I a l
a
a
NUREG/cR-5843 SAND92-0167
CORCON-MOD3: An Integrated l computer Model for Analysis of
Molten ore-Concrete Interactions a
User’s Manual *8610039*
a Prepared by D. R. Bradley, D. R. Gardner, J. E. Brockmann, R. O. Griffith
SANDIA NATIONAL LABORATORIES
TECHNICAL LIBRARY
Sandia National Laboratories Operated by Sandia Corporation
prepared for U.S. Nuclear Regulatory Commission
a
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NUREG/CR-5843 SAND92-0167
CORCON-MOD3: An Integrated Computer Model for Analysis of Molten Core-Concrete Interactions
User’s Manual
Manuscript Completed: August 1993 Date Published: October 1993
Prepared by D. R. Bradley, D. R. Gardner, J. E. Brockmann, R. O. Griffith
Sandia National Laboratories Albuquerque, NM 87185
Prepared for Division of Systems Research Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 NRC FIN L1434
ABSTRACT
The CORCON-Mod3 computer code was developed to mechanistically model the important core-concrete interaction phenomena, including those phenomena relevant to the assessment of containment failure and radionuclide release. The code can be applied to a wide range of severe accident scenarios and reactor plants. The code represents the current state of the art for simulating core debris interactions with concrete. This document comprises the user’s manual and gives a brief description of the models and the assumptions and limitations in the code. Also discussed are the input parameters and the code output. Two sample problems are also given.
NUREG/CR-5843
Contents
IkJ&
l. O Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
l.ZBroad CapabilitiesofCORCON-Mod3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2l.31mprovements inCORCON-Mod3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.OBriefDescriptionsofthePhenornenologic.al Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.12.2
2.3
2.4
Overview ofCORCON Phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4System Componenta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Debris Poll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.2 Concrete Cavity . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72,2.3 Atmosphere andSurmmdings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Physical Pr ocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.12.3.22.3.-3
2.3.42.3.52.3.62.3.72.3.8.2,3.92.3.102.3.11
2.3.122.3.132.3.142.3.15
Energy Generation ...,.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Melt/ConcreteHeatTransfer.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12CoohmtHeatTmnsfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...19Crust Formation and Freezing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Bubble Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2SInterlayer Mixing, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Pool Surface HeatTmnsfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Concre& DecmnpositionandAb lation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Time-Dependent Melt Radius... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Mass Transfer andEnergyTransfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Energy Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Cavity Shape Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Aerosol Generation and RadionuclideRelease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46.Aerosol Removal ByOverlyingWater Pools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 .
Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4.1 Thermodynamic Properties.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.4.2 Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602.4.3 Liquid-SolidPhase Transition.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612.4.4 Coolant Saturation Line..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.0 Aasumptionsand Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.0 User Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1 ATypicd Calculational Cycle inCORCON-Mod3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.2 DeacriptionoftheInputParameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.1 Discussion ofSelected Input Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.2.2 ReumunendedValuesandDefault VahmsforInputQuantitiea . . . . . . . . . . . . . . . . . . . . 93
v NUREWCR-5843
Contents (continued)
5.0
6.0
7.0
4.3
4.44.5
Description of the Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Numerical Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.3.2 Graphica 10utpu t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Description ofthe WamingandError Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Geaeral Programming g Information . . . . . . . . . . . . . . . . . . . . . . . . 8........ . . . . . . . . . .
Codinghfolmation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 DeacriptionofSubroutines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2 uaeofcommon . ..o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3 DefinitionaofPrinciprd Variablea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Problema . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.i ’Ihe CORCON Standard Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2 AdditionalSample Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Referemes. d o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. OF . . . . . . . . . . . . . . .
97
9799
100IN
112
112112112
160
161
253
NuREG/cR-5843 vi
EitB!E .r!!kk2
2.12.22.32.42.52.62.72.82.92.10
2.11
2.12
2.132.142.152.16
4.14.24.34.4
6.16.26.36.46.56.66.76.86.96.10
6.116.126.136.146.156.166.176.18
xdmwofhmtfluxonmti~~~m~m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Approximation toheatflux asafimction ofinterface temperate . . . . . . . . . . . . . . . . . . . . . . . . . . 21Enthalpy ofconcrete andits decomposition products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Patbofgas through pool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Pathofmetal throughpool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Pathofoxide throughpool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Normal surface .~ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Circle intersection pro@tionmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Enhanced recession forinsidecomer point, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Sensitivity of the ikxxmtamination factor to bubble size (pool depth is3m,V(rel)/V(rise)isl.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . .’ . . . . . . . . . . . . 53
Sensitivityoi’the decontwninationf actor topcmldeptb (bubble diameterislcm.v@el)/v(rise)isl.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Sensitivity ofthedecontaminaticm factor ofthe velocity mtio(pool depth i:; 2m,bubbiediame&x Is l am)...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., 55Two-phase cmstruction formkture . . . . . . . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . . . . . . . 56Liquiduaand solidustemperature fits forCr-Fe-Nisystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Example liquidusand solidustemperature foroxidicmixturea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Alternate phase diagram iortheoxidephase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
F’lowdiagram forCORCON-Mod3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Initial cavity geometry -cylinderwith hemispherictdbsse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Ihitial cavity geornetr y-wbitraryshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95hitialc avitygemnet~-cy linderwith flat base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Axial ablation mtectdculated forthe CORCON standardproblem . . . . . . . . . . . . . . . . . . . . . . . . . . 164Axial andradial ablation distance calculated forthe CORCON standard problem . . . . . . . . . . . . . . . . . 165Layer temperatures calculatedforthe CORCONstandard emblem . . . . . . . . . . . . . . . . . . . . . . . . . . 166Cumulative gasgeneration calculated forthe CORCON standard problem . . . . . . . . . . . . . . . . . . . . . . 167Gasgeneration ratecalculated forthe CORCONstandard emblem ...,. . . . . . . . . . . . . . . . . . . . . . 168Energy terms calculated fortheCORCON standard problem.........,.. . . . . . . . . . . . . . . . . . . 169Aerosol concentration (ambient conditions) calculated forthe CORCONstandard problem . . . . . . . . . . 170.Aerosol cmcentration (STP)calculated forthe CORCONstandard problem . . . . . . . . . . . . . . . . . . . . 171Aerosol generation rate calculated forthe CORCON standard problem . . . . . . . .. . . . . . . . . . . . . . . . 172Axial ablation rate calculated forthe BWR sample problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...173Axial and radial ablation distances calculated for the BWR sample problem . . . . . . . . . . . . . . . . . . . . . 174Layer temperatures calculated forthe BWR sample proble m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Cumulative gas generation calculated for the BWR sample problem . . . . . . . . . . . . . . . . . . . . . . . . . 176Gasgeneration ratecalculated forthe BWR sample problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177Energy terms ctdculated forthe BWR sample problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Aerosol concentration (ambient conditions) calculated for the BWR sample problem . . . . . . . . . . . . . . . 179Aerosol concentration (STP) calculated for the BWR sample problem . . . . . . . . . . . . . . . . . . . . . . . . 180Aemsolgeneration ratecalculated forthe BWR sample problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
vii NuREG/cR-5843
X&k
Tables
2.12.22.32.42.52.6
4.14.2
5.15.25.35.45.55.65.7
6.16.26.36.4
Chemical speci=included in CORCON master species list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Chemical species included inthe VANESA apecies list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Chemical compositions ofdefaultconcretes (Values inw/o) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Meltingranges ofdefaultconcretes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Decay-heat elements andgroupings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Chemical apecies includedinthe CORCONchemical equilibrium solution . . . . . . . . . . . . . . . . . . . . . . 34
Input instructionsfor CORCON-Mod3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75CORCON-gemnWed Warningand error measageaforeach subroutine . . . . . . . . . . . . . . . . . . . . . . . . iOl
ListofCORCON subroutines.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Subroutineacalled byeachprogram routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Pmgramroutineswhich calleach routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123COMMONblockscontainedby each program routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Program routinescantainingeach COMMON block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Variabkac ontainedi neachCOMMON block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Dictionary ofprincipal variablesinCORCON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Inputlisting forthe CORCONstandard problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182Outputlistingforthe CORCONstandard problem . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 184Inputlisting forthe BWRsampleproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203Outputlisting fortheBWRsample problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
NUREGICR-5843...
VIII
Nomenclature
a
A
[A]
Aii
c
CP
c
c,
C*
c,,
cd
d
D,
E
E-
f
fefi
8
81
G
AG
h
4’
4
Laplace constant (= [u/g@,-pJ]’~
Area; initial mass concentration of condensingvapor
Aerosol wncentration
Oxide phase interaction parameters
Speed of sound in the gas
Specific heat
Cunningham slip correction factor
Heat capacity of layer i for the new mass at theold tempemture
Coefficient used in the boiling heat transfermodel
Coefficient used in the boiling heat transfermodel
Drag coefficient
Diameter
Diffusion coefficient for species i
Dimensionless entrainment volume due tobubble bursting
Dimensionless droplet entrainment flux
Fraction of evolved gas entering bubbles
Free energy function for species i
Gravitational acceleration ( = 9.806 mk~
Gibbs free energy of species i
Gibbs free energy
Free energy of formation
Convective heat transfer coefficient; spcificenthalpy
Enthdpy of vaporization
Meld phase interaction panuneter
H
AH
AH~
j
Ja-
k
K
&l,i
%*
&i
K,
Ku
P
L
m
M
M,
n
N
N.
N~
N@~
Nu
P
ix
Total enthalpy
Change in enthalpy; latent heat of fusion
Heat of ablation
Superficial velocity (volumetric flux)
Dimensionless variable in Equation (64)
Thermal conductivity; Boltzmann’s constant
Extinction coefficient
Effective rate constant for formation of vaporspecies i
Gas phase mass transport coefficient
Rate constant for condensed phase masstransport
Vaporization rate constant
Dimensionless number in the Kutateladze.correlation
Liquid layer thickness
Characteristic length; layer thickness; radiationpath length
Maas
Morton number (= gp4Aplp2c?)
Molecular weight of species i
Number concentration of aerosol particles
Number of sixe segments used to describe theaerosol particle siiz distribution
Avogadro’s number (6.023 x I@ atoms/mole)
Number of moles of species k
Dimensionless gas viscosity
Nusaelt number (= hL/k)
Pressure
NuREG/cR-5843
Nomenclature
P
P,
F
Pr
q
Q
Q*
r
R
R
Ra
Re
%
i
s
Sh
t
:t
T
m
AT
u
u
Vd
vi
v
Vw
Powa
Partial pmaure of species i
Product of P3k3tialpressure times fugacitycoefficient
Prandtl number (= pc#)
Heat flux
Heat flOW
Heat tranaf~ mhancexmztt factor
Radius; radial coordinate
Radial melt di3nea3aion
universal gas constant
Rayleigh number (= @ATL3/ua)
Reynolds number (= puL/p)
Specific entropy of species i
Surface mcesion rate (ablation rate)
Vohunetric heat source
Sherwood number (= &d/DJ
Time
Tirnestep
Temperature
Temperature correction
Tempera@e difference; temperature change
Flow velocity in the film
Velocity of rising bubbles
Droplet settling velocity
Molar volume of species i
Volume
Transition gaa velocity
NUREG/CR-5S43
Metal phase interaction parameter
Weight fraction of species j
Weber number (= U%Oc/aJ
Spatial location
Position of c43ncrete surface
Mole fraction of species i
Position of solidification and melting fronta;edalpy change in temperature units
Axial (vertical) inordinate
Thermal diffusivity; gas volume fraction;parameter in melt radius solution
Droplet volume fraction
Coefficient for aerosol removal by diffusion
Coefficient for aerosol removal by impaction
Coefficient for aerosol removal bysedimentation
Thermal expansivity
Temperature difference ratio
Activity coefficient for species i
Film thickness
Emisaivity
Dimensionless gas velocity
Wall inclination
Melting and solidification constants
Dynamic viscosity; mean particle size
Chemical potential of species k
Kinematic viscosity
Normalized excess bubble volume
Nommclature
P Density
Molar density of the condensed phase
Surface tension, geometric standard deviationof aerosol particle size distribution
Stefan-Boltzmann constant (= 5.668 x 104W/m’ K9
VolunE t%wtion solids in a slurry
Flux
Volume fraction of species k
Dimensionless bubble volume
Implicitness factor (fully explicit = O; fullyimplicit = 1)
Subscri~ta
a
abl
A
b
B
c
Cln
Crit
CHF
d
e
eff
enter
4
f
Based on the Laplace constant; atmosphere
Ablation
Atmosphere
Bubble
Bubbling film; bottom
Concre@, convective
coolant
Convective
Critical
Critical Heat Flux
Droplet
Elemental; eatrainme nt; equivalent
Effective
Entering
Equilibrium
Fluid
F
fg
g
gas
i
in
I
P
leave
liq
L
Leid
m
max
mp
o
out
P
P
r
react
ml
rise
R
s
sat
Film
Vaporization
Gas phase
Gas sparged
ith species or layer
Incoming
Interface
Liquid phase
Lawing
Liquidus
Laminaq laye~ condensed phase
Leidenfrost (film cxilapse) point
Melting; mixture
Maximum
Melting point
Overall
Outgoing
Pool; Aemaol particle
Penetration
Radiative; radial
Chemical reactions
Relative
Rise
Radial
Net radiation
Surfacq solidification
Saturation
xi NUREWCR-5843
sol
source
stable
sub
Sur
s
tot
T
tr
unstable Unstable thermal gradient
w Ablating concrete surface (wall)
z Axial
Solidus
Decay heat source
Stable thermal gradient
Subeaoled
Surmmdings
Stokes
Total
Turbulent; top
Transition
1 Initially molten phase; component 1 of binarymixture
2 Substrate; umnponent 2 of b- mixture
sUDWSCliDtS
k kth temperature range in thermal equation ofstate
e Liquid; Iiquidus
m Melting state
n ntb time level
o Undisturbed or unperturbed state
s Solid; solidus; slag
Xs Excess
Projected
A Property for new eanposition at old
o Initial
NuREG/cR-5s43 xii
1.0 Introduction
A proper assessment of the risks to the public associatedwith the operation of nuclear power plants requires arealistic evaluation of the important accident sequences.The Reactor Safety Study’ demonstrated that the risksassociated with light water reactors (LWRS) aredominated by core meltdown sequences. In thesehypothetical accident sequences, loss of normal andemergency cooling systems leads to melting and slumpingof the core. If uninterrupted, this is followed by failureof the pressure vessel and deposition of molten core andassociated stmctural materials onto the concrete floor ofthe reactor cavity.
The interaction of the resulting pool of debris with theancrete has beers identified as an important part of theaccident sequence. The debris is maintained at elevated
temperatures by decay heat from non-volatile fissionproducts retained in the melt. The temperatures and heatfluxes involved are sufficient to decompose and ablateconcrete; such attack could fail containment by basernatpenetration. This would result in a release of radioactivematerials to the soil underneath the reactor building.
Potentially more important are the various mechanismswhich can lead to above-ground failure of containmentand release of radioactive materials to the atmosphere.The most obvious of these involve the large amounts ofwater vapor and carbon dioxide which are produced by
the decomposition of concrete. These gases can then bereduced to hydrogen and carbon monoxide in chemicalreactions with the core debris. (Small quantities ofhydrocarbons and other species are also formed.) Allfour major gases contribute to the risk of eventualoverpreasurization of containment. Hydrogen and carbon
monoxide are also combustible, presenting an additionalrisk of sudden overpressurintion if they are ignited.Also, ablative attack may cause the failure of internalstructures in the containment building such as the reactorpedestal in a boiling water reactor (BWR); the resultingmechanical disruption could fail the containment itself.Finally, heat lhm the debris may be sufficient by itselfto cause the failure of containment. This might happen,for example, by degradation of the containmentpenetration seals in a BWR or by overheating of thedrywell liner in a BWR Mark I containment.
The CORCON-Mod3 computer code was developed tomechanistically model the important core-concreteinteraction phenomena, including those phenomenarelevant to the assessment of containment failure andra&onuclide release. The code is sufficiently flexiblethat it can be applied to a wide range of severe accidentscenarios, and reactor plants. As such, the coderepresents the current state of the ah for simulating coredebris interactions with concrete.
1.1 Historical Background
A research program to investigate molten corekoncreteinteractions was initiated at Sandia Natioml Labomtorieain July 1975, under the sponsorship of the Reactor SafetyResearch Division of the U.S. Nuclear RegulatoryCommission. This program was initially experimental,but its scope was soon broadened to include thedevelopment of computer models to describe theinteractions. A preliminary model, based on limited dataand using untested assumptions, was quickly developedby W. B. Murfin in 1977? This model, INTER1, wasintended as a qualitative tool, suitable for sensitivitystudies; ita use for quantitative prediction was specificsdlydiscouraged by its author.z
Following the release of INTER1, work was begun ondevelopment of an improved computer code, CORCON.This program was intended to provide a moredetailed--and more mechanistic-description of thephysical processes involved in molten corekoncreteinteractions. The first version of the code,CORCON-Modl $ was released in 1981. It lackedmodels for the freezing of core debris and forinteractions between debris and a coolant (water), whichlimited its applicability to the early stages of accidentsinvolving dry raictor cavities. hter development WOrkhas concentrated on removing these limitations. Also, asexperience with the code accumulated, severaldeficiencies in the existing modeling became apparent andimprovements were made to correct them.
It was decided that CORCON-Modl would be supportedas originally issued. That is, errors which prevented thecode from performing as intended (as indicated by the .users manual) would be corrected, but improved modelswould not be issued until an entirely new version of thecode was completed. In the second version of the code,
CORCON-Mod2$ the restrictions mentioned above wereremoved by the inclusion of freezing and coolant models.Heat transfer and viscosity models were improved, andthe code was brought into conformity with the 1977ANSI standard for FORTRAN programrning.sCORCON-Mod2 WSS rekased in 1984.
Since its release, CORCON-Mod2 has been usedextensive y to analyze coreamcrete interactionexperiments, such as SURC-4,6 and to analyizcore-concrete interactions in various severe accidentscenarios. It is incorporated in the systems-level &CONTAIN and MELCOR~ which are used to aMlyZ4Scontainment response and overall accident progression,respectively.
1 NuREG/cR-5843
Introduction
This experienu with CORCON-Mod2 and the improvedknowledge of coreumcrete interactions gained since therelease of the code, have revealed some deficiencies in
CORCON-Mod2. For example, the difficultiesemcamtered by coreumcrete interaction codes insimulating the results of International Standard Problem24 (ISP-24)? which is baaed on the SURC+ experiment,grevealed the need to include condense&phase chemicalreactions and improved heat transfer models.
In CORCON-Mod3, many of the deficiencies previouslyidentified have k removed, and several significant newfeaturea have h added. A summary of modelimprovemtmta and additions is provided in Section 1.3 ofthis report.
1.2 Broad Capabilities ofCORCON-Mod3
CORCON is a general computational model describingthe intemctiom between molten me materials andconcn?te in LWRS. The molten core debris is assumed tolie in an axisyrnmetric concrete cavity, with gravityacting parallel to the axis of symmetry. Several standardconcretes may be used, or the user may specify anon-standard concrete. Coolant (water) may be present.The user also may specify addition of core materialand/or cuolant as a function of time.
The model includes heat transfer between the corium andthe cmncrete and between the corium and the atmosphere.If coolant is present, then the heat transfer from thecorium to the molant, and from the coolant to the
-h-, is modeled.
For heat transfer between the corium and the concrete,the user may select to model the interracial region as agas film or a slag film. Heat transfer across the gas filmis by wmbined radiation and convection (the models in
the code are identical to those used in CORCON-Mod2).The model for heat transfer across the slag film is basedon analysis of transient slag and crust growth at theinterface during intermittent contact between the coriumand the concrete. Convective heat transfer between thebulk melt and the film (gas or slag) is modeled using heattransfer conditions derived for boiling and gasbarbotage.
while the effects of subcooling and gas barbotage areincluded in the film boiling models. The transitionboiling regime is treated using a log-linear interpolationbetween the critical heat flux and the L.eidenfrost points.
Models have been added to simulate the mixing betweencorium layers which occurs via droplet entrainment.Melt stratification via de-entrainment has been added aswell. The user may choose to disable the mixingcalculation, forcing the corium to remain stratified intodistinct oxidic and metallic layers. Here, as inCORCON-Mod2, the layering configuration isdetermined by the relative densities of the layers.
Both gas-phase and condense&phase chemical reactionsare modeled. The model assumes chemical equilibriumbetween the oxides, metals, and gases in each layercontaining metals. Chemical reactions between gases andoxides in a purely oxidic layer are not treated, The usermay disable the oxide-metal condensed phase reactions ifdesired.
CORCON-Mod3 models the generation of aerosols andthe release of radionuclides using the VANESA model,10which has been fully integrated into the code. TheVANESA model, which was developed originally as astand-alone code, treats aerosol generation byvaporization and by mechanical prowsses (e.g., bubblebursting). Kinetic limitations to the vaporization processare mnsidered. VANESA also models aerosol removalby an overlying water pool.
CORCON-Mod3 includes a much broader range of useroptions than were available in CORCON-Mod2.Through input the user can modify many of the momimportant models and param~rs in the code. Thiscapability allows the code to be applied to a broaderrange of accident conditions. It also allows the usergreater flexibility in modeling uncertain phenomena.
The features described above allow CORCON-Mod3 tomodel a wide range of coreamcrele interactionphenomena and allow the code to be used to simulate theeffects of core-concrete interactions in a wide range ofsevere accident scenarios. CORCON-Mod3 is astateaf-the-art computer code for simulating theinteraction of molten core debris with concrete in LWRS.
The heat transfer model for the coolant includes arepmeatation of the full pool boiling curve. The effect 1.3 Improvements in CORCON-Mod3of ambient pressure is included in the models for film,nucleate, and transition boiling. The effect of coolant Many improvements have been made to CORCON-Mod2subcooling is included in the nucleate boiling model, during the development of CORCON-Mod3. Several of
NuREG/cR-5843 2
Introduction
the phenomenologicxd models in CORCON-Mod2 wereimproved, and several new models were added.
The model improvements include:
●
●
●
the debrkoncrete heat transfer models now alloweither a stable gas film or an unstable gas film withintermittat melt-concrete contact,
the coolant heat transfer model now includes theenhancement of film boiling heat transfer by gasbarbotage md coolantsubcooling, and
the models for bubble phenomena (bubble size, risevelocity, and void fraction) have been upgraded toreflect our improved understanding of bubblebehavior.
The new models include:
● an integrated version of the VANESA modelto that
includes models for aerosol generation andradionuclide release from the melt, and scrubbing inoverlying water pools.
●
●
●
●
the models for condensed phase chemical reactionsbetween oxide and rne4als,
activity coefficient models for the condensed phaaea(used in the aerosol generation and radionucliderelease calculation),
an aerosol scrubbing model for subcooled pools, and
a parametric treatment of core debris spreading acrossthe concrete floor of the ractor cavity:
In addition to these model chang~, CORCON-Mod3provides the user with the capability of modifying a widerange of models and model parametem. This additionalflexibility allows the code to be used in a broader rangeof applications.
The new and improved models are described briefly inSection 2. A more detailed description of the currentphenomenologicxd models will be provided in the .forthcoming CORCON-Mod3 models and correlationsreport.
3 NUREGK2R-5S43
2.0 Brief Descriptions of the Phenomenological Models
2.1 Overview of CORCONPhenomenology
CORCON-Mod3 is a mechanistic computer model thatdescribes the core-concrete interaction phenomenarelevant to the assessment of containment failure andradionuclide release. In this section, we present a briefdescription of the principal interaction phenomenamodeled in the code.
A great deal may be understood about core/concreteinteractions from a very simple picture. The attack ofcore debris on concrete is largely thermal in a light-waterreactor. Energy is generated in the core debris fromradionuclide decay and from chemical reactions, and maybe lost either through its top surface or to the adjacentconcrete. (In many experimental studies, externallysupplied induction or joule heating is substituted for thereactor decay heat.) In either case, so long as the heatsource is sufficiently large, the situation rapidlyapproaches a quasi-steady state where the losses from thecore debris balance the internal sources. The partition ofinternally generated heat between concrete and surfacz isdetermined by the ratio of the thernud resistances of thecorresponding paths. In this simple view, pool behavioris dominated by conservation of energy, withheat-transfer relations providing the most importantconstitutive relations.
Under most circumstances, the heat flux to the mncreteis sufficient to decompose it, releasing water vapor(adsorbed and from hydroxides) and carbon dioxide(from carbonates), and to melt the residual oxides. Thesurface of the concrete is ablated at a rate which istypically several centimeter per hour. The moltenoxides and molten steel from reinforcing bars in the
concrete are added to the pool. The gases are stronglyoxidizing at pool temperatures and will be reduced,primarily to hydrogen and carbon monoxide, on contactwith metals in the pool. Ultimately the reacted andunreacted gases enter the atmosphere above the pool.These gases may or may not bum immediately,depending on their temperature and on the relativeconcentrations of oxygen, steam, and combustible gases.Combustion of these flammable gases are an importantconsideration in the assessment of containment failureduring a severe reactor accident. Modeling of theseatwve-pool phenomena is not included in CORCON-Mod3.
Gas released at the bottom of the melt pool rises throughit in the form of bubbles. Gas released at the sides ofthe melt also form bubbles and rise to the surface. Athigh gas release rate-s a stable gas film may form ateither the bottom or side surfaces. The presence of gasbubbles in the pool increases the volume of the pool, andincreases the interracial area in contact with concrete.
Vaporization of melt constituents into the rising bubblesleads to aerosol generation when these vapors condensein the cooler atmosphere above the melt. Aerosolpatiicles are generated also when the bubbles rupture atthe surface of the melt and are entmined by the risinggases. The aerosols that are produced by these processesinclude both radioactive and non-radioactive species.Radionuclide release during core-concrete interactionscan be an important contributor to the radionuclidesource term arising from the accident.
Because the concrete thermally decomposes at depthswell below the surface, the thermal response of theconcrete is complex. The released gases produce internalpressures which drive flows of carbon dioxide, steam,and liquid water through the pores of the concrete.Experiments have shown that at low incident heat fluxes,the concrete may be heated to substantial depths prior tothe onset of ablation. At higher heat fluxes, however,penetration of the thermal front will be minimal prior tothe onset of ablation. In either case, a steadytemperature profile is eventually attained and ablation
assumes a pseudo-steady character. Given the high heatfluxes expected during core-concrete interactions, wehave always assumed steady state ablation in CORCON.This is true also of CORCON-Mod3.
Experimental evidence 11*1zshows that the VtiOUS oxidic
species in the melt are highly miscible, as are themetallic species, but that the two groups are mutuallyimmiscible. In the absence of gas bubbling, the coredebris will strati& into distinct layers based on theirrelative densities. A stratified layer configuration hasbeen assumed in previous versions of CORCON.
Mixing of the immiscible layers can occur at high gasfluxes or when the densities of the layers are close.’3Mixing occurs when droplets of the lower (denser) layerare entrained by bubbles passing through the interfacebetween the layers. Once entrained into the mixture, thedroplets will settle out. Therefore, during a cme-
NUREG/CR-5843 4
concrete interaction, there may be times in which themolten core debris is mixed and other times in which thedebris is stratified. CORCON-Mod3 models bothentrainment and droplet settling (deentrainment). Theuser may disable the mixing calculation and force thecore debris to remain fully mixed or fully stratified.
If water is present, it will form an additional layer at thetop of the pool. Though explosive intemctions have beenobserved when molten material has been poured throughWak,, 14~t expfi~nts have shown that explosive
interactions are unlikely when water is Pured onto meltscomposed of prototypic LWR core materials. 1s’16(Thereader should note that there have been experiments inwhich emergetic events have been observed in this~nfiWmtion. ‘7.18 However, the-se were @StSusing
highly superheated metallic melts under vigorous gassparging. We do not expect these conditions to exist inLWR accidents.) If the water does not react violentlywith the molten material underneath it, it will provide anenhanced heat sink. This is likely to cool the top of themelt below the solidification temperature, resulting in asolid crust on the surface. It has been suggested thatthese crusts will progressively fragment and allow wateringression until the core debris is completely quenched. 19This progressive quenching of the melt has not beenobserved in any experiments to date. CORCON-Mod3treats heat transfer to the coolant using pool boilingcorrelations. It does not allow for either steamexplosions or the progressive quenching of a molten poolto a cuolable debris bed.
An overlying coolant pool will also trap aerosolsgenerated during the core-concrete interaction.Depending on the depth of the pool and its degree ofsubcooling, there may be a factor of ten or morereduction in the amount of aerosol released into thecontainment atmosphere. 15
As time progresses, the debris pool grows; its surfacearea increases, and decay heating decreases. Therefore,pool temperatures and heat fluxes decrease, and thepossibility of refreezing arises. Substantial freezing ofthe metallic phase may occur. However, the largeinternal heating and small thermal conductivity of theoxidic phase prevent the existence of steady crusts morethan a few centimeters thick. The bulk of this phase willremain liquid, probably for weeks. 1lf
Coupling between the molten pool and the rest ofcontainment is rather one-sided; the pool serves as asource of mass and energy while being only weaklyinfluenced by conditions in the containment.Containment pressure affects the propxties of gases inthe pool and of any water over the molten debris.
Model Descriptions
However, the effects on gas-related heat transfercoefficients, on equilibrium gas compositions, and on thetemperature and latent heat of the water are relativelysmall. Heat loss from the top of the molten debris isdominated by radiation to containment structures or to theoverlying water. Because of the fou~-powertemperature dependence of the radiative flux, this loss israther insensitive to containment temperatures (unlessthey are very high). In the absence of a water layer, theoptical properties of the atmosphere rpay becomesignificant. Molecular absorption by atmospheric gaaeais a relatively small effect, IIf but ~rosol concentrations
may be great enough that the atmosphere is optically~ck.lb
Because CORCON-Mod3 is not intended to serve as afill containment code, no attempt is made to modelabove-pool structures. Tbe surroundings, tempemture,and atmospheric pressure are user-specified and may begiven as functions of time. The decrease in radiativeheat transfer from the pool surface to the surroundings,associated with atmospheric attenuation by aerosols, isapproximately accounted for. The calculation is baaed ondiffusion theory for gray, infinite parallel plates, and-anaerosol concentration is calculated internally for thepurpose of determining the atmospheric extinctioncoefficient during the intemction.
2.2 System Components
The principal components of the CORCON system arethe core debris, the concrete, and the atmosphere andsurroundings above the debris. The code will also treatan overlying coolant pool if one is present. Thecomposition of each component is specified through userinput in terms of a “master list” of chemical species.The list, presented in Table 2.1, is divided into four
groups: oxidic compounds, metals and other elemeats,gases, and miscellaneous cmmpounda. Aa noted in thetable, not all of the species in the master list are availableto the user for specification of initial compositions. Thealuminates (species 12 to 17) am a hold-over from theviscosity modeling of CORCON-Modl and are not usedin CORCON-Mod3. The fission-product pseudo species(oxides 24 to 28, metal 47 and gases 82 to 83) are usedin the decay-heat generation model. The initial fissionprcduct composition is determined within the code fromthe concentration of fission products in the fuel. Thefission product composition is then updated during thecalculation to aoxnmt for addition of core material intothe reactor cavity and release in the form of aerosols.
Although we believe that the list of available apeciea ismore than ample for describing the physical and chemicalprocesses pertinent to the interaction of molten LWR
NUREG/CR-5843
Model Descriptions
Table 2.1 Chemical species included in the CORCON master species list?
Metals andOxides other elements Gases Miscellaneous
123456789
1011121314151617181920212223242s262728293031323334-42
SiOzTiOzFeOMnOMgOCaoSroBaOLizON~OLoKA102NaAIO,BaA1204caA1204MgAlz04MnAlz04F~OJA1203uo~zfo2Crz03NiOTpMO,(c)TpMOj-@OxTpAlkMet(c)TpHalogn(c)F~04Mn,o,PU02U03U308Blank
4344454647484950515253545556575842
FeCrNiZrTpMMnc(c)AluSiUA13uA12NaCa-’XBlank
6364656667686970717273747576777879808182838485868788899091-99
Tacudo species representing four condenacdphase fission productgroups.
c(g) 100 HZO evapCH, 101 HZO themco 102 caco3C02 103 Ca(OH)z~H, 104 HZO ct’n
C2H4 105-109 Blank
G&HH,HZONNH3Nzo02OHCHOCHZOCfo,(g)TpMO,(g)TpM03(g)Al*o*(g)A120(g)Alqg)OAIH(g)AIOH(g)OAIOH(g)
~oz(g)Blank
_Incrt oxidlc apcciestreatedas an element “X” in chemicalquilibrium calculation.
Aluminates,apccicn12-17, not uacd in CORCON-Mod3.
‘Actualspeciesoarncauaadin the codehave all uppercase Iettcmand no aubacripla(e.g., SiOz = S102).
NUREG/CR-5843
Model Descriptions
core materials (and coolant) with concrete, blank space-shave been left in the list for future additions. Suchadditions to the list might be required, for example, fortreatment of the sodium chemistry associated withcorekoncrete interactions in Liquid Metal Fast BreederReactor (LMFBR) accidents.
The VANESA model was developed using a somewhatsimpler description of the melt, and considers only themajor condensed phase species. VANESA fmussedprimarily on gas phase chemistry and it thereforeincludes a much more extensive species list for thegas phase. The VANESA species list is shown inTable 2.2.
2.2.1 Debris pool
CORCON models the debris pool as consisting of anumber of layers contained in a concrete cavity. Theselayers are, from bottom up, a heavy (i.e., dense) oxidephase (HOX), a heterogeneous mixture of heavy oxidesand metals (HMX), a metallic phase (MET), aheterogeneous mixture of metals and light oxides (LMX),a light oxide phase (LOX), a coolant (CLN), and theatmosphere (ATM). The three-letter mnemonics areuseful in describing the pool structure, and have beenused in appropriate variable names throughout the code.hyer volumes, including the swelling effects of gasbubbles, determine the elevations of layer interfaces andof the pool surface.
These seven layers are always present in the datastructure but may be “empty” in the sense of containingno material. Note that the coolant (CLN) is treated inthe same manner as the debris<ontaining layers.
Many different layer configurations are possible now thatCORCON-Mod3 allows for the existence of mixturelayers. Mixing, stratification, and density changesresulting from material addition can lead to changes inthe layer orientation during a calculation.
If an overlying coolant layer is present, it will form alayer overlying the core debris. The user may specifythe presence of a coolant layer at the start of thecalculation or may specify addition of coolant at somelater time. Currently, water is the only acceptablecoolmt.
2.2.2 Concrete Cavity
The concrete cavity containing the core debris is assumedto be axisymmetric. Several simple geometries areavailable to describe its initial shape. The user mayspecify a cylinder with either a flat base or a
7
hemispherical base. A general (axisymmetric) initialshape may also be defined by Specifying the initialposition of each body point. The shape of the cavity isrepresented and tracked by the position of a number ofpoints, termed “body points, ” on its surface.
The composition of the concrete must also be specified,and may be chosen as one of the three built-in defaultconcretes. These are referred to as “basaltic aggregateconcrete, ” “limestone aggregate common sand concrete,”and “limestone aggregate concrete. ” The mnpositiona ofthese concretes are given in Table 2.3; they are W onmeasured compositions reported by Powera. 1lb Thesolidus and liquidus temperature “for these wncretea,also included in internal data, are given in Table 2.4; theuser must Speci& an ablation temperature somewherebetween these limits.
Alternatively, provision is “made for the user to detine a“non-standard” concrete. In this case, the compositionand melting range of the concrete must be user-specified,in addition to the ablation temperature. The concretecomposition may be specified either in terms of CaCO~and Ca(OH)2, or in terms of their deccmpsition “products, CaO, COZ, and HZOCHEM (chemically boundwater). The latter form is used internally, with the code
performing the conversion if nwesaary.
Steel reinforcing bar in the concrete is also permitted; ifpresent, it is assumed to be pure iron (Fe). Alternatively,CORCON-Mod3 allows the user to specify thecomposition of the rebar to be something other than iron.This option was included to enable the user to simulateexperiments with zirconium rods embedded in theconcrete. m Concrete, with or without reinforcing rods, is .treated as a homogeneous material.
2.2.3 Atmosphere and Surroundings
The atmosphere above the pool and ita surroundingsserve as sinks for mass (evolved gases) and energy(convection and radiation from the pool surface).CORCON-Mod3 contains very simple madels for thesecomponents. The atmosphere is described by a specified(constant) temperature and (timedependent) pressure.The surroundings are described by a specified(timedependent) temperature and (time- ortemperaturedependent) emiaaivity. Within the code, thepool surface (bottom of the atmosphere) is treated as amajor computational interface. Very limited information,restricted to mass flows and (linearized) heat transferrelations, is passed across the interface. Thus, becausethe interface is well-defined and actively used in thestand-alone cude, a more detailed above-pool model-or afull containment response code-could be easily
NUREG/CR-5843
‘i’nhle 2.2 Chwnicnl species included In the VANK!SA species list
J 1 2 3 4 s 6 7 8 9 10I
1
2
3
4
s
b
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
23
y(g)
Fe(c)
Cr(c)
al(c)
m(c)
Ru(c)
Sri(c)
WC)Te(c)
Ag(c)
#ho{c)
-c)
M2q(c)
Me#(c)
K#(c)
Sqc)
Uo#c)
Zrl+(c)
cs#c)
See(c)
Sro(c)
Lafi(c)
cd+(c)IIMl(c)
cd(c)
H#J)
FeO(c)
Cr##c)
Mfo(c)
au
IAJ
w
ml
w
au
IAJ
Ml
IAl
IN
IaJ
IAl
Zd:l
w
w
ml
w
w
w
w
H(o)
Fe(o)
c?(g)
Iti(m)
MO(9)
W(9)
Sn(m
Sb@)
b(g)
As(o)
W9)
Cc(o)
Al(o)
no(g)
K(g)
Si(o)U(9)
Zr(u)
Ca(g)
28(O)
Sr(g)
La(g)
Cc(g)
HMO)
CeI(9)
owe)
FeO(0)
cm(g)
w
aoo(9)
Rag)
slag)
w
Teoco)
A@(g)
IWJ(9)
W(9)
AlO(g)
Ma(g)
m(o)
sit)(g)
m(e)
Zro(g)
Cal(e)
sa9)
sro(9)
Leo(s)
ceo(9)
llho(9)
1(9)
0(9)
MM(o)
CrcQ(o)
Ilioll
aoo2(9)
AU02(U)
s-l(o)
mm(e)
W+(o)
WtI(o)
I&In
Couw)AU3ti(0)
MO(g)
m(e)
sio#J)Uo#
zro@
Ceo(s)Sdm(g)
Srtnl(e)Ld!tl(o)
Cetwg)
alloM(9)
lit(o)
02(9)
FeCUI)2(g)
Cf’tyil)
lli(olo2
lbo#9)
RtID@)
sn(ow#l)
sb(oll)#l)
Te##)
Ag(OH)2(g)
nfmnl(o)
CO(OW)2(9)
At#(g)
K2(O002(iI)
Sitnl(g)
Uo#o)
zf’ow(9)cepl)#9)
se(al)#i)
Sr(OW2(9)
La(OU)2(g)
Ce(CW2(9)
lnwn)2cln
12(9)
copw
l$cro~(e)lliHI12MO04(9)
R@6(9)snt~e)SiY2(s)tealAgTe
MxO#l)
Cell
AlC+(g)
MI(9)
KH(9)
si(o$l)2(o)
tl$Jo4(9)
Zr(011)2(0
ce#clJ)
WI
Srll
Le$
1%IlbO@)
10
CO(9)
la!
crow
ml
(moo3)2
Rlm
Sl#
Sbf(fl)
TCO(OW2(9)A@
w
%Al#g)
ne@)
K2(g)
sin
Uaa
Zrm
CC@
ml
w
(LCO)2
(Ceo)z
w
IN*w
Cr(0tl)2
w
(lwy~
RU(OII)2
sna4
Sin@)
Te2(9)
A%
w
ml
Al(OW2(g)
w
w
siH4
U(OH)2
w
cdl
w
w
w
w
w
W*
w
w
w
\
%
-
H2Te(9)
A%
w
w
AIO(CM)(g)
w
w
si2
w
w
C*
Ku
w
w
w
w
●NU . Not Uwd
Model Descriptions
Table 2.3 Chemical compositions of default concretes(Values in w/o)
LimestoneBasalti aggregate Limest
Speci c one
Specie es aggrega common aggreg
s no. te sand ate
concret concrete concree te
SiOz 1
Ti02 2
MnO 4
MgO 5
CaO 6
Na20 10
KZO 11
Fez03 18
A1203 19
Cr203 22
CO* 66
HZO 100
evap
H20 101them
54.84 35.80
1.05 0.18
0.OO 0.03
6.16 0.48
8.82 31.30
1.80 0.082
5.39 1.22
6.26 1.44
8.32 3.60
0.00 0.014
1.50 21.154
3.86 2.70
2.00 2.00
3.60
0.12
0.01
5.67
45.40
0.078
0.68
1.20’
1.60
0.004
35.698
3.94
2.00
Table 2.4 Melting ranges of default concretes
Temperature (K)
Concrete Solidus Liquidus
Basaltic 1350 1650Aggregate
Limestone 1420 1670Aggregate-
Common Sand
Limestone 1690 1875Aggregate
9 NuREG/cR-5843
Model Descriptions
substituted. This is typically what is done whenintegrating CORCON into integral accident analysiscodes such as CONTAIN’ and MELCOR.8
Heat transfer fmm the pool surface is by convection andradiation with the latter mode ordinarily dominant.Convective heat transfer is calculated using thetemperature of the atmosphere while radiative heattransfer uses the temperature of surrounding surfacea. Ifdesired, CORCON-Mod3 computes atmospheric aerosolconcentration for the purpose of estimating the opticalthickness of the cavity atmosphere above the pool.
2.3 Physical Processes
A number of physical processes are included in thenxxleling of molten-fuelkcmcrete interactions; theseinclude internal energy generation, mass and heattransfer, chemical reactions, concrete response, andbubble phenomena. The models are described in thefollowing subsections. The level of detail is “intended tobe sufficient for understanding of the basic concepts andthe code implementation; for details, the reader shouldconsult the references.
In several cases, one or more phenomena are tightlywupled and must be considered simultaneously. Forexample, concrete response determines gas generation,which affects heat transfer and the heat flux to concrete,which in turn feeds back to determine concrete response.We will note such coupled interactions in the discussionwhich follows.
2.3.1 Energy Generation
The entire fuel/concrete interaction process is driven bydecay heat generated in the pool, including actinides,decay products and irradiated structural materials.Because of the loss of some of the more volatile fissionproducts before the pool is formed (i.e., during thein-vessel core melt progression), use of the ANS
Standard decay curve is not appropriate. While decayheating could be calculated using detailed decay chains,as described in the Users’ Manual for CONTAIN,7 theisotopic information is not needed for fission-producttracking in CORCON-MCX13. Therefore, we haveincluded a much simpler decay heat model in the code.
BennetP has shown that the decay power for typicalreactor cores in the 1-hour to lOday time-frame is nearlyproportional to operating power and relatively insensitiveto bumup. Therefore, a SANDIA-ORIGEI@’ calculationwas performed for a reference core representative of alarge PWR core at equilibrium bumup (3320 MWt and33000 Ml@/ MTU). From the results of thiscalculation, we identified 27 elements (excluding noblegases) which account for essentially all the heatproduction in the reference core in the time-frame ofinterest. We assume that the initial intact-core inventoryis proportional to core operating power, as specified bythe user. The initial pool inventory of fission products isthen determined by the fraction of the core contained inthe melt, as given by the mass of U~ and theuser-specified core sire, multiplied by a “retentionfraction” for each element. (Note that as a result of thisscheme, UOZ must be present for decay heat to berepresented.) These retention fractions account forpartial loss of the more volatile species during the in-vessel melt progression phase. The elements, theirassumed chemical ford’ and concentrations in the core,and the default retention fraction’ for each species’ aregiven in Table 2.5. The retention fractions may beoverridden by the user if desired.
The radionuclide release model in the code requires theinitial fission product composition of the core debris tobe specified. The user has two options for specifying thefission product composition. The default is to use thefission product composition determined for the decaypower calculation. Aa another option, the user mayspecify the fission product composition. ‘his option isuseful when performing experiment simulations since themelt has a given composition of fission productsimulants.
The decay power is calculated using the furtherassumption that the specific decay power (W/g-atom)associated with each element is a simple fiction of timeatler SCRAM. The values of the decay power associatedwith each element (also taken from the referenceSANDIA-ORIGEN calculation) are tabulated at eighttime points: 0.5, 1.0, 2.0, 4.0, 10.0, 24.0, 72.0, and 240hours. A power-law interpolation (i.e., log-power isassumed to b linear in log-time) is then used todetermine the decay power at intermediate times. Ifneeded, the decay power may be extrapolated to earlieror later times.
‘Bennett, D. E., “PowerI.evel-BumupParametricStudy,”tmnmrandumto M. Berman,SandiaNationnlLaboratories,Albuquerque,NM, September10, 1979.
%Imters,D. A., privatecommunication,1980.
NuREG/cR-5843 10
Model Descriptions
Table 2.5 Decay-heat elements and groupings
Massconcentra
tion RetentPseudo-ele Element [g-atom/M ionment w fraoti
(thermal) on1
FPM
Metals Mo
Tc
Ru
Rh
Sb
Te
FpOx
MonoxidesSr
Ba
Dioxides Zr
Ce
Np
cm
Nb
Pu
Am
FpAlkMet
Me~#f~liRb
Cs
FpHalogn Br
Halogens I
Zr, ZrOz Zr
.6053
.1545
.3885
.0690
.00244
.0627
.2155
.1915
.7352
.3870
.0422
.00204
.01139
.7921
.00593
.1099
.1662
.1446
.4638
.0539
.01705
.0819
.3776
.00530
.0320
l%iw
l%%
.97
.97
.97
.97
.85
.85”
.90
.90
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.19
.19
.10
.10
( structural)
11 NUREGICR-5843
Model Descriptions
There may be fwther losses from the melt during theinteraction due to further vaporimtion and to mechanicalsparging and aerosol generation driven by concretedecomposition gases. The user has two options fordetermining release from the melt: a completeradionuclide release and aerosol generation calculationusing the VANESA model, or the simple release modelemployed in CORCON-Mod2 and retained in CORCON-Mod3. The detailed treatment in the VANESA model isdescribed in Section 2.3.14 and will not be discussedhere. The simple CORCON-Mod2 model is discussedbelow.
CORCON-Mod2 considered only vaporization of alkalimetals and halogens. It is extremely unlikely that eithergroup will be present in elemental form because thealkali metals boil (at one atmosphere) slightly below 1000K and the halogens boil below 500 K. The halogens willprobably be present as alkali halides (e.g., CSI) withboiling points of 1500 to 1600 K. Under ordinaryconditions, the melt will contain more alkali metal thanhalogea; the excess will most probably occur ashydroxidea with boiling points comparable to the halides.However, the retention fractions may be specified suchthat the amount of halogen present exceeds the amount ofalkali metal. If this occurs, the model inCORCON-Mod3 will eliminate the excess halogen duringinitialization; an appropriate message is written to theoutput file. The remaining halogens and alkali metals arethen removed exponentially in time with an arbitrary butreasonable half-life of 10 minutes. Except in the decaypower model, the fission products and actinides aregrouped as four pseudo elements, as follows:
FpM - metals which may oxidize, and whoseoxides may volatilize
FpOx - chemically inert oxides
FpAlkMet - alkali metals
FpHalogn - halogens.
Thus, the composition of the melt is represented in termsof these four pseudo elements which are resolved intoactual elements only for the calculation of decay power.
2.3.2 Melt/Concrete Heat Transfer
Heat transfer between molten core debris and reactorcavity concrete is controlled by the bubbling of concretedecomposition gases through the melt. This process issimilar to nucleate boiling or gas barbotage except that at
the interface between the core debris and the concrete,gas is being released coincident with melting of the
concrete surface. The molten concrete is miscible inmolten oxidic core debris, but is immiscible in metalliccore debris. At bubble departure, drops of concrete slagare displaced from the surface of the concrete by thebuoyancy of the concrete slag in the denser molten corematerial and the suction caused by the low pressureregion in the wake of the rising bubbles.
Coincident with gas bubbling and concrete melting at theinterface, the molten core debris may begin to solidi~ asa crust adjacent to the melting concrete surface. Thiscrust may be stable or unstable depending on its growthrate, its strength propertia, and the dismptive forcesacting to destabili~ it. If the crust is unstable, it willfragment and be carried away by the rising bubbles. Ifthe crust is stable, it will continue to grow at a ratedetermined by the local tmergy balance. Eventually, itmay provide a barrier to the flow of gases and concreteslag. If this occurs, the flow of gas and slag will then beparallel to the concrete surface.
At extremely high gas generation rates, it may be
possible to form a stable gas film at the melt-concreteinterface. This is the description assumed in previousversions of CORCON. When a stable film is present,
heat transfer across the film is by combined radiation andconvection.
In order to adequately represent melt/concrete heattransfer in the cases described above, models are
r~ui~ for bubble-driven hat t~sfert slag layergrowth and removal, crust growth and stability, and heattransfer across a stable film. Models for bubbledrivenconvection heat transfer are described in Section 2.3.2.1.The models for interracial heat transfer phenomena arediscussed in Section 2.3.2.2.
2.3.2.1 Bulk Pool Heat Transfer
Heat is removed at the boundaries of the pool, which areits top surface snd its interface with concrete.As discussed in Section 2, the internal temperature of thepool adjusts quickly so that these heat losses balance theinternal heat generation, and the heat transfer approachesa steady state. Therefore, we use quasi-steady modelsfor heat transfer in CORCON-Mod3. The principaladvantage of quasi-steady models is that heat fluxes atany time depend on the current state of the pool and noton its history. For example, fully developed flow isassumed in convective correlations and the temporaldevelopment of boundary layers is not considered.
In CORCON-Mod3 we employ a multi-layered poolmodel (Section 2.2. 1) for which it is convenient toconsider heat transfer one layer at a time. Given a trial
NuREG/cR-5843 12
set of interracial temperatures, a solution is found(independently) for each layer. Newton’s iteration isthen used to revise the interracial temperatures to satis~the requirement that the heat flux must be continuous atall interfaces between layers. The solutions for theindividual layers are repeated at each step. Theheat-transfer model allows for several possibleanfigurations in each layer: the layer may becompletely molten, it may have a solid crust on one ormore surfaces, or it may be completely solid. In thissection, we will address heat transfer in a liquid layer orthe liquid portion of a partially-solidified layer. Themodifications neceaaary to account for crusting orfreezing will be described in the next section.
Heat transfer coefficients are required from the interiorof a liquid layer to its surfaces. If the layer were a rightcircular cylinder, there would be three such coefficients:to the upper, lower, and radial surfaces. InCORCON-Mod3, these three heat tmnsfer coefficient-sare evaluated for a cylinder whose thickness and volumematch those of the layer. Boundaries with other layersare assumed to be horizontal, and the corresponding heattransfer coefficients employed directly. For the boundarywith concrete, an appropriate combination is constructed,as described in Section 2.3.2.2, to account for the actualinclination of the surface.
The analysis includes the effects of the passage ofconcrete decomposition gases through the liquid. Modelsare included for gas injection at the bottom surface of themelt, and gas agitation along the sides of the melt. Thebulk pool heat transfer model in CORCON-Mod3 hasevolved from those used in CORCON-Mod 1, andCORCON-Mod2. The model in CORCON-Modl wasbased on the correlation recommended by Blottne#which was a modification of a correlation by Konsetov.nCORCON-Mod2 retained this model for the radial(vertical) surface, but utilized the empirical correlationdeveloped by Ginsberg and Greene” for axial (horizontal)interfaces.
Early comparisons between CORCON-Mod2 predictionsand the remdta from experiments demonstrated veryclearly that the heat transfer models in the cede were notaccurate. Because of this, Bradle~ initiated amassesament of the heat transfer models in the code. Hisrecommendations formed the basis for selection of themodels implemented into CORCON-Mod3.
For the bottom interface of the melt pool, where gasbubbles may be injected from the incoming concrete, theheat transfer coefficient for a liquid layer is calculatedusing the correlation devised by Kutateladze. TheKutateladzex correlation is given by:
Model Descriptions
Nu, = 1.5 x 10-3 Kum f(q) (1)
where Nu, is the Nusselt number baaed on acharacteristic length equal to the Laplace constant a,
a = {u(/[g@t - pa)l}’n ,
Ku is a dimensionless number detined as
Pr p j’Ku=—
gP
q is a dimensionless gas velocity defined by
(2)
(3)
(4)
and f(q) is given by
f(q) =
{
1, ifq<l (5)
q-in if q> 1
In these equations, j’ is the superficial velocity for thegas entering the melt, Vw is a transition velocitycorrelated by
v, = 4.0 x lo-%tlpt (6)
Ut is the surface tension of the liquid, pt is the deaaity ofthe liquid, p’ is the density of the gas, p is the pressure
at the interface, and Pr is the Prandtl number for theliquid. For many fluida, the transition velocity calculatedusing the above equation is comparable to the velocity fortransition from bubbly to chum-turbulent flow. The heattransfer comelations have been formulated such thatalternate equations for the transition velocity can beeasily substituted into the model.
In CORCON-Mod3, a smooth transition for N% throughthe value q = 1 is effected by using
Nu,, /q + NUC2qNu. = (7)
I/q + q
where Nu,l and Nua are defined as follows
13 NUREGICR-5843
Model Descriptions
Nual = 1.5 x 10-3 Kum (8) Nu = rnax (0.54 Its’”, 0.14 lta’~) , (11)
Nu,z = 1.5 x 10-3 Kum q-’n
Results from experiments with gas agitation of heated for axial heat transfer in an unstable thermal gradient,surfaces suggest that heat transfer along vertical walls is andless scmsitive to the superficial gas velocity than isindicated by the Kutateladze correlation.n~’ Theexperiments show also that at high gas velocities
atvective heat transfer at horizontal and verticalsurfaca is nearly the same. These results suggest that amodified form of the Kutateladze correlation should beused for calculating the heat transfer coefficient to theside of a liquid layer. We have chosen, therefore, torepreaat convective heat transfer along the verticalsidewalls using only the churn-turbulent (i.e., q > 1)form of the Kutatelad.ze correlation. This form of thecorrelation depends on the superficial gas velocity raisedto the one-sixth power. This dependence is in the rangeof literature valuea which indicate a 0.14 to 0.33dependence on gas velocity.~n
For liquid layers within the melt pool, a correlationdevised by Greenez is used to calculate the heat transfercoefficient in each layer, except for the uppermost meltlayer. Greene’s correlation is
Nu = max (0.59 Ral’4, 0.10 Rain) (12)
for radial heat transfer. Here
Nu = ht/k (13)
is the Nusselt number, baaed on the layer thickness, f,md
Ra = j#3ATt3/m (14)
is the Rayleigh number. AT is the temperaturedifference, fluid to boundary. In Equations (11) and(12), the first expression in parentheses corresponds tolaminar (low Rayleigh number) convection and thesecond to turbulent (high Rayleigh number) convection.
h = 1.95 k @e Pr)O”n/r~, (9) The heat transfer coefficient at a surface where thetemperature gradient is stable is calculated directly fromEquation (12). If the temperature gradieat is stable at
where k is the thermal conductivity, Re is the Reynolds one interface but unstable at the other, convective flowsnumber for the liquid baaed on the characteristic length r~ driven by the unstable gradient steepen the stable~d the superficial gas velocity j’, Pr is the Prandtl gradient. To acmmt for the resulting increase in heatnumber for the liquid, and r~ is the average bubble radius transfer, the heat transfer coefficient for the stablein the layer. gradient is then calculated from
For the uppermost melt layer (adjacent to the atmosphereor coolant), the heat transfer coefficient is calculatedusing a modified form of the Kutateladze correlation
Nu_=l+
[
1 +2Nu 1IAT~l ‘“’
(Equation (l)), which accounts for the greater surfaw “’-’m (15)
ama of the unstable surface. For the upper melt surface,the Kutateladze correlation is simply multiplied by anarea enhancement derived by Farmer? Kulacki and co-worker#-33 have developed correlations
for convective heat transfer in internally heated fluidlayers. The model in CORCON-Mod3 reproduces the
A“ = 1 + 4.5 ‘~ (lo)q various correlations with a maximum error of 30 perceat
and an average error closer to 10 Percent.’]d
At sufficiently low gas velocities, heat transfer in molten The natural convection limit is imposed indebris is dominated by natural convection. This process CORCON-Mod3 by choosing the greater of the Nusseltis modeled in CORCON-Mod3 by conventional numbers calculated for bubble+mhanced and for naturalNusselt-Rayleigh correlations in the fortmm convection. The actual implementation assumes that
c&cene, G. A., privateconununication,March, 1991.
NuREG/cR-5843 14
Model Descriptions
Equation (15) may be applied even when N&tib isevaluated for bubble-enhanced convection.
For very thin or very viscous layers, the naturalmnvection correlations above can yield smaller heatfluxes than would result from simple conduction.Therefore, an approximate conduction limit is impaed inCORCON-Mod3, in the form of a lower limit in theNusselt number. The formulation is based on theaverage temperature of the liquid layer, T, which isconsistent with CORCON usage and is normal practicefor convective heat transfer. For convection, there is an(usually unstated) assumption that the boundmy layers arethin and that the lwd temperature is essentially equal tothe average temperature. The assumption fails at or nearthe conduction limit, where the temperature profile isquadratic (for a uniform volumetric source). This is thereason that we have chosen an “approximate” limit ratherthan an “exact’ one. A fill discussion is contained inReference 1le.
In the radial direction, the exact conduction resuh for aquadratic temperature profile is
q#‘u’ + k(Tt . T,)
4t=—
R(16)
where Nu~ is the Nusselt number baaed on layerthickness, and R is the average radius of the layer. Thisprovides the desired lower bound on radial heat transfer.
The exact axial conduction result is
~ = X[Tt - T~ + (-T~ + 2T/ -T#t
% = -2k [Tt - 1T~ + (-T~ + 2Tt - T~) /t
(17)
(18)
where the fluxes are positive up, and subscripts “B” and“T” refer to the bottom and top surfacea, respectively.Note that qs in Equation (17) does not necessarily havethe same sign as (TB - T() and similarly for ~ and (T, -Tr) in Equation (18), which would greatly complicate anattempt to impose the ‘exact” limit. In order to avoidthis, we have employed the approximations
~ = 2k{Tt - T~(19)
+ 2 [max ((T/ - TJ(Tt - T,), 0)] ’’j/t
and
q~ = -2k{T( - T~(20)
+ 2 [max ((T~ - TJ(Tf - TJ, 0)] ’~)//
which have the desired properties, and the same values asEquations (17) and (18) for the limiting cases of nointernal heating (T = (TB + T~)/2) and of large internalheating (TB - Tt = T~ - Tf). In fact, as discussed inReferenoe 1le. the approximation errs only in thetemperature at which steady state is achieved for givesboundary temperatures and VOhlXMtriC heating. ThiS
error is unavoidable if we wish the heat fluxes to havethe same sign as the temperature” differences. In anycase, if the conduction limit in a liquid is reached, thelayer must be relatively thin, and tie maximum error inthe average temperature, one third of the temperaturedifference across the layer,l]O must be relatively small. Itrepresents only a minor error in the seasible heat contentof the layer and has no other cmaequences. Equations(19) and (20), rewritten in the form of Nusselt numbersbased on layer thickness, are employed in CORCON-Mod3 as lower bounds in the Nuaaelt numbers in a liquidlayer.
2.3.2.2 Interracial Heat Transfer
At the time CORCON-Mod2 was released, it wasassumed that gas releaae from the decomposing concretewas sufficient to form a stable gas film betwem theconcrete and the debris pool. There was no convincingexperimental evidence to support or disprove thisassumption. Conaequemtly, CORCON-Mod2 employed amodel for meltkcmcrete heat transfer that assumed theboundary region was dominated by a stable gas film andthat on horizontal and nearly horimntal surfaces theTaylor instability leads to formation of bubbles whichenter the melt, while on more steeply inclined aurfwesthe gas forms a flowing film.
Since that time, the assumption of an initially stable gasfilm has been shown to be incorrect under most realisticaccident conditions.fi Instead, gas release is usually farless than that required to forma stable gas film, andintermittent debrisumcrete contact occurs. Thisintermittent contact results in periodic growth andremoval of slag from the interface, and, depending on thetemperature of the molten debris, may also lead toperiodic growth and removal of debris crusts. Simplifiedmodels for these processes have been developed andimplemented in CORCON-Mod3. The stable gas filmmodel implemented in CORCON-Mod2 has beenretained, and the user can select either the slag or gasfilm model at the start of a calculation. No transitionfrom one model to the other is included.
15 NuREG/cR-5843
Model Descriptions
The following is a brief discussion of the slag film andgas film models. For further discussion of the slag filmmodel the reader is referred to Reference 2S.
SlagFilm Model
Simultaneous concrete melting and molten core debrissolidification can be modeled using an analysis similar tothat used by Epstein~ to model freezing of molten reactorfuel on the surface of stainless steel cladding. Epstein’smodel comiders four regions: the initially molten phase,the solid substrate, the solidified molten phase crust, andthe layer of melting substrate. The energy equation ineach of these regions has the form:
m, ] aTi=—— (21)
= ai at
where Ti is the temperature in region i, ai is the thermaldiffuaivity of region i, x is the spatial location, and t istime. (Note that internal heating of the molten phase dueto decay heat has been neglected. It can be easily shownthat during a bubble cycle, internal energy generation canbe neglected.)
The energy equation is solved subject to the followingboundary conditiomx continuity of temperature at eachinterface, continuity of heat flux (including effects ofphase change) at each interface, and the temperature ofthe melt and substrate at “infinity” is fixed at the initialtemperature of the region.
Given these boundary conditions, the temperature of eachof the four regions has the general form
the interface between the core debris and concrete can bedetermined from the following equation:
(24)
where Ti is the interface temperature, Tim and T- arethe melting points of the initially molten phase and solidsubstrate, and u is the following function of materialproperties:
f -1 In
(2s)
where k and a are the thermal conductivity and thermaldiffusivity of the respective regions, and the subscripts 1sand 2m refer to the solidifying molten phase and meltingsubstrate, respectively.
Under some conditions, solidification of the molten phasedoes not occur. The equation for the interfacetemperature is then derived following the same procedurebut with three regions rather than four. The resultingequation for the interface temperature is
T,O - T, @
T,O - T- = u + erf(~(26)
where TIO is the initial temperature of the molten phase,and u is now based on the thermal conductivity andthermal diffusivity of the molten phase rather than thecrust.
[1The preceding analysis is implemented in
T, = A1+Bied & (22) CORCON-Mod3 by treating the transient slag layer2(a#1n growth and removal process as a heat transfer resistance
in series with convective heat transfer within the molten
with the positions of the solidification and melting fronts pool. At the interface between the slag layer and the
given by equations of the following form: molten pool
Xi(t) = 2 Ai (ai t)’n (23) hPCP-Ti)=h,ci-TJ (27)
In these equations, &, B*, and ~ are constants where h is the convective heat transfer coefficient, anddetermined by applying the boundary conditions. the subscripts p, i, c, and s refer to the debris pool, the
interface, the concrete surface, and slag layer. The poolApplication of the boundary conditions results in a set of heat transfer coefficient is determined using the equationsalgebraic equations for the constants. By algebraic discussed in the preceding section. The concrete surfacemanipulation, this set of equations can be reduced to two temperature is simply the user-specified ablation
dental equations for A, and &simultaneous tranacen temperature. The interface temperature is determinedAfter A, and & have beem determined, the temperature at using the analysis described above. Solving this equation
for the slag heat transfer coefficient yields
NuREG/cR-5843 16
Model Descriptions
.hTP-Ti The result may be cast in the form of a Nusselt numberh,
‘Ti-T (28) baaed on film thickness asc
=h, y
NUB =h, 6B
= 0.804 (32)
The overall heat transfer coefficient (between the molten~
debris and the concrete surface) is given bywhere h~ is the heat-transfer coefficient, & is the film
h, h, thickness, and ~ is the thermal conductivity of the gas.hO=— (29)
h, + hP The factor 0.804 is the fraction of the surface notoccupied by bubble sites md, therefore, available forheat transfer. The film thickness satisfies
Substituting for ~ into this equation results in
6; = 15.05 Ren L3 (33)
ho = hp (+) (30)
Here Lisa material property
Bradleyx found that the value of -y/(-y+ 1) is relatively
[1In
insensitive to the material properties of the core debris. L=P: (34)
Whether the core debris is metallic or oxidic, y/(-y+ 1) 8P’(P, - P,)was found to fall within a narrow range of 0.29+0.07.In light of the uncertainty in the heat transfer models, we where g is the acceleration of gravity, subscripts t and gdecided to implement the model assuming a constant refer to pool material and film properties,. respectively,value of y. The value of 7 corresponding to a value of andy/(y + 1) equal to 0.29 is 0.41. Hence, the slag heattransfer coefficient is aasumed to be given by Re = ptj’a
B— (35)
h, = 0.41 h, (31)P’
Currently, the code provides a lower limit to the slagheat transfer coefficient of 1000 W/m2 K. This valuesimulates conduction-limited heat transfer across a thin (1mm) slag layer. Calculated results should be relativelyinsensitive to this value since it is likely to be invokedonly when a debris crust exista at the interface with theconcrete. Therefore, heat transfer would be controlledby conduction through the crust, and the contributionfrom the slag thermal resistance would be small.
Stable Gas Film Model
For a stable gas film, two models for heat transfer areused, one for nearly horizontal tihns in which there isessentially no gas flow parallel to the concrete surface,and one for inclined films in which there is gas flowparallel to the concrete surface. A film is classified as“nearly horhmntal” if its inclination is less than 15degrees.
For a stable gas film on a nearly horizontal surface, heattransfer is computed from a mechanistic model based onmomentum balance in a Taylor-instability bubbling cell.35
is the Reynolds number baaed on the I#mx comtant(defined in Equation (2)), and the superficial velocity j’with which gas enters the film. Note that if the processmodeled were really film boiling, the equations would beclosed through the relations
(36)
where ti~gis the effective heat of vapori~tion. Relativelysimple manipulation can then be used to reduce thepresent model to a form similar to Berenson’#correlation for boiling on a flat plate,
‘=068[k’%$:~J~’37)This bubble model is used for inclinations less than 15degrees in CORCON-Mod3. Above 30 deg~ we use aflowing-film model, and consider both laminar andturbulent films. The transition model used between 15degreea and 30 degrees will be described later. The filmmodels are mechanistic, based on momentum balancks in
17 NuREG/cR-5843
Model Descriptions
an inclined flowing film, with the Reynolds analogy usedfor heat transfer in the turbulent case. The results,expm.saed as Nuaselt numbers, are
(38)
for the huninar case and
N% = ~ ~fi, = ().()325 pr’n l?e~ (39)
for the turbulent case. In these equations, Pr is thePrandtl number for the film, and R% is the Reynoldsnumber baaed on film thickness:
(40)
with U the average flow velocity in the film. l%e filmthicknesses satis~
& .5.61 ReF L3/si33 o (41)
& = 0.0469 ReY L’/sin 0 (42)
where 0 is the inclination of the film from the horizontal.
In CORCON-Mod3, we employ a simple transitionbetween the 1* and turbuknt flOW regimes whichwill ensme continuity of iilm thickness and heat-transfercoefficient with the appropriate limits:
(45)
where the various film thicknesses and Nusselt numbershave been defined above.
A transition between the bubbling model and thefilm-flow model is also required. We have incorporateda mechanistic model l’; based on a momentum balancewith a fraction, f, of injected gas going into bubbles andthe rest into establishing the film. The results have theform
/i3 = C5;+ f(sin 150/sin e) a: (46)
h = [fN~ + (1 - f)N~] kg/ti . (47)
A transition is achieved by decreasing f linearly with sin0 from 1 at 15 degrees to O at 30 degrees.
Bwmw of the high temperatures involved, heat transferby radiation across the gas film must also be included.The radiative component accounts for about one half ofthe total heat flux in many CORCON calculations. Weuse the form for a transparent gas between infiniteparallel gray walls
U5 (T: - T:)
~ = (l/&p + l/cw - 1) “(48)
Here us is the Stefan-Boltzmann constant, TA and TWarethe temperatures of the pool side of the gas film and ofthe ablating concrete surface, respectively, and ~ and Qare the comesponding emissivities.
The convective heat-transfer coefficients above involvethe superficial velocity of gas entering the interfaceregion and, in film flow regions, the film-wise massflow. The latter is determined by the entering gas flowat all upstream points. The superficial gas velocity isdetermined by the concrete response, which isdetermined by the total heat flux. This, in turn, involves
the heat-transfer coefficients themselves. Aself-consistent solution has been found advisable fornumerical stability; this is obtained through a simpleiteration.
Note that Pcu/i is the mass flow per unit width of film,which satisfies
(49)
where r is the local radius of the cavity, s is the pathlength measured along the film, and f is the interpolationfactor which imposes the transition from bubbling to filmflow.
We solve this equation by use of a simplepredictorumector method. An inner iteration, asdescribed above, is required to solve the non-linear(because of radiation) energy balance at each point. Incases where the spacing between body points is too greatto resolve the development of the gas film,
NUREGICR-5843 18
Model Descriptions
intermediate points are consideredroutine.
Numerical Solution Technique
by the integration
H@ transfer through the (slag or gas) film is formulatedin terms of the temperatures of ita surfaces. On the meltpool side, this temperature, T,, is delemnined implicitlyby the requirement that the heat flux be continuous. Thesubroutine SURFEB is used to perform a surface energybalance at the interface betweem the melt and the film andto evaluate its temperature at each spatial point. Thenonlinear equation
(50)
is solved for TA using Newton’s iteration. (Note that theradiation term disappears if the slag film model isselected by the user. This greatly simplifies the solutionfor T..) A complete solution, including the fillevaluation of pod-side heat transfer within the iterationloop, would be extremely expensive in computer timebecause the energy balance is typically performed athundreds of points along the podconcrete interface.
T%e crust formation modeI in CORCON-Mod3 wasdeveloped originally for CORCON-Mod2. This modelintroduces a discontinuity in behavior when TA passesthrough the solidification temperature, T,. Thequalitative dependence of ~ on T~ is shown inFigure 2.1. When T~ is slightly greater than T,, no crustexists md the derivative dq/dTA is given by a convectiveheat-transfer correlation. When T~ is slightly less thanT,, a crust must be present. when a crust is present, thederivative is small because a small change in surfacetemperature merely changes the (steady) crust thicknesswith very little change in the heat flux. The discontinuityin slope must be accounted for to prevent unphysimlresults or failure of the iteration which determines T~.
As in CORCON-Mod2, CORCON-Mod3 uses apiecewise linear approximation to qP as a function of T~.There are two casea, as shown in Figure 2.2, dependingon whether or not a crmt was present (TA was less than
T~ when within-pool heat transfer wss last evaluated. Ifso, ~ is evaluated as
qp=t#’’+~(T-TAd), (51)dTA A
for TA 5 T,. For T* > T,, ~ is extrapolated linearly toxero at TA = T~, where TM is currently taken as the
temperature of the liquid center of the, layer. Thisisillustrated in Figure 2.2A. If, on the other hand, nocrust was previously present (TA was greater than T~,Equation (51) is used to evaluate ~ for T. > T,. ForT~ < T,, the heat flux ~ is assumed to be constant asshown in Figure 2.2B.
2.3.3 Coolant Heat Transfer
If a coolant layer is present, CORCON-Mod3 calculateboiling heat transfer. l%e boiling heat tninafer model inthe code includes the full boiling cuwe, baaed onstandard pool boiling correlations as summarized byBergles.n Corrections are made for the effects of gasinjection at the meltkoolant interface and coolantsubcooling. The various correlations involved are notused directly in CORCON-Mod3. This is possiblebecause the boiling heat transfer coefficient for a givesfluid, water in this case, is a fimction of pressure andtemperature only, with all of the detailed depedena ofmaterial properties on temperature md pressure containedin the one function. A series of calculations wasperformed outaide the code, using thermal and -rtproptxties from the Steam Tables,= to generate tablea ofvaluea. These were then fit by simple analytic formswhich reproduce the tables within 3 percent over thepressure range of 10 kpa to 10 MPa (saturationtemperatures from 320 K to 580 K). The principaladvantage of using these fits is that extensive libraries ofwater properties need not be included in the code.
Nucleate boiling is treated by using the Rohseno@correlation for the temperature rise and the Zubefi41correlation (with Rohsenow’s coefficient~ for the criticalheat flux to calculate the values of ~ and of TW- T- atthe point of critical heat flux (where TW,as used here, isthe temperature of the debris surface). These arerepresented as
%nP=1.50 x loqlo-sp)”””s (52)
1.0 + 5.97 x lo-qlo-~p)’”’”
~w - Tm)m =1.71 x 10 C,f (lo-sp)4””2 (53)
loo + 7.02X ltYO(10-5p~’” ‘
where all values are in S.1. units (i.e., q is in W/m2, p isin Pa, and T is in K) and the surface coefficient, Cd, istaken as 0.01. The nucleate-boiling portion of theboiling cume is then represented as
NuREG/cR-5s43 19
Model Descriptions
NuREG/cR-5843
CRUST 1NO CRUST
adx-2 I1, Ib I3z I
II
TS
INTERFACETEMPERATURE,TA
Figure 2.1 Dependence of heat flux on surfam tempexatuw
20
Model Descriptms
-.
a. 7A“d < T~
okI1-.I
?$ II.4k I
1- 1I I5 Ix I I
III
k~Aola
‘s ‘M\
INTERFACE TEMPERATURE, TA
I
t-awz
——’9=—9=— —
I
I III
III
I I
Ts TAO’d\ \
INTERFACE TEMPERATURE,TA
Figure2.2 Approximation to heat flux as a function of interface temperature
21 NuREG/cR-51343
Model Descrmtions
q = %[(L -Lt)(’L - Luwra (54) with temperature as the 3/4 power of (TW- TJ. Weassume that this dominates the implicit temperaturedependence through material properties, so that ~ may
where the exported is that attributed to Rohsemm in be calculated as
Refereme 37.
qc=qquii[(’L- TJ(L - L)H~ “(61)
The effect of suhcooling on nucleate twihng is included,using the expression recommended by Ivey:a
The mdiative contribution, ~, is givcm for intinite
%aw,d%a%d “ 1 + %Fnl - ~.~ ‘(55) parallel gray walls by
where T~ is the bulk temperature ot the fluid and the % (T: - T:)%=
(62)
coefficient C- is given by l/&w + l/&, - 1 “
f ~ W4 where & is the ernissivity of the wall and q that of the
c’ IIk+ q.* = 0.1
(56) cmlant.-
x~”CORCON-MocU includes the effects uf gas barbotage
This coefficient is calculated aa a fiction of pressure and coolant subcooling on film boiling heat transfer.
fkom the fit Both gas barbotage (i.e., noncondenaible gas injection atthe interface) and coolant subcooling can greatly increase
4.77 x lo”qlo-’p)+”mthe film boihng heat flux, while also increasing the
CM = (57) temperature at which the vapor film collapses (theLO -6.29 X 10-3(10-~~W “ Leidenfrost point).
The film boiling regimeis baaed on the BerensoncmeJation# for the heat-transfer wefficient in filmboiling and for the teqemtm differenw at theLeidenfrost tempemtw @inimum tilm-boiling point).These have heat fit for use in CORCON-Mod3 ss
1.88 x Id(lo-$p)ow (58)% “ 1.047.58 X 10-s(lO-~)O’m
(’rW- TJW =8.56 x 10’(lO-*)”M (59)
1.0 + 1,38 X 10-’(10~)0”* “
Above the Leidenhst point, the total heat flux includingradiation is repmaented, in accordance with Reference37, as .
.
q = % (ol)’n + % “(60)
Here ~ is the convective heat flux in the abseace ofradiation, and the factor (qJq)in accounts for the tict thatthetotalheat flux amtribukw to the vaporhtion rate,which determines the thickneaa and thermal resistance ofvapor film. l%e heat flux ~ has an explicit variation
Gas barbotage increases film boiling heat transfer byincreasing agitation of the mcdant, and by increasingagitation of the melt surface. In CORCON-Mod3, theenhancement to the film boiling heat flux due to gasbarbotage is included as a multiplicative factor. Thefactor used depends on whether the* underlyingthe coolant is solid or liquid.
If the surface underlying the coolant is liquid, then theenhancement factor is calculated ttaittg a correlation ofexperimental results advanced by ~reane.d l%eexperimental results were for freon and water on threedifferent molten metals, bismuth, lead, and Wood’smetal. The expression proposed by Ckeerte is
Q:=fi11+11085[+10”’’(1 +2j;)where Q is the ratio of the measured heat flux to theheat flux calculated using the Berenson cmddkm, j; =
j,~., j, is the mpw!kid gas velocity, U- is theterminal rise velocity of the noncondenaible gas bubblesin the liquid metal, and Ja*is defied by
‘Oman%0. A., prlvuo oonununlomlon,Sbbnmy, 1990. ,]
NURWER-S843 22
Model Des nptions
- AT~Ja” = ~P’”
h(t + 0.5 C,.vAT:(64)
where ATti is the wall superheat TT - T@, and CA, is thespecific heat of the vapor at constant pressure.
If the surface underlying the coolant is solid, then theenhancement factor is calculated using a correlationadvanced by Duignan. u This correlation is W onexperiments in which gas was injected through heated,drilled plates in contact with an overlying water pool.The correlation used in CORCON-Mod3 is
Q.”=~+04j;/Ja-T’(65)
where all variables hab e been previously defined.
When the temperature of the core debris is calculated tolie between the solidus and liquidus temperatures of thedebris mixture, the two enhancement factors shownabove are weighted by the surface solids fraction. Thesolids fraction is estimated using
the thickness of the vapor film. The reduced filmthickness permits greater heat transfer by conduction.
The enhancement to heat transfer owing to coolantsubcoohng in the film boiling regime is included as amultiplicative factor. The factor is calculated using m
equation of the form proposed by Siviour and EA# andDhir and Purohit:4
~: = 1 + C (ATJ’’’:~AT# (69)
where Q;b is the coolant subaohng factor, AT~ is thetxmlant subcooling (i.e., T@ - T~, and C is chosen tobe 0.98, baaed on comparison to expernnental msuha inReferences 46 and 47,
By reducing the thickm.a.wof the vapor film, thesubcooling of the coolant reduces the atability OSthe film,and increases the minimum film boiling temperature.The effect of coolant subcoohng on the muumum filmboiling temperature N calculated using a simple linearcorrelation of experimental data:~q’a
AT-* = ATWO + 8.OAT_ (70)
where T* is the liquidus temperature, T~ is the sohduatemperature, and T., is the surface temperature. The gasbarbotage enhancement factor is then calculated from
Q*=Q:(I-cP)+CL*C$ (67)
The increased agitation of the melt-coolant interfacecaused by gas barbotage destabilizes the vapor film,
thereby increasing the temperature at which the filmcollapses. The effect of gas barbotage on the minimumfilm boiling temperature is accounted for by the equation
AT_m = ATN,O + 463.1 j}w’ (68)
where ATtiw is the minimum film boiling superheat inthe presence of gas barbotage, AT-O is the minimumfilm boiling superheat in the absenw of gas barbotage,and jc is the superficial gas velocity.
Subcooling of the overlying coolant pool can alsoenhance heat transfer in the film boiling regime. Whenthe overlying coolant pool is subcooled, energy isremoved from the gas film by the overlying subcooledwhmt. ‘I12enet effect of this cooling is a reduction in
where AT~ = T~ - T4 is the minimum !ilm boilingsuperheat in the presence of coolant subcooling, andAT-O = T~ -T. is the minimum film boiling superheatin the absence of coolant subcuoling.
In the absence of experimental data for the combinedeffects of coolant subcooling and gas barbotage, we haveimplemented the following simple equations to describethe combined effect of these phenomena on the filmboiling heat flux and minimum film boiling temperature:
Q:=1 + [(~ - ]~ + (Q: - l~]’n , (71)
and
[(AThu = ATW,O + ATW - ATWO )2 (72)
(.+ ATM ~ - ATWO )’l’n .
The transition-boiling regime is represented by a simplelinear interpolation in h q vs. h AT- between thecritical heat flux and the Leidenfrost point. The latter isadjusted to account for the effects of coolant subcocdingand gas barbotage.
23 NuREG/cR-5843
2.3.4CrustFomnation and Freezing
After sume period of interaction, core debristemperatures WIli fdi m the point where solidificationbegins in the eariy stagea, we assume that crests wiliform at one or inure mterfwes with the interior of thelayer remaining ilquid. (This is not the only possibility:the crusts may be unstable, or the entire meit may form aslurry.) At kiter times, considerable f%eezirtg may occur.If part or aii of a iayer becomes frozen, heat can beremoved from it by conduction oni y, which is ordinarii yfar ieas effective than convection. Because of intemaiheating and the fact that cooiing cannot continue unieasheat iosaes exceed sources. freezing is iargeiyseif-iinuting.
For some accident scenarios, the core debris may imtialiybe soiid or partially solid. !f the degree of solidificationis such thai internally-generated heat cannot be removed.the debris temperature wiii rise and material wiii meltuntil convective heat transfer is sufficient to aiiow abaiance to be achieved. in general, meiting wiii proceedoutward from the center of the debris.
A complele formulation of the probiem invoiveatransient, twodirnemsionai heat transfer with conduction,umvection, and change of phase. The ~tiai resolutionmust be sufficient to resolve centimeter-thick crusts onlayers with dimensions of meters. A numerical solutionof the fidi probiem wo,uid be very difficuit, if notimpossible.
A major effect of the presence of .soiid crests on heattransfer is the iirnitation of convective losses because theboundary temperature of the liquid cannot faii beiow thesolidification temperature. Aiso, a crust provides anaddihorud thermai resistance between the interior of thepooi and ita surroundings. Both effects tend to reduceheat ioaaes and siow internal cooling rates (or forcereheating) so that a steady state is approached. We haveretained in CORCON-Mod3 the relatively simplequasi-steady-state model deveioped for inciusion inCORCON-Mod2.0 The model is described in thefollowing paragraphs.
The modei is formulated in terms of the averagetemperature of the iayer, which is known from ita massand energy content, although it assumes the existence ofa temperature profile within the iayer. The basicapproach is to constmct a steady-state soiution to theheat-transfer equations in a right circular cyiinder whoseaverage temperature, boundary temperatures, thickness,and voiume ali match those of the actuai iayer. Theresulting heat fluxes at the boundaries are then used at
the corresponding boundaries of the actual iayer. Asdescribed above, the state of a layer wili evoive toward a ~situation where heat losses balance unemai heatgeneration. The avemge temperature and the boundaryheat fluxes at this steady state are determined by theinternal heating and the boundary temperatures for thelayer.
AS a tirther simplification, the problem is reduced to twoindependent onedlrneasionat problems, one axial and oneradial, by performing mriiai and axial averages,
rtspectiveiy, of the fuii two-dimensional problems. Thisis a famiiiar approximation for convedive heat transfer inan almost isothemai liquid layer with thin thermalboundary iayers, and its accuracy is seidom qu~tioned.It might be expected to be iess accurate in the oppositeiimit of conduction in a sohd. Therefore, the modei wastested by comparing its predictlona with tie exactsolution for steady-staie conduction in a right circularcyiinder with uniform volumetric heating and specifiedSurfalx temperatures. 1lh me agreement between tie two
calculations was found to be good: ditienmces in thepartition of heat and in the effect of boundarytemperatures on the average temperature were ie.ss than10 percent, and the calculated temperature rises due tointernal heating differed by less than 20 percent.Therefore, we beiieve that the onedimensionaisimplification is sufficiently accurate for use inCORCON-Mod3.
Within a one-dimensional calculation, a iayer may beentirely liquid, entireiy soiid, or liquid with a soiid crust.For the axiai case, a crust may exist on the top, on thebottom, or both. in iiquid regions, heat transfer is byconvection (natural or bubbie-enhanced) with aconduction limit as described in Section 2.3.2.1. In soiidregions, it is by conduction. The aii-iiquid case employsthe resuits of Section 2.3.2.1 directiy, whiie the ali-soiidcase uses the tmaiytic resuits for steady-state conductionwith a constant volumetric source which foiiows from
%= -kdTldz (73)
dq#iz = S,
q, = -kdT/dr
d(rq~ldr = rS r.
(74)
(75)
(76)
Here the heat flux, q, is positive upward or outward, andS is the volumetric heat source. These reiations iead to
NUREGICR-5843 24
Model Descriptions
fiuniliar quadratic temperature profiles. In terms ofboundary and average temperatures, the heat fluxes are
q, = k(-4T~ + 6~ - 2T,)/L , (77)
q. = k(-2T, + 6~ - 2T~)/L , (78)
q, = 4k(; - R)/R , (79)
with subscripts B, T, and ~ referring to the bottom, top,and radial surfaces. Here T is the average temperatureof the layer, and L and R are its thickness and radius,
respectively. Note that the volumetric source does notappear m these results; the implications of this are furtherdiscussed in Reference 1lh.
In the case of a liquid with crusts, the liquid sublayer issolved first using assumed values of its averagetemperature and thickness of radius, T~ and t or R~. andappropriate boundary temperatures. For any surface atwhich a crust exists, the boundary temperature isassumed to be the solidification temperature. Conductionin a crust is again governed by Equations (73) through
(76), and the tempemture profile is again quadraticwithin the crust. We require continuity of the heat fluxat the interface with the liquid and set the volumetricsource in the crust equal to that in the liquid,
s, = (% - q,p , (80)
s, = 2qrlR, , (81)
This leads to crust thicknesses and average temperaturesof
~, = (2T~ + T,)/3 + qu ti,/6k(85)
~~ = (2T~ + TJ/3 - ~, dT/6k (86)
(87)
for those crusts which are~re-sent. Here T, is thesolidification temperature, T= is the average temperatureof crust x, and ~f is the heat flux at its interface withthe liquid, where “x” may be B, T, or R. In some cases,one or more of Equations (82), (83), and (84) may haveno real solution. For this to happen the effective SOUIW(divergence of the heat flux) must be negative, whichmay occur if a layer is being heated by an adjacent layer.The solution is to repeat the calculations with the soumemade less negative by increasing the assumed liquidtemperature and/or dimensions.
In general, neither the total layer thickness (or radius)nor the overall average temperature thus determined willbe correct for the layer. This requires an iteration on thethickness and temperature of the liquid sublayer. Atwo-variable form of Newton’s iteration has been foundeffective for this. A ‘bound and bisect” backup has kincluded for reliability.
2.3.5 Bubble Phenomena
Gases that rise through the debris pool as bubblesinfluence the heat transfer in the pool, as described inSection 2.3.2. The bubble properties and behavior alsoaffect mixing between the layers and the aerosol andfission product release.
Owing to the importamx of the bubble properties in theinterlayer mixing models developed by Greene’3 and now “implemented in CORCON-Mod3, the bubble behavior
models have been improved in CORCON-Mod3. Thenew models are described in this section.
Bubble rise velocities are computed for three regimesbased on bubble geometry and size. Regime 1 applies tosmall spherical bubbles with internal gas circulation.Regime 2 applies to ellipsoidal bubbles with internal gascirculation. Regime 3 applies to spherical cap bubbles.
The equation for bubble rise velocity U~ used in Regime1 is derived using classical hydrodynamic analysis:m
g 42 P,u,=—12A
(88)
2s NUREGICR-5843
Model Descriptions
where g is the acceleration due to gravity, ~ is thebubble diameter, p] is the density of the surroundingliquid. and p, is the viscosity of the aumwnding liquid.
The equation used for bubble rise velocity in Regime 2id’
[ 1m
2. 14utUb . + 0.505 gd, (89)
Pt d.
where u, is the surface tension of the liq~id, and ~ is theequivalent direr of the bubble.
The equation used for bubble rise velocity in Regime 3 isthe Davies-Taylor formulan
(90)
when r. is the radius of an equivalent spherical bubblewith the same volume as the spherical cap bubble.
CORCON-Mod3 determines the appropriate regime by!irat mnparing the rise velocities for regimes 1 and 2.If the regime 1 velocity is greater than the regime 2velocity, the bubble is not spherical, and is, instead, ineither regime 2 or 3. (If the converse is true, the bubbleis spherical and the regime 1 value is appropriate.) Thislogic can be used because there is an inflection in thebubble rise velocity curve at the transition t%om sphericalto ellipsoidal bubbles. Next the regime 2 and 3 velocities
are ampared. If the regime 2 value is greater than theregime 3 value, the bubble must be a spherical cap,otherwise the bubble is an ellipsoid. The regime 2 valueis used for ellipsoidal bubbles, while the regime 3 valueis used for spherical cap bubbles.
The volume of the debris pool is inflated by the volumeof the gas bubbles, a phenomenon known as ‘levelswell. ” CORCON-Mod2 used a form of the drift-flux
cormlationn to determine the level swell of the melt.BrockmannS found that this correlation overpredicted thelevel swell for steel melts, and he developed a correlationthat appears to be accurate for a wide range of materialproperties. Brockmann’s correlation is
(Y= O.128M 4W (j,*~W
where a is the volume fraction, j-’ is a dimensionlesssuperficial gas velocity, given by
NUREGICR-5843
(91)
and M is the Morton number, given by
(92)
(93)
The volume t%wtion is limited to a maximum of 0.42, assuggested by Blottner.Z
Accurate prediction of bubble size is critical to thecalculation of interlayer mixing (see Section 2.3.6). Thebubble medel used in CORCON-Mod3 treats threebubble formation mechanisms. In this formulationbubble size depends on the superficial gas velocitythrough the layer.
At low gas velocities, bubbles form at the surfau andthen depart when their buoyancy overcomes surfacetension. A simple force balance yields the equation forthe bubble diameter *S3
J (94)
% = ‘“01056 8(Ptu. PJ ‘
where 0 is the contact angle (in degrees) between themelt and the surface; in CORCON-Mod3, the cmtactangle is assumed to be 120 degrees.
At higher gas fluxes, bubbles grow to larger sizes beforedeparting from the surfaw.. The bubble size correlationimplemented in CORCON-Mod3 is baaed on theDavidson-Schule# equations for the bubble volume,where both high and low viscosity liquids are considered.For low viscosity liquids,
[1.1.2
vu = :43 = 4.1369 X 10-s ~(95a)
g.
while for high viscosity liquids,
[“13t4
VW = U d; = 0.01094 ~ (95b)x P,g
where j’ is the superficial gas velocity in mJsec and g isthe actxleration of gravity (9.8 m/#). The code uses the
26
Model Descriptions
maximum of the bubble sizes predicted using these two) correlations.
At very high gas fluxes, a stable gas film may form. Fora gas film, the equation for bubble radius implemented inCORCON-Mod3 is identical to the one used incoRcoN-Mod2:
where the leading coefficient is based on the experimentsof Hosler md WestWater.ti Literature values for thiscoefficient range from 2.2 to 4.2.XM The lower valuesare inconsistent with bubble sizes observed in melt-~ncrete experirwnts at Sandia National Laboratories andelsewhere.
CORCON-Mod3 calculates the bubble size for each ofthe three regimes. The Davidson-Shuler equation is usedin most cases. The low gas velocity equation provides alower bound to the bubble size, while the gas filmequation provides an upper bound.
The bubble size is recalculated at each layer interface.The effects of chemistry and changes in temperature andpressure are accounted for, but bubble coalescence is notmodeled. The aveinge of the radii of the bubblesentering and leaving the layer is used to calculate a singleterminal velocity for the layer.
The gas flux at any elevation is calculated using the localcross-sectional area and the total flow of gas from lowerin the pool. A local gas volume fraction is thencalculated, and the elevations of layer interfaces aredetermined from the integral of the non-gas volume
%mL= ! (1 - a(z)) A(z) dz (97)PL ~
where ~ is the mass of the non-gas in the layer, pL isthe density of the non-gas in the layer, a(z) is the localgas volume fraction at elevation z, A(z) is the debris poolarea at elevation z, and ~ and ~oP are the elevationsof the bottom and the top of the layer, respectively.
2.3.6Interlayer Mixiig
Though CORCON-Mod2 included mixture layers in itslayer stmcture, it lacked mechanistic models for mixingbetween the layers of the debris pool. We havedeveloped and implemented an interlayer mixing modelin CORCON-Mod3 based on the experimental and
analytical work of Greene. ‘3”S7SsThe mechanistic modelsand their implementation into CORCON-Mod3 aredescribed below.
Two mixture layers are possible, a layer of “light= oxidewith suspended metal drops or a layer of metal withsuspended “heavy” oxide drops. Mixture layers can be
created in one of two ways. First, a mixture layer canbe created by the entrainment of one layer, the denser ofthe two, into another. A mixture layer can also becreated when an overlying layer becomes more densethan the layer beneath it. The latter case was handled inCORCON-Mod2 by assuming that a ‘layer nip”occurred; in other words, the demser oxi& layer wasassumed to migrate instantaneously through the metallayer and combine with the overlying oxide layer.
When a mixture layer is formed by an unstable densityarrangement, mixing is assumed to occur instantaneously;that is, during a single CORCON time step. Theadjacent layers are assumed to merge to form the mixturelayer.
When a mixture layer is formed by entrainment, theentrained drops are assumed to be carried to the top ofthe overlying layer before floating free of the entrainingbubble. As a result, the overlying layer immediatelybecomes a mixture layer, and it is redefined by the code.
CORCON-Mod3 calculates also the creation ofsingle-phase layers due to droplet settling(deentrainment), Therefore, mixture layers mayeventually stratify into distinct metal and oxide layers ifdensity differences become greater or the gas flowthrough the melt decreases.
To illustrate the treatment of interlayer mixing in thecode, consider the following example: molten coredebris is initially stratified with an oxidic phase on thebottom (HOX layer), and a metallic phase on top (METlayer), and is rapidly ablating concrete. The gas flowrate is assumed to be sufficient to begin entraining theoxide into the metal. Once entrainme nt begins, dropletsof the HOX layer are carried to the top of the METlayer, so the MET layer is redefined as an HMX layer(HMX implying suspended heavy oxide in a lessdenaemetal layer). There will be a net loss of oxide from theHOX layer until the rate of entrainment equals the rate ofdroplet settling out of the HMX layer. Completeentrainment of the HOX layer may occur as the HOXdensity decreases due to the addition of lower densityconcrete oxides (from ablation). If the density of thesuspended oxide in the HMX layer subsequently becomesless than the density of the metals, the HMX layer is ,redefined as the LMX layer (or is combined with the
27 NuREG/cR-5843
Model ihcriptions
LMX layer It one M preaeat). Metals m the LMX layerwill then begin to settle out of the mixture Complete
atratificahon may occur as the gas flow rate continues todecrease, resulting in a debris configuration with a metallayer (MET) on the bottom and a less dense oxide layer(LOX) on the top. Note that the beginning and eadingdebris configurations in this example are the same aswhat was generally observed using CORCON-Mod2.The evolution of the final configuration is, however,more realistic.
The above example represents just one of many scuuuiosthat may occur depending on the reiative deasitiea of theoxide and metal phases, and the gas flow through themelt. (Another example is provided in the BWR sampleproblem shown in Section 6.0.) The comments providedin subroutines ORIENT and .4DDLYR are sufficientlydetailed for the user to understand the various casestreated by the cude.
As the deaaities of the metallic and oxidic phases and gasflows change, the oriatatlon of the layers may alsochange. Coding has been included to handle all possiblechanges in the layer oriedation.
In the eattrainmnt calculation, two criteria am used todetermine whether entminmen t is possible;” these are
where PI is the density of the material in the upper layer,and p2 is the deasity of the material in the lower layer.In Equation (98), w is the dimensionless bubble volume,&fined by
(99)
where V~ is the bubble volume and VbP is the bubblevolume required for penetration of the interface, given by
v [13.90,2 3n (loo)&Fal=
8(P, - PJ
in which Ulz is the surface tension of the liquid-liquidinterface, g is the acceleration due to gravity, Pt is thedensity of the liquid sumounding the bubble, and p’ k the
density of the gas in the bubble. VbO in Equation (98) isthe minimum bubble vol~’ for entrainment t, given by
[ 13n
7.8 Ulzv (101)ho =
i?(3P, - P2 - 2PJ
If either criterion defined by Equation (98) is notsatisfied, thea entrainment cannot tiur. In practice, thesecond criterion of Equation (98) is the more restrictiveof the two.
If both conditions for ent rainment are satisfied, then theentrained drop volume per bubble is calculated using thecorrelation developed by Greene’3
Ve— =~ t“”’”Rd’””@’m . (102)V_ 806
In Equation (102), Ve is the entrained drop volume perbubble, and V_ is the theoretical maximum volumethat could be entmmed and is given by
v =v,(P, -PJ - (u,,/g) (12Z-’V,)’P (103)O,llmx
(P, - P,)
Re, are R% in Equation (102) are the Reynolds numbers
(baaed on bubble diameter) for bubbles rising in thelower and upper fluids, respectively, and ~ is thenornudiud excess bubble volume above that required forentrainment
(104)
Note that, as defined in Equation (103), V.- goes tomm at the foUowing value for V~:
[13n
4.91U,2v
(105)&& =
go, - P’)
This value for V~ is more limiting than that given byEquation (100). Therefore, it is used along withEquation (101) to determine whether entrainment ispossible.
Given the superficial gas velocity through the surface, jg,and the bubble volume, V~, the bubble flux (number ofbubbles per unit area per unit time) is calculated as
Since -h bubble has associated with it an entraineddrop of a known volume, the mass flux of entmined
(10s)
NuREG/cR-5843 28
Model Descriptions
material can be calculated. Multiplying the mass flux ofentrained material by the interracial area and time stepgives the mass entrained during the time step. This massand its associated enthalpy are transferred into themixture layer. If no mixture layer is available to acceptthe entrained mass, one is created to contain it.
Deentrainment is calculated by first calculating the dropsettling velocity using the droplet drag coefficientcxxrelations proposed by Greene.’3 The comelationsfollow the drag curve for spherical drops until a criticalvalue for the settling velocity is reached. At the criticalsettling velocity, Greene observed droplet oscillationswith a coincident increase in the drag coefficient.
In the absence of drop oscillations, the drag coefficient isdetermined from the following set of correlations byBeard and PmppachecW
cd= 1 + 0.102 Re0w5 (107a)
r 4s
for 0.2< Re < 2.0
cd= 1 + 0.115 Re””m
r(107b)
d.s
for 2.0< Re <21.0
cd= 1 + 0.1879 Re0”Q2 (107C)
r 4s
for 21.0 c Re <200.0. In these equations, C&s is thedrag coefficient for Stokes flow:
cd.s=24/Red (108)
and Red is the Reynolds number for the droplet based onthe droplet diameter.
Greene developed the following criterion for the onset ofdroplet oscillations:
(109)
III this equation, Wed and Reti, are the Weber andReynolds numbers, respectively, at which droposcillations were first observed. Coincident with theoscillations was a dramatic increase in the droplet drag
coefficient. The observed drag coefficients are correlatedby
[11.12
cd Red (110)—=—Cd,ti, Red,
where Cd,dt is the drag coefficient at the onset of dropletoscillations.
A consistent droplet settling velocity v~ and dragcoefficient are determined by iteration. Given v~, thevolume fraction ad of drops in the mixture layer, and thedensity of the drop material p~, the mass flux of settlingdrops is calculated using the equation
+, = vdad12d (111)
Multiplying the mass flux by the interracial area and thetime step yields the mass of drops settling out of themixture during the time step. This mass and itsassociated enthalpy are transferred out of the mixturelayer and into the layer below it. If no separated layerexists to accept the deentrained mass, one is created atthe start of the next timestep.
In CORCON-Mod3, the user has the option of selectingwhether to begin a calculation with a stratified or a fillymixed debris pool, and the user can select whether thecode will perform the entrainment and deentrainmentcalculations. This allows the user the flexibility to begina calculation in a fully mixed configuration and themallow the code to calculate entrainment anddeentrainrnent, or the user can force the debris pool toremain mixed by bypassing the mixing calculation.Similarly, the user can begin a calculation with astratified debris pool and then allow the code to calculateentrainment and deentrainment, or the user can force thepool to remain stratified by bypassing the mixingcalculation.
Average thermophysical properties (thermal conductivity,viscosity, surface tension, etc.) are calculated usingvolume fraction or mass fraction weighing of theindividual metal and oxide phase properties. SeparateIiquidus and solidus temperatures are calculated for themetallic and oxidic phases. The mixture layer solidustemperature is assumed to be the lower of the metal andoxide phase solidus temperatures, while the mixtureliquidus temperature is chosen as the maximum of themetal and oxide phase solidus temperatures. Crustformation occurs only when the lead temperature dropsbelow the solidus temperature. Between the solidus andliquidus temperatures, the mixture is assumed to forma
29 NUREG/CR-5843
Mdel Descriptions
slurry. The solids fraction for the mixture is determinedby mass-weighing the solids fraction of the metal andoxide phases, where the solida fraction of each phase isbaaed on the appropriate solidus and Iiquidustemperature for that phase.
2.3.7 PmI Surface Heat Transfer
We anticipate that CORCON-Mod3 will be coupled to
integral system codes such as MELCORS andCONTAIN.7 To simpli~ such effo~, the pool surfacehas been treated as a major computational interface inCORCON-Mod3, with limited information passed in awell-defined way betweea above- md below-aurfawmodules. Othenvise, these modules are quiteindejnmdenti in particular, the need for simultaneoussolution of above-surface and below-surface heat transferrelations has bees avoided. The treatment inCORCON-Mod3 is identical to that in CORCON-Mod2.
Each half of the problem (above- and below-surface)defines an upward heat flow, Q, as a function of thesurface temperature, T,. An energy balance at thesurface of the pool requires finding that T, for whichthese heat flows are equal; this generally involvessolution of a nonlinear-and perhaps verycomplicated--equation. This may be viewed somewhatdifferently: for each half of the problem, the boundarycondition at the pool aurfaw is the heat flow vstemperature characteristic of the other half, and theobject is to find a simultaneous solution. Each“half-problem” is solved with a boundary condition
representing the reaponae of the other half, linearizedabout the most ready calculated surface temperature.The calculation is described in more detail below.
First, the end-of-timeatep response of the pool, linearizedabout ita start-of-timestep value, T:,
Q, = Q:IM + #[b, (T, - T,”) , (112)s
is calculated in ENRCN1 and passed to the above-poolmodule, ATMSUR. This response includes contributionsfrom the implicit terms in the pool energy equation,involving the change in layer temperatures with change inend-of-tirnestep heat loss from the surface. InATMSUR, it is used as a boundary condition for the fullnonlinear problem involving atmosphere andaurmundings, resulting in a provisional end-of-timestepsurfhce temperature, ~+’. This, together with thelinearization of above-surface response about ~+’,
Q, = Qc”l~r +:lsur (T, - ~~”) , (113)s
is passed back to the below-surface modules. Thelinearization ultimately serves as a bounday condition foranother nonlinear calculation which results in the finaltmd-of-timestep value ~+’. This procedure hasadvantages with respect to the energy-conamvationequations, as will be discussed in Section 2.3.12.
In the version of ATMSUR included in CORCON-Mod3,heat loss from the pool surkce includes convective heattransfer to the atmosphere and radiative heat transfer tothe surroundings. Thermal radiation is the dominantmechanism. If desired, the radiative effects of aerosolsin the atmosphere may be included in the calculation,with an atmospheric opacity determined from calculatedaerosol concentrations. Once the optical thickness of theatmosphere is known, the onedimensional diffusionequation is applied for infinite, parallel, optically grayplates giving
‘B(T:- ‘:)%3- =
(114)I/c, + l/&w- 1 + 0.75 KL
where T, is the surface temperature, TM is thesurroundings temperature, K is the extinction coefficient,L is the average path length for radiation in the cavityatmosphere, and c, and e,. are emissivities of the surfaceand surroundings, respectively.
Note that Equation (114) reduces to the transparentatmosphere equation as either the extinction coefficient orthe average path length approaches zero.
Convection produce-s additional heat transfer from thepool surf-. Unless the atmosphere is tmly transparent,however, convection and radiation are strongly coupled;
the radiation tends to increase thermal stability andreduce Convection.m In most cases, however, we havefound the convection contribution to be small.Therefore, we have included only a very simpleconvection model in CORCON-Mod3. The convectiveheat transfer from the pool surface to the atmosphere isgiven by
(115)
where T, is the bulk temperature of the atmosphere. Theheat transfer coefficient, ~, is assumed to be constant at10 W/d K.
NUREGICR-5843 30
Model Descriptions
The total beat flux from the pool surface is given by
% =%i-+b (116)
This equation is solved for T, simultaneously with thelinearized pool response, Equation (112), to determinethe provisional end-of-timestep surface temperature fi+’.
2.3.8 Concrete Decomposition and Ablation
The response of concrete exposed to high heat fluxes iscomplex. Concrete is an inhomogeneoua material whichundergoes changes in composition as it is heated. Themost important of these changes are the vaporization ofinterstitial and adsorbed water at about 400 K, thedecomposition of calcium and magnesium hydroxidesnear 700 K, and the decomposition of calcium andmagnesium carbonates between about 1000 and 1100 K.The carbon dioxide, water vapor, and liquid waterproduced within the solid concrete flow through the poresof the remaining matrix in response to pressure gradients.Finally, the remaining oxide matrix melts, at atemperature which ranges from about 1350 K to 1900 Kfor representative concretes. In the context ofmoltenare/cxmcrete interactions, the molten andsemi-molten materials are removed from the surface intothe pool, as the surface recedes.
We have retained in CORCON-Mod3 the simplifiedmodel for the concrete response that was used inCORCON-Mod2. This model is based on a steady-state,onedimensional energy balance, and is described below.
If a steady temperature profile exists in the concrete, asimple heat balance at the concrete surface yields
q = p=AH~ dx,ldt (117)
where q is the net heat flux to the concrete, p= is thedensity of concrete, AHti is the ablation enthalpy ofconcrete, and x, is the position of the concrete surface.
The heat flux q must, of course, be reconciled with theinterracial heat transfer model of Section 2.3.2.2. Ingeneral, this procedure will involve an iteration todetermine the temperature of the pool side of theinterracial film (gas or slag), allowing for the fact thatthe thermal resistance of that film may depend on the gasgeneration which results from the ablation. If thistemperate is below the ablation temperature, theconcrete is treated as an adiabatic boundary with q (anddx./dt) set equal to zero.
We emphasize that the pseudo-steady temperature profile,which is used to justifi Equation (1 17), does not appearin the equation. The sensible heat and chemical energy(and changes in these quantities) associated with thetemperature profile are ignored. This is not a problem incases where the pool contains a high temperate liquidmelt: studies by ACUREX, using a more complexablation code, have shown that the ablation processnxtches a quasi-steady state within about 1 minuted’ Atvery late times, or early times with initially solid debris,the inaccuracies could be greater.
The quasi-steady model is also used to calculate thegenemtion of decomposition gases; that is, the massgeneration rate of each gas is taken as its partial densityin the concrete times the ablation rate. Gas released inadvance of the ablation front is thus ignored; thisassumption neglects the initial burst of gases associatedwith establishing a steady profile in the concrete by a hotmolten pool. The model is also in error at early timesfor solid debris, because no gas is generated beforeablation begins, as well as at late times if ablation ceases.The ablation enthalpy for concrete in Equation (117) iscalculated internally, and consists of both sensible andchemical energies. The sensible energy is computed asdescribed in Section 2.4.1. It includes the energynecessary to raise gaseous decomposition products to theconcrete ablation temperature to acumnt for the soalled“transpiration cooling” effect. The chemical energy isincluded using experimentally determined heats ofdecomposition for three reactions: evaporation of theewater (11 kcal/mole), release of chemically bound water
from hydroxides (25 kcal/mole), and release of CQ fromcarbonates (40 kcal/mole). The enthalpy of limestoneaggregatdcommon sand concrete (including decom-position products where appropriate) is illustrated inFigure 2.3 as a fiction of temperature.
The ablation temperature of concrete is not preeiselydefined because ablated material may not be completelymolten. In CORCON-Mod3, we consider a meltingrange defined by the concrete liquidus and soliduatemperatures, with the ablation temperature ordinarilychosen by the user to lie between them. The choiceaffects the calculated heat of ablation, as may be seenfrom Figure 2.3. Concrete decomposition products eaterthe interracial film or the pool at the ablationtemperature, with the enthalpy appropriate to thattemperate. Therefore, because all enthalpies arecomputed from the same data base, the choice of ablationtemperature has no effect on overall conservation ofenergy.
31 NuREG/cR-5843
if,-
.
uto
o
XN+
) o“I VI
./
ic 1’ 10 I
;;e4
N 1~, t
II /
L
: v’ cONcRETE 1LIMESTONE/COMMON SAND
I1 1 1 I I I [ I I I 1 I 1 I
500 1000 1500 2000TEMPERATURE (K]
Figure 2.3 Enthalpy of ammete and Its dccomposltlmt products
Model Descriptions
If the concrete contains reinforcing steel, the energynecessary to raise it to the concrete ablation temperaturesincluded in the “concrete” ablation enthalpy.
2.3.9 Time-Dependent Melt Radius
Inprevious versions of CORCON, it was assured thatthe melt pool, comprising the core debris, coolant,ablated concrete decomposition products, and ablatedmaterials from the surroundings, completely fills thebottom of the reactor cavity. The assumption limits theutility of the code and may cause numerical problems ifsmall masses of core material are required to be spreadthinly over the surfaw concrete. For example, it is notpossible, under this assumption, to simulate the transientevents accompanying the initial pmr of core debris ontoa concrete basemat and the subsequent spreading of themolten debris across the basemat floor. CORCON-Mod3allows the user to specifi a time-dependent radius of themelt that is less than the dimension of the confiningcavity. This feature extends the range of severe accidentscenarios that can be simulated.
The spreading of a viscous liquid across a solid surface isa complex physical process. If the liquid begins tosolidify while flowing, this wmpounds the complexity ofthe process. If a crust begins to form on the uppersurface of the spreading liquid, the crust may be stable ormay be broken up and mixed into the liquid. In the lattercase, the resulting slurry has a high viscosity and a highsurface tension. Ultimately, the shear stresses requiredto maintain the flow are greater than those driving theflow, and the flow stops. The molten material continuesto solidify in place and may attack the substrate.
Mechanistic modeling of the spreading process describedabove is not attempted in implementation of thetimedependent melt radius option in CORCON-Mod3.Instead, the user enters a table of times andcorresponding radii, and values of maximum andminimum allowable melt thickness. This approachallows considerable flexibility in mimicking the spreadingprocess delineated above, but also allows the user tospecify physically unreasonable melt configurations. Theoption, as currently implemented, will adjust the meltradius to keep the melt thickness between the maximumand minimum thicknesses specified by the user.Alternatively, by setting the maximum and minimummelt thicknesses to be equal, a constant melt thicknesscan be specified, and the appropriate melt radius will bedetermined at each time step. A rudimentary criterion isincluded to determine when the melt contains too muchsolid material to allow the melt to continue to spread:when the total crust thickness is greater than a half of themelt thickness, spreading stops.
Each layer of the melt pool is assumed to have the sameradius until the melt reaches the sidewall. Mass may beadded to the melt pool, either additional core debris orconcrete ablation products. With the option,’ it ispossible to fix the radius at a particular value, and tohave the melt repose on the concrete floor as anon-spreading glob. As currently implemented, thetimedependent melt radius feature is restricted tocylindrical cavities with flat floors (IGEOM = 2).
Coolant may be present in the cavity when thetimedependent melt radius option is invoked. Thecoolant is treated correctly as long as the quantity ofcoolant is sufficient to cover the melt. Programexecution stops when the coolant no longer covers themelt. Treating the case where the cucdant does not fullycover the melt would necessitate extensive modificationsto CORCON to add a radial layer structure and allowsimultaneous heat transfer from the melt to a radial waterlayer and the surroundings. We believe that suchmodifications are not warranted at this time.
Additions to the energy equations to account for the “exposed melt edges are described in section 2.3.12.
2.3.10 Chemical Reactions
In CORCON-Mod2 it was assumed that the principalchemical reaction involved in cordconcrete interactions isthe oxidation of metals in the pool by concretedecomposition gases These gases, water vapor andcarbon dioxide, are reduced in the process, primarily tohydrogen and carbon monoxide. It is possible to furtherreduce carbon monoxide to atomic carbon. This ispredicted by CORCON-Mod2 in many cases involvingmetallic zirconium.
In CORCON-Mod3 we treat not only the reactions ofmetals with gases from the concrete, but also condensedphase reactions between oxides and metals. The latterwere added to the code based on the results of theSURC-4 experiments In this experiment, a vigorousinteraction was observed between metallic zirconium anda silicious concrete with low gas content. Thisinteraction could only be explained by consideringcondensed phase chemical reactions between thezirconium and molten oxides from the concrete. Thedriving chemical reaction was
Zr + SiQ-Si + Zfl + 2.1 MJ/kg Zr
Condensed phase reactions are particularly important forcore debris interactions with high silica, low gas,concretes such as the one used in the SURC4experiment. They are much less important for calcareous
33 NuREG/cR-5843
MAel Descriptions
concretes that have a low silica content and high gascontent. The user stables condensed phase chemistryusing the input flag, ICHEM.
To include condemsed phase chemical reactions, it wasnweaaary to expand the master species list to includeuranium, aluminum, calcium, and silicon metals. Theseand other additions to the master species list are shown in
Table 2.1.
CORCON-Mod3 assumes that chemical equilibrium isachieved between the reactants during each tirneatep.The chemical equilibrium solver minimizes the Gibbsfree mergy for 56 chemical species and 15 elements.These species, which are shown in Table 2.6, include allrelevant condensed species (the rm%als, their oxides, andcondensed carbon), the mincipal gaseous mecies of water
vapor. hvdrogen, carbon dioxide, and carbon monoxide,
and a variety of leas-important gases such as light
hydrocarbons. The subroutine employed, MLTREA, hasevolved from an implementation by Powers’ ‘c of themethod of Van Zeggeren and Storey.m It performs asimple first-order steepest descent minimization of theGibbs function subject to constraints on massconservation and on non- negativity of concentrations.The version included in CORCON-Mod3 ia essentiallythe same as that included in the third amrection set forCORCON-Mod2.a For a more detailed discussion of theequilibrium solver, the reader is refened to Referencesllfand 62.
The solution procedure has a number of significantadvantagea: (1) it is extremely general; (2) reactionsneed not be specified; (3) convergence does not require agood initial guess (although it is much faster if one isavailable); and (4) the resulting FORTRAN code isrelatively small for the number of species considered.The condensed phase reactants and oxidic products are
Table 2.6 Chemical species included in the CORCON chemical equilibrium solution
Metals andOxides Other Elements Gases
FeO Fe c(g)MnO Cr CH,A1Z03 Ni coU02 Zr co,zro2 FpM- W2CrzO~ Mn ~H4NiO c(c) ~H,FpMOJ Al HFpM03* u wF~Od Si HZOMn~04 UA13 NSiOz uAl~ NHJUJO* Ca NzCao x- 0
O*OHCHOCHZOCro,(g)FpMOz(g)”FpM03(g)”Al,o,(g)Al*o(g)Ale(g)OAIH(g)AIOH(g)OAIOH(g)Ale,(g)
%eudo-species representing condensed phase and gas phase fission product groups%efi oxide species treated as element “X” in the chemical equilibrium calculation
NuREG/cR-5843 34
Model Descriptions
treated as ideal solutions in MLTREA; that is,entropy~f-mixing terms are included in their chemicalpotentials, and the activity of each species is equal to themole fraction in the phase.
It should be noted that non-ideal solution chemistry hasbeen included in the vaporitiion release model inVANESA. (See the discussion in Section 2.3.14.) Thisinformation could be made available to the MLTREAsubroutine, but this has not yet bees done. Althoughnon-ideal solution chemistry is important for calculationof vaporization release from the core debris, we currently
do not believe it to be important for the calculation offlammable gas production or energy generation, whichare the primary results from the MLTREA calculation.
The ICHEM flag, which is used to enable the condensedphase chemistry calculation, is also used to disable theproduction of condensed carbon (C(c)) during thereaction of carbon dioxide with reactive metals such aszirconium or aluminum. This reaction, which is oftenreferred to as “coking” or “carburimtion, ” is predictedby CORCON-Mod2, but has not been observed to anysignificant extent in previous melt-concrete experiments.To disable the coking reaction, the chemical potentials ofC(c) is artificially set to a large value (currently 10’Scal/g-mole). With this change in place, the code wasfound to predict substantial production of acetylene(~H~. Since significant acetylene production also hasnot been observed in any paat experhneats, we havesuppressed the formation of acetyhme by setting thechemical potential of ~Hz to a large value (also10’5 cal/g-mole) whenever the coking reaction isdisabled.
As with earlier versions of CORCON, CORCON-Mod3contains coding to calculate the reduction of oxides at the
pod surface by the oxygen-pm atmosphere above themelt. l%is feature was implemented and tested duringdevelopment of CORCON-Modl, but was bypassed inreleased versiona of the code because of the incompletetreatment of the atmosphere. We have retained it,still
bypassed, in CORCON-Mod3.
The thermodynamic-properties package (Section 2.4. 1)employs the standard thermochemical reference point ofseparated elements in their standard statea. With thisreference point, heats of formation of all species areautomatically included, and all heats of reaction areimplicitly contained in the enthalpy data. In fact, theyare calculated only for edit purposes.
2.3.11 Mass and Energy Transfer
Processes involving mass transfer are of ’considerableirnpmtance in the modeling of molten corekoncreteinteractions. These include injection of concretedecomposition products (condensed and gaseous) into thepool and further additiona of core materials, structuralmaterials, or cuolant entering from above. It isconvenient to include chemical reactions in the samecalculational structure, because these reactions affect thenature of transferred masses.
These transportprocaaes mdfy both the mass
inventories and the energy contents of the various poollayers. The cmeaponding terms in the mass and energyequations are evaluated in subroutine MHTRAN. Thestructure of this routine closely miffors our picture of thephysical processes it models, as described in the
following paragraphs.
The masses and enthalpies of all pool layers are updatedfor mass transfer and associated heat transfer in twopasses. (Note that a calculation will not begin until thereis some debris present in the pool.) The first paas, “upward through the pool, follows the rising gases andrising condensed-phase materials from concretedecomposition or ccmcrete/melt/gaa reactions. Thedirection of motion is determined by the density relativeto the local layer material and/or the driving forces forentrainment. The compositions and enthalpiea of theserising materials are followed and modified for chemicalreactions. The materials are thermally equilibrated withany layers they pass through, and their energy kultimately added to the layer where they remain. Anyheat of reaction remains with the layer where the reactionoccurred.
The second calctilonal pass, the downward pass, issimilar to the firat: it follows any mnterial entering thepool from above in addition to sirdcing reaction products,concrete ablation products, and droplets settling out ofmixture layera. Entering metallic species are added tothe firat layer of the core debris containing metals. If nolayer with metals is present, a metallic layer is created.Addition of oxidea and coolant is treated in a similarfashion. Aa with other material movements inCORCON, mass added to the cavity is assumed toequilibrate thermally with each layer through which itpasses or eventually resides. Figures 2.4 through 2.6show this in more explicit detail. In these figures, Qdenotes thermal equilibration, O/M/G refers to theoxidelmetallgaa oxidation reaction, and MX denotesinterlayer mixing. The total heat capacity of a layer isassumed to be much greater than that of materials passingthrough it so that thermal equilibration takes place at’ the
35 NuREG/cR-5843
Model hSCli@iOllS
s
m
de
ure
1 OAAIG I
\\\\\\] Metal(MET)
1.
re
e
Figure 2.4 Path of gas through pool
NuREGlcR-5a43 36
Model Descriptions
. . ...” . . . . . .. ..” ..”. .
.“. . .“. . .“. .. .. . . . .. ...” . ...” . . .
..“
“. “... ”.”. “...”. ”O .. ”.”.. . . . . . . . . . . . . . . . . . .
. . . ““. . . . . . . . . .. . . .
. . . . . . . . . . . -. ”... . . .
..
. .
. ...
I O/M/G I
.....
Surroundings
AtmosphereATM
Coolant(CLN)
LightOxide(LOX)
\L ...... ........... .. ...... ...... . ... . ... ... . .. . ..... .... ...
:
ELight Mixture(LMX)
Metal(MET)
Heavy Mixture(HMX)
Heavy Oxide_ (HOX)
lag of Gas Film
Concrete
Pigurc 2.S Path of metal through pool
37
Model Ikcripticms
s
II !
.
ght OJdde(LOX)
M Mixture(LMX)
Metal(MET)
avy MMure(HMX)
i \
v+’’’’’’’’’’!.’{> Heavy Oxide. .
“. . (HOX). . .
“..... OO
. . . . . .. . . . . .*” .
\● ✎ ✎ ● ✎ ✎ ● ✎ ✎,.” ,.” ..”
. ..” . I. Slag or Gas Film.“** .“**
Conaete
Figure 2.6 Path of oxtde through pool
NUREGICR-5843 38
start-of-timestep layer temperature. The awxxiatedchange in layer enthalpy is given by
AH~ = H(%, T~) - H(m~~ T-) (118)
where H is enthalpy, T is tempemture, m is mass(including composition), and the subscripts “Lm, “in”,and “out” refer to the layer, to material entering it, andto material leaving it, respectively.
Because the enthalpy package employs the standardthermochemksl reference point of separated elements intheir standard states, this equation will al= holdincluding the effects of chemical reactions. If, forexample, the composition of the gas which leaves thelayer differs from that of the gas which entered, theentire energy effect is accounted for through the differentcompositions associated with ~ and ~.
2.3.12 Energy Conservation
The energy equation to be solved for each layer of thepool is given by
HP’ = Hla + AH- , - AHhW ,
I-q=
AL, =
AH~ , =
AH- , E
AH_ , =
%1 =
Qsi =
Qrl=
+AH-l+AH_l (119)
-Qw, +Qs, -%-Qiu
the total enthalpy of layer i at timelevel n
the enthalpy of materials enteringduring the time-step
the enthalpy of materials leavingduring the time-step
the enthalpy gain from chemicalreactions
the enthalpy gain from decay heatsources
Qlu=
Model Descriptions
the heat transfemd to the exposedmelt edges if the timedependent meltradius option is used.
As discussed in Section 2.3.11, the “entering, -“leaving, ” and “reaction” terms are naturally associated.The “reaction” term is included implicitly in the othertwo for the thermochemical reference point employed.llw.se terms are calculated in subroutine MHTRAN asdiscrete changes, involving all of the material whichmoves during a time-step. Residence times are notconsidered. In other words, all materials which resultfrom ablation are assumed to be completely relocatedduring the same timestep.
Energy generation from mdionuclide decay powerchanges slowly. llerefore, the corresponding term inthe energy equation is evaluated explicitly (in thenumerical methods sense) as a beginnmg-of-timesteppower multiplied by At. The remaining three terms inEquation (119) involve heat flows which are driven bytemperature differences The heat loss to concrete is alsoevaluated explicitly, but the remaining terms are treatedusing a linearized-implicit algorithm. These termsinvolve the axial heat flows to the upper and lowersurfaces of the layer (with the exception of the bottomlayer for which the lower surfmx is adjacent to concrete),and are taken as weighted averagea of the VSIW at timen and the linearly-projected valuea at time n + 1. Thisresults in the equation
(120)
where the tilde “ -” denotea the linearized projection
described below, and, of CQurse, ~+’(~) includes theterms (~, - ~ JAt, The implicitness factor (1 isprogrammed as a variable, but is set equal to 1.
The following discussion of the terms in the energybalance is divided in two sectiom. The discussion in thefirst section applies for cases in which the timedependentmelt radius option is not invoked. The second sectionapplied if the user chooses to invoke the timedependent ‘melt radius option.
the heat loss to ablate concreteMelt Radius Option Not Invoked
the heat transferred from the bottomsurface (zero for the bottom layerwhere this is part of Q), and
the heat transferred to the top surface.
When the timedependent melt radius option is notinvoked, ~ = O, and the terms in the energy equationare determined as in CORCON-Mod2.
39 NUREGICR-5843
Model DescriptionB
We calculate the projected end-f-timestep heat fluxes
if i is not the top layer in the pool. or from
(121)
(122)
if it is. Here ~@x is the upward heat flux at the top(bottom) of layer i, T~ is the temperature of layer i, T, isthe temperature of the interface, Al is its area, and wand (dQ/dTJ~ define the linearimtion of above-poolheat transfer described in Section 2.3.7. The subscriptsB, T, and L refer to the bottom and top of a layer, andto the layer average, respectively. It is important to notethat dq#Tm may not equal d~/dTi. An example ofthis occurs for a primarily molten layer with a thin crust.An increase in the average temperature increases theliquid temperature and the heat flux to the crestedsurface, while an increase in the surface temperaturemerely decreases the crust thickness with little change inheat flux (under the quasi-steady assumptions ofCORCON-Mod3).
The temperaturesof the interfaces (other than the topsurfaoe) are eliminated, and the change in thetemperature of layer i during the timestep approximatedin terms of the change in enthalpy by
(~Ti s= xi a H/’+’- H)ci . (123)
Here fIi is the total enthalpy at temperature ~ of thecontents of the layer at time n+ 1, and Ci is thecorresponding heat capacity. When coolant is present,Equation (123) is valid only so long as the coolantremains aubcocded. When boiling occurs, ~+’ must bethe saturation temperature T*, and the final enthalpy ofthe coolant will determine what fraction of it hasvaporimd during the time-step. This is handled initiallyby treating ~~~ and ~~~ as independent variables.
Equations (120) through (123) result in a set of linearequations for the layer entbalpies at time n+ 1. As codedin subroutine ENRCN 1, the equations are written interms of the X’s (which may be thought of as enthalpychanges in temperature units) in the form
They are solved as
(xi = x:’) + X;2J ‘p’1 _ T,”) + X?) ~T+ (125)8
with ~+’ - ~) and ATch Ietl undetermined.
If no coolant is present, so that all the ~o) are O, theheat flow at the top surface, including the effects of allimplicit terms in the energy equation, now has the form
Qfl’dQ
(= Q: + :1 f:” -
dT, poolT:) . (126)
This is the linearized pool response mentioned in Section2.3.7. Specifically, the derivative is
(g
dT, ‘ pool =
This equation
@T _dQT~1 topi
x:) , (127)+ dTL’ topi
is solved simultaneously with theabove-pool-thermal response in subroutine ATMSUR todetermine T ~+’. The final evaluation of layer enthalpies
and the corresponding layer temperatures is thenperformed in subroutine ENRCN2. This allows theimplicit nature of the equations to he maintained acrossthe pool surface even though above- and below-surfm
heat transfer are not evaluated simultaneously. It is thestabilizing effect of the implicit algorithm which makespossible the relatively long timesteps routinely employedin the code.
If coolant is present but remains subcooled l-l!!!: andAT* are related through Equation (123), and ATA maybe eliminated from both Equations (12S) and (126)through the relationship
(x: + x$) ~:+1 _
iiTA =T:) (128)
1 - Xg)
NUREG/CR-5843 40
Model Descriptions
This possibility is tested, using the above-pool thermalresponse from the beginnhg of the tirnestep
Q:” =Q:+ ~ Iwr (~:+’- T:) (129)
9
to close the set of equations. If this results in a ~~~below saturation, the elimination of ATA is accepted, andthe solution proceeds as for the no-coolant case. If, onthe other hand, this calculation results in a ~j~ abovesaturation, we assume that sufficient boiling occurredduring the time-step to hold the temperature to saturationand set ~=~~ equal to Tm. In this case, we use theabove-pool thermal response from the start of thethnestep,Equation (129), to complete the solution insubroutine ENRCN 1. The resulting enthalpy of thecoolant corresponds to a liquid/vapor mixture at thesaturation temperature. The partition of mass betwtxmthe two phases is evaluated, and the vapor component isadded to the gases which left the pool during thetime.step. As before, the calculation is completed throughATMSUR and ENRCN2, but with the derivative dQ~/dT~set very large (negative). This procedure assures thatATMSUR will determine a value for ~+’ very near toTm.
A special case arises when the coolant layer is totallydepleted during a timestep, and the calculation justdescribed results in a layer enthalpy greater thm that forsaturated vapor. In this case, we assume that all vaporwas generated at saturation and decrement the mass andenergy of the cuolant layer accordingly, but we do notupdate the enthalpies of other layers at this time. Theentire calculation is repated, with the coolant layer nowabsent. Because of the detailed balance of heat-flow
terms in Equation (120), energy is conserved exactly.
Although the total enthalpy of the coolant is not mro atthe start of the recalculation, ita final enthalpy must bezero. Inspection of the equation will show that the resultof the implicit calculation is to force the net heatdelivered to the coolant layer during the timestep to beexactly sufficient to vaporize it at its saturationtemperature.
The major approximation in this treatment of the coolantis the use of saturation conditions at the beginning of thetimestep mther than at the end. This could result in anapparently super-heated liquid coolant or in one which isapparently subcooled but boiling. In practice, nosignificant problems have been observed.
Melt Radius Option Invoked
Consider now the case when a timedependent meltradius is used. We must account for heat transfer fromthe melt edges to either the atmosphere or the coolant.First, we consider the case where coolant is absent.
The interface temperatures are determined in routineINTEMP. Temperatures of horimntal interfaces withinthe melt are determined as in the previous section. Thetemperature of the uppermost interface, between the meltand the atmsphere, is also determined as before. Sincethe heat flux to the atmosphere is known, this flux can beused to determine the temperatures of the exposed layeredges as follows. The linearized atmosphere response ~is
(130)
where Tw is the temperature of the edge of layer i and T,is the provisional surface temperature (assumed know).~ must match the heat flux at each layer edge,
where T~ is the current temperature of the edge of layeri, 6TN is the change in temperature required to produceequality of the fluxes, Tu is the fixed temperature oflayer i, and a is a parameter. The value of a=Ocorresponds to an adiabatic “edge, while a= 1 matches the
fluxes. Then linearizing, with
q;= %h d~- = q, + d~/dT, (T; - T) , (132)
aqm aT d%q;+_
aTm “ = aq’●+a—iiTm.
dT,
Solving for the temperature correction 6Tfi,
41 NUREG/CR-5843
Madel Descriptions
l%e new edge temperature of layer i is then
{minT; + 6TN, Tu) ; (134)
this Comtram‘ t is imposed so that the radial heat transferis always outward (i.e., positive).
The procedure described above k implemented at the endof the main interface temperature iteration loop inINTEMP. Following convergence of the interfacetemperatures, new values of the average surfacetempmture T. and the constant flux q, are required. Thenew values are given by
[
khl-1
%=; A%q,+ ~ A.%1“
(136)l-l
where T~ is the temperature of the horizontal interfubelween the melt and the atmosphere, ~ is the area ofthe interfac8, and ~ is the flux from the uppermost meltlayer to the atmosphere through the top interf-. AM isthe area of the edge of layer i, and A is the total meltarea exposed to the atmosphere.
The layer temperatures are updated in routine ENRCN1.
To account for the energy loss from the melt to theatmosphere, the energy equation for each layer becomes
Hfli = H~’(explicit)
-(d:’- Q:)} ,
where the last term on the right-hand side of the equationaccounts for heat transfer from the melt edge, ~+’ is theenthalpy of layer i at the time step n+ 1, ~’ (explicit)is the explicit part of the update, f) is the implicitnessfktor (set equal to 1), and At is the length of the timestep. Qsl, ~, and Qm ate the bottom, top, and radialheat transfer, respectively, of layer i at the appropriate
-eindicated by the superscript. The term, w~:t -C&, IS gwen by
Q;’ - Q: . & I 1*(T:’-T:)+#. “38)Fb Li
Equation (135) is then solved in the same way asEquation (120).
Once the layer temperatures Tu at the new time havebeen determined, the new provisional surface temperatureVI, the new provisional heat flux ~+’ and derivatived~/dT, and the surface emissivity are updated using areaaverages over the exposed surface of the melt.
Consider now the case in which the timedependent meltradius option is invoked and coolant is present. Theinterface between the melt and the coolant now includescontributions from all the exposed layers. Thetemperatures of the layer edges are determined in thefollowing way. The temperatures of the horixmtalinterfaces within the melt are determined as in the casewith no time-dependent melt radius. At the meltumlant
interface, we have the energy conservation equation
where Tv is the current temperature of the bottom(x= B), layer (x= L), top (x= T), or edge (x=R) of layery, which maybe coolant (y=c), the top layer of the melt(y=t), or the layer i (y=i). ~ is the area of the tophorizontal interface of the melt, & is the exposed areaof the edge of layer i, and A is the total exposed area ofthe melt. Equation (138) is solved by first setting /iT~ =6Tm and r~ = ~,, and initially setting 6TW = O. l%enlinearizing,
kh-1+ E Awq; ,
1-1
NUREG/CR-5843 42
Model Descriptions
The coolant overlying the melt is treated as a layer, andthe appropriate heat fluxes are determined as described inSection 2.3.3. The quantities q: and 6q~~T~ are thenused to determine the edge temperature of each meltlayer by matching heat fluxes as
where a=O implies an adiabatic edge, and U= 1 matchesthe heat fluxes. Thus
and the new edge temperature for layer i is
(143)
where the minimum constraint is imposed so that the heattransfer is radially outward (i.e., positive). Theparameter a is programmed as a variable but is currentlyset equal to 0.0 in the code.
The layer temperatures are updated in routine ENRCN1.The energy equation for each melt layer is Equation(137), as in the case with no coolant. When coolant ispresent, however,
where ATm is the change in the edge temperature overthe timedep, and ATU is the change in the layertemperature. By analogy with the expression for AT1,the change in the temperature of the horizontal intedkeI, the expression for ATM is
The energy equation for the molant layer is then
(145)
R“”’ = H~’(explicit)
{+QAt (Qgl- Q&)
}+ ;;l (Qti’ - Q;) ,
(146)
when the summation on the right-hand side accounts forthe heat transfer from the exposed edges of the nwltlayers. Equation (146) with Equation (137) for thenonaohnt layers are thea solved in the same way asEquation (120).
As noted in Section 2;3.9, the timedependent melt radiusis limited to cases where the coolant completely coversthe melt. When the coolant is insufficient to cover themelt, the code reports an enor and execution stops.
2.3.13 Cavity Shape Change
The shape of the cross-section of the cavity is defined forcomputational puqmes by a series of %xiy points. ”Thaw are the intersections of a fixed series of rays withthe cavity surface as shown in Figure 2.7. Given thecavity geometry at the start of a timestep, the shapechange procedure providea a new cavity shape at the endof the tirnestep. The normal recession rate is used ateach body point, as calculated by the concrete ablationmodel. The methods used in CORCON-Mod3 are thesame as those developed for CORCON-Mod2. Theshape change procedure evolved from the CASCET “model written for CORCON-Modl by
ACUREX/Aerotherm Corporation,dl under contract toSandia. We fit assure that the concrete recessionfollows the local normal at each body point and thenproject the resulting surface points back onto the rays.The projection is performed by passing a circle througheach normally receded point and its two nearestneighbors, and defining the new body point as theintersection of this circle with the corresponding ray asshown in Figure 2.8. A solution will exist so long as nobody point is allowed to cross the neighboring ray duringa timestep. In fut, there are two solutions, and we pickthe one which is nearer to the normally receded @nt.
With one exception, the rays emanate from an origin onthe vertical axis of symmetry of the cavity. We haveretained the so-called ‘tangent ray” from CASCET. Thisis a single ray, parallel to the axis, which defines theedge of the flat bottom of the cavity. Because the
43 NuREG/cR-5843
Model kiC@iOiM
NuREG/cR-5843
Fii 2.7 Normal surface resession
44
Model Descriptions
1;
PROJECTED~ RECESSION
(NEW BODY POINT)
F- 2.8 Circle intersection projection method
45 NuREG/cR-5843
Model Deacriptiona
corresponding body point moves vcntically, the bottom isconstrained to remain flat as is required by the ablationmodel. When the cavity surface passea through a pointwhere the tangent ray cresses an ordinary ray, theordering of the body points is changed appropriately.
In tke calculations, the “normal” at each body point ischosem as the bisector of the angle formed by lima fromthe body point to its neareat neighbors on each side.Another modification was made to prevent numerical
~g of comers projecting into the cavity. In thiscase, shown m Figure 2.9, if the normal ablation duringa thnestep is As = AAt, the point defining the comermoves As/c047/2). (Projection back onto the ray systemis not included in this Figure. ) In CORCON-Mod3. thecorrection is made for recession of all body points forwhich y > 0.
2.3.14 Aerosol Generation and RadionuclideRelease
Asgasea from decomposition of concrete pass throughthe melt and leave the pool, aerosols are generated bymechanisms such as vaporimtion/condensation andbubble bursting. These aerosols were observed in earlyexperimental work, and were hypothesized to be animportant mechanism for radionuclide release from thecore debris. The VANESA model’” was developed topredict aerosol genemtion and radionuclide release duringcore-concrete interactions. VANESA has now beenintegrated into CORCON-Mod3 .
The VANESA nmdel is called from CORCON-Mod3 aspart of the upward pass in subroutine MHTRAN (seediscussion in Section 2.3.11). VANESA requiresinformation on: the composition, temperate, andmaterial properties of the core debris; the flow rate andcomposition of gasea sparging the melt; the depth andtemperature of any overlying coolant; and the ambientpressure. This information is provided by the remainderof CORCON and is passed to VANESA after first beingconverted to the form required by VANESA. Thefollowing conversions are made in subroutine CVFAC:
● CORCON’S debris composition (including fissionproducts) is converted to a VANESA composition bystoring CORCON’S oxide, metal, and fission productmasses in the VANESA composition array XM.
● Average metal and oxide debris temperatures aredetermined for VANESA by mass-weighting thetemperatures of the metals and oxides in the CORCONlayers.
●
●
●
The metal and oxide material properties used inVANESA are calculated by mass-weighting theproperties of the metals and oxides in the CORCONlayers. The same is true for the bubble properties usedby VANESA. All material and bubble properties areconverted to c.g.s units for use in VANESA.
The gas flow rate and composition used in VANESAare determined from the gases exiting the surface ofthe melt. In other words, VANESA uses the resultsfrom the chemical equilibrium solution performed inthe CORCON calls to MLTRF.A from REACI’. (Notethat subroutine SRG, which is used in the stand-aloneversion of VANESA has been eliminated in theintegration of VANESA into CORCON.) CORCONgas species that are not tracked by VANESA areincluded in the total flow rate, but are not included inthe VANESA gas composition. These gases areeffectively treated as inert in the vaporization releasecalculation performed in VANESA.
The coolant depth and temperature, and ambientpressure are pk to V~ESA after first convertingthe depth and pressure to units required by VANESA(i.e., centimeters and atmospheres),
It should be noted that because VANESA is called duringthe upward pass in MHTR4N, the debris compositionpassed to VANESA does not include any debris added byuser-specified mass addition. Since this mass is added aspart of the downward pass in MHTRAN, it is added afterthe call to VANESA. Consequently, the CORCON andVANESA debris compositions pMted in the output willbe slightly different whtmever the mass is being added tothe core debris.
The implementation of the VANESA model included inCORCON-Mod3 calculates the following features ofradionuclide release and aerosol generation:
●
●
●
●
●
●
The rate and total mass of aerosol generated.
The concentration of aerosols in the evolved gases.
The composition of the aerosol, including the ‘contributions of non-radioactive materials, as well asthose of radionuclides.
The mean size and size distribution of the aerosols.
The msterial density of the aerosol.
The effects of coolant pools overlying the core debrison the production and nature of the aerosols.
NUREG/CR-5843 46
Model Descriptions
I-1
/I
1
/’
‘new normal
F- 2.9 Enhsnced recession for imide cormr point
47 NuREc3/cR-5843
Model Descriptions
After completing the above calculations, VANESA passesthe calculated results for the mass and composition of thereleased aerosols back to the rest of CORCON-Mod3.CORCON-Mod3 uses these results to adjust the mass,composition, and enthalpy of each layer. The fissionproduct content of each layer is also adjusted in order tocorrect the decay power generation for fission productrelease during the timestep. It should be noted thatchanges to the gas composition resulting from thevaporintion reactions treated by VANESA (seediscussion below) are not passed back to CORCON. Asa tit, the VANESA gas composition reported in theoutput is slightly different from the gas compositionreported by the rest of CORCON.
The VANESA models for aerosol generation,radionuclide release, and water pool saubbing are brieflydescribed below. The reader is referred to Reference 10for a more detailed discussion of the models.
Model for Vaporization Release
Vaporization is the most important of the releasendmisms. This is especially true during the earlyphases of the interaction when the temperatures are thehigh-t and the oxygen potential of the core debris is thelowest. The VANESA model includes both athermochemical analysis of vaporization and an analysisof the kinetic factors which may prevent the equilibriumlimit from being reached.
Vapor formation proceses can be quite complex.Consider, for example, the formation of vapor from acondeased phase species MO=. Vapor formation mayoccur by unary vaporization, which is described by thefollowing simple stoichiometry:
Vaporization may also result from reactions between the
condensed phase and the adjacent gas phase. Forexample, the following reaction stoichiometries mayOccuc
[MO=] + HZO + MOX+,(g) + H2
~Ox] + xH, + M(g) + xH,O
A general reaction stoichiometry for vaporization into asteamlhydrogen atmosphere can be written as
~0~ + (w-x) H,O + MO~ + (w-x-y/2) H, .
For this reaction, the equilibrium pressure of the vaporspecies MOW is given by:
-AG(rxn) . ~
ROT
(w-x+)P ● (MO#Y)[P - (H)]
((147)
X “(MOX)[P *(HZO)](W-X)
where F(i) and X*(i) are given by:
‘(i) = P(i)@(i) and ~(j) = x(j)-yfi)
where P(i) and @(i) are the partiat pressure and fugacitycoefficient for vapor species i, x(j) and y(j) are the molefraction and activity coefficient for condensed phasespecies j, and AG(rxn) is given by
AG(rxn) = AG~MO~Y) - AG@fOx)+ (w-x - y/2) AG~H) (148)
- (w-x) AG~~O)
and AG~i) is the free energy of formation for species i.
Expressions of this type must be written for each of thevapor species involved in the vaporization proax3s. Theevent of vaporintion of the condensed phase species,MO,, is then determined by the partial pressures of allvapor species composed of element M. As is shown inthe above equation, vaporization release is a strongfunction of temperature and composition of evolvedgases. Because the rising bubbles provide the surfacearea available for vaporization, release depends also onthe gas flow rate through the meh.
The current implementation of VANESA assumes thatthe fugacity coefficients for all vapor phase species areequal to 1.0. In other words, the vapor phase is assumedto be ideal. Non-idealities are, however, umaidered forthe condensed phase. The code calculates the activitycoefficients of metallic species using a subregularsolution model. For oxidic species, an associatedsolution model is used.
In the subregular solution rndel, the activity coefficientof the metal phase constituents is determined from
_ ~ x, aG”
k-1 axk-1
where the excess Gibbs free energy is given by
(149)
NuREG/cR-5843 48
Model Descriptions
N-1 N
G“=zx~ [w,, X, + ~ij ~j] (150)i.1 j-i.l i J
where Wij and hij are the interaction parameters thatdescribe the chemical interaction betweem metallicconstituents i and j. The interaction coefficients areassumed to be linear functions of temperature; thereforetwo parameter values are needed to specify each i,jcoefficient. Tabulated values for these parameters areincluded in BLOCK DATA INTCOF. The tabular entrywas simplified by making use of the followingrelationships between W,j and h,~:
Thus, it was only necessary to enter values into the upper(or lower) diagonal of each array.
The associated solutions model for the oxide phase hasnot yet been completed. It takes into account a richerchemistry with more constituents than are currentlytreated in VANESA. The chemical equilibrium of theoxide phase is solved and the associated solution modelapplied to this richer chemistty. Effective activitycoefficients for the species treated in VANESA are thencalculated and returned to VANESA. Although the datanecessary to use the model are not yet completelyavailable, the model has been formulated and theframework for its solution is included in VANESA.Until the implementation is complete, CORCON-Mod3should be run with the user flag IDEAL set equal to 1.The model is briefly described below.
The associated solution model adopted for the oxidicphase k Won a model suggested originally byBottinga and Richert.Q In this model, the chemicalpotentials of species in the system are derived byassuming regular solution interactions between pairs ofspecies, and recognizing that the molar volumes of theconstituents can be very different. Given this basis, thefollowing equation is derived:
where p ~ is standard state of the pure liquid species k,#~ is the volume fraction of species k in the mixture, v,is the molar volume of species k in the liquid phase, and
~ is the interaction coefficient for species k-jinteractions. The volume fraction of ~ies k isdetermined from
~, = NNk“~ N, Vii.1
where N; is the number of moles of i in the mixtunz
152)
Equation’ (151) can be written in terms of the activitycoefficient:
IIN
‘k ~‘jInyk=ln “
~ N, V,i-l
+~+i[l-~]i.1 v.
(153)
Tables of the oxide phase interaction coefficients, ~,will be included in a later update.
The VANESA model also considers kinetic limitations tothe vaporization release. The model treats the followingthree proceses:
●
●
●
Transport of the volatile constituent of the condensedphase to the free surface.
Conversion of the condensed phase constituents to the .vapor phase
Gas phase mass transport of vapor species away fromthe free surface
The following equation for the molar flux is solved foreach vapor species:
@Jj=K——A dt
..,, r% - p,) (154)
where the ~HJ is the effeetive rate constant for formation
of vapor species j, P~ is the equilibrium partial pressureof j over the condensed phase, and PJ is the partial
pressure of j in the bulk gas phase. The effective rateconstant, ~n~, is given by
49 NuREG/cR-5843
Model Descriptions
K1
e4TJ = P* 1 ROT (155)
%1 Ll&t xi ‘q+q
where ~ M the rate constant for condensed phase mass
-n. P* is the molar deuaity of the condensedphase. A is the mole fraction of ccmatituemt i in the bulkcondensed phase, ~,U is the vaporimtion rate constant,and ~ is the gas phase mass transport coefficient ofvapor species j. In this equation, the aubscripta i and jrefer to the condensed and vapor phaaea, respectively.
The rate constant for condensed phase mass transport iscalculated in the VANESA model using
!% DiK#T (156)
where Sh is the Sherwood number, D, is the umdensed
phase diffusion coefficient, and d is the diameter of therising bubbles. The condensed phase diftiaioncoefficied is detmmined using the Scheibel@ modificationof the Wilke-Chan~ correlation:
[4]n~+ 3VL
(157)
D, - 8,2xlo-10 T vi1/3
PL ‘{
where vL is the 3nolar volume of the condeased phase, v,is the molar volume of i, and PL is the viscosity of thecondensed phase. The Sherwood number is determinedfrom one of several different correlations depending onthe bubble geometry (e.g., size, shape, etc.). For adiscussion of these cormhtions the reader is referred toReference 10.
The vaporizxttion rate constant is calculated using a formof the Hertz-Knudsen equation, m In this model, K,ti isdetemined t%om
“u=+ (158)
where ai is the condensation coefficient (currently setequal to 1.0 in the code), Ml is the molecular weight ofspecies i, and T is the vapor phase temperature (assumedequal to the temperature of the melt).
The gas phase mass transport coefficient is calculatedfrom
(159)
where DJ is the gas phase diffusion coefficient for vaporspecies j, and ~ is the equivalent spherical bubblediameter. me gas phase diffusion coefficient iscalculated using the equation proposed by Singh andSingh:n
where MJ and M’ are the molecular weights of apecka jand the gas phase mixture, v] and v’ are the molar
volumes of species j and the gas mixture, and P and Tare the pressure and temperature of the gas phase.
Model for Mechanical Release
Mechanical generation of aerosols by entrainment andbubble bursting is important late in a reactor accident,when the core debris temperature has fallen such thataerosol generation by vaporimtion is minimal. Bothdroplet entrainment and bubble bursting are modeled inthe code.
Droplet eatrainmen t is n30deled using a correlationdeveloped by Kataoka and Ishii:a
H/+-P’ (161)E ● = 0.002 (j,”)3 N(@l’n ~
L
where ~ is the dimensionless entrainment flux
i“ =j’
[1
1/4q 8 (PI - P’)
P:
and N@J is a dimensionless gas viscosity
(162)
(163)
NuREG/cR-5843 50
Model Descriptions
“’”m ““)The VANESA model calculates aerosol generation bybubble bursting using the following correlation byAzbekm
3 K,
{}
NUMER ‘n
‘=2x P’~ DENOM
where NUMER is
[ 1d: 9 ~’ lnNUMER= 1-— ——
21$ + 16 K;
[1
dl?_l
‘q
DENOM is
3 42DENOM=l+. —
4K7
-’[i? 19 d: ‘n1-— ——
2% + 16 K:
the dimensionhxa entrainment volume, E, is
E._ PI v,
P’ Vb
(165)
(166)
(167)
(168)
where V, and V~ are the volume of the entrained aerosoland bubble, K, and Kz are
1.15% u,K,= -
(169)
~ is the diameter of the bubble, and c is the speed ofsound in the gas.
If the user chooses to bypass the VANESA calculation,but still wishes to consider the effects of aerosolgeneration on radiant heat loss from the upper debrissurface, the empirical correlation used inCORCON-Mod2 is used, This correlation is given by:lid
[A] = (33 + 240j~ exp(-19000K/T) (170)
where [A] is the concentration (g/n$ STP) of aerosol inthe evolved gas, T is the tempemture of the melt (K),and jg is the superficial gas velocity through the melt(m/s STP). Note that both the superficial velocity andthe concentration in this expression have been reduced tostandard temperature md pressure (STP).
The temperature T in Equation (170) is assumed to be thetemperature of the top layer of the melt. The gas flow(in bubbl=) through the pool is converted to a superficialvelocity at STP, and the aerosol concentration is adjustedto the temperature and pressure directly above the pool,with the temperature taken as that of the top layer. Ifcoolant is present, we assume that it is effective inscxubbing aerosols from the evolved gases, and set theconcentration in the atmosphere equal to zero.
The empirical aerosol concentration is calculated solelyfor the purpose of determining the radiative properties ofthe atmosphere; no composition is calculated for it, apdita mass is not charged against the pool inventory.
2.3.15 Aerosol Removal By Overlying WaterPools
Tbe VANESA model also treats the decontamination ofaerosol-laden gases passing through an overlying waterpool. Aerosol removal is assumed to be due to thefollowing mechanisms: sedimentation of aerosol particleswithin gas bubbles, impaction and adherence of aerosolparticlea on the bubble walls, and difiion of aerosolparticles to the bubble walls. If the water pool issubcooled, a fourth mechanism is assumed to be active:collapse of bubbles due to steam condensation in the
subcooled pool. This model assumes that either thesteam condtmaea completely immediately after the bubbleforms in the subcooled water pool or that steamcondensation is just complete when the bubble reachesthe water-atmosphere interface.
The VANESA model for aerosol removal is baaed on themodel formulated by Fuchs.m The aerosol removal rateis given by:
dm(d,,x)
dt= - [a,(d) + al(d) (171)
+ aD(d~] m(dP,x)
where m(c$,x) is the mass of aerosol having dhmeter ~at elevation x above the debris surface; and as(~,
51 NUREGICR-5843
Model Descriptions
a~~, and a~dJ are the coefficients for removal bysedimentation, impaction, and diffusion.
The sedimentation coefficient is given by Fuchs:m
where J(W is given by
J(d) =I? PP42C
18 P,
(172)
(173)
D~ is the diameter of the bubbles, U* is the rise velocityof the bubbles in the water pool, pp is the materialdensity of the aerosol particles, p, is the viscosity of thegas, C is the Cunningham slip correction factor
C=’+6 [1x7+004exd-0”:dpll(174)
where A is givem by
d, is the diameter of a gas molecule, P is the local
Pressure, and N~ is Avogadro’s number. The equationfor the sedimentation coefficient neglects the effects ofwater condensation on the aerosol particles. This wouldincrease the effective particle diameter, and therebytic- aerosol removal by sedimentation. Note,however, that this effect would be compensated to someextent by the reduction in the material density of theaerosol .
The coefficient for particle diffusion is also given byFuchs:rn
[1In
86aD(dJ = 1.8 — (176)
Uti ~’
where 9 is given by
~_ kTC
3r p, d,(177)
and k is Boltzmann’s constant. The equation for theparticle diffusion coefficient neglects the effect of steamproduction on the bubble surface. A flux of steam fromthe surface would, of course, reduce diffusion ofparticles to the surface.
The impaction coefficient describes loss of aerosol fromthe bubbles due to impaction on the bubble wall. Thisoccurs because the particles cannot stay within theinternally circulating gas flow. This mechanism isaffected by many different processes; consequently, manyof the correlations in the literature are quite complex.The VANESA model uses the relatively simplecorrelation shown below:
where r is given by
/2’ 42cT
= 18 p’
(178)
(179)
and U=, is the relative velocity of the particles. The ratioU=,/UA is a parameter that depends on many variablessuch as bubble shape, internal circulation velocity, etc.The user may supply a value through input or may selectthe default value of 1.5. Values t%om 1.5 to 4.2 arereasonable. (The upper end of this range corresponds tospherical cap bubbles. For spherical bubbles, thegeometrical basis for the impaction model is probablyinvalid.) Figure 2.12 illustrates the sensitivity of thepool decontamination factor (DF) to variations in thisratio.
Aa the above equations illustrate, the aerosol removal issensitive to many factors including: particle size, bubblesize, bubble rise velocity, and pd depth. Thesensitivities of the calculated pool DF to these variablesare shown in Figures 2.10 through 2.13.
The figures show a significant dependence of the poolDF on the size of the aerosol particles Small particles(< lpm) are trapped efficiently because they diflbequickly to the bubble wall. Large particles (> 1 pm)are trapped efficiently because of efficient sedimentationand impaction. It is important, therefore, that the codeuse accurate models for calculating the particle diameterof the aerosols. These models are described below.
Aerosol formation and growth processes are extremelycomplex. Important processes include: homogeneous
NuREG/cR-5843 52
t-L)
if
17
13
9
s
1
F&m 2?10
0.5 1.0
PART I CLE SIZE (Umj
Ssdtfdtyofthed amtamhwtbnfktorcobahhkshz @oddcpthls3rq v(mwv(rlse)
1.5
Is M)
17
13
9
s
1
700 CM
100 CM
—
PARTICLE SIZE (urn)
Figarc 2.11 Sensltidtyof the decontandnat~ factor to pool depth @abbk dlamcter Is 1 q V(rd)/V(rlse) IS 13
● ● ● ● ● ● ● ● 9 ● ●
17
13
9
5
1
Flgwc 212
..
V(relyv(risi?) = 5.
.
.-1
I I I 1 I I 1 I 1 1 I I I I I03 1.0 1s
PARTICLE SIZE (WI)
LIOUIDUS~~-
“ //
=-9”/
/
/
/
/
>“/
JSO LIDUS
——. - -
ME Ct4 ANt CAL MIXTURE
LIOUIOUSI SO LIDUS
CONSTRUCTION
TEMPERATURE
Figure Z13 Wphaw amstrudon for mixturv
Model Descriptions
nucleation in the vapor phase, condensation of vapor onnucleated particles and other surfaces, and coagulation ofparticles in the vapor stream. The VANESA manual’”provides an excellent summary of the models proposed toanalyze these processes.
Givem the complexity of the required models and theuncertainty associated with these models, the developersof the VANESA model decided to adopt an empiricalapproach to the calculation of the particle size. Thismodel begins with the assumptions that a.) particle size isdictated by condensation of vapora on nucleated andcoagulated particles, and b.) the temperature of the gasstream is low enough that essentially all of the vapor willcondense. Given these assumptions, the mean particlesixe is
[11/3
d,= 6A (1 80)
7r pP n(t)
where A is the initial mass concentration of thecondensing vapors (g/m’ gas), pP is the material densityof the particles (g/cd), and n(t) is the numberconcentration of the particles (pafiicles/cm3). Based onexperimental results which indicate a mass-weightedmean particle size of 1.2 ~m at vapor concentration of 50to 150 g/cm3, the number density of the aerosol particis estimated to be 1(Y particles/cm3. Thus, the meanparticle size in micrometers is calculated by
[11/3
dP = 0.266 A (<
For calculations, such as pool decontamination, thatrequire a particle si~ distribution, a log normaldistribution is assumed with a geomelric standard
es
81)
deviation of 2.3. (The user may specify alternate valuesfor the particle size and/or geometric standard deviationif desired.)
The aerosol scrubbing model divides the supplied aerosolsize distribution into size chase-s containing equalfractions of the total mass. The upper limit to theparticle size in each class is determined from
*= O”’l’+eTRll 1 ‘182)where N is the number of sim segments, Di+, is theupper limit to the size in class i, p is the mean particlesize, and u is the geometric standard deviation. Withineach class, the characteristic size is determined such that
half the mass lies above the characteristic size and halflies below.
The code solves for the aerosol removal as a function ofposition in the pool, and integratea the positiondependentremoval to determine the total aerosol removed from thegas stream. Since particle removal is sine depeadent, thecode tracks the changes in the size distribution withposition in the water pool.
2.4 Material Properties
Calculation of the physical processes described in thepreceding sections requires values for a wide range ofthermodynamic and transport properties. Theseproperties are treated as functions of composition and oftemperature. However, the dependence is not alwaysexplicitly included in the CORCON-Mod3 model; forexample, the values used for surface tensions areindependent of temperature.
In most cases, properties are required for the mixtures ofspecies which make up the components of the CORCONsystem, although the calculation of chemical equilibriumrequires the chemical properties of the individual species.With a few exceptions, such as the viscosity of oxidemixtures with large silica contents, mixture properties arecalculated from those of the constituent species.
The property models described below are the same asthose used in CORCON-Mod2 with a few exceptions. Auser option for specifying the phase diagrams of themetallic and oxidic phases is now provided inCORCON-Mod3. Also, properties used by the
CORCON-Mod3 implementation of the VANESA modelhave been included.
2.4.1 Thermodynamic Properties
The thermodynamic properties calculated are density,specific heat, enthalpy, and chemical potential.
Ik!dY-P (wd
Condensed Dhases:
Mixture densities are computed from
Pm = lC$ m~/Z (mivi/Mi)i
(183)
where the molar volumes of the individual speci~ aregiven by
57 NuREG/cR-5843
Model Descriptions
“i = “; [1 + c,(T -1673 K)] . (184)
Values for v ~ and CJapplicable to the liquid phase arestored in subroutine DENSTY for all condeusedspxies. ““n The temperature range of the data fromwhich this mhtionahip was generated varies considerablyfor the different species. For many of the oxides, it is!Yom 1200 to 1800”C, while for others it covers the
subroutine CONFND, with one or more temperatureranges for each species. A single range is used for allgaseous species, and the fits are valid from 298.15 to6000 K. The fits for condensed species include both theliquid and one or more solid phases; in some casea, tworanges are defined for a single phase. Thus, each speciesrequires fmm two to five sets of coefficients. The upperlimit of validity is above 2500 K in most caaea, althoughit is as low as 2000 K in others.mn
entire range km melting to boiling. However, Equation In any case, the data for the highest temperature range(184) is applied at all temperatures. Tlkis disregards the included are used for all temperatwes above thechange in density which accompanies &zing. minimum for this range. Mixture specific heats are
computed by mass averaging asSeparate tablea of deasities and molecular weights arestored (in BLOCK DATA XNDAR) and used in the Cp = 4186.8 ~ (micP)/m~ , (189)VANESA model. The tabka include values for both .
condemed phase species and gas phase species. For thespecies considered by VANESA, the molar volume is where the constant providw the conversion to S.1. units.
calculated fmm these values by Specific heats are computed in subroutine CPENTH.
. . )3nthalDy - h (J/kg)%“i. _ (1 85)A Speci* enthalpies are computed from integrals of the
corresponding spcific heats. The conventional
where M, is the molecular weight of species i. Thethermochemical reference point of separated elements intheir standard states (25”C, 1 atm) is employed; i.e., the
molecular weight of a mixture is calculated by molar enthalpies correspond to the JANAF tables. The resultweighing of the species molecular volumes. may be expressed in the form
43- us~hsse :
~hi(T) = hJT ‘) + ~~dT’CP, (T’)
Densities are computed from the ideal gas relationship
=Ki+AIk (T - T~)Pm = l@PM.~OT (186)
(+ 10-3Bik T2 - T~)/2
where ~ is the mixture molecular weight: ( )+ 10-cCik T3 - Tlu /3
(187)M==~xl Ml . - l@DY (1/T - VT;)
1
SOecific Heat - q (J/kg K)
The specific heat of any species, condensed or gaseous,is represented in the form
cP,
= Al + 10-3BiT + 10-6CIT2
(188)
+ 10DIIT2 .
Within the calculation, unitq are calhnol K, reflecting theoriginal data soumea; a conversion to S.1. (J/kg K) ismade before return from the calculational package.Values of the constants& B,, Cl, and Di are tabulated in
(190)
for Tin the kth temperature range for species i (i.e., ~<T CT~+’). The {T:} are the break points in thespecific heat fits. The first is 298.15 K and the last istreated as infinite. Thus, the first integration constant,~, is the standard enthalpy of formation of species i.Any others required are computed internally, subject tothe condition that the discontinuity in enthalpy at fi bethe appropriate heat of tmnsition, A~,m, if a phasechange occurs at T,, and zero othewise. SubroutineCONFND contains tables of these heats of formation andof transition. The integration constants are evaluatedinternally during an initial call to CONFND from routineSETUP in order to assure full-word accuracy onmachines of different word length. This is done to avoidthe possibility of negative discontinuities in h(T), which
NuREG/cR-5843 58
Model Descriptions
could cause numerical problems. At this time, thediscontinuities in entludpy are also replaced by smoothtransitions over an arbitrary temperature range of 10 K.As with specific heat, the enthalpy of a mixture iscomputed by mass averaging:
hm(T) = 4186.8 ~ [mih,(T)~mm . (191)
Mass averaging of specific heats and cmthalpies is reallyappropriate only for mechanical mixtures in which eachspecies is unaffected by the others. Because of mutualsolubilitie.s, actual mixtures of metallic or oxidic speciesform one or more phases. The principal effect is achange in melting behavio~ rather than the individualspecies melting independently at their own melt points,theentire mixture melts over a range of temperatures.
We account for this effect--at least partially--inCORCON-Mod3. The melting range, defined by theliquidus and solidus tempemtures, is prescribed byexternal models for mixtures of condensed species.Specific heat and enthalpy are calculated in three ranges:
1.
2.
3.
For T < P, the calculation is as described abovewith the exception that extrapolated solid propertiesare used for any species which would ordinarily beliquid. This is simply accomplished by ignoring thepmseuce of the sets of coefficients and integrationconstants for temperature ranges in which the speciesis liquid, so that the last set describing a solidcontinues to be used above the melting point.
For T( < T, extrapolated liquid properties are usedfor any species which would ordinarily be solid byignoring the presence of data for the solid.
For ~ < T < T’, linear interpolation in enthahw isused between the liquidus and hlidus. The con~btslope is returned as the specific heat. The effect ofthis construction is indicated in Figure 2.13.
Enthalpies are computed in subroutine CPENTH,
Chemical Potential - g (J/kg K)Chemical potentials for the species are required in thecalculation of chemical equilibrium and are computedfrom the molar Gibbs fimction
gi=hl-Ts, , (192)
where s is the entropy and may be computed attemperature T and at the reference pressure of oneatmosphere from
Si(-r) = S~T’) +\
‘dT’cP, (T’)/T’T’
= ~: + A’ In (T@ + 10-3B; (T - T;)
+ 10-W: (T2 - Tlu)/2
- l@D~ (1~’ - l/Tlu)/2 (193)
for T in the kth temperature range for species i (i.e., ~< T < T~+‘). The first integration constant, K~l, is the
standard entropy of formation of species i and, as withthe cdhalpy, any others required are computedinternally, subject to the condition that the discontinuityin enthalpy at T! be the appropriate entropy transition ofAH~,m/T~, if a phase c@nge occurs at Tf and mmotherwise. Again, subroutine CONFND contains theneceamry data tables and calculates integration constantsduring the initial call from SETUP. The chemicalpotentials, evaluated in subroutine CHEMPO, are usdonly as internal variables in the chemical equilibriumsubroutine MLTREA, which employs chemists’ uniis ofcal/mole. Therefore, no conversion to S.1. is made.MLTREA itself converts the standard chemical potentialsfor pure gaaea at one atmosphere pressure to mixtureconditions using the ideaI gas result
where ~ is the partial ptwsure of gaseous species i. No
pressure Correction is made for condensed species.
FM Mew Function - fef (cal/gmole K)
The VANESA model tabulates and uses free energy datain the form of free energy fictions. The free energyfunctions are related to the gibbs function and edtalpyby
fefl = -gl(T) - hi(298. 15)
T(195)
where 4(298. 15) is the enthalpy of species i at thereference temperature, 298.15 K. The data for thespecies free energy functions were fit to an equation ofthe following form
59 NuREG/cR-5843
Model Descriptions
where x = T/10000. The seven coefficients for eachVANESA chemical species are tabulated in BLOCKDATA BARRAY.
2.4.2 Transport Properties
The transport properties computed in CORCON-Mod3am the dynamic viscosity, the thermal conductivity, thesurface tension, and the emissivity. Detailed models areincluded for condensed-phase species and mixtures only.Gas-phase viscosity and thermal conductivity (requiredfor calculation of heat-transfer coefficients at themelt/c43ncrete interface) are treated as umstants usingrepresentative values defined in subroutine GFLMPR.
Dvnamic Viscosity - p (kg/m/s)
Oxidic Dhase:
The viscosity of molten oxides is quite mmplex,particularly when significant amounts of silica (SiO~ arepresent. For low-silica mixtures, the viscosity iscomputed from the Kendell-Monroe expre.ssion.~n
(197)
The viscosities of the species are determined using anAndrade formn
where the constants p: and ai are determined byempirical correlation.
Values of these coefficients are included (in subroutineVISCTY) for only a limited number of species. Thevalues for FeO, AlzOJ, and UOZ are based on publisheddata;z’s that for CaO is based on our own unpublished
theoretical estimate. The values for ZrOz and Cr20J arebased on analogy with UOZ and FeO respectively. Theseare irnpmtant contributors to the viscosity because theymay be dominant species in either the fhel-oxide layer orthe lightmxide (slag) layer. Only these species areconsidered in the Kendell-Monroe calculation, and theresulting composition is renormalized.
For mixtures with a higher silica content, the viscositycan be greatly increased by the formation of stronglybonded chains of Si04 tetrahedral. The viscosity iscalculated from a model proposed by Shaw.n This wasoriginally generated as a fit to the correlation developedby Bottinga and Weill baaed on geologic data,m and wasshown to give good agreement with it within the original
data base. Shaw’s model has an extremely simple form,for which good extrapolation properties are built in:
/’% = exds (1~/T - l.so) - 6.40] . (19)
Here the viscosity, p, is in poise (1.0 poise =0.1 kg/m-s) and s is a function of mixture compositiongiven by
( ,)s = Enixi s,O/Znixi Xsa . (200)
i ,
Data are included in subroutine VIS~ for TiOz, FeO,MgO, CaO, Li20, N~O, KZO, F~OJ, and AIZOJ; thesevalues are taken from Shaw’s paper. Also included aredata for UOZ and Zr02 based on an assumed analogywith TiOz, and for CrzOJ based on an assumed analogywith F~OJ. Again, the composition in terms of thesespecies is renormalized for use in Equation (199).
The Shaw model is restricted to mixtures with relativelyhigh silica contents; it is matched to the low-silicaKendell-Monroe form by simply accepting the greater ofthe two values calculated from Equations (197) and(199). The transition, where the two values are equal, istypically at a composition of 20 to 30 percent silica.
The maximum viscosity is limited to that for basalt,which is computed from
p(basalt) = 1.94 x 10s exp [20950/Tl
where p(basalt) is the viscosity in kg/m-s and T is inKeMns.
Metallic Phase:
We assume that the viscosity of the metallic phase can berepresented by the viscosity of iron (the majorconstituent) as given by the expression
Pm = 1.076 x 10-3 exp(3313/T) . (201)
coolant:
The coolant viscosity is computed fromn
P-M = 2.414 X 10-s 10”
a = 247.8 /(T-140) .
(202)
NuREG/cR-5843 60
Model Descriptions
Two-Phase, Solid-Liauid Slurry
CORCON-Mod3 contains a model for the enhancementof viscosity by suspended solids, in the form
1%
[1
(203)‘P. ;’~
where p,, is the slurry viscosity, A is the viscosity of thepure liquid mixture, and 4 is the volume fraction ofsolids.
This form was suggested by Kunitz” for slurriescontaining less than 50 percent solids by volume. InCORCON-Mod3, the expression is assumed to apply upto 50 percent solids. The solids fraction is computed bylinear interpolation between the mixture Iiquidus, T’, andthe mixture solidus, T’, as
(p(q-) . T’-T
T’ - T’”(204)
This equation is applied whenever the temperature isbetween the liquidus and solidus pointa.
Recent experiment.# suggest that the slurry viscositypredicted using the above equation may be significantlysmaller than the true viscosity of prototypic mixtures offiel and concrete oxides. However, these are onlypreliminary results, so we have made no codemodifications in this area.
Thermal Conductivity - k (W/m K)
Values for thermal conductivitynn’75’”*n forcondensed-phase species are stored in subroutineTHKOND. No temperature dependence is included.Mixture values are computed from the species values bymole-fraction averaging.
It should be mentioned that CORCON uses the samethermal conductivity for both the solid and liquid phases -- literature values for the solid phase thermal conductivityare tabulated in the code. While this is a fairlyreasonable assumption for the oxide phase, it may be inerror for the metal phase. For example, aluminum at900 K (33 K below the melting point) has a thermal
conductivity of 210 W/m K, while at 1000 K, thethermal conductivity is only 93 W/m K.= Most othermetals have thermal conductivities in the solid phase thatare approximately twice their thermal conductivities inmolten phase. To help correct for this potential problem,we have provided the user with the option of specifying a
multiplier to be applied in the calculation of the metalphase thermal conductivity. It should be noted, however,that this modified thermal conductivity would still beapplied to both the solid and liquid phases.
Surface Tension - u (N/m)
Values of surface tensionn’’’”qm for cxmdensed-phaaespecies are stored in subroutine SIGMY. No temperaturedependence is included. Mixture values are CQmputedfrom the species values by mole-fraction averaging.
Emissivity - c (-)
The calculation of radiative heat transfer requiresemissivitie.s for the radiating surfaces. In theCORCON-Mod3 code, only the emissivity of water .(coolant) is stored as internal data. Values are input bythe user for the ablating concrete surface, for the oxidicand metallic melt phases, and for the surroundings abovethe pool. The first is specified as a constant, while thelast three may be input as functions of either surfacetemperature or time.
Etnissivities are computed in subroutine EMISIV.
2.4.3 Liquid-Solid Phase Transition
In order to model solidification effects, we must be ableto determine the Iiquidus and solidus temperatures formetallic and oxidic mixtures. Melting temperatures and
latent heats of fusion are readily available for a widerange of materials. Values for all the condensed-phasespecies in the CORCON Master List (Table 2. 1) arecontained in the thermodynamic property tables describedin Section 2.4.1. The situation is quite different for themixtures encountered in melticoncrete interactions; dataare lacking, and the mixtures are too complex fordetailed analysis. Therefore, we have developedrelatively simple procedures for estimating the liquiduaand solidus temperatures of the various mixturesencountered in CORCON-Mod3. These temperatures arealso usexl in the construction of a single melt transition inthe enthalpy of such mixtures, as described in Section2.4.1.
%&he, M. Presentationat the ACE TechnicalAdvisoryCommitteeMeeting, ArgonneNationalLaboratory,June 1991.
61 NUREG/CR-5843
Model Description
Concrete:
The melting of concrete is strongly influenced by thepresence of trace species such as alkali oxides.However, melting ranges for typical concretes have beendetermined experimentally, and are included as part ofthe internal data in CORCON-Mod3 for the three built-inconcrete varietiea. For user-specified concretes, theIiqmdus and solidus temperatures must also be input bythe user the valuea for the built-in concmtea, Table 2.4,should provide some guidance.
M*I ic Mixtures:
For metallic mixtures (at least late in the auident whensolidification is likely) the principal constituents shouldbe Cr, Fe, and Ni from stainless steel. Therefore, wehave constmcted a simple fit to the iron-chromium-nickelternary phase diagram,” with due consideration to theassociated binary phase diagrams. The Iiquidus andsolidus temperatures are fit as
T 1. ~ (2130 - 510w~@- 1140w~1,
1809- 90WC, - 440W~1,(205)
1728- 200WC, - 40W%,
1793 - 230WC, - 130W~)
and
T ‘ = ~ (2130 - 730Wm - 3310W~1,
1809- 90WC, - 560W~l,
1728- 2SOWC, - 100WW, (206)
1783- 310WC, - 140W~,,
1613 )
where We,, W~, and W~l are the weight fractions of Cr,Fe, Ni, respectively, These expressions agree with theoriginal curves within a few tens of degrees. Theconwponding contour maps are shown in Figure 2.14.As implemented in CORCON-Mod3, the presence ofother elements is ignored, and the weight fractions ofchromium, iron, and nickel are renormalized so that
Wcr + w~o + WN, = 1.0.
Other metals such as zirconium or silicon, which may be
present in significant amounts at various times during theinteraction, may substantially depress the melting
temperature of the metal phase. We currently do notaccount for this effect in CORCON-Mod3. We have,however, provided the user with the option of specifyingthe solidus temperature for the metal phase. If thisoption is invoked, the liquidus temperature is set at 10 Kabove the userdefined solidus temperature.
Oxidic Mixtures:
The melting behavior of oxidic mixtures is far morecomplicated than that of the metals. The majorcxmstituents of concrete, CaO, SiQ, and A120j, form acomplicated ternary system (see, e.g., Reference 73).The fuel oxidea, UOZ and Zroz, appear to form arelatively simple system, but it is really a single-line inthe far more complicated uranium-oxygen-zimoniumternary system. Because consideration of the wmplete
phase diagram for concrete oxides plus fuel oxides seemsto be out of the question, the melting behavior of oxidicmixtures is treated in an approximate manner.The user may select from two different representations ofthe oxide phase diagram: one that assumea an idealsolution for the solid phase, and one that assumeseutectic interactions also occur. In both cases, the oxidicmixture is treated as a pseudo-binary system in which thefiel oxides form one “component” with concrete andstad oxides forming the other.
If the two components are assumed to form idealsolutions in both liquid and solid phasea, the following
equations for the liquidus and solidus temperatures areapplicable:
XIeXP[-HHl,20+$exp [-*[+ -+]]=1
XIeXPIHHll,20+~exp [++1=1where A is the mole-fraction of component i, ~is itamelting temperature, and AM is its heat of fusion.
This formalism may be applitxi to a mixture of mixturesby treating TIMas T~, the liquidus tempemtim of mixtum
NUREGICR-5843 62
1
18ST
IS3 Ss
Fo 1s30
rF&Qc214 UquldmsandsdidOS~ w h CPFdUl system s“=.
ii
Model Descriptions
i, in the Iiqudua equation, and as ~, the solidus
temperature of mixture i, in the solidus Equation (207).
lle melt properties for the fuel oxides (UO, + ZrO) aretaken aa~
AH = 208CWX + 17700 (1 - X)(209)
-5050 x (1 - x)
and
T ~ = T ‘ = AH/(20800x/2950(210)
+ 17700 (1 - x)/3123)
where AH is the component latent heat in Cal/mole, T’
and T’ are in K, and x is the mole fraction of Zfi- in theU02 + zro~ mixture.
For the second mixture, concrete oxides + steel oxides,we use concrete properties with T and T’ from either
built in data (for the three default concrete-s) or from userinput data (for a nonstandard concrete). The mixturelatent heat, AH, is internally calculated from built-inenthalpy data as
where
~ = (T” + T’)/2
and
~t.fi= Zmiii~ (T)/m
I
(211)
(212)
(213)
Here ~@) are the enthalpies of the liquid and solidphases of the constituent spies, extrapolated, ifnecsssry, as described in Section 2.4.1.
An example of the resulting phase diagram, for U~ +35 mol/o ZrOz and Lime-stone Aggregate/Common SandConcrete is shown in Figure 2. 15).
Recxmt ex~rimentsr have shown that the phase diagramcalculated assuming ideal solution interactions may be
fRoche, M. Pnwcnfationat fhe ACE Technical AdvisoryCommitteeMeeting, kgonnc NationalLaboratory,Juna 1591.
significmtly in error for the LWR debris compositions ofinterest. These experimerms clear] y show that eutecticinteractions occur in the oxide nuxture. As a result, thesolidus tenqwrature of the oxide phase decreases muchmore rapidly with the addition of concrete oxides thanshown in the figure. The experiments show that at onlyabout 10 or 20 mole percent concrete, the solidustemperature of the mixture has fallen to nar the concretesolidus temperature.
As one of the user flexibility options in CORCON-Mod3,the user may choose the ideal solution phase diagram (thedefault selection) or select an alternate parametricrepresentation that accounts (at least approximately) forthe observed melting behavior. In the latter, the liquidustemperature is assumed to be the same as for the idealsolution model. The scdidus temperature, which is themore critical value, is calculated assuming that thesolidus temperature decrease-s linearly with concreteaddition to a user-specified concrete mole fraction. Athigher concrete concentrations the solidus temperature isfixed at the concrete solidus. (The resulting phasediagram is shown in Figure 2.16.) While extremely
simple, this parametric model provides a fairly accuraterepresentation of the experiment data.
NUREGICR-5843 64
Model Descriptions
fI I 1 I 1 I I I I I
Ll?vlESTONE/CONIMON SAND
I I 1 1 I 1 I 1 1
0.0 0.5” 1.0U02 + Zr02 MOLE FRACTIONCONCRETE CONCRETE
Fuure 2.15 Example Iiquidus and solidus temperatures for oxidic mixtures
65 NUREGICR-5843
Model Descriptions
3000
LIMESTONE/COMMON SAND1
\
\\
\\
\\
\
-\
\\
\\
\
\polldus
t 1 I I I 1 1 1 I
0.0U02+Zroa
0.6 1.0MOLE FRACTION CONCRETE CONCRETE
NuREG/cR-5843
Figure 2.16 Alternate phase diagram for the oxide phase
66
2.4.4 Coolant Saturation IJne
If a coolant is present, CORCON-Mod3 considers thepossibility that it may vaporize. The calculationalprocedure, described in Section 2.12, requires knowledgeof the saturation line for the coolant-that is, thetemperature at which it boils at any givem pressure.data in the Steam Tabl# were fit by a nonlinearoptimintion program as
p= (T) s 1.292 x 10’0 exp[1
-3880,4
m
The
(214)
Model Descriptions
in S.1. units (pmsaure p in Pa, temperature T in K).This simple exp=ion reproduces the original datawithin 0.5 percent for T < 573 K, corresponding to pm< 8.5 MPa (which is far in excess of containment failurepmssurea), and is in error by only 5 pement at thecritical point. This accumcy aeOma more than adequatefor a code such as CORCON-Mod3. In addition to itsextremely compact and efficiemt form, Equation (213) hasthe vittue of an exact analytic inverse
T- (p) = 43.15- 3800.4. (215)
h (p/1.292 X 10!O)
67 NUREGICR-5843”
3.0 Assumptions and Limitations
The CORCON-Mod3 code has been designed to be usedfor the anal ysis of both reactor accident sequences andmelthxmcrete interaction experirnemts. The code input,described in Section 5.0, is sufficiently flexible to allow auser to describe problems of either type. Accidentcalculations provide information for assessment of therisks of operation of LWR’S. Calculations ofexperiments are useful both for planning and forinterpretation of results. The comparison of experimentand calculation is valuable for guiding further efforts inboth areas.
The user, however, should be aware of a number ofassumptions, approximations, and simplificationsemployed in the modeling which may affect the accuracy(or at least the interpretation) of CORCON-Mod3calculations. It is also woxth noting that a number ofsensitivity parameters are available through input to allowthe user to readily explore the extent of importance ofsome of the approximations noted below. Theseparameters are listed and briefly discussed in Table 4.1.Among the more important of these are:
1. The atmosphere and surroundings above the poolsurface serve only to provide boundary conditions forheat and mass transfer from the pool, as CORCONdoes not include calculational procedures to uphttethe temperature, pressure, or composition of theatmosphem or the temperature of the surroundings.(However, if these quantities are updated by othercode modules coupled to CORCON, the currentvalues will be used.) The calculation of radiative heat
loss from the pool surface is based on a one-dimensional model, and the convective loss iscalculated using a constant heat transfer coefficient.
2. The calculated concrete response is based on one-dimensional steady-state ablation, with no con-sideration given to conduction into the concrete or todecomposition in advance of the ablation front. Thisassumption is probably not a source of serious errorin the analysis of reactor accidents, at least for thesequences with long-term interactions be4ween corematerials and concrete. The heat fluxes involved aresufticientl y large that quasi-steady ablation is
approached within the first few minutes of interactionif the pool is molten; the process continues for aperiod of hours to days, sustained by decay heat fromthe fission products in the melt. The steady-stateablation assumption makes it difficult to apply thecode to transient intemctions that occur in the first
few minutes following reactor vessel failure. Thecode may also be inaccurate for analysis of verylong-term interactions where the debris temperaturemay be close to the concrete ablation temperature.
3. The solidification model is preliminary. It assumesthat a crust forms on any surface whose temperaturefalls below the solidification temperature. Themechanical stability of the crusts is not considered.We believe that both the mechanical strength of thecrust and the loads imposed on it by concretedecomposition gases are important in determining thetrue solidification behavior of the core debris.
The code assumes also that the crust has the sameproperties as the bulk liquid phase. This may not betrue if the liquid phase composition is changing withtime. Consider for example the formation of an oxidecrust early in the interaction (before significantconcrete ablation). This crust material will have asolidus temperature near that of the fuel oxidemixture. As concrete is incorporated into the moltenphase, the molten phase solidus temperature will “decrease. The cede assumes that the same change inthe solidus occurs for the crust. Clearly, this is notcorrect.
4. If the gas-film model is used, it is used for radial heattransfer even after the melt solidifies, even though theassumptions on which the model is based are nolonger valid. In particular, no radial gap developsaround a layer of the melt which has completelysolidified. Thus, radial ablation continues with the“solid” layer continuing to conform to the changingshape of the cavity rather than behaving as a rigidpenetrator. As coded, the model also assumes thatthe frozen materiat remains gas-permeable. Becausethe total amount of concrete eroded is largelydetermined by energy considerations (the availabledecay energy), the effect of these modelingassumptions is primarily on the calculated shape ofthe cavity.
5. There is no treatment of chemical reactions betweenthe melt and the atmosphere, or of reactions in theatmosphere. We do not consider these to besignificant limitations. Melt-atmosphere interactionsare probably insignificant due to the limited surfacearea and relatively low temperature of the surface.Reactions in the atmosphere do not affect the progressof the core-concrete interaction and so can be
69 NUREG/CR-5843
Assumptions
neglected in a computer model such as CORCON.Modeling of atmosphere reactions would, however, beuseiid where comparing code predictions to experimentresults, since the gas stream in the experiments issampled at some distance from the melt surface.
6. The de assumes ideal chemistry where calculatingbulk phase chemical reactions.
7. The code uses flat plate pool boiling correlations tonmdel heat transfer to an overlying coolant pool.Recemt experiments show that heat transfer is greatlyeahanced during the initial pour of coolant. Thisenhanced heat transfer may lead to rapid cooling ofthe melt surface, and a transition to nucleate boiling.The code predicts lower early heat fluxes than in theexperiments, and long-term heat transfer by filmboiling. Interestingly, the code predicts well the
longer term (steady state) cuolant heat fluxesmeasured in the experiments.
8. The timedependrmt melt radius m(xlel allows the userto mimic the spreading of a melt across a horizmtalfloor, but it is not a mechanistic model of spreading.
9. The de uses the same Fe-Cr-Ni phase diagram forthe metal phase that was in CORCON-Mod2. Thistreatment neglects important metallic components suchas Zr, Si, or Al that may be present in the melt atvarious tirnea during a core-concrete interaction. Ingeneral, these constituents will reduce the meltingrange of the metal phase relative to the rangepredicted by the code. Through input the user canmodi~ the phase diagram for the metal phase byspecifying a constant solidus temperature. TheIiquidus temperature is then assumed to be 10 Kgreater than the specified solidus.
NUREG/CR-5843 70
4.0 User
In this chapter we describe a typical calculational cycle ofthe CORCON-Mod3 computer code. We discuss theinput parameters and describe the output. Finally, weprovide general prog ramming information for the code.
4.1 A Typical Calculational Cycle inCORCON-Mod3
We have designed the calculational cycle in CORCON toreflect our view of the interrelationships of the variousphysical and chemical phenomena described in Chapter 2,The description of a typical calculational cycle inCORCON will aid user in understanding how thephenomena are modeled in the code.
At the start of a timestep, CORCON has a complete“snapshot” of the problem, that is, it has current valuesof all the relevant computational variables, including thecavity geometry; the physical, chemical, and thermalstate of the melt pod; and the transport properties for thepool, For the first timedep, the “snapshot’ comes fromthe initialimtion procedure. For later tirnesteps, the“snapshot” comes from the results of the precedingttitep.
The variablea describing the state of the melt pool areadvanced to their valuea at the end of the timestep by thecalculational procedure described below. The basic logicis also given in Figure 4.1, which is a flow chart of themain program in CORCON-Mod3,
1. Calculate a timestep. This may be either constant orvariable, m specified by the user.
2. Calculate the internal mass transport, melt/gas and
condensed phase chemical reactions, and theassociated energy terms.
Injection rates of concrete decomposition produets(already known) are assumed to remain constantover the timeatep, and the calculation proceeds intwo passes.
The first pass follows rising gaaea and condensedphase materials (e.g., concrete slag or entrainedmaterial), layer by layer. If the material shouldremain in the current layer, ita mass and energy areadded to that of the layer; otherwise, it isequilibrated thermally with this layer and passed onto the next. Gas passing through a metakontaininglayer is equilibrated chemically with the metal, andthe oxidic reaction products are added to the risingoxides, with any heat of reaction rernainin gin thelayer. When the surface of the pool is reached, the
Information
3.
4.
5,
6.
71
rising gases are passed to an interface routine whichdisposes of them and initializes any downward massflows, such as added coolant or additional corematerial falling into the pool. It is in the first passthat the VANESA subroutine is called. TheVANESA model calculate radionuclide releaM andaerosol generation, which are included in the upwardflow of material exiting the pool.
In the second pass, tilling condeaaed-phaae materialsare followed downward layer by layer, beingequilibrate in each layer, until they are added to theappropriate layer.
Finish the explicit time-advmcement of the layerenergy equations.
This step includes the addition of decay heat andsubtraction of heat lost to the concrete. It alsoaccounts for interlayer heat transfer and 10SSfromthe pool surface baaed on rates at the start of thetimeatep. If coolant ia preseat and is boiling, thecalculation ia completed at the step; othenviae, thematrix equations for an implicit calculation of theinterlayer and surface energy terms is set up. Alinearized representation of the pool then.ualreqxmae, surface heat flux VS surface temperature,is conatmcted.
Determine a provisional end-of-tirnWep value forthe tempemture of the surface of the pool bymatching heat fluxes to and from this surface.Constxuct a linearkl representation of theabovepool thermal reqmnse, as surface heat flux vasurface temperature.
In matching the heat fluxes, the Iinearimd pool
response and the “exact” relationships for theabovepool heat transfer are used. If desired, thechange of temperature in the atmosphere andsurroundings during the timeatep are included hereand made comistemt with the heat flux. The simpleroutine provided could easily become part of theinterfaw to a more general model,
Comphe the solution of the implicit interlayer heattransfer equatiom, using the provisionalcmd-of-timeatep surface temperature, to determinethe final layer ertthalpiea. Reconcile th~ with theknown layer masses and compositions to determinethe new layer tempemtures.
Calculate the new cavity shape, using the ablationratea at the start of the timestep. These ablationrates, are treated as constant over the tirneatep.
NuREG/cR-5843
userInformtim
L-JPROGRAM
CORCON
vINITIALIZE AND/OR DEFINE PROGRAM CONSTANTS
IAND COEFFICIENTS
I
+READ ALL INPUT DATA, MATCH INPUT SPECIES WITH MASTER LIST
I AND DETERMINE INITIAL CAVITY GEOMETRY DATAIM I
+COMPLETE INITIALIZATION OF ALL NECESSARY VALUES INITL
FIRST APPROXIMATION TO ABOVE-POOL THERMAL RESPONSE ATMSUR
I
CALCULATE:
AVERAGE GAS MIXTURE PROPERTIES IN THE GAS FILM GFLMPR
POOL LAYER DENSITIES, SOLIDIFICATION AND LAYER FLIPS PLLAYR
MELT LAYER TRANSPORT PROPERTIES MLTPRP
LEvEL SWELLS, INTERFACE LOCATIONS
AND LAYER AVERAGE VOID FRACTIONS LEVSWL
VOLUME HEAT SOURCES SOURCE
INTERFACE HEAT TEMPERATURES AND HEAT FLUXES INTEMP
PO IN TWISE AEILATION”??ATES ALONG
THE MELT-CONCRETE INTERFACE MASRAT.
I
NuREG/cR-5s43
++EDIT:
WRITE DATA TO PLOT TAPES IF APPROPRIATE PLOt8
PRINT OUTPUT IF AT AN EDIT TIME EDIT
A
Figure 4.1 Flow diagram for CORCON-Mod3
72
User Information
A
CALCULATE:——
NEW TIM ESTEP TIMSTP
+
uPDATE:LAYER MASSES AND ENTHALPIES FOR EFFECTSOF TRANSPORT, CHEMICAL REACTIONS. ANO .AEROSOL GENERATION. MHTRAN
~
EXPLICIT UPDATE OF LAYER ENERGY EOUATIONS.
ADVANCE TIME
TIME= TIM E+At
i
UPDATE:
ATMOSPHERICAL SURROUNDINGS, IN CLUOINQ MASS
ANO ENERGY TERMS ATMSUR
+
FINISH IMPLICIT PART OF POOL ENERGY; Calculate
NEW TEMPERATURES ANO SPECIFIC HEATS ENRCN2b
‘ UPDATE:i
CAVITY GEOMETRY BY CALCULATING NEW
POSITION OF BOOY POINTS RECEDE
Fwure 4.1 Flow diagram for CORCON-Mod3 (continued)
73
User Information
7.
8.
9.
10.
11.
120
calculate the new layer densities. Determine if theprevious layer ordering is still appropriate. If it isnot, reorient the layer configuration. Uyer flipsoccur in this step as well as creation of mixturelayers.
Calculate new layer transpoti properties (viscosity,thermal conductivity, etc.) from the newcompositions and temperatures.
Calculate bubble-rise velocities and (from knowngas-flow rates) pointwise void fractions in the pool.From the void fractions, the known volume ofcondensed phases in each layer and the cavity shapedetermine the elevation of each layer interface.
Evaluate decav or externally-imposed heat source-s.
Evaluate heat transfer between layers and theresulting interlayer heat fluxes.
The linearized above-pool response which wascalculated in Step 4 is used in this calculation. Thefinal temperature of the pool surface determined herewill differ slightly from the provisional valuecalculated in step 4.
calculate pointwise ablation rata along themeltumc&e interface.
The thermal resistance of the gas film, if it exists, iscalculated bawl on the local conditions of gas flowand the rate at which gas is entering the film, This
rate is made consistent with the local heat flux andablation rate.
At this point, CORCON onw again has a mnplete“snapshot” of the problem, for the end of the timestep.
At this point in the calculational cycle, all the calculatedvariablea have been evaluated at the same time level,
allowing the generation of a consistent printed edit of thestate of the system, if this is desired.
In the main program, the above steps are executed in theorder 7-12, edit if required, check for end of problem,14, and roped. This order is used because steps 7-11am also required as part of the initialization.
4.2 Description of the InputParameters
CORCON-Mod3 expects input to be provided in a filecalled “canod3.in” (Unit 5)0 The data cards needed for
input by the code are described in Table 4.1. Note that
the input is compatible with the inputs used forCORCON-Mod2, in the sense that any input deck used
for CORCON-Mod2 will also be accepted by CORCON- 4Mod3. There are, of course, numerous data cards thathave been added to the input for the many additionalfeatures in CORCON-Mod3. Also, some models thatwere inactive in CORCON-Mod2 have been activated in
CORCON-Mod3 (e.g., time-dependent mass addition).Finally, the reader should note that the user may now (
include comments within the input deck to explain aparticular eatry, or to provide a short description of thecalculation. Comment lines are assumed by the code if a
9$” appears in the first column.
A given problem will not require all the data cards and (
fields described. In fut, some fields and cards are notyet operational and these are indicated by **[...]** in thetable. This has been done to reserve space for furtherupgrades of the code, and to provide the adventurouscode modifier with information concerning partiallyimplemented features.
Data cards are initially read in subroutine DATAIN, andare echoed to the output file, and to a scratch file called“echo.filg (Unit 7). The cards are subsequently readfrom the scratch file by routines CONPRP, DATAIN,DCYINT, INCOOL, INGEOM, INPCON, INPGAS,MELTRD, and BCLTOV, which interpret the actual datafields.
4.2.1 Dwussion of Selected Input Quantities
Most of the input for CORCON is fairly self+xplanatory,especially to the user who is fhniliar with the type ofproblems it solves. However, experience has shown thatsome portions of the input require further discussion.
Edit and Timestep Control
‘Ihe parameter TPRIN (card 3) provides the user withdetailed printout after time has passed TPIUN. This is ofinterest primarily in the diagnosis of code problems; theadditional information is pMted in ~~ of FORTRANvariables and requires detailed knowledge of the internalworking of the cude for its interpretation.For routine calculations, TPRIN should be set greaterthan the problem end time TIMEND.
For both the variable timestep cmntrol (card group 3A)and the variable edit control (card group 3B), the lastspecification is assumed to apply to the end of theproblem if TIMEND is greater than the last TEND orTED, respectively. Each group is terminated by a blankcard rather than by a spxified count. This facilitates theinsertion of additional control intewals at significant or
NuREG/cR-5843 74
User Information
Table 4.1 Input instructions for CORCON-Mod3
‘ cardGroup# Field Format Variable Name Description
SECTION 1. PROBLEM IDENTIFICATION, COMPUTATIONAL OPI’IONS AND CONTROLPARAMETERS
PROBLEM TITLE
1 1-80 A80 80 Column run identification
COMPUTATIONAL OPTIONS INDICES
2 1-5 15 ILYR Index apecifiing number of initial melt layera:o-1-2-3-
**[4 -
>10 -
1 oxidic layer& 1 metallic layer1 metallic layer1 oxidic layer1 heterogenoua mixtuti layer2 oxidic layera 421 metallic layer]**Mixing models enabled; Initial layer configuration
6-10 15 ICOOL
11-15 15 IGEOM
16-20 15 ICON
21-25 15 ICHEM
26-30 15 IFP
31-35 15 ISUR
36-40 15 **[IABL]
set by ones digit (e.g., ILYR= 10 indicatea twolayers with mixing on)
Coolant index:o- no coolant1- coolant
Cavity geometry index:1- Cylinder with herniapherical baae2 -- Cylinder with flat baae
**[3 - Cylinder with spherical-aegrneat basel~x4 - Arbitrary shape
Concrete composition index:o - Nonstandard concrete1 - Baaaltic aggregate concrete2 - Lhnestone aggregate; common sand concrete3 - Limestone aggregate concrete
(Ming and condensed phaae chemistry (CPC) index:o - Coking off & CPC off1 - Coking off & CPC on
10 - Coking on& CPC off11 - Coking on& CPC on
Decay Heat (power) generation index:o - Decay power axnputed internally2 - Power deposited into oxidic and metallic layera
input veraua time
Index specifying surface temperature history ofattnoaphere surroundings:** ()[ - surface teqwature history computed internally]
1 - surface temperature inpvt Versus time
Index apeci~ing rnaaa addition to pool due to ablation ofsurroundings
o -- No maas addition**[1 - Mass addition ratea computd internally]**
75 NuREG/cR-5843
userInformation
Table 4.1 Input imtructions for CORCON-MOD3 (continued)
cad {GrouP# F&Id Format Variable Name Description
41+5
46-50
51-55
56-60
6145
66-70
71-75
76-80
2A 1
2-5
6-10
15
15
15
15
15
15
15
u
Al
15
15
ISPLSH
IPINC
IFILM
IRSTRT
IMOV
IPG
ISRABL
IAOPAC
‘&’
ITIMR
IFVAN
11-15 15 IVANFP
16-20 15 IUSER
NUREGICR-5S43
Melt/coolant splashout index:– No splashout from pool
** 1[0 - Metallic and oxidic phase splashout mass flow ratesinput versus time]**
Print increment index:>0 – Print output every IPINC time steps
so – Print controlled by Card Group 3B
Meltumcrete heat flow index:o – Bottom and side use slag film correlations1 – Bottom uses slag film& side uses gas film
10 – Bottom use-s gaa film& side uses slag film11 – Bottom and side use gas film correlations
Restart option index:o - Run starta from beginning
**[ 1 -- Restart calculation based on previously computedresults]**
Cavity shape plot index:o - No plots desired1 – Plots are desired
Index specifying plots of prescribed variables versus time:o -- No plots desired1 – Plots desired
Index specifying mass addition to poolo – No mass addition1 – Mass addition rates input versus time
Index specif@g radiative treatment of atmosphenxo – Treated as transparent1 – Opacity due to aerosols computed& included
The anqxxsand specifies the inclusion of this card.
Time dependent melt radius (TDMR) index:o – TDMR option not used
1 - TDMR option in use (IGEOM = 2 only)
Index speci~ing that a complete VANESA calculation is to beperformed
o -- No VANESA calculation1 – Perform complete VANESA calculation
Index specifying form of fission product information used byVANESA:
o– Fission product composition from CORCONl– Fission product composition to be specified
Index specifying inclusion of additional user flexibility input:o– No user flexibility inputl– User flexibility input to be provided
76
User Information
Table 4.1 Input imtructions for CORCON-MOD3 (continued)
card/GrouP# Field Format Variable Name Description
CONTROL PARAMETERS
3 1-1o E1O.O DELTIM Time-step control:> 0.0-- DELTM is the time step (s)<0.0 – Time step controlled by Card 3A
11-20 E1O.O TIMEO Initial time at which calculations are to begin (s)
21-30 E1O.O TIMEND Final time at which calculations are to cease (s)
31-40 E1O.O DPRIN **[Diagnostic print interval - pcint diagnostic messages everyDPRIN seconds starting at TIME = TPRIN (s)]**
41-50 E1O.O TPRIN Time at which diagnostic output is to begin (s)
Variable time-step control. Include Card 3A only if DELTIM <0.0
3A 1-1o
11-20
21-30
Variable edit control.
3B 1-1o
11-20
E1O.O DTMN Minimum time step for interval (s)
E1O.O DTMX Maximum time step for interval (s)
E1O.O TEND End time for interval (s)
Repeat Card 3A for a maximum of 10 intervals, terminate with DTMN <0.0
Include Card/Group 3B only if IPINC <0.0
E1O.O DED Time between edits for interval (s)
E1O.O TED End time for intend (s)
Repeat Card 3B for a maximum of 10 intervals, terminate with DED <0.0
SECTION 2. PROBLEM INITIAL Conditions
CONCRETE CRUCIBLE INITIAL GEOMETRY
4 1-5 15 NRAYS Number of rays (maximum of lot))
6-15 F1O.O RO- R-coordinate of center of ray system (m)
16-25 F1O.O ZO Z-coordinate of center of my system (m)Measured positive downward.Reference is arbitrary.
●Only permitted value is 0.0
Cylinder with hemispherical base – see Section 4.1.1 (Figure 4. 1). Include card 5 only if IGEOM = 1.
5 1-1o F1O.O RS Radius of hemispherical base (m)
11-20 F1O.O HC Height of cylindrical top section (m)
21-30 F1O.O RW External radius of concrete crucible (m)
31-40 F1O.O HBC Height from external base of cmcible to base of cylindricalsection (m)
77 NUREGICR-5843
Table 4.1 Input instructions for CORCON-MOD3 (continued)
-..
%&# FWd Fomat Variable Name Description
6. 1-1o F1O.O ZT Z-uxxdinate of cylinder top edge (m)
11-20 F1O.O RAD Radiua of cylinder (m)
21-30 FIO.O HIT Height of cylinder (m)
31-40 F1O.O RADC Radius of comer (m)
41-50 F1O.O RW External radius of concrete cmcible (m)
51-60 F1O.O HBB Height from external baae of crucible to baae of cavity(flat bottom) (m)
6145 15 NBOT Number of ray pointa equally spaced along flat bottom ofcavity
66-70 15 NCORN Number of ray pointa equally spaced around comer(not including tangent points)
*~Cylinder with spherical-segment baae - NOT OPERATIONAL. No input for IGEOM = 3.]**
Arbitrary shape - see Section 4.1.1 (Figure 4.3). Include cards 7, 8 and 9 only if IGEOM = 4.
7 1-5
6-15
16-2S
26-35
8 1-1o
11-20
9 1-1o
11-20
10 1-1o
11-20
21-30
31-40
15 NBOT Number of ray points equally spaced along flat bottomof cavity
F1O.O RTANG R-coordinate of tangent point (m)
F1O.O RW Extend radiua of concrete crucible (m)
F1O.O HTOTL Height from external base to top of crucible (m)
F1O.O R(1) Racwdinate of body point #1 (m)
F1O.O z(l) Z-coordinate of body point #2 (m)
F1O.O R(l) R-coordinate of body point I (m) for(I = NBOT + 2, NRAYS)
F1O.O m Z-coordinate of body point I (m) for(I = NBOT + 2, NRAYS)
(’Therewill be (NRAYs - NBOT - 1) carda in card Group 9)
CONCRETE COMPOSITION AND PROPERTIES
E1O.O TIC Initial temperature of concrete (K)
E1O.O TW Temperatum of concrete surface (K)(Ablation temperature)
E1O.O EW Emissivity of concrete surface (-)
E1O.O RBR Mass fraction of reinforcing steed in the concrete(mass fraction: kg_FE/kg_concrete)
NUREGICR-5843 78
User Information
Table 4.1 Input instructions for CORCON-MOD3 (continued)
Card/GrouP# Field Format Variable Name Description
Include card/group 11, 12 and 13 only if ICON = O.
11
12
13
13A
13B
14
15
16
1-5
1-8
11-20
1-1o
11-20
21-30
1-5
1-8
11-20
1-5
6-10
11-20
21-30
1-8
11-20
1-8
11-20
15 NINP Number of species in concrete mixtumonly species available in the Maater Species List may beincluded.
A8 NAMSP Name of concrete species (left justified)
E1O.O SM Maas fraction of concrete species (kg/kg_CONC)
mere will be NINP cards in group 12.)
E1O.O RHOC Demity of concrete (kg/m3)
E1O.O TSOLCI’ Concrete aolidus temperature (K)
E1O.O TLIQCr Concrete liquidus temperature (K)
Include cadgroup 13A and 13B only if RBR <0.0
15 NRBRSP Number of metallic species in rebar
A8 NAMSP Name of rebar apeciea
E1O.O SM Maas Iinction of rebar apeciea @g/kg rebar)
CORE MELT CONSTITUENTS
INITIAL MASSES, COMPOSITIONS, AND TEMPERATURES
15 NOSI Number of melt oxidic apeciea to be inpu$ only apecieaavailable in the Maater Species List may be included
15 NMSI Number of melt metallic apeciea to be inpuo only speciesavailable in tbe Maater Species List may be included
E1O.O TOI Initial oxidic melt temperature (K)
E1O.O TM Initial metallic melt tempemhue (K)
A8 NAMSP Name of oxidic apeciea (left justified)
E1O.O SM Masa of oxidic species (kg)
(l’here will be NOSI carda in card/group 15.)
A8 NAMSP NanM of nwtallic apeciea (left justified)
E1O.O SM Maw of metallic apeciea (kg)
(There will be NMSI cards in card/group 16.)
NURIWCR-5843
User Information
Table 4.1 Input imtructiom for CORCON-MOD3 (continued)
Group? Field Fommt Variable Name Description
INTACT CORE SIZE AND POWER, AND NUMBER OF RETENTION FRACTIONS TOBE MODIFIED
Include card/groups 17 and 18 only if IFP = O.
17 1-1o
1i-20
21-25
18 1-4
11-20
E1O.O XMTU Core size (metric tons of uranium)
EIO.O XMWTH (he operating power (MW thermal)
15 NUM Number of radioactive species in the intact core inventoryfor which the retention factor will be modified @UJM < 27)
A4 IFP1 Name of radioactive species whose retention factor is to bemodified (left justified)
E1O.O RET1 Retention factor of radioactive Speci= IFP1
(There will be NUM cards in card/group 18.)
COOLANT INITIAL MASS, COMPOSITION, AND TEMPERATURE
Include c.ardlgroups 18A md 18B only if ICOOI = 1.
18A 1-1o E1O.O TCI Initial coolant temperature (K)
18B 1-8 A8 NAMSP Name of coolant species (left justified) (H20 or H20CLN)
11-20 E1O.O FMCI Maas of coolant species ()
ATMOSPHERE INITIAL VOLUME, PRESSURE, TEMPERATURE, AND COMPOSITION
19 1-1o E1O.O VA Initial gas volume (m**3)
11-20 E1O.O PA Initial gas pressure (N/m*%2)M - Constant for problems O – Gas pressure specified by cardlgroups 20A&
20B
21-30 E1O.O TA Initial gas temperature (K)
31-35 15 NGSINP Number of gaseous species in the atmosphere;only species available in the Master Species List may beincluded (NGSINP < 18).
20 1-8 A8 NAMSP Name of gaseous species (left justified)
11-20 E1O.O SM Mole fraction of gaseous species (-)
(There will be NGSINP cards in group 20.)
Include card/groups 20A and 20B only if PA <0.
20A 1-5 15 NATMPR Number of points in table of pressure of gas atmosphereveraus time (1 < NATMPR < 10)
NUREGICR-5843 80
User Information
Table 4.1 Input instructions for CORCON-MOD3 (continued)
CawGroup# Field Format Variable Name Description
20B 1-1o E1O.O TPA(l) Table of gas pressure (PA) versus time (s); alternating valuea11-20 E1O.O PAT(1) of time, TPA (J) and pressure,
21-30 E1O.O TPA(2) PAT(J) for J = 1, NATMPR.
314 E1O.O PAT(2) If NATMPR = 1, pressure is constant at PAT (l).. .
. .
. ●
EIO.O TPA(NATMPR) Up to four pairs per card. May requi~ up to 2 cards tocmmplete the table.
E1O.O PAT(NATMPR)
SECTION 3. MELT INTERNAL HEAT GENERATION
DECAY POWER FOR OXIDIC AND METALLIC PHASES
Include card/group 21 only if IFP = 2.
21 1-5 15 NDECO
6-10 15 NDECM
Include card/group 22 only if NDECO > 0.
22 1-1o E1O.O TIql)11-20 E1O.O PIql)21-30 E1O.O TIq2)
31-40 E1O.O PIO(2). ●
. ●
. .
E1O.O TIO(NDECO)
E1O.O PIO(NDECO)
Include card/group 23 only if NDECM >0.
23 1-1o E1O.O TIM(1)11-20 E1O.O PIM(l)21-30 E1O.O TIM(2)
31-40 E1O.O PIM(2). .● ●
. .
E1O.O TIM(NDECM)
E1O.O PIM(NDECM)
Number of points in table of oxidic phase power veraua time(O < NDECO s 30)
Number of points in table of metallic phase power versustime (O < NDECM < 30)
Table of oxidic phase power (W’) versus time (s);alternating values of time, TIO(J) sod power, PIO(J) forJ = 1, NDECO.
If NDECO = 1, power is constant at PIO(l).
Up to four pairs per card. May require up to 8 cards tocomplete table.
Table of metallic phase power (W) vemus time (s);alternating values of time, TIM(J) and power, PIM(J) forJ = 1, NDECM.
If NDECM = 1, power is constant at PIM(l).
Up to four pairs per card. May require up to 8 cards tocomplete table.
81 NuREG/cR-5843
Usel Information
Table 4.1 Input instructions for CORCON-MOD3 (umtinued)
Group Field Format Variable Name Description
SECTION 4. BOUNDARY Conditions OF PROBLEM ATMOSPHERE SURROUNDINGS
SURROUNDING TEMPERATUREHISTORY
Include cardgroups 24 and 25 only if ISUR # O.
24 1-5 15 Number of points in table of surroundings temperatureversus time (NTP < 10)
25 1-1o E1O.O Trs(l) Table of surroundings temperature (K) versus time (s);11-20 E1O.O TMPS(l) alternating Vdlles of time, TTS(J) and temperature, TMPS(J)21-30 E1O.O lTs(2) for J = 1, NTPo31-40 E1O.O TMPS(2)
. .
. .
.
EiO.O Trs(NTP) Uptofourpairs percard. Mayrequire upto3 cardstocomplete table
E1O.O TMPs@JTP)
RATES OF SPECIES MASS ADDITION TO POOL
Include cadgroups 26, 27, 28 and 29 only if ISRABL # O.
26 1-5
6-10
27 1-8
28A 1-5
6-10●
●
●
15 NSPG Number of species in mass addition table;only species available in tbe Master Species List may beincluded (NSPO s 20).
15 IFPOPT Option flag for input of fission product mass addition0- fission product composition calculated internally1- fission product composition specified by user
A8 NAMSP Nama of species in mass addition table (left justified)
(The will be NSPG cards in card/group 27.)
15 NMP(l) Number of points in table of mass flow rate versus time forfirst species as defied in card/group 27.
15 NMP(2) Number of points in table of mass flow rate versus time foro seumd species as defined in cardlgroup 27..
Ii NMP(NSPG) Number of points in table of mass flow rate versus time forlast species as defined in card/group 27. (NMP(l) s 10,I = 1, NSPG)
NuREG/cR-5843 82
User Information
Table 4.1 Input inatructioms for CORCON-MOD3 (continued)
cadGroup# Field Format Variable Name Lkcription
28B 1-1o11-2021-303140
●
.
.
.●
1-1o11-20
●
●
.
●
✎
29A 1-5
6-10
11-15
29B 1-1o11-2021-3031-40
.●
●
●
.
29C 1-1o11-2021-3031-40
.
.
.●
●
E1O.OE1O.OE1O.OE1O.O
●
.
E;O.OE1O.O
E1O.OE1O.O
.
.●
E1O.OE1O.O
15
15
15
E1O.OE1O.OE1O.OE1O.O
.●
E;O.OE1O.O
E1O.OE1O.OE1O.OE1O.O
.
.
E;O.OE1O.O
TMs(l,l) Tables of maa flow rate (kgh) of species I versusFMS(l,l) time (s) for esch apecieaas defined in card/group 27;TMS(2,1) alternatingvalues of time, TMS(I,J) and rate, FMS(I,J) for (I
FMS(2,1) = 1, NMP(J)) and (J = 1, NSPG).●
●
tis(NMP(l),l)FMS(NMP(l),l)
TMs(l ,2) Start a w card 28B for each w species.FMS(1,2) May require more thao one card for each apeciea.
.
.●
TMS(NMP(NSPG),NSPG)FMS(NMP(NSPG),NSPG)
NOTS
NMTS
NCI’S
TIOTS(l)TOTS(1)TIOTS(2)TOTS(2)
●
●
TIiTS(NOTS)TOTS(IWTS)
TIMTS(l)TMTS(I)TIMTS(2)TMTS(2)
.
.
TI*MTS(NOTS)TMTS(NOTS)
Number of points in table of temperature versus time for ~added oxi& phaae.
Number of points in table of temperahm vwaus time foradded metallic phaae.
Number of pointa in table of tempemtum veraua tim foradded coolant phaae.
Tables of time (s) veraua tempemtum (K) for addedoxide p-,aknating valuea of time, TIOTS(I) and temperature,TOTS(I) for (1 = 1, NOTS)
Tablea of time (s) veraua temperature (K) for addedmetal phasetaknating VdlJW of time, TIMTS(l) and temperature,TMTS(I) for (I M 1, NOTS)
83 NUREG/CR-5843
User Information
Table 4.1 Input instructions for CORCON-MOD3 (continued)
cardGroup# Field Format Variable Name Description
29D
30
31
32
33
1-1o11-2021-3031-40
.
.
.
.●
1+
5-8
9-12
1-5
6-10
11-15
1-1o11-2021-3031-40
.
.
.
.●
1-1o11-2021-30314
.
.
.
.
.
E1O.OE1O.OE1O.OE1O.O
.●
.
E1O.OE1O.O
TIcrs(l) Tables of time (s) versus temperature (K) for added
TCXS(l) coolant phase;TICTS(2) alternating values of time, TICTS(I) and temperature,TCTS(2) T~S(I) for (1 = 1, NOTS)
.
.
TI”~S(NOTS)TCTS(NOTS)
EMISSIVITIES FOR RADIATION HEAT TIUINSFER COMPUTATIONS
A4
A4
A4
15
15
15
E1O.OE1O.OE1O.OE1O.O
.●
E;O.OEIO.O
E1O.OE1O.OE1O.OE1O.O
.
.
.
E1O.OE1O.O
IREO
IREM
IRES
NEO
NEM
NS
TORT(1)EO(l)TORT(2)EO(2)
.
.
.
TORT(NEO)EO(NEO)
TORT2(1)EMM(l)TORT2(2)EMM(2)
.
.●
TORT2(NEM)EMM(NEM)
Variable name (either TIME or TEMP) for table of oxidicphase emissivity versus IREO.
Variable name (either TIME or TEMP) for table of metallicphase emissivity versus IREM.
Variable name (either TIME or TEMP) for table ofsurroundings emissivity versus IRES.
Number of values in table of oxidic phase emissivitiesveraus IREO (1 < NEO < 5).
Number of values in table of metallic phase emissivitiesversus IREM (1 < NEM < 5).
Number of values in table of surroundings emissivities versusNS (1 s NS s 5).
Table of oxidic phase emissivity (-) versus time (s) ortemperature (K);alternating values of emissivity, EO(I) and time ortemperature, TORT(I) for I = 1, NEO.
If NEO = 1, emissivity is constant at EO(l).
May require up to 2 cards to complete table.
Table of metallic phase emissivity (-) versus time (s)or temperature (K);alternating values of emissivity, EMM(I) and time ortemperature, TOR12(I) for I = 1, NEM.
If NEM = 1, emissivity is constant at EMM(l).
May require up to 2 cards to complete table.
NUREGICR-5843 84
User Information
Table 4.1 Input instructions for CORCON-MOD3 (untinued)
Card/GrouP# Field Format Variable Name Description
34 1-1o11-2021-30314
.
.
.●
.
E1O.OE1O.OE1O.OE1O.O
.
.
.
E1O.OE1O.O
TORT6(1) Table of surroundings emissivity (-) versus time (s) orEs(1) temperature (K);TORT6(2) alternating values of emissivity, ES(I) and time orES(2) temperature, TORT6(I) for I = 1, NS.
●
. If NS = 1, emissivity is constant at ES(l).●
TORT6(NS) May require up to 2 cards to complete table.Es(m)
Include cadgroup 34A only if IAOPAC # O.
34A 1-1o E1O.O RADLEN Characteristic path length (m) for atmospheric opacitycalculation.
SPLASHOUT OF POOL CONSTITUENTS
**[Include card/groups 35, 36 and 37 only if ISPLSH # O.]**
SECTION 5. TIME-DEPENDENT MELT RADIUS
Include card/groups 38 and 39 only if IGEOM = 2 and ITIMR =1.
38 1-5 15 NORAD Number of points in table of melt radius versus time(O < NORAD S 12)
6-15 F1O.O HTMIN Minimum allowable melt thickness (cm).(HTMIN >0.1 cm)
16-25 F1O.O HTMAX Maximum allowable melt tbickrmss (cm).(HTMAX S Id cm)
85 NUREG/CR-5843
User Information
Table 4.1 Input inatructioms for CORCON-MOD3 (continued)
Group# Field Format Variable Name Description
39 1-1o11-2021-3031-40
.
F1O.OF1O.OF1O.OF1O.O
.●
FiO.OF1O.O
TIMRAD(l) Table of melt radius (m) versus time (s);RADTIM(l) alternating valuea of time, TIMRAD(I) and melt radiua,TIMRAD(2) RADTIM(l) for I =’ 1, NORADRADTIM(2)
●
● .●
TIMRAD(NORA May require up to 3 cards to complete table.D)RADTIM(NORAD)
.
.
SECTION 6. USER FLEXIBIL~Y
Include cardigroup 40A and 64 only if IUSER = 1.
40A 1-5 15 IBHTB Index specifying modification of the bulk heat tranafercoefficient for the bottom surf-
6-10 15 m-m Index specitjing modification of the bulk heat tranafercoefficient for the side surface
11-15 15 Index specifying modification of the interlayer heat transfercoefficient
16-20 15 ICHT Index specifying modification of the coolant heat fluxcalculation
Index indicating modification of the minimum film boilingtemperatw
21-25 15
26-30
31-35
36-40
4145
15
15
15
15
IEON
IERT
IDRT
Index for modification of the entrainment onset criteria
Index for modification of the entrainment rate calculation
Index for modification of the droplet settling calculation
ICDC Index for modification of the condensed phase diffusion
coefficie4N
46-5051-55
5640
61-65
66-70
71-75
15
15
15
15
15
15
IVDC
ICNCD
mmIBR
IKO
Index for modification of the vapor phaae diffusion coefficient
Index for modification of the condensation rate coefficient
Index for specification of the mean aerosol particle size
Index for modification of the bubble size models
Index for modification of the metal phase thermal conductivity
Index for modification of the oxide phaae thermal conductivity
NuREG/cR-5s43 86
User Information
Table 4.1 Input instructions for CORCON-MOD3 (continued)
GrQup# FkJd Format Variable Name Description
40B
41A
41B
42A
42B
43A
43B
44A1
1-5
6-10
11-15
16-20
21-25
2b-3(’)
31-35
36-40
41-45
1-1o
11-20
21-30
1-1o
1-1o
11-20
21-30
1-1o
1-1o
11-20
21-30
1-1o
1-5
15
Is
IS
15
15
15
15
15
IS
E1O.O
E1O.O
E1O.O
E1O,O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
15
IVSM Index for modification of the M phase viscosity
Ivso Index for modification of the oxide phaaeviacuaity
ISTM Index for modification of the metal pbaae surface tension
ISTO Index fbr modification of the oxide phxse audke tmaion
IRHOM Index for modification of the oxide phaae deaaity
IRHOO Index for modification of the metal phaae deaaity
IPHM Index for modification of the mtal phase diagram
IPHO Index for modification of the oxide pbaae diagram
IZIP Index for modification of the chetilicd equilibrium cutoff
Include cardgroup 41A only if IBHTB = 1,
Coefficients A,B, and C in:
BHTB Nu-ARe~~
CHTBInclude cardgmup 41B only if IBHTB <0,
XBM Multiplier applied to bulk convective beat traaafbr coefficientfor the bottom surfaw of the melt
Include cadgmup 42A only if IBHTS = 1.
AHTs Coefficients A, B, and C in:
BHTS Nu=AR#~
CHTs
Include cadgroup 42B only if IBHTS <O.
XSM Multiplier applied to bulk convective heat tranafer coefficientfor the radial (side) surface of tbe melt
Include caud/group 43A only if IIHT =1.
Al Coefficients A, B, and C in:
BI Nu - A Ret p+
CI
Include card/group 43B only if IIHT <1,
Multiplier applied to intdayer bent tranafer coefficied
Include card/group 44A only if ICHT = 1.
NCHT Number of entries in table for coolant heat flux vs. AT-@IcHT 4 20)
87 NUREC3KR-5843.
User Information
Table 4.1 Input instructions for CORCON-MOD3 (continued)
cadGrwP# Field Format Variable Name Wption
44A2
44B1
44B2
45
46
4’7
48
49
50
51
52
53A
1-1o11-20
.●
.
1-5
1-1o
11-10.
.
●
1-1o
1-10
1-1o
1-1o
1-1o
1-1o
1-1o
1-1o
1-1o
E1O.OE1O.O
E1O.O
E1O.O
15
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
DTCHT(l) Table of coolant heat flux (w/m~ vs. AT-; alternating valuescm(l) of AT- and heat flux
DTCHT (NCHT)CHT (NCHT)
Include card/group 44B only if ICHT <O.
NCHT Number of entries in table for the coolant heat flux vs. AT-(NCHT s 20)
DTCHT(l) Table of cuolant heat flux multiplier vs. ATW; alternatingvalues of ATW and heat flux multiplier
cm(l)
DTCHT (N~H)
CHT(NCHT)
Include card/group 45 only if ITMFB = 1.
TMFB Minimum film boiling temperature (K)
Include card/group 46 only if IEON = 1.
ECRIT Critical bubble size for entrainment
Include card/group 47 only if IERT = 1.
XEM Multiplier applied to calculated entrainment rate
Include card/group 48 only if IDRT = 1.
XDM Multiplier applied to calculated droplet settling flux
Include card/group 49 only if ICDC = 1.
CDM Multiplier applied to the condensed phase diffusion coefficient
Include card/group 50 only if IVDC = 1.
VDM Multiplier applied to vapor phase diffiion coefficient
Include card/group 51 only if ICNDC = 1.
CNDM Multiplier applied to the condensation rate coefficient
Include card/group 52 only if IMU = 1.
PSDMU Mean aerosol particle size (micrometers)
Include card/group 53A only if IBR = 1.
BR1 Multiplier for the Fritz bubble size
NUREGICR-5843 88
User Information
Table 4.1 Input instructions for CORCON-MOD3 (continued)
Card/Group# FieJd Format Variable Name Description
11-20
21-30
53B 1-1o
54A 1-5
54B 1-1o11-20
.
.
.
55A 1-5
55B 1-1o11-20
.
.
.
56A 1-5
56B 1-1o11-20
.
.
.
E1O.O
E1O.O
E1O.O
15
E1O.OE1O.O
E1O.O
EIO.O
15
E1O.OE1O.O
E1O.O
E1O.O
15
E1O.OE1O.O
EIO.O
E1O.O
BR2 Multiplier for the Davidaon-Schuler bubble size
BR3 Multiplier for the gas film bubble size
Include card/group 53B only if IBR C O.
BRFIX Fixed bubble radius (m)
Include card/group 54 only if KM = 1.
NKMM Number of entries in the table of thermal conductivitymultiplier vs. temperature (NKMM < 10)
TKMM(I) Table of thermal conductivity multiplier vs. temperature (K);XKMM(I) alternating values of temperature and thermal conductivity
multiplier
TKMM
(NKMM)
XKMM(NKMM)
Include card/group 55 only if IKO = 1.
NKOM Number of entries in table of thermal conductivity multipliervs. temperature (NKOM < 10)
TKOM(l) Table of thermaI conductivity multiplier vs. temperature (K);XKOM(l) alternating values of temperature and thermal conductivity
multiplier
TKOM (NKOM)
XKOM (NKOM)
Include card/group 56 only if IVSM = 1.
NVSMM Number of entries in the table of viscosity multiplier vs.temperature (NVSMM < 10)
TVSMM(l) Table of viscosity multiplied vs. temperature (K); alternatingVSMM(I) values of temperature and viscosity multiplier
TVSMM(NVSMM)
VSMM
(NVSMM)
Include card/group 57 only if IVSO = 1.
89 NUREG/CR-5843
User Information
Table 4.1 Input instructions for CORCON-MOD3 (mntinued)
Group# Fdd Format Variable Name Description
57A
57B
58
59
60
61
62
63
64
1-5
1-1o11-20
.
.
.
1-1o
1-1o
1-1o
1-1o
1-1o
1-1o
1-1o
15
E1O.OE1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
E1O.O
NVSMO Number of entries in table of viscosity multiplier vs.temperature (NVSMO < 10)
TVSMO(l) Table of viscosity multiplier vs. temperature (K); alternatingVSMO(l) values of temperature and viscosity multiplier
TVSMO(NVSMO)VSMO(NVSMO)
Include cadgroup 58 only if ISTM = 1.
STMM Multiplier applied to the metal phase surface tension
Include card/group 59 only if ISTO = 1.
STMO Multiplier applid to the oxide phase surface tension
Include card/group 60 only if IRHOM = 1.
RHOMM Multiplier applied to the metal phase density
Include card/group 61 only if IRHOO = 1.
RHOOM Multiplier applied to the oxide phase density
Include card/group 62 only if IPHM = 1.
TSOLMT Constant value for the metal phase solidus temperature (K)
Include card/group 63 only if IPHO = 1.
XEUT Mole fraction of concrete oxides at which the oxide phasescdidus temperature has decreased to the concrete solidus
Include card/group 64 only if IZIP = 1.
ZIP Value of the ZILCH parameter in MLTREA = cutoff forinclusion in the chemistry solution (default: 1. E-5 moles)
NUREG/CR-5843 90
userInfmmtiOIlTable 4.1 Input instructions for CORCON-MOD3 (continued)
11-15 15
16-20 15
CawGrmp# Field Format Variable Name Description
SECTION 7. VANESA INPUT
VANESA INPUT OPTIONS
65 1-5 15 IBUB Bubble diameter option indexO -- Fixed bubble diameter is user specified
1- Bubble diameter is calculated internally
6-10 15 KATIS Mechanical release option indexO -- Fixed release1-- Azbel, Ishii & Kataoka comelations are calculated
internally.
INOPL INOPL optionO – No pool calculation
1- Pool calculation activated
IDEAL Non-ideal chemistry indexO -- Calculate activity coefficient for use in VANESA1 -- Assume ideal chemistry
BCL COMPOSITION
Include cardlgroups 66A, 66B and 66C only if IVANFP = 1.
66A 1-1o11-2021-3031-4041-5051-6061-7071-80
66B 1-1o11-20
21-3031-4041-5051-6061-7071-80
66C 1-1o11-2021-3031441-5051-60
61-7071-80
E1O.OE1O.OE1O.OE1O.OEIO.OE1O.OE1O.OE1O.O
E1O.OE1O.O
E1O.OE1O.O
EIO.OE1O.OE1O.OE1O.O
E1O.OE1O.OE1O.OE1O.OE1O.OE1O.O
E1O.OE1O.O
CESIODXENKRYTEBASNRU
MOSR
RBYTCRHPDLA
CEPRNDStdPuAG
SBNB
Maas of Cesium melt constituent (kg).Mass of Iodine melt constituent (kg).
Mass of Xenon melt constituent (kg).Mass of Krypton melt constituent (kg).Mass of Tellurium melt constituent (kg).Mass of Barium melt constituent (kg).Mass of Tin melt constituent @g).Mass of Ruthenium melt constituent (kg).
Mass of Molybdenum melt constituent (kg).Mass of Strontium melt constituent (kg).
Mass of Rubidium melt constituent (kg).Mass of Yttrium melt constituent (kg).Mass of Technetium melt constituent (kg).Mass of Rhodium melt constituent (kg).Msss of Palladium melt constituent (kg).Mass of Lanthanum melt constituent (kg).
Maas of Cerium melt constituent (kg).Mass of Praseodymium melt constituent (kg).Mass of Neodymium melt constituent (kg).Mass of Samarium melt constituent (kg).Mass of Plutonium melt constituent (kg).Mass of Silver melt constituent (kg).
Mass of Antinomy melt constituent (kg).Mass of Niobium melt constituent (kg).
Include card/group 67 only if INOPL # 0.
91 NUREG/CR-5843
User Information
Table 4.1 Input instructions for CORCON-MOD3 (continued)
cdl
Group# Field Format Variable Name Description
67 1-1o
11-20
21-30
31-40
41-50
5140
IlO 11=NOSC Number of size segments used to describe the aerosol size
distribution (4 < NOSC < 50) (If 11 < 0, use default:NOSC = 20.)
F1O.O F1=GSD Geometric standard deviation of si= distribution of aerosolsentering water pool (If F1 < 0, use default: GSD = 2.3)
110 12= IDMF Switch that controls the diffusion mechanism for aerosolentrapment by the water pool.O – Diffusion mechanism inactive+0 - Diffusion mechanism active
110 13=IMPF Switch that controls the impaction mechanism for aerosolentrapment by the water pool.O -- Impaction mechanism inactive40-- Impaction mechanism active
F1O.O F2 = BSIZI Diameter of gas bubbles at base of the water pool (cm)
(If F2 <0, use default: BSIZI = 1.0 cm)
F1O.O F3 =VROVR V(rel)/V(rise), the ratio of gas velocity within the bubble tothe rise velocity of the bubble.(If F3 <0, use default: VROVR = 1.0)
NUREG/CR-5843 92
User Information
interesting points in the development of the calculation,without providing unneeded detail during the remainderof the problem. The actual timesteps employed maydiffer from those specified, if necessary, to produce edits
at the requested times.
Edits are produced at times which are integral multiplesof the edit intmval DEDIT(I), rather than a DEDIT(I)from the previous edit. This minimizes the effect of theinsertion of additional edits, which is valuable if onemust compare the outputs from several calculations at thesame times. To clarify this, consider as an example acalculation performed with edit controlled by an inputcard such as
1200.0 21600.0
This will produce printed output every 1200.0 s (20minutes), at times of 1200.0 s, 2400.0 s, 3600.0 s, etc.Suppose that some interesting phenomenon is observed atabout 3000 s, and that more frequent output is desirableto study it. The set of input cards
1200.0 3000.O60.0 3300.0
1200.0 21600.0
will prmke additional printed output at 3000.0 s, 3060.0s , . . . . 3300.0 s. However, the later edits will still bewritten at times of 3600.0s, 4800.0s, etc., rather thanbeing shifted to 4500.0 s, 5700.0 s, etc.
If variable tirnestep control is specified (DELTIM < O)but no intervals are specified, then the calculation will beterminated following input.
If variable edit control is specified (IPINC < O) but nointernals are specified, then the calculation will be run
but no ptited output will be generated. This might bedesired by a user who is interested only in plots of theoutput data.
Tables
All input tables are automatically linearly interpolatedduring execution. This is true for tables given as a
fimction of time and those specified as a function oftemperature.
Initial Cavity Geometry
The definitions of most of the variables used to describethe initial cavity geometry (cards 5 to 9) should beapparent from Figures 4.2 through 4.4, or from the
definitions of the variables in Section 5.2. However, thevariables NBOT and ITANG warrant firther discussion.
The cavity-shape description introduces a “tangemt ray”
parallel to the csvity axis through the tangent pointbetween the flat bottom of the cavity and the curvedsides. This ray is used in the shape-change calculation tomaintain the flat bottom of the cavity as required by themodels.
For the flat-bottomed cylinder, IGEOM = 2, or thearbitrary cavity shape, IGEOM = 4, there is already anormal ray through this tangent point, which is numberedNBOT. The tangent ray, numbered lTANG =NBOT +
1, defines an additional body point which initiallycoincides with that defined by the ray NBOT, but whichdiverges from it as the surface recedes. The number of
the rays is changed as the calculation proceeds, to reflecttheir actual ordering along the cavity surface. (Note that“normal” points can cross over the tangent ray.)
In the case of a hemispherically baaed cavity, IGEOM =
1, a flat bottom is assumed to exist with a radius that isone percent of the sphere mdius RS, and only a single
point is defied with the number ITANG = NBOT = 2.
The Size and Power of the Intact Core
The size and power of the intact core (card 17) is used todetermine the concentration of fission products in the fielif IFP = O. This concentration, as modified by retentionfactors for each element included, together with the U~
mass in the pool, is used to evaluate the initial~fission-product invento~ of the melt. If the initial mass
exceeds the size of the intact core, a warning is issued.
4.2.2 Recommended Values and DefaultValues for Input Quantities
Recommended values for some of the input quantities aredescribed below. Except for the default concretecompositions listed in Table 2.2, default values are notused in CORCON. That is, if a required input value isnot defined, then in general code execution is terminatedwith an appropriate warning or error message.
Timestep Values
The timestep for CORCON is controlled by user input(card 3 and, optionally, group 3A). In selected valuesfor the timestep, the user should remember that theCORCON model is explicit in time for the calculation ofablation ratesand convective mass and energy flows.Therefore, if the tirnesteps employed are too large,
NUREG/CR-5843 93
U= Information
IGEOM = 1
r-R
z QI
(RO,ZO)*
I I
I
1=I
RS
*RO 20 MUST BE AT CENTER OF HEMISPHERE9
NUREG/CR-5843
F~ure 4.2 Initial cavity g~me~ - cylindw with hemkphtid haw
94
User Information
1-R
(RO* ,ZO)
*RO MU
I
‘r
ZTI
& RAD+
CAVITY
RADC
\1
ST BE 0.0
Figure 4.3 Initial cavity geometry - arbitrary shape
95
HIT
HBB
NuREG/cR-5843
User Information
IGEOM= 4
f —--l?
I‘RWTI
(ROqf,20)
(R(l),2(1))
1
CAVITY
1I = NBOT + 2, NRAY
R(i), Z(l))I
I , “TANG
f
*RO MUST BE 0.0
NUREG/CR-5843
Fwure 4.4 lNtial cavity geumetry - cylinder with flat base
96
A
HTOTL
User Information
unphysical results may be generated or the calculation using a greater number of rays tn achieve better
may fail completely definition of the cavity shape.)
Based on experience during the development and testing 4.3 Description of the Outputof CORCON-Mod3 and on experience with previousversions of CORCON, we recommend timestep values inthe range of 10 to 60 s. Short timesteps should be used
4.3.1 Numerical Output
whenev-er conditions are changing rapidly such as duringPriods of high heat transfer (rapid cxmcrete ablation),
The output from CORCON-Mod3 is stored in the file,
vigorous exothermic chemical reactions, or rapidCCMod3.OUT. This file contains several majorsections.
intedayer mixing. Conditions such as these are mostlikely to occur at early times. At later times, it may be
The first section is an echo of the input data; it is anpossible to increase the timestep without incurringnumerical problems. TimeStep control is accomplished
uninterpreted reproduction of the records comprising the
using card group 3A.input stream. This provides a compact, permanent
record of the data used in a particular calculation, and is
Concrete Ablation Temperature
The ablation temperature for concrete, TW, is not clearlydefined and must be specified by the user. The user islimited to values between the liquidus and solidustemperatures for the concrete selected. Based on pastexperience in simulating experiments with CORCON-Mod3, we currently recommend that the ablationtemperature be selected at or near the Iiquidustemperature for the concrete. This selection implies thatconcrete is not displaced from the interface until it isalmost completely molten. The liquidus and solidustemperatures for the default concretes are listed in Table2.3.
Initial Problem Time
When using the internally calculated decay heat
generation, the initial time, TIMEO, corresponds to thetime following reactor shutdown (SCRAM) that the meltis deposited into the reactor cavity. If a specific time isnot known, a value of TIMEO in the range of two to five
hours would be reasonable.
Cavity Coordinate System
In the specification of the ray system (card 4), the originmust lie on the axis of symmetry (RO = 0.0). Based onsensitivity calculations, we recommend that 20 be chosento maximize the number of rays whose intemection withthe cavity surface is close to perpendicular, which avoidssmall-angle intersections. In any case, the origin must lieabove the bottom of the cavity. The ray spacing shouldbe chosen so that the separation between body points(i.e., intersections of rays with the cavity surface) isinitially in the mnge of three to 30 cm. Although up to100 rays may be specified, most applications will requirefewer than 60 rays. (Given the uncertainty in modelingheat transfer to the concrete, there is no real benefit to
useful for finding input errors.
The second section contains the input data as interpretedin CORCON. It contains a description of the concretecavity, the composition of the concrete (either default oruser-specified), the fission product inventory for the melt
and the initial conditions for the melt, the identity andquantity of the coolant (if any), the composition of theatmosphere above the melt pool, the type of boundaryconditions, the composition and mass flow rate ofmaterial entering the melt pool, and the radiativeboundary conditions for the melt pool. Error messagesare printed in this section if errors are detected. If errorsare detected, code execution continues to the end of thissection, and then terminates. This can reduce thenumber of passes needed to find all the emors in an inputdeck.
The third output section presents a temporal snapshot ofthe state of the core-concrete interaction. This isgenerated at the start of the problem, TIMEO, and atsubsequent times as specified in the input. Theinformation is presented in several sections, each startingon a new page of output, with a running header toidentify the version of the code in use, the problem title,the problem time, and the timestep number. The sectionsare a general summary, and summaries of gasgeneration, cavity geometry, heat transfer, chemical
reactions, melt pool geometry, melt pool composition,melt layer properties for the melt pool, aerosolgeneration and radionuclide release, and aerosol removalin an overlying water pool. The latter two sections areprinted only if the user has chosen to perform theVANESA calculation. These sections are described ingreater detail below.
Various informational messages, such as those describingchanges in melt layer orientation or warnings concerningthe number of iterations required in various routines, areprinted between the snapshot edits. A fourth section of
97 NuREG/cR-5843
UserInformation
output may be generated by use of the TPRIN variableon Card 3. This section contains extensive diagnosticinformation, and is intended primarily for debugging thecode; it is labeled in terms of FORTRAN variable namesand assumes that the user has detailed knowledge of thecode. Under ordinary circumstances, this output shouldbe suppm.saed by specifying TPRIN greater than theproblem emd time, TIMEND.
Gelled summary
The general summary section of the snapshot editcontains the pool configuration, the maximum depth andradius of the cavity, an approximate energy budget, andquantities needed to check the accuracy of the numericsof the code.
The pool configuration is given as the number of layersin the pool, the configuration of the layers, and thepresence of cuolant.
The maximum depth and radius of the cavity are given inmeters, with the locations of the points of maximumdepth and maximum radius, and the remaining axial andradial concrete thicknesses.
The energy budget is a summary of the mtes of gain orloss of energy (in watts) from the pool through variousmechanisms. The budget is not exact: some rates arecurrent and some are averages over the precedingtirneatep. In some ~, approximations have been madein the calculation of the rates given in the energy budgetwhich are not used in the internal CORCON calculations.For these reasons, the printed energy budget may notbalanu exactly, although the error is usually small (onthe order of a few percent). However, largediscrepancies may appear following a major discontinuityin the physical phenomena, such as problem initiation,depletion of the coolant, or layer flip. The energybudget is for debris-containing layers only; it does notinclude the coolant or the concrete.
Detailed checks on mnservation of mass and energy inthe entire pool (including coolant, if present) are madeand printed in this section. The printed values are thediscrepancies between the sums of layer contents and thevalues required by conservation within the poolboundaries, and are presented as relative errors in massand enthalpy. Normally each value should be nearmachine round-off for single-precision arithmetic.
Gas Generation Summary
The gas generation summary section of the mapshot editcontains generation rates and cumulative releases for all
the condensable and noncondensible gas species in theproblem. These are presented as masses and moles, andinclude the gases in bubbles, the gas film, and vaporizedcoolant .
Cavity Geometry Summary
The cavity geometry summary section of the snapshotedit presents the locations of the body points defining thecavity shape, the distance of each body point from thebottom center along the concrete surfaq the local slopeof the wall, and the angle of the ray which defines thepoint. Also, the cumulative volume and surface areabelow each point, the average void fraction at theelevation of the point are presented for each point. The
-<flotations of interface-s between pool layers are also given..’O;:‘“Heat Transfer Summary
The heat transfer summary section of the snapshot editpresents, for each body point, the local normal wncreteablation rate, the film conditions, the temperature of thepool/film interface or of the pool/concrete interface, thefilm thickness, film-wise mass flow rate, the averagevelocity of the gas in the film (if a gas film is present),the Reynolds number, the film flow regime, thecontributions of radiation and convection to the heat flux,and the heat transfer coefficient. If no gas film ispresent, the film thickness, film-wise mass flow rate, the
average velocity of the gas in the film, and the Reynoldsnumber will all be zero or very small numbers.
Chemical Reactions Summary
The chemical reactions summary section of the snapshotedit presents the results of the chemical reactions in eachlayer during the timestep. For a metal layer, the resultsof the metal/gas or metal/gas/concrete oxide reactions areprinted. For a heterogeneous layer, the results of thebulk metal/oxide/gas reactions, are printed. For thefilm, the results of the film metal/gas reactions during the
timestep are printed. The quantities of the reactants and
products are printed in moles for each of the oxide,metal, and gas species involved in the reactions.
Melt Pool Composition Summary
The melt pool composition summary section of thesnapshot edit presents the mass of each species present ineach occupied layer of the pool and the total mass ofeach species present in the pool.
IwREG/cR-5843 98
User Information
Melt Pool Geometry Summary
The melt pool geometry summary section of the snapshotedit presents the radius and thickness of the melt pool.This section is printed only if the timedependent melt
radius option is used.
Melt Layer Properties Summary
The melt layer properties summary section of thesnapshot edit preaenta the values of thermophysical andtransport properties for each layer in the melt pool.Also, quantities related to gas bubbles, such as the bubbleradius and velocity, are presented, and heat transfercoefficients, crust model quantities, and axial interface
temperatures and layer edge temperatures are presented.Important terms in the layer energy equation are given.
All quanthksare evaluated at the current time, with theexception of the heat of reaction entry, which is anaverage over the preceding timestep.
Interlayer Mixing Summary
lle interlayer mixing summary is provided if a mixturelayer exists; it is not necessary for the mixing option tobe active. The summary lists properties for each phasein a xnixtum layer. This information supplements thelayer property information provided in the preceding editsummary. Also included in this summary are the massesof oxide or metal entrained and de-entrained during thetimestep.
Aerosol and Radionuclide Release Summary
The aerosol and radionuclide release summary isprovided if the user has chosen to perform the VANESA
calculation. This output summary provides the aerosolrelease rate, aerosol concentration in the gas stream,aerosol composition, aerosol material density, aerosolparticle size, and the temperatures and gas compositionused in the VANESA calculation.
Aerosol Removal in an Overlying Water Poolsummary
TMs section is provided only if the user has chosen toperform the VANESA analysis and an overlying waterpool is present. The output in this section includesparticle sizedependent deumtamination factors and massdistribution. Also printed are the overall decontaminationfactor and total mass of aerosol emerging from the waterpool.
4.3.2 Graphical Output
Output files for generating graphical depictions of thedata are obtained by setting IPG to a non-zero value toobtain a set of tiles for plotting such things as gas
genemtion rates and melt temperatures as timctions oftime, or setting IMOV to a non-zero value to obtain afile of cavity shape data for making movies of theevolution of the cavity shape.
The quantities written to the various output files forplotting are described below. Except as noted, eachquantity is written at each edit time.
Unit 30 (movie.dat)
The quantities written to Unit 30 are the number of rays,the outer radius of the concrete crucible [m], and theaxial coordinate of the bottom of the crucible [m] (on thefirst line of the file). Then tbe time [s], therz-coordinates of each body point, the radius of the topsurface of the melt pool or coolant, and the axial locationof this surface (all in meters) are written. Thisinformation can be used to generate plots of the temporalcavity shape, but doing so requires that the user develophis/her own post-processor.
Utit 31 (Ccmodlplt)
Thequantitkswritten to Unit31 include the time [s] andthen, for each layer, the layer temperature [K], the layermass ~g], the layer density ~g/m ], the layer voidfaction [-], the temperature of the lower layer surface[K], and the heat transfer from the lower surface ~.Also written are the coordinates [m] of the locations ofmaximum radius and maximum axial depth of the meltpool, the maximum axial and radial erosion distances, the
axial erosion rate at the first body point (i.e., at thecavity centerline), the cumulative gas generated [g-mole]by species, and the rate of gas generation [g-moles/s] byspecies.
If a VANESA calculation is performed, Unit31 is alsoused to store tirnedependent information on radionuclide
release and aerosol generation. The quantities written toUnit 31 are the aerosol generation rate [g/s], and the
aerosol concentration at ambient conditions [g/d].
The quantities written to this file may be mad by anyFORTRAN program that includes the appropriate
unformatted read statements. An example of the requiredread statements for each time point follows:
99
real time(npta),ttay(npts,6),amtay(npta,6)real adot(npta),dz(npts),drfnpts)
NUREG/CR-5843
User Information
c
10
tad outgaa(npta,4),doutga(npta,4),q(npta,6),aaum(6),aetfnpta,3)dcuble prwision xmas
mad(ntp2)tintcs(jpt)do 10i=l,6
read(ntp2)Uay(jpt,i),amtay(jpt,i),x! ,x2,x3,x4continuemad(nQ2)Z1,rl ,r2,z2mad(ntp2)adot(jpt)rud(ntp2) &(jpt,dr(jpt)tcad(ntp2)(outgaa(jpt,i),i= 1,4)mad(otp2)(doutga(jpt,i),i= 1,4)md(ntp2) (q(jpt,i),i = 1,5)m.ad(nQ2)aer(jpt,l),aer(jpt,2),xmas●ertjpt,3)=xnus
4.4 Description of the Warning andError Messages
CORCON-Mod3 performs a number of error checksduring execution. First the input data are examined forobvious errors or inconsistence. Then variousintermediate results of the transient calculation are testedto detemnine if they are physically realistic within thelimits of the models in CORCON-Mod3 and if they have
converged numerically.
When an error condition is detected, an appropriatemessage is issued. Subsequent action depends on theseverity of the erro~ execution may
● continue with a warning, or
● terminate at the end of the timestep, or
● tetinate immediately.
lle messages that the user may encotmte: are listed inTable 4.2, together with the action taken by the code.
Most of the error messages are self-explanatory. In afew cases, additional comments have been added toclarify the meaning of the message.
Examination of the code listing will reveal several otherlocations where an error or warning message could beprinted and execution terminated by a call to FAIL. Ingeneral they correspond to errors which, short ofmachine error, cannot exist in CORCON- Mod3. Thesemessages might appear if incorrect modifications weremade to the code, and are included for that reason.
4.5 General ProgrammingInformation
CORCON-Mod3 is coded in FORTRAN which conformsto ANSI Standard X3.9-1978 (“FORTRAN 77”).5 Theonly changes in language from CORCON-Mod 1 are theuse of type CHARACTER for alpha-numeric data, and
the use of BLOCK IF structures in the newer routines.The code contains approximately 23600 source linea,including 6200 lines of COMMENTS.
In cases where constants are required to have fitllmachine accuracy, they are evaluated by execution of ashort routine called SETUP.
The cmle reads data from a file named “wnod3.in,”which must exist at the start of the run. (On UNIXsystems, the file name should be in lower case.) ASCIIoutput is written to a file named “ccmod3.0ut, ” whichwill be creatwl with “unknown” FORTRAN status. Onsome systems, this will cause art existing file with thename “ccmod3 out” to be ovenvritten. Additional binaryfiles, “movie.dat” and “ccmod3.pit, ” may be created andwritten for post~xecution printing and plotting.
NUREG/CR-5843
User Information
Table 4.2 CORCON-generated warning md error messages for each subroutine
ABLATE——
“* * * ABLA~ * * * I~RpoLA~oN FOR MASS ~Dm(_jN
() AT ( ) OFF HIGH END OF TABLE ()”~arning only]
ADDLYR.--. ——. -
‘* III * ADDLYR * * * CONVERGENCE FAILURE.
L, HTOT(L),TLAY(L) = (), (), ()”~arning only]Convergence failure for layer temperature in call to TMPFND.
ATMPRO
n* * IIIATMPRO * III * I~RpoLA~oN FOR A~oCJpHER]c
PRESSURE AT () OFF LOW END OF TABLE 0“~aming only]
●☛ ☛ ☛ A~pR() * III * I~E~oLA~oN FOR A~ospHE~c
PRESSURE AT () OFF HIGH END OF TABLE ()”~aming only]
ATMSUR——
‘* * * ATMSUR * * IIIINTJ7~o~~ON FOR SURROUNDINGS
TEMPERATURE AT () LOW END OF TABLE ()”warning only]
“* * * A~suR * * * 1~~~’rIoN FOR SURROUNDINGS
TEMPEIWTURE AT () OFF HIGH END OF TABLE ()”~aming only]
‘* * III ATMSUR * * * CONVERGENCE FAILURE*
flmmediate termination]Failure to match the above-pool heat transfer to the pool surface.
101 NuREG/cR-5843
User Information
Table 4.2 CORCON-generated warning and error messagea for each subroutine (continued)
CHEKCV
‘I@ * * CHEKCV ● * * No MORE cx)L~o -
@mediate termination]
“* * * LEVSWL\CHEKCV * * * NOT ENOUGH COOLANTTO COVER THE MELT AT () SECONDS. “[Immediate termination]
-III * IIIENRCN l\cHEKcv * * * NOT ENOUGH cooLA~
TO COVER THE MELT AT () SECONDS. “@unediate termination]
CONFND——
** * * coNFND III * * INSERT = () EXCEEDS Dimensions
[Immediate termination]Can only occur if data tables have been changed.
“* * * CONFND * * * IOPT = () OR IN = () NOT IN MASTER LIST”
[Immediate termination]Can only occur if data tables have beem changed.
CONPRP
W* * * CONPRP * III IIICONCRETE INPUT SPECIES () N(JT IN MASTER LIST’
[Deferred termination]
●III I@* CONPRP * * IIIREBAR INPUT SPECIES () NOT IN MASTER LIST”
~ferred termination]
CPENTH.--—
“** * CPENTH * * * IOPT = () IS IN ERROR”[Immediate termination]
CREATE
W* * IIIPLLAYR III x * CONVERGENCE FAILURE.
L, HTOT(L),TLAY(L) = () () ()”[Immediate termination]
NuREG/cR-5s43 102
User Information
Table 4.2 CORCON-generated warning and emor messages for each subroutine (continued)
CYLIND-.. —.. —
-* * * CYLIND * * * N~YS = () LESS THAN NBOT + NCORN + 3“
[Deferred termination]Too few mys or two many bottom and comer pointa in cavity definition.
DIMACH
“DIMACH – I OUT OF BOUNDS”[Immediate termination]Incorrect index in calling statement: 1 .LE. I .LE. 5. Can only occur if the code has been modified incorrectly.
DATAIN
‘* III* DATWN III* * NO DATA ON UN~ 5n
[Immediate termination]
‘* * IIIDAT~N * III * T(x) MANY ~MEsTEp I~ERVA~n
[Deferred termination]
“* * * DATATIN * * * NO TIMESTEP INPUT”[Deferred termination]
** * * DATAIN * * III Too MANY EDIT I~J7RvA~n
[Deferred termination]
“* * * DATAIN * * * INVALID IFP = ()”
[Immediate termination]
“* * * DAT~N * * * IREO = () IREM = () IRES = ()”
[Immediate termination]Improper type for emissivity tables. Should he “TIME” or “TEMP”.
DCSEVL--------
“DCSEVL NUMBER OF TERMS LE O“[Immediate termination]
“DCSEVL NUMBER OF TERMS GT 1000”[Immediate termination]
“DCSEVL X OUTSIDE (-1, + 1)”[Immediate termination]
103 NuREG/cR-5843
User Information
Table 4.2 CORCON-generated warning and error messages for each subroutine (continued)
DCYINT
‘III III * DCYINT * III *, PROBABLE ERROR. POOL CONTAINS () PERCENT OF CORE”
~aming only]Input haa specified a maas of U02 greater than the entire core.
DHGEN.-—
m* * * DHGEN III III III INTERpoLA~oN FOR SOURCE POWFR IN
OXIDE AT () OFF LOW END OF TABLE ()”warning only]
‘* * * DHGJ2N * * * INTERpoLA~ON FOR SOURCE POWER IN
OXIDE AT () OFF HIGH END OF TABLE ()”
~arning only]
n* * * DHGEN * * * INTERPOLATION FOR SOURCE POWFR IN
METAL AT () OFF LOW END OF TABLE ()”warning only]
● III * * DHG)7N * * * I~ERpoLATIoN FOR SOURCE POWER IN
METAL AT () OFF HIGH END OF TABLE ()”~arning only]
EDIT
EMISIV——
‘* * * EMISIV * * *, INTERPOLATION FOR SURROUNDINGS
EMISSIVITY AT () OFF LOW END OF TABLE ()”~aming only]
“* III * EMISIV * * IIII~RpoLA~ON FOR SURROUNDINGS
EMISSIVITY AT () OFF HIGH END OF TABLE ()”~arning only]
‘* III * EMISIV * * IIIINTFRpoLA~oN FOR OXIDE
EMISSIVITY AT () OFF LOW END OF TABLE ()”~arning only]
‘* !@ * EMISIV * * * INTE~oLATION FOR OXIDE
EMISSIVITY AT () OFF HIGH END OF TABLE ()”marling only]
NUREG/CR-5843 104
User Information
Table 4.2 CORCON-generated warning and esmr messagea for each subroutine (continued)
** III * E71SIV * * * I~~LA~oN FOR METAL
EMISSIVITY AT () OFF LOW END OF TABLE ()”~aming only]
‘III * * )7MISIV * * * I~Rpo~~oN FOR METAL
EMISSIVITY AT () OFF HIGH END OF TABLE ()”~aming only]
“* * * EMISIV * * * NSPL,NSPU = O ()”
[Immediate termination]Invalid species range.
ENRCN1——
‘* * I@ENRCN1 * I@* MASS IN LAYER ()”
[hmnediate termination]Improper layer. Can only occur if the code has been modified incorrectly.
“* * * ENRCN1 * * * BAD DQDT, LLO, DQTIYIT(LLO), LUP, DQBDTB(LUP) =
00000”[hnmediate termination]Some heat flux vs temperature relation has a negative slope.
‘* * IIIE~cNl * * IIIMA~x AMTRJ( Is SINGULAR As DETF7ED By s~Ba
[Immediate termination]The equations for the solution of the implicit energy equations are singular.
ENRCN2
‘* * * ENRCN2 * * * CONVERGENCE FAILURE. L, HTOT(L),TLAY(L) = () () ()”
~mmediate termma“ tion]Failure to determine new layer temperature after energy update.
FILM
“* * * FILM * * * CONVERGENCE FAILURE. JBODY,LYR,EMDO,EMD = () () () 0“[Immediate termination]Failure to determine consistent film properties (heat transfer coefficient and gas generation).
105 NuREG/cR-5s43
User Information
Table 4.2 CORCON-generated warning and emor messages for each subroutine (continued)
HTRCLN
‘* * * HTRcLN * * * CONVERGENCE F~Lu~=
Ummediate termination]Failure to determine radiative contribution to the boiling heat transfer.
“b4’’b~c~***NcL. ()”
[Immediate termination]Invalid cuolant. Can only occur if the code has km modified inumectly.
HTRLAY
-x * * HTRLAY * * * AXIAL CONVERGENCE FAILJJREO L,Kou~,Lo@L,LoopT = () () () on
~arning only]Failure to determine state of layer consistent with boundary conditions. Has only been observed for vanishingly thin
liquid sublayers, and usually in early iterations of INTEMP (so that the result does not affect the end-f-timestepresults). Code continues, using conductive heat transfer for layer.
‘* * * ~Ay * * * AXIAL SOLID coRE/LIQuID SURFACE
WITH L,TS,TB,TL,lT = ()()()()09warning only]Solid layer is being melted from the top md bottom. Has only been observed in early iterations of lNTEMP (so that theresult does not affect the end-of-timestep results). Code continues, using convective heat transfer to the solidustemperature.
“* * * HTRLAy * * * RADIAL CONVERGENCE FAILURE. L, KOUNT,LOOPL,LOOPT . () () () ()”
pwrning only]Failure to determine state of layer consistent with boundary conditions.
“* * * HTRLAy * * *, ~1~ SOLID c(_jRE/LIQuID SURFACE
WITH L,TS,TLTR = ()()() ()”Ununediate termination]Solid layer being melted from outside.
INCOOL—.
‘* * * INCOOL * * * COOLANT () NOT IN MASTER LIs’rn
[Deferred termination]
NUREG/CR-5843
User Information
Table 4.2 CORCONqperated warning and error mesages for each subroutine (continued)
INGEOM
“* * * ~GEOM * * * NRAYs . (), G~ATER THAN LIMIT OF 100”
[Immediate termination]
W* III * INGEOM * * * Ro = (J MUST BE 0.0”
[Immediate termination]
INITL
‘III * * IN~ * * * INv~IJj ILYR = ()’
[Deferred termination]
INPCON
‘dI * 10 INPCON * * * OXIDE () NOT IN MAs~R LIST”
[Deferred termination]
nib * * lNPCON III * * METAL (j NOT IN MASTER LIST”
~efefred termination]
INPGAS—. —-.
“* * * INPGAS * * * GAS (j NOT IN MASTER LIST”@eferred termination]
“* * III INPGAS * III * INTERp(_)LA~ON FOR ATMospHE~c
PRESSURE AT () OFF LOW END OF TABLE ()’~arning only]
‘* * * INPGAS * * * I~ERpoLA~oN FOR ATMOSPHERIC
PRESSURE AT () OFF HIGH END OF TABLE ()”~arning only]
INTEMP
‘* * * ~Mp * 8 * MA~I)( AMTRX Is SINGULAR As DE~~D By SAXB-
[Immediate termination]Tbe equations for determining interface temperatures are singular.
107 NUREG/CR-5843
User Information
Table 4.2 CORCON~enerated warning and error messages for each subroutine ”(continued)
~dI * III I~Mp III III III CONVERGENCE F~LuREa
~arning only]Newton iteration to determine interface ternperaturea failed to converge in 20 iterations.
LEVSWL
‘* * * LEvs~ III * III FIRST OCCUPIED ~yER .GT. ()”
@unediate termination]Can only occur if the code haa been nwdified incorrectly.
‘* * I@~vs~ III * IIIcAvI~ T(x) tJMfiJ FOR MELT-
[Immediate termination]Need to specify a larger cavity (rememlwr level swell).
MASRAT—..
‘III III III MAs~T III I@ III FIRST OCCUPIED LAYER OCT. ()”
[Immediate termination]
** III III MASRAT I@ III III CONVERGENCE F~Lu~w
[Immediate termination]Failure to match film heat transfer results to pool heat transfer at the bottom of the pool.
MASSEX——
“* * * MASSEX * * * ICALL = ()”
~mmediate termination]Invalid call to MASSEX. Can only occur if the code haa been modified incorrectly.
MELTRD
n41 III * MELTRD * * * NORAD = ()”
~mmediate termination]The number of entries in the time-radius table is greater than the maximum allowed number (MAXIUD).
“* * * MELTRD * * * RADTIM() = () IS NEGATIVE. ”
[Immediate termination]
“* * * MELTRD * * * TIMRAD() = () IS NEGATIVE. ‘
~mmediate termination]
NuREG/cR-5843 108
User Information
Table 4.2 CORCON-generafed warning and errer messages for each subroutine (continued)
‘* * * MEL~ * * * ~MRAD() > ~M~oa
[Immediate termination]
The entries in the time table must be increasing with time.
‘III III * MELTRD III * III RAD~M() > RAD~Moa
[Immediate termination]The entrkx in the radius table must be increasing with time.
‘* x * MEL~ I@ * * Too FEW E2~ ]N ~M&RAD~s
TABLE. EXECUTION TERMINATED. “~mrnediate termination]
MHTMN
‘* * III M~ * III III MASS IN LAYER ()”
[Immediate termination]Can only occur if the code has been modified incorrectly.
MLTPRP
‘* * * ML~Rp III III * MASS IN LAYER ()-
[Immediate termination]Can only occur if the code has been modified incorrectly.
MLTREA
“* * * MLWA * * * REDOING SOLUTION FROM NEW STARTING GUESS”
The equations for determining g the next correction to the equilibrium composition are singular or failed to converge. Anew starting guess will usually avoid the problem region.
‘III * * ML~tf * * III MATRIX AK Is SINGULAR IN FIRST cfiL TO s~=
~rmnediate termination]The equations for determining the next correction to the equilibrium composition are singular despite a new starting
-.
‘* * * ML~A * III III APPARENT CONVERGENCE F~LuRE
RELATIVE ERROR IN TOTAL MASS = ()”
warning only]Failure of the chemical equilibrium routine. “Apparent” because error is often insignificant, although the code fails torecognize this. Check to verify that no serious violation of mass consemation has occurred.
109 NuREG/cR-5843
User Information
Table 4.2 CORCON-generated warning and error messages for each subroutine (continued)
PLJ.AYR
S* * ● p~~ * * * MASS ~ LAYER ()”
[Immediate termination]Can only occur if the code has been modified inconectly.
PRTGAS
“INVALID IRE = O IN PRTGAS”[Immediate termination]Can only occur if the code has ham modified incorrectly.
REACT.—
‘* * * REA~ * * III IMPROPER REACTION NUMBER = ()”
[Immediate termination]Can only occur if the code has been modified incorrectly.
SOLLIQ—---
‘* III * SOLLIQ * III III NSPL, Nspu = () ()”
~xnmediate termination]Invalid value for NSPL or NSPU. Can only occur if the code has been modified inccmectly.
SPHCYL——
~* * * SpHCYL * * * IGEOM = 3 NOT OpERA~ONALS
[Immediate termination]
SURFEB——
S* III * SURFEB * * * CONVERGENCE FAILURE.
ICOUNT,’ITA,QP,DQPDTA,QW,DQWDTA = ()()()()() ()”flmmediate termination]Failure to match film heat transfer results to the pool heat transfer.
NuREG/cR-5843 110
User Information
Table 4.2 CORCON-generated warning and error mmsnges for each subroutine (continued)
SVLAAR
w* * I@ sv~ ● * IIICONVERGENCE F~LJJ~”
Dnunediate termination]Failure to determine liquidus and solidus temperatures for oxidic mixture.
TMPFND
“* * * ~pFND * * * MASS IN LAYER ()”
[Immediate termination]Can ooly occur if tbe code has tieen modified incorrectly.
VISCTY
“* * * VIS~ * * * NSPL,NSPU = () ()”
[Immediate termination]Invalid value for NSPL or NSPU. Can only occur if the code baa been modified incorrectly.
111 NUREG/CR-5843
5.0 Coding Information
5.1 Descriptions of Subroutines
Subroutines developed specifically for CORCON arelisted in Table 5.1 with brief descriptions of the functionsthey perform. Also included are routines such as SAXBwhich are used by CORCON but were not developed
specifically for CORCON.
Also provided is a variety of coding information that mayassist the user in understanding the timction of thevarious subroutines in the code and the overall programflow. Table 5.2 is a list of subroutines called by eachroutine. Table 5.3 is a list of program routines whichcall each subroutine.
5.2 Use of Common
Most of the internal data in CORCON-Mod3 arecontained in and communicated through namedCOMMON blocks. To assist the user in understandingthe flow of information between subroutines, we provideTables 5.4, 5.5, and 5.6. Table 5.4 lists the COMMONblocks contained in each program segment. Table 5.5lists the program segments containing each COMMONblock. A list of
the program variables in each COMMON block is givenin Table 5.6; the variables are defined in the nextsection.
5.3 Descriptions of PrincipalVariables
Table 5.7 provides a dictionary of the principalFORTW4N variables used in CORCON-Mod3. Forarmys shown in the table, the different amay elements
may correspond to different layers, to different chemicalspecies, etc. This is indicated by the index used, asfollows:
I- speciesJ - body pointK- elementL- layer or layer interfaceM- temperatureN- time
Interface L is the interface between layer L and layerL-1.
NUREGICR-5843 112
Coding Information
Table 5.1 List of CORCON subroutines
ABLATE
ACTMET
ACTOXD
ADDLYR
AERPTL
ANGAVL
ARBINP
ATMPRO
ATMSUR
BARRAY
BCLTOV
BLKDTA
BUBBLE
CHEKCV
CHEKHT
CHEMPO
COMBIN
COMBN2
CONFND
CONPRP
CORCON
CPENTH
CREATE
CVFAC
Computes mass flow rate of each species in surroundings material as it ablates and falls into pool
Computes the activity coefficients for metal phase constituents
Computes the activity coefficients for oxide phase constituents
Combines two layers into a third layer
Determines aerosol particle size, mass concentration, and evolution rate.
Finds body angle at each ray (body) point
initializes an arbitmry cavity shape
Determines bulk properties of the gas mixture (atmosphere) above the molten pool
Updates atmosphere and surroundings, or serves as an interfacs to a containment response code
Contains parametric values for fits to the free-energy functions
Groups fission product elements and converts masses from g-mol to kg
Contains data tables, including master species list, master molecular weight list, stoichiornetriccoefficients and phase table for MLTREA, and various pointers and global constanta
Determines bubble sizes and velocities where gas enters the pool and within pool layers
Computes the critical volume of coolant needed to cover the melt when the timedependent melt radiusoption is used
Checks for valid melt thickness when the timedependent melt radius option is used
Computes enthalpy, entropy, and Gibbs free energy of each species required for the melt/gas chemicalreaction calculation in MLTREA
Adds one mixture to another to produce a single mixture mass, composition, and eathalpy
Combines the mass and enthalpy of two layers to form a new layer.
Initializes data tables and finds coefficients for specific heat, enthalpy, and entropy for a species asnecessary for calculations in CHEMPO or CPENTH
Initializes concrete composition and properties
Controls program flow
Computes specific heat and enthalpy of condensed melt phases for both single- and two-phase(liquid-solid) mixtures
Creates separated layers if a mixture layer ha.. lost a phase due to deentrainment
Translates CORCON variables into VANESA variables
113 NUREG/CR-~843
Coding Information
Table 5.1 List of CORCON subroutines (continued)
CYLIND
DATAIN
DCOEFF
DCYINT
DCYPOW
DENSTY
DENTRN
DF
DHGEN
EDIT
EMISIV
ENRCN 1
ENRCN2
ENTRN
EXPRNT
FAIL
FDZ
FIIRAD
FILM
FPUPD
GEOM
GFLMPR
Initializes a flat-base cylindrical cavity shape
Handles the input of data for the program
Calculates drag coefficients for stable droplets in the melt
Sets up the initial intact core inventory of radioactive species and associated retention factors, andinitialims decay product pseudo-species
Evaluates the decay power of each radioactive element as a function of time
Computes the density of the condensed pha%s in the pool (the metallic and oxidic melt mixtures andcoolant
calculates the deentrainment (settling) of suspended liquid droplets
Calculates the aerosol mass gradient in the pool
Computes the decay heat generated within each pool layer
Manages the printed output of the code
Determines the emissivities of the condensed pha~ of the condensed phases of the pool from inputtables of emissivit y vs time or temperature
Performs the explicit update of the layer energy equations, including boiling of the coolant, and sets up
the implicit terms
Finishes the update of the layer energy equations by adding the implicit terms, and calculate new layertemperatures
Calculates bubbledrive entrainment of a heavy fluid by a less dense fluid
Controls the generation of extra debug printed output
Performs error handling when called by a subroutine which detects abnormal data or an invalidcomputation
Calculates exp(z) for SRPP
Finds the index of the body point close..t to the edge of the melt
Advances the state of the gas film from one point to another and integrates results
Updates the fission product composition of each group given the initial composition and changes incomposition due to mm.. addition or fis..ion product release
Determines the volume, surface area, and strmm length of the concrete cavity as a fiction of bodypoint
Computes the average gas mixture propertied.. in the gas film at each body point
NUREG/CR-5843 114
Coding Information
Table 5.1 List of CORCON subroutines (continued)
HCBBOT
HCBINJ
HCBSID
HCBTOP
HSPCYL
HTRCLN
HTRLAY
HTRLIQ
HTRN
INCOOL
INGEOM
INITL
INPCON
INPGAS
INTEMP
INVERF
LEVSWL
LININT
LOSSES
MASLOS
MASRAT
MASSEX
MECLOS
MELTRD
MHTRAN
.
.
.
.
.
Calculates the bubble+mhanced liquid-liquid heat transfer coefficient at the bottom of a layer
Calculates the heat tnmsfer coefficient for bubble injection at the bottom of the pool
Calculates the bubble-enhanced heat transfer coefficient at the side of the pool
Calculates the bubble-enhanced liquid-liquid heat transfer coefficient at the top of a layer
Initializes a cylindrical cavity with a hemispherical bottom
Evaluates heat transfer in the coolant layer, including boiling
Evaluates heat transfer in a layer, including conduction in solid regions
Computes heat transfer coefficients in a liquid layer or sub-layer, including bubbledancedconvection, natural convection, and conduction
Computes gas film heat transfer coefficients in all regimes
Inputs the initial mass, temperature, and identity of the coolant
Inputs and defines the initial geometry of the concrete crucible
Initializes necessary variables before entering the main computational loop
Inputs initial masses of core constituents and their temperatures
Inputs and defines the initial composition and state of the atmosphere
Computes temperatures and heat flows at layer interfaces
Computes the inverse of the error function
Calculates pool level swell, layer interface locations, and layer average void fractions
Performs linear interpolation or extrapolation from tables
Calculates aerosol losses by vaporimtion
Computes mass loss from the melt due to volatilization of fission products
Determines concrete ablation rates (mass loss rates)at body points
Serves as an interface for mass exchange with atmosphere and surroundings
Computes aerosol 10SWSby mechmical processes
Input data for the timedependent melt radius
Updat= layer species masses and evaluates effects of mass transport and chemical reactions on layerenthalpie.s
115 NuREG/cR-5s43
Coding Information
Table 5.1 List of CORCON subroutines (continued)
MLTPRP
MLTREA
ORIENT
PAGEHD
PHSPRP
PLLAYR
PLOTS
POOLV
PRTGAS
QMELT
REACT
RECEDE
RFBS
RLUD
SATP
SAIT
SAXB
SE~L
SETUP
SIGMY
SOLLIQ
SOURCE
SPHCYL
SRPP
Determines transport propetiie.s of metallic and oxide phases of the melt
Solves the problem of chemical equilibrium iteratively by a constrained first-order steepest descenttechnique, to minimize the free energy
Changes the layer configuration if density differences warrant a c~an~e
Prints a page header with code version identification and the problem title
Determines layer phase properties for aerosol calculations
Calculates layer densities and determines need for reorientation of layers
Writes data files for a post-processor plotting program
Integrates aerosol losses in the pool and determines aerosol size distribution
Prints results from the metal/gas/oxide reactions
Evaluates the local heat flux on the PI side of the gas film
Sets up neuxxary reactants for MLTREA and distributes the products returned
Computes the concrete normal recession and relocation of body points during a timestep
Module of the equation solver SAXB
Module of the equation solver SAXB
Evaluates saturation pressure as a function of temperature
Evaluates saturation tempwature as a function of pressure (an ENTRY in SATP)
Solves a system of real linear algebraic equations AX = B (a Sandia Mathematical Library routine)
Calculates the drag coefficients for stable and unstable drops in deentrainment
Performs code set up requiring execution (as opposed to DATA statements) including the evaluation of
machine round off
Computes surface tensions of the condensed phases of the pool
Sets up the components of pseudo-mixtwe-s of oxides or metals and calls either SSMELT or SVLAARto calculate the mixture solidus and liquidus temperatures
Evaluates the decay heat source in the pool
Initializes a cylindrical cavity with a spherical-segment bottom
Calculates the equilibrium partial pressures of vapor species
NUREG/CR-5843 116
Coding Information
Table 5.1 List of CORCON subroutines (continued)
SSMELT -
SUBSIZ -
SURFEB -
SVLAAR -
THKOND -
TIMSTP -
TMPFND -
TMPSET -
TRADII -
UCOEFF -
UDU -
UNDEFN -
VANESA -
VANFP -
VBUBL -
VCFAC -
VIS2PH -
VISCTY -
VOUTP -
VSCRIT -
XNDAR -
Calculates the liquidus and solidus temperatures of a metallic phase based on stainless steel (Cr-Fe-Niternary)
Sections the aerosol size distribution and calculates the size range and characteristic size
Performs a surface energy balance at a point on the cavity surface to determine mass flux of ablatedconcrete at a point
Performs a Schroeder-von bar pseudo-binary construction of the liquidus and solidus temperatures ofan oxidic phase
Determines the thermal conductivity of the condensed phases in the pool
Determines the new timestep
Determines the mixture temperature, given the composition and enthalpy
Initializes tempmture.s for newly-created layers
Determines the timedependent melt radius from a linear interpolation within the input table
Calculates the droplet drag coefficient for an unstable drop
Module of equation solver SAXB
Sets layer temperatures and property values to zero when a layer disappears following an orientationchange
Controls the aerosol calculations
Calculates the fission product content of the melt for use in aerosol calculations
Calculates bubble properties for use in aerosol calculations
Prepares the VANESA aerosol calculations for use in CORCON
Computes the Kunitz two-phase viscosity multiplier for suspended solids in the melt
Computes the viscosity of the metallic and oxidic phases of the melt
Prints VANESA aerosol calculation output to the output file
Computes the critical superficial gas velocitiai into the pool for use in determining bubble sizes
Initializes species molecular weights, and densities for condensed species
117 NUREG/CR-5843
Coding Information
Table 5.2 Subroutines called by each program routine
ABLATE cdks
ACI’MET calls
A~OXD CS]]S
ADDLYR calls
AERPTL calls
AERPTL calls
ANGAVL calls
ARBINP calls
ATMPRO dk
ATMSUR CJA]]S
BARRAY mlk
BCLTOV cds
BLKDTA ctdls
BUBBLE calls
CHEKCV ctd]s
CHEKHT calls
CHEMPO cal]s
COMBIN calls
COMBN2 calls
CONFND calls
CONPRP calls
CORCON Ulk
CPENTH UdlS
CREATE calls
CVFAC calls
LININT FAIL
COMBIN COMBN2 DENSTY FAIL SOLLIQ TMPFND UNDEFN
AERSOL LOSSES
LININT FAIL
ATMPRO EMISIV EXPRNT FAIL LININT
VSCRIT
FAIL
CONFND
FAIL
CPENTH DENSTY FAIL SOLLIQ
ATMSUR DATAIN EDIT ENRCN1 ENRCN2 GFLMPR INTEMPINITL LEVSWL MASRAT MHTRAN MLTPRP PLLAYR PLOTEXPLOTIN PLOTS RECEDE SETUP SOURCE TIMSTP
CONFND FAIL
ADDLYR CPENTH FAIL SOLLIQ TMPSET UNDEFN
NUREG/CR-5843 118
Coding Information
Table 5.2 Subroutines called by each program routine (continued)
CYLIND
DIMACH
DATAIN
DCOEFF
DCSEVL
DCYINT
DCYPOW
DENSTY
DENTRN
DERF
DERFC
DF
DFDZ
DHGEN
EDIT
EMISIV
ENRCN1
ENRCN2
ENTRN
EXPRNT
FAIL
FDZ
FIIRAD
FILM
FPUPD
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
FAIL
BCLTOV CONPRP FAIL INCOOL INGEOM INPCON INPGASMELTRD
DCYPOW FAIL VANFP
SE’ITL
DIMACH DCSEVL DERFC INITDS
DIMACH DCSEVL INITDS
DCYPOW FAIL LININT
PAGEHD PRTGAS VOUTP
FAIL LININT
CHEKCV CPENTH EXPRNT FAIL MASSEX SATT SAXBSOLLIQ
EXPRNT FAIL TMPFND
EDIT
FAIL HTRN SURFEB
119 NuREG/cR-5s43
Coding Infofmstion
Table 5.2 Subroutinescalledby each programroutine (continued)
GEOM calls
GFLMPR ctdls
HCBBOT calls
HCBINJ calls
HCBSID CSlh
HCBTOP calls
HSPCYL calls
HTRCLN calls
HTRLAY calls
HTRLIQ CSIIS
HTRN Cslls
INCOOL calls
INGEOM CllllS
INITDS calls
INIT’L calls
INPCON calls
INPGAS calls
INTEMP calls
INVERF calls
LEVSWL calls
LININT calls
LOSSES calls
MASLOS calls
MASRAT Cdk
MASSEX calls
NuREG/cR-5843
ANGAVL
EXPRNT
EXPRNT
HCBBOT
FAIL
ARBINP
ATMSUR
DCYINT
FAIL
EXPRNT
DERF
BUBBLE
MECLOS
CPENTH
CPENTH
CPENTH
FAIL
FAIL
HCBINJ
CYLIND
CPENTH
FAIL
LININT
FAIL
CHEKCV
EXPRNT
FAIL
HTRLIQ
HTRLIQ SAXB
HCBTOP
FAIL GEOM HSPCYL SPHCYL
DENSTY FAIL SOLLIQ
FILM , HTRCLN HTRLAY SAXB
EXPRNT FAIL TRADII
FAIL FILM
FPUPD LININT SOLLIQ
I20
Coding Information
Table 5.2 Subroutines called by each program routine (continued)
MECLOS
MELTRD
MHTRAN
MLTPRP
MLTREA
ORIENT
PAGEHD
PHSPRP
PLLAYR
PLOTS
POOLV
PRTGAS
QMELT
REACT
RECEDE
RFBS
RLUD
SATP
SATT
SAXB
SE’ITL
SETUP
SIGMY
SOLLIQ
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
calls
Calls
calls
calls
calls
calls
calls
calls
FAIL
BUBBLE COMBIN CPENTH CVFAC DENTRN ENTRN EXPRNT
FAIL MASLOS MASSEX POOLV REACT SOLLIQ VANESA
CPENTH EMISIV EXPRNT FAIL SATT SIGMY THKOND
VISCTY VIS2PH
CHEMPO EXPRNT FAIL PRTGAS SAXB
ADDLYR
CREATE DENSTY EXPRNT FAIL ORIENT
DF INVERF SUBSIZ
FAIL PAGEHD
CPENTH EXPRNT FAIL MLTREA SOLLIQ
GEOM
FAIL
FAIL
FAIL RFBS RLUD UDU
DCOEFF UCOEFF
CONFND
FAIL SSMELT SVLAAR
121 NUREG/CR-5843
Coding Information
Table 5.2 Subroutines called by each program routine (continued)
SOURCE ah
SPHCYL UlllS
SRPP calls
SSMELT calls
SUBSIZ calls
SURFEB dk3
SVLAAR C.S]k
THKOND C51k
TIMSTP calls
TMPFND calls
TMPSET calls
TRADII calls
UCOEFF dk
UDU calls
UNDEFN dk
VANESA calls
VANFP calls
VBUBL calls
VCFAC calls
VIS2PH calls
VISCI-Y calls
VOUTP calls
VSCRIT calls
XNDAR Calls
DHGEN
FAIL
FDZ
DERF
FAIL QMELT
FAIL
EXPRNT
CPENTH FAIL SOLLIQ
CHEKCV CHEKHT FIIRAD
AERSOL PHSPRP SRPP VBUBL VCFAC
FPUPD
FAIL
PAGEHD
NuREG/cR-5843 122
Coding Information
Table 5.3 Program rnutines wbkb call each routine
ABLATE
ACTMET
ACTOXD
ADDLYR
AERPTL
AERSOL
ANGAVL
ARBINP
ATMPRO
ATMSUR
BARRAY
BCLTOV
BLKDTA
BUBBLE
CHEKCV
CHEKHT
CHEMPO
COMBIN
COMBN2
CONFND
CONPRP
CORCON
CPENTH
CREATE
CVFAC
CYLIND
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
VANESA
VANESA
CREATE ORIENT
AERSOL
VANESA
GEOM
INGEOM
ATMSUR
CORCON INITL
DATAIN
LEVSWL MHTRAN
ENRCN1 LEVSWL TRADII
TRADII
MLTREA
ADDLYR MHTRAN
ADDLYR
CHEMPO CPENTH SETUP
DATAIN
CONPRP CREATE ENRCN1 INITL MASLOS MASRAT MASSEXMHTRAN MLTPRP REACT TMPFND
PLLAYR
MHTRAN
INGEOM
123 NUREG/CR-5843
Coding Information
TaMe 5.3 Program routines which call each routine (continued)
DIMACH
DATAIN
DCOEFF
DCSEVL
DCYINT
DCYPOW
DENSTY
DENTRN
DERF
,-..DERFC
DF
DFDZ
DHGEN
EDIT
EMISIV
ENRCN 1
ENRCN2
ENTRN
EXPRNT
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
FAIL is called by
FDZ is called by
FIIRAD is called by
FILM is called by
NUREG/CR-5843
DERF DERFC
CORCON
SEITL
DERF DERFC
INPCON
DCYINT DHGEN
ADDLYR CONPRP INITL PLLAYR
MHTRAN
INVERF SUBSIZ
DERF
POOLV
SOURCE
CORCON
ATMSUR
CORCON
CORCON
MHTRAN
ATMSURMASRAT
ABLATECPENTHENRCNIINITLMELTRDRFBSTMPFND
SRPP
TRADII
INTEMP
FIIRAD
MLTPRP
ENRCN1
MHTRAN
ADDLYRCREATEENRCN2INPCONMHTRANRLUDVISCTY
MASRAT
ENRCN2MLTPRP
ATMPROCYLINDFILMINPGASMLTPRPSAXB
124
HTRCLNPLLAYR
ATMSURDATAINHTRCLNINTEMPMLTREASOLLIQ
HTRLAY
REACT
CHEKCVDCYINTHTRLAYLEVSWLPLLAYRSPHCYL
INTEMP LEVSWLTIMSTP
CONFND CONPRPDHGEN EMISIVINCOOL INGEOMMASIWT MASSEXPRTGAS REACTSURFEB SVLAAR
Coding Information
Table 5.3 Program routineswhich call each N)utine (continued)
FPUPD
GEOM
GFLMPR
HCBBOT
HCBINJ
HCBSID
HCBTOP
HSPCYL
HTRCLN
HTRLAY
HTRLIQ
HTRN
INCOOL
INGEOM
INITDS
INm
INPCON
INPGAS
INTEMP
INVERF
LEVSWL
LININT
LOSSES
MASLOS
MASRAT
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
M@SEX VCFAC
INGEOM RECEDE
CORCON
HTRLIQ
HTRLIQ
HTRLIQ
INGEOM
INTEMP
INTEMP
HTRCLN HTRLAY
FILM
DATAIN
DATAIN
DERF DERFC
CORCON
DATAIN
DATAIN
CORCON
POOLV
CORCON
ABLATE ATMPRO ATMSUR DHGEN EMISIV INPGAS MASSEX
AERSOL
MHTRAN
CORCON
125 NUREG/CR-5843
Coding Information
Table 5.3 I%gram routines which call each routine (continued)
MASSEX
MECLOS
MELTRD
MHTRAN
MLTPRP
MLTREA
ORIENT
PAGEHD
PHSPRP
PLLAYR
PLOTS
POOLV
PRTGAS
QMELT
REACT
RECEDE
RFBS
RLUD
SATP
SATI’
SAXB
SETTL
SETUP
SIGMY
SOLLIQ
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
ENRCN1 MHTRAN
LOSSES
DATAIN
CORCON
CORCON
REACT
PLLAYR
EDIT PRTGAS VOUTP
VANESA
CORCON
CORCON
MHTRAN
EDIT MLTREA
SURFEB
MHTRAN
CORCON
SAXB
SAXB
ENRCNI MLTPRP
ENRCN1 HTRLAY JNTEMP MLTREA
DENTRN “
CORCON
MLTPRP
ADDLYR CONPRP CREATE ENRCN1 INITL MASSEX MHTRANREACT TMPFND
NUREG/CR-5843 126
Coding Information
Table 5.3 ~ratn routines which call each routine (continued)
SOURCE is called by
SPHCYL
SRPP
SSMELT
SUBSIZ
SURFEB
SVLAAR
THKOND
TIMSTP
TMPFND
TMPSET
TRADII
UCOEFF
UDU
UNDEFN
VANESA
VANFP
VBUBL
VCFAC
VIS2PH
VISCI-Y
VOUTP
VSCRIT
XNDAR
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
is called by
CORCON
INGEOM
VANESA
SOLLIQ
POOLV
FILM
SOLLIQ
MLTPRP
CORCON
ADDLYR CREATE ENRCN2
ADDLYR CREATE
LEVSWL
SEITL
SAXB
ADDLYR CREATE
MHTRAN
DCYINT
VANESA
VANESA
MLTPRP
MLTPRP
EDIT
BUBBLE
127 NUREG/CR-5843
Coding Information
Table 5.4 COMMON block contained by eachprogram routine
ABLATE
AClldET
ACTOXD
ADDLYR
AERPTL
AERSOL
ANGAVL
ARBINP
ATMPRO
contains
contains
contains
contains
contains
contains
contains
contains
contains
ATMSUR contains
BCLTOV contains
BUBBLE contains
CHEKCV contains
CHEKHT
CHEMPO
COMBIN
COMBN2
CONFND
CONPRP
CORCON
CPENTH
CREATE
CVFAC
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
CYLIND contains
NUREG/CR-5843
A42
ACTIV
ACTW
A45Two
BCL
BCL
A3
A3
A21
(
Two MASTER
BO B1 B2 B8 MASTER MX
CNDCON CTOV VAN VANPRP VPL XND
CTov VAN VANPRP XND
ONE T’WNEIT CNSTNT
ONE TWNEIT
Two ATMDAT
HEATEX ATMDATA20 A23
COMP XND
A32 BO
A3 BOMRCI
B1 CNSTNT
PFDAT
MASTER
CNDCON A32
B4 ONE
MASTER
A45 BO
ARGLST TWOMASTER BCLMX VAN
A3 ONE
BO B1VAN CTov
BCL A31
B1 B3
BI CNSTNT
MRCR MRCI
B3 MASTER
Two
B1 B2
BO B1CTov CTOPVANPRP
FORTN TWNEIT
128
Two CNSTNT A4
TWNTWO CNSTNT
ONE Two MRCR
SPECNM
MASTER MX Two
B2 B6 B6AVToc CNDCON
CNSTNT
Coding Information
Table 5.4 COMMON blocks contained by each prngram routine (continued)
D1 MACH contains
DATAIN contains A43 MA23 A42SPECNM TITLEVAN BCL
DCOEFF contains
DCSEVL contains
DCYINT contains B6A B6B
DCYPOW contains B6
DENSTY
DENTRN
DERF
DERFC
DF
DFDZ
DHGEN
EDIT
EMISIV
ENRCN1
ENRCN2
ENTRN
EXPRNT
FAIL
FDZ
FIIRAD
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
MASTER
BO B1
CDF
A4 A17
A3 A4BI B2Two THREECONSRV SPECNM
Two A19
HEATEX A4B9 TWOMRCR MRCI
HEATEX BO
BO B1
ONE TWO
ONE TWO
A3 ONE
A4 A9B1 ONECNDCON CTOVCDF VPL
A31 M
CNSTNT MX
BO B1
A32 A39B5 B8
A17 A19 A20Two THREEcroP COMP XNDMRCR MRCI
Two MASTER SPECNM
Two
B2 M MASTER
A44 A45 BOB9 ONE
FOUR TWNTWO GASEDT MASTER CNSTNTMRCR MRCI MX
A20 B9 MASTER
BO B1 B2 B5 B7MASTER IMP CONSRV MX
B1 IMP CONSRV
CNSTNT MX
B4
TWNEIT MRCR MRCI
129 NUREG/CR-5843
Coding Infofmstion
Table 5.4 COMMON blocks contained by each program routine (continued)
FILM contains ARGLST A4
FPUPD contains MASTER B6
GEOM
GFLMPR
HCBBOT
HCBINJ
HCBSID
HCBTOP
HSPCYL
HTRCLN
HTRLAY
HTRLIQ
INCOOL
INGEOM
INITDS
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
A3
A32
B1
B1
B1
BO
A3
BOMRCI
B1
BO
MXB1
B9
ONE
ONE
A39
CNSTNT
CNSTNT
CNSTNT
B1
ONE
B1
B5
B1
A4CNSTNT
FORTN
INrrL contains HEATEX A3BO B1B9 ONE
MX MRCR
INPCON contains A4 AlO
INPGAS contains AlO A21
INTEMP contains HEATEX ARGLSTB8 Two
INVERF contains
A32 B1
B6A B6B
FOUR FORTN
ONE
CNSTNT
FOUR FORTN
B5 B8
B8 Two
CNSTNT
A32 BO
CNSTNT
A4 AIOB2 B3TWNTWO GASEDTMRC1
A31 B6
A31 MASTER
A3 A32CNSTNT A4
CNSTNT
TWNEIT CNSTNT
TWNEIT CNSTNT
B9 CNSTNT MRCR
CNSTNT MRCR MRCI
B5 B8 A39
A31 A32 A45B5 B8CNSTNT CONSRV MASTER
MASTER SPECNM
SPECNM TWO
BO B1 B5MRCR MRCI
NuREG/cR-5843 130
Coding Information
Table 5.4 COMMON blocks contained by each program routine (continued)
LEVSWL contains A3 A32TwNTwoMRCI
LININT contains
LOSSES contains BCL CTov
MASLOS contains BO B1Crov VToc
MASRAT contains ARGLST A3B3 B5MRCR MRCI
MASSEX contains B6A BOCONSRV A31
MECLOS
MELTRD
MHTRAN
MLTPRP
MLTREA
ORIENT
PAGEHD
PHSPRP
PLLAYR
contains
contains
contains
contains
contains
contains
contains
contains
cmtaina
A4
BCL
A3Two
A4B8VAN
BO
A4
A4
ONE
BCL
A45
CTOv
A4MRCR
A32MASTER
B1
PFDAT
BO
Two
VANPRP
BOMASTER MX
PLOTS contains A32 BEONE TWO
POOLV contains CDF POOL
PRTGAS contains A4 A45
QMELT contains B1 B5
A44 BO B1 B3
TWNEIT CNSTNT A4 Two
B2 B6 Two CONSRV
A32 CNSTNT MASTER BOTwo TWNTWO TWNEIT ONE
B1 B2 B7 B9B6 A42 A43 Two
VAN VANPRP XND
BO B1 CNSTNT ONEMRCI
BO BI B2 B3CONSRV ‘IWO MX CTov
B2 BE MASTER B9
RNDOFF
B1 MX
TITLE
XND
MASTER
B1 B2 BE B9A4
A3 A4 BO B1CNSTNT MASTER MRCR MRCI
cToP VPL
PFDAT MASTER SPECNM
BE
ONEMRCR
MASTER
B1
MASTER
mn
B7
Mx
Two
B2
131 NUREG/CR-5843
Coding Infonnstion
Table 5.4 COMMON Mocks contained by each program routine (continued)
REACI’
RECEDE
RFBS
RLUD
SATP
SAXB
SEITL
SETUP
SIGMY
SOLLIQ
SOURCE
SPHCYL
SRPP
SSMELT
SUBSIZ
SURFEB
SVLAAR
THKOND
TIMSTP
TMPFND
TMPSET
TRADII
UCOEFF
UDU
contains
contains
contains
contains
A4GASEDT
A3
contains
contains
contains
CNSTNT
CNSTNT
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
contains
A32
BO
B
A32
ONE
BO
B1
A3MRCR
RNDOFF
A45 TwoONE PFDAT
ONE Two
RNDOFF
B9
B]
MASTER
Two
Two THREE
B1 B2
B8
A4 BOMRCI
BoMASTER
FOUR
FOUR
B9
B1 B2 B7CONSRV MX
TWNEIT
TWNEIT A3
Two MASTER MX
B8 CNSTNT ONE
NUREG/CR-5843 132
Coding Information
Table 5.4 COMMON blocks contained by each program routine (continued)
UNDEFN
VANESA
VANFP
VBUBL
VCFAC
VIS2PH
VISCI’Y
vow
VSCRIT
contains
contains
contains
contains
contains
contains
contains
contains
contains
BO B1
A4 VAN
XND B
B6 COMP
BCL CTov
BCL XND
MASTER B9
A4 XNDCNDCON CTOV
CNSTNT
MX
BCL CNDCON CTOV croP VPLVANPRP
B6B
VAN VANPRP XND
VToc MASTER CNDCON B6 B6A
VAN BCL VPL CDF POOLCTOP TITLE
133 NUREG/CR-5843
Coding Infonnstion
Table 5.5 program routines containing each COMMON block
AlO
A17
A19
A20
A21
A23
A3
A31
A32
A39
A4
A42
A43
A44
A45
A9
ACTIV
ARGLST
ATMDAT
B
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
INITL INPCON INPGAS
EMISIV
CHEKCVINITLRECEDE
INITL
EDITLEVSWL
HTRN
DHGENINPCONMLTREATRADII
MASSEX
EDIT
INTCOF
lNTEMP
VANESA
DATAIN DHGEN
DATAIN EMISIV
ATMSUR DATAIN
ATMPRO INPGAS
ATMSUR DATAIN
ANGAVLGEOMMELTRD
ARBINPHSPCYLPLOTS
CYLINDINTEMPTIMSTP
INPCON
FILMMASRAT
EDITINTEMPORIENTVANESA
INITL
VANESA
MASRAT
EDITLEVSWLTRADII
INPGAS
GFLMPRMHTRAN
ENRCN1LEVSWLPLLAYRVOUTP
PLLAYR
FIIRADMASRAT
MASSEX
HTRNPLOTS
FILMMASSEXPLOTS
PRTGAS
is contained in
is contained in
BCLTOV DCYINT
BUBBLEINITLSOLLIQ
CONPRPINTEMPSURFEB
is contained in
is contained in
EDIT GFLMPR
ATMSURHTRNMELTRDPRTGAS
DATAININILMHTRANREACT
is contained in
is contained in
is contained in
is contained in
ABLATE DATAIN
DATAIN MASSEX
EDIT LEVSWL
ADDLYRREACT
CREATE
is contained in
is contained in
is contained in
is contained in
is contained in
DATAIN
ACTMET ACTOXD
FILM
ATMSUR
SRPP
CVFAC
ATMPRO
BARRAY
NuREG/cR-5843 134
Coding Information
Table 5.5 Program routines containing each COMMON block (continued)
BO
B1
B2
B3
B4
B5
M
B6A
B6B
B7
B8
B9
BCL
CDF
COMP
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
ADDLYRCVFACENTRNINTEMPMHTRANSOURCE
ATMSURDENTRNHCBTOPLEVSWLMLTPRPTMPFND
BLKDTADHGENHTRCLNMASLOSORIENT
TRADII
BUBBLEEDITHTRLIQMASRATPLLAYRUNDEFN
CHEKCVENRCN1HTRNMASSEXPLOTS
CREATEENRCN2INITLMELTRDREA(X
ADDLYRCVFACENRCN2
HCBTOPINTEMPMHTRANREA~
ATMSURDATAINENTRNHTRCLNLEVSWLMLTPRPSOURCE
BUBBLEDENTRNFILMHTRLAYMASLOSORIENTTMPFND
CHEKCV
DHGENHCBBOTHTRLIQMASRATPLLAYRTMPSET
CHEKHTEDITHCBINJHTRNMASSEXPLOTSTRADII
CREATEENRCN1HCBSIDINIT’LMELTRDQMELTUNDEFN
ADDLYRINmPLOTS
CREATEMASLOSREACT
CVFACMASSEXTMPFND
DHGENMHTRAN
EDITMLTPRP
ENRCN1PLLAYR
BUBBLE CONPRP INITL LEVSWL MASRAT MHTRAN
BLKDTA CORCON FAIL
EDITINTEMP
ENRCNIMASRAT
HTRCLNQMELT
HTRLAY HTRN INITL
BLKDTAFPUPD
CVFACINPCON
DATAINMASLOS
DCYINTMASSEX
DCYPOWVANFP
VCFAC
DHGENVCFAC
CVFAC DCYINT FPUPD MASSEX
DCYINT FPUPD VANFP
ENRCN1 MASSE)( MHTRAN REACT
ADDLYR
INTEMPTMPSET
EDIT
MHTRAN
TRADII
HTRCLNMLTPRP
HTRLAY
PLLAYR PLOTS QMELT
BLKDTAINmVISCTY
EDITMASSEX
EMISIVMLTPRP
ENRCN1PLLAYR
HTRCLNSOLLIQ TMPFND
MECLOSAERPTLPHSPRP
BCLTOVVANESA
CVFACVBUBL
DATAINVCFAC
LOSSESVOUTP
DATAIN DF POOLV VOUTP
BCLTOV DATAIN VANFP
135 NUREGICR-5843
Coding Information
Table 5.5 l%ogram routines containing each COMMON block (continued)
CONSRV
CNDCON
CNSTNT
is contained in
is contained in
is contained in
EDITMHTRAN
AERPTLVOUTP
ANGAVLCYLINDHCBBOTHTRLAYLEVSWL
TRADII
DATAIN
AERPTLMASLOS
CYLIND
EDIT
EDIT
ATMSUR
ENRCN1
ABLATECREATEEMISIVMASLOSPLLA1-RVCFAC
CHEKCV
HTRCLN
MELTRD
CHEKCVHTRCLN
MELTRD
ADDLYRENTRNPLLAYR
ENRCN1REACT
ENRCN2 INITL
DATAIN
BUBBLEENT’RNHCBTOPINGEOMPLOTS
VOUTP
CVFACVANESA
INGEOM
RECEDE
INITL
CONFNDDENSTYINITLMHTRANREACT
EDITINTEMP
EDITINTEMP
DENTRNMHTRANUNDEFN
MASLOS
VANESA
CHEKCVFILMHSPCYLINITLSETI’L
DATAINVBUBL
TIMSTP
INTEMP
CONPRPDHGENINPCONMLTPRP
SOLLIQ
ENRCN1
LEVSWL
ENRCN1LEVSWL
EDITMLTPRP
MASSEX
VCFAC
CHEKHTGEOMHTRCLNINTEMPSETUP
LOSSESVOUTP
CPENTHEDITINPGASORIENTTMPFND
FIIRAD
MASRAT
FIIRADMASRAT
ENRCN1ORIENT
CONPRP CVFAC
ATMSURDENTRNHCBINJHTRLIQMASRATVSCRIT
BLKDTAEDITHCBSIDHTRNMELTRD
CTOP
CTov
is contained in
is contained in
POOLV VANESA
AEROSOLMECLOS
ATMSURMHTRAN
is contained in
is contained in
is contained in
is contained in
is contained in
is contained in
GEOM HSPCYLFORTN
FOUR GEOM HSPCYL
GASEDT lNITL
ENRCNI ENRCN2HEATEX
IMP
MASTER
ENRCN2
BLKDTA
DCYINTFPUPDMASSEXPRTGAS
ADDLYRCVFACENRCN 1MASRATPLOTSVISCTY
MRCI is contained in
is contained in
is contained in
is contained in
CHEKHTHTRLAY
PLOTS
DATAINlNITL
TRADII
MRCR CHEKHTHTRLAYPLOTS
DATAININITLTRADH
MX CREATEHTRNREACT
CVFACINITLTMPFND
BLKDTA CHEMPO MLTREA PRTGAS REACTPFDAT
NUREG/CR-5843 136
Coding Information
Table 5.5 Program routines containing each COMMON block (continued)
CHEKCVFAILINITLREA~
UDU
DATAIN
TIMSTP
VOUTP
CYLINDMELTRD
INITL
ATMSURDCYINTFAILMASRATPLOTS
ATMSURVBUBL
CVFAC
POOLV
VCFAC
BCLTOVVCFAC
CORCONFIIRADLEVSWLRECEDE
DCYINT
FIIRADRECEDE
LEVSWL
CHEKCVDENTRNHTRLAYMASSEXREACT
CVFACVOUTP
MECLOS
VANESA
DATAINVOUTP
ONE is contained in ANGAVLEDITHSPCYLPAGEHD
ARBINPEXPRNTINGEOMPLOTS
CYLIND DATAINGEOM GFLMPRMASRAT MELTRDTIMSTP TRADII
POOL is contained in
RNDOFF is contained in
SPECNM is contained in
POOLV VOUTP
SETUPMLTREA
BLKDTAINPGAS
CONPRPPRTGAS
EDIT INPCON
THREE is contained in
TITLE is contained in
TWNEIT is contained in
DATAIN EDIT
DATAIN PAGEHD
ANGAVLLEVSWL
ARBINPMASRAT
GEOM HSPCYLTIMSTP
TWNTWO is contained in
Two is contained in
BUBBLE EDIT MASRAT
ADDLYRCVFACENRCN1LEVSWLPAGEHDTIMSTP
ATMPRODATAINEXPRNTMASLOSPLLAYRTMPFND
CORCON CREATEEDIT EMISIVINPGAS INTEMPMELTRD MHTRANRECEDE SOURCE
VAN is mntained in AERPTL
MHTRANAERSOLVANESA
DATAIN MECLOS
VANPRP is contained in AERPTLVBUBL
AERSOL PHSPRP VANESA
VPL is contained in
VToc is contained in
XND is contained in
AERPRL DATAIN
MASLOS
AERSOL
VOUTP
CVFAC
AERPTL MECLOS PHSPRPXNDARVANESA VBUBL
137 NUREG/CR-5843
Coding Information
Table 5.6 Variables contained in each COMMON block
A1O
A17
A19
A20
A21
A23
A3
A31
A32
A39
A4
A42
A43
A44
A45
A9
ACTIV
ARGLST
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variahlm
VA, PA, TA, TMI, TOI
NDECM, PIM(30), TIM(30), PIO(30), TIO(30),NDECO
TEMPM, TEMPO, TEMPS
EMM(5), EO(5), ES(5), NEM, NS,NEO, TORT I(5), TORT2(5), TORT6(5), RADLEN
NATMPR, TPA(IO), PAT(10)
NTP, TMPS(10), TIX(10)
DDODS, R(1OO) Z(loo) , RMAX , ZB,IMAXR, VOL(1OO), ‘X(1OO) , ZMAX , ZT,IMAXZ, RW , HANGL(1OO), FLMANG(1OO), SDOT(1OO)
CONINP(109)
DELH , OMSI , RHOC , S1 , EWRHOPCT, GDPMWT, TSOLCT, TLIQ~, HF~’,Tw , TIC
GFCP(1OO), GFKOND(I(M)), GFMWT(ICK3), GFPR(lMI), GFRHO(l(M)),GFVISC(IOO)
ICOOL , IGAS, IMOV, IREAC, ISRABL,IMIXICHEM : ICOK,IFP , ILYR, IPG , IAOPAC, IFILM,IFILM?3, IFILMS
NSPG, NMP(20), NSR(20), FMS(10,2O), TMS(10,2O),IFPOPT
NMTS, NOTS, NCTS, TIMTS(10), TIOTS(10), TICTS(10),
TMTS(IO), TOTS(10), TCTS(IO)
ALPHZB(1OO)
IRE, IBALF1, IBALF2, IBALF3
FMM(IO), TMM(10), NSP1, FMO(10), TMO(10),NSP2
ACMET(26), ACOXD(26), AIJ(26,26), HO(26,26), H1(26,26), H2(26,26), WO(26,26),W1 (26,26), W2(26,26)
JBODY, LYR , IM , HCN, DEL, RYNLD, ‘lTA, EMD, FF,WFILM, WGIN, WCNDIN
NUREG/CR-5843 138
Coding Information
Table 5.6 Vanablea contained in each COMMON block (continued)
ATMDAT
B
BO
B1
B2
B3
B4
B5
M
MA
B6B
B7
B8
B9
contains variables PATM
contains variables B(25, 10,8)
contains variables NLAY, IHOX, IHMX, IMET, ILMX, ILOX, ICLN, IATM,NLAYER, LAYER(6)
contains variables ALPLAY(7), THKLAY(7) , ARINT(8) , TINT(8) ,AMLAY(7) , PLAY(7) GFLINT(8) , ZINT(8)BETLAY(7), RHOLAY(7) ; VISLAY(7) , GMWINT(8): AMSTRT(7),
CPLAY(7) , SIGLAY(7) , QABL(7) , PINT(8) HTOT(7) ,
EMLAY(7) , TLAY(7) UBUB(7) , QINT(8) ; QPOOL(7) ,
QDCY(7) TSOLLA(7) : TLIQLA(7) ,QREAC(7) ; VISLIQ(7) , TS1DE(7) ,TSOLTD(7) , TSTART(7) ,VSGINT(7) , BUBRAD(6)
contains variables SMOXY(40,5), SMMET(l 5,5), SMGATM(30),SMGGEN(30), DELSMG(3)
contains variables BAR , FCDP(7) , FG(7) FMMRBR(15), HTG(7),HMIN , HCDPIN , FMGDCY(30),’FMDOCY(40),FGFL(7), HTGFL(7)
contains variables KSTP
contains variables DQBDTB(7), DQBDTL(7) , DBQD1-I’(7) , DQTDTB(7) , DQTDTL(7),DQTD’IT(7), QZEROZ(7), DQZDTA(7), QZEROR(7), DQRDTA(7),HCBO’IT(7), HCSIDE(7) , HCINTB(7) , HCIIVIT(7) , DQRD~7)
contains variables IU02, IZR02, IZR, NFPEL, NGRP, CNCTRN(25), ILAST(4),NMASTR, IMASTR(8), IGROUP(8), FRACTO(8), VOLRAT(8),
IU, IAL
contains variables CNTRNO(25), XMOLG(4), XMOLP(4)
contains variables FPA’IWT(25), IGRP(4)
contains variables FOTRN , SMOTRN(40) , TOTR , HTOTRN ,FMTRN, SMMTRN(15), TMTR, HTMTRN,FMSAV , SMMSAV(15) , TMSV , HTMSAV ,FGTRN , SMGTRN(30) , TGFL , HTGTRN ,FGFLM , SMGFLM(30) , TGTR , HTGFLM ,FGSAV , SMGSAV(30) , TGSV , HTGSAV ,FCTRN , SMCTRN , TCTR , HTCTRN
contains variables CRUSTB(7), CRUSTI’(7), CRUSTR(7), TLCNTZ(7), TLCNTR(7)
contains variables 1H20L , IH20G, NCL , NCGTC1 FMCI , TSAT, HSCLIQUHSCGAS ‘
139 NUREG/CR-5843
Coding Information
Table 5.6 Variables cnntained in each COMMON block (continued)
BCL
CDF
COMP
CONSRV
CNDCON
CNSTNT
CTOP
C’rov
FORTN
FOUR
GASEDT
HEATEX
IMP
MASTER
MRCI
MRCR
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
contains variables
XM(25, 10), XI-(25,3), P(2S, 10), IRST, SXMP(25,2),YKG(2S,2)
GSD, BSIZ1, VROVR, IDMF, IMPF, NOSC
CES, IOD, XEN, KRY, TE, BA, SN, RU, MO, SRRB, Y , TC , RH , PD, LA, CE, PR , ND, SM:PU, AG, SB ,NB ,NBO
TOTALM, TOTALH, RELERM, RELERH
WF(6), CH20G, CC02G,
PI , PI02 , P103 ,GRAV, RNOT, SIGMA
DEPTH, PRESS, TEMP
WFRBR, CAOMGO
TMET, TOXD, ST2, FLAR, COART, GMOL, HYSPR, OXMOL,CMOL, RVM , RVO,IFVAN, IVANFP
RO, 20
THET(1OO)
AMOLD1 (56,5), FMOLI(56,5), IR31(5), ITGAS1(5),AMOLD2(56) , FMOL2(56) , IR32 , ITGAS2 ,AMOLD3(56) , FMOL3(56) , IR33 , ITGAS3
OMEGA, DTIME, ASRF, EMSRF, TSN, QSN, TSNP1, QSNP1,DQSDTS
HTHAT(6), DHTLDT(6), BORX(6,3)
N03, NM1 , NM2, NGI ,NG2, SPEMW(109)
IRAD, ITIMR, ITOPR, NORAD
AFLUX, CAVHIT, CAVRAD, CVCOOL, HTMIN, HTMELT,HTMAX, RADT , TIMECR, TIMESD, RADTIM,TIMRAD,EJAREA,QSIDE , RINT
NUREG/CR-5843 140
Coding Information
Table 5.6 Variables contained in each COMMON block (continued)
Mx contains variables
PFDAT contains variables
ONE contains variables
POOL contains variables
RNDOFF contains variables
SPECNM contains variables
THREE contains variables
TITLE contains variables
TWNEIT contains variabltx
TWNTWO contains variables
Two contains variable..
VAN contains variables
VANPRP contains variables
VPL contains variables
VTOC contains variables
XND contains variabl~s
FOENT , FMENT , FODNT , FMDNT ENTO(5) ,
ENTOMX(5), ENTM(5) , ENTMMX(5), DENTo(5), hTM(5) ,RHOM(5) , RHoq5) , VOLM(5) VOLO(5) , AMM(5) ,
AMO(5) RDROP(5), TSOLM(5) : TSOLO(5) , TLIQM(5),TLIQO(5) : SIGM(5) S1GO(5) VISM(5) , VISO(5) ,THKM(5) , THKO(5) : HTM(5) : HTO(5) , CPM(5) ,cPq5)
NOP1 , NMP1 , NMP2 , NGP1NUMSPE , IPNT(56), SG(56), NUMELE, ‘ANE(56, 15)
IFLOR, IGEOM, IRSTRT, JT, NRAYS
DSSG(MNOSC), APM(MNOSC), RSIZ(MNOSC), DLCC, DNMS,DNGSD , ENM , EGSD
URO
ISPNAM(109)
lDELT, NDELT, T1MDT(10) , DTMIN(IO), DTMAX(10),IEDIT , NEDIT , TIMED(10), DEDIT(10)
ITITL
ITANG, NBOT, RTANG
BUBMLI(1OO), DELL(IOO) , GFLMFL(IOO),HCON(IOO) , IMOD(1OO), REYNLD(IOO), TEMPA(1OO)
DELTIM, IPINC , TIME, TIMEO, TPRIN,DPRIN , TEDIT, TIMEND
VAPOR, BURST, AER1 , AER2, GOXD, IBUB, BUBDM, BUBDO,KATIS , DC , BUBD, PTBB, PTDIA, INOPL
BUBNM, BUBNO, DMETP , DOXP G(2S,1O), GMET ,PMETP , POXP , PVAR , QMETP : Qoxp , SMETP, SOXP,BNM , BNO , RTM , RTOSTM , STO , VISMET, VISOXD,’VMET , VOXD
SIZ, XMAS, DEN
XMLS(14), XOLS(33), ICVSPE(49), ICVFP(25)
XN(25, 10), DARR(25,2)
141 NuREG/cR-5843
Coding Information
Table 5.7 Dictionary of principal variables in CORCON
FORTRAN Algebraicsymbol symbol Desu+ption units
ACMET(I)
ACOXD(I)
AER1
AER2
AFLUX
AG
ALPHZB (J)
ALPLAY (L)
AM(l)
AMLAY (L)
AMM (L)
AMo (L)
AMOLD1 (l,L)
AMOLD2 (I)
AMOLD3 (1)
AMSTRT (L)
ANE (I,K)
APM (N)
ARINT (L)
ASRP
B (I,N,K)
BA
BAR
BETLAY (L)
%
l’i
Ag
a(Z)
u’
. .
m~
. .
. .
. .
m~
. .
. .
A
As
Ba
. .
PL
The activity coefficient for metal phase constituents
The activity coefficient for oxide phase ecmstituents
The concentration of aerosol particles created byvaporization and bubble bursting
The concentration of aerosol particles created byvaporization and bubble bursting, for gas at standardconditions
The fraction of the top melt surf= heat flux used insetting the melt edge temperatures for a timedependeatmelt radius
Quantity of silver (Ag) in the fission product inventory
Local axial void fraction at Z(J)
Average void fraction
Amount of species
Mass
Mass of metal phase in new layer produced by thecombination of two old layers
Mass of oxide phase in new layer produced by thecombination of two old layers
Amount of species in layer at start of timeatep
Amount of speeies in atmosphere at start of timedep
Amount of species in gas film at start of timestep
Mass at start of timeatep
Stoichiometric coefficients
Aerosol mass in distribution range N to N+ 1
Interface area
Melt surface area exposed to atmosphere or coolant
Array containing parametric values for fits to the free-energy fimctiona
Quantity of barium (Ba) in the fission product inventory
Weight fraction of rebar in the concrete
Volumetric coefficient of expansion
gkc
glee
g-mol
. .
g-ml
kg
kg
kg
g-mol
g-ml
g-mol
kg
g
m2
m2
g-mol
I@
NuREG/cR-5843 142
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symbol Ileacription units
BNM
BNO
BSIZI
BUBD
BUBDM
BUBDO
BUBMLI (J)
BUBNM
BUBNO
BUBIUiD (L)
BURST
CAOMGO
CAVHIT
CAVRAD
CC02G
CE
CES
CH20G
CMOL
CNCIRN (I)
CNTRNO (I)
COART
. .
.-
. .
. .
. .
. .
. .
C5
Cs
. .
Morton number for the metal phase in aerosolcalculations
Morton number for the oxide phase in aerosolcalculations
Initial bubble size in aerosol calculations
Fixed input bubble diameter, used in aerosolcalculations
Bubble diameter for rhe metal phase, used in aerosolcalculations
Bubble diameter for the oxide phase, used in aerosolcalculations
Molar flux of gas entering bubbles
Number of bubbles passing through the metal phase, inaerosol calculations
Number of bubbles passing through the oxide phase, inaerosol calculations
Average bubble radius
The concentration of aerosol particles generated bybubble bursting
Maas fraction of CSO in CaO and MgO
Axial location of the original cavity floor (time-dependent melt radius)
Radius of the cavity, until the melt reaches the cavitywall (timedependent melt radius)
Mass fraction of original concrete CO
Quantity of cerium (Cc) in the fission product inventory
Quantity of ceaium (Cs) in the fission product inventory
Mass fraction of chemically bound and evapmnble waterin the concrete
Total quantity of carbon, used in aerosol calculations
Fission product quantity
Original fission product quantity
Maaa rate of addition of concrete to the melt
cm
cm
cm
cm
g-mol/m2-s
-.
m
m
m
g-ml
g-mol
g-mol
g-mol
g-mol
gls
143 NUl&GICR-5843
Cading Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description uNts
CHPOT (I)
CONINP (1)
CPLAY (L)
CRUSTX (L)
CVCOOL
DARR (I,K)
DDODS
DEDIT (N)
DELH
DELL (J)
DELSMG (1)
DELTIM
DEN
DEPTH
DHPOW
DHTLDT (L)
DLCC
DMETP
DNGSD
DNMS
DOXP
DPRIN
DQBDTx (L)
DQRDTA (L)
P;
m
C?L
6‘L
6
. .
At
--
.-
. .
. .
-.
--
dqm/dTx
d~/dTA
Standard state chemical potential
Initial mass of condensed species
Specific heat
Crust thickness of face x (= B, bottom; = T, top; =R, radial)
Critical volume of coolant required to cover the melt(timedependent melt radius)
Array containing the densities for the condensed species
Ratio of normal recision to normal distance to adjacentray
Time between printed edits
Heat of ablation of concrete
Gas film thickness
Mass of gaseous species generated during timestep
TimeStep
Aerosol density
Depth of coolant, used in aerosol calculations
Decay heat power
Total heat capacity of new mass at old temperature
Linear correlation coefficient in the aerosol model
Maas density of the metallic phase in aerosol
calculations
Geometric standard deviation of the aerosol particle size
distribution
Mean particle sim for tbe aerosol particle sizedistribution
Mass density of the metallic phase in aerosolcalculations
Time interval for diagnostic prints
Rate of change of upward heat flux at the bottomsurface with respect to temperature x ( = B, bottom;= L, laye~ = T, top)
Rate of change of outward heat flux to the radial surfacewith respect to the surface temperature
Ulllg-mol
kg
J/kg-K
m
m3
kg/m3
s
J/kg
m
kg
s
glee
cm
w
Jtkg-K
glee
pm
glee
s
W/m2-K
W/m2-K
NuREG/cR-5843 144
Coding 122formatioo
Table 5.7 Dictionary of principal variabka in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description uNta
DQRDTL (L)
DQSDTS
DQTDTx (L)
DQZDTA (L)
DSSG (N)
DTIME
DTMAX (N)
DTMIN (N)
GSD
EJAREA
EMD
EMLAY (L)
EMM (M Or N)
EMSRF
EMSUR
ENM
EO(Mor N)
ES(Mor N)
EW
FCI’RN
FG (L)
FGFLM
FGSAV
FGTRN
FLAR
Rate of change of outward heat flux to the radial surfacewith respect to the layer temperature
Rate of change of the heat flux tdfrom the pool surfacewith respect to the surface temperature
Rate of change of upward heat flux at the bottomsurface with reapxt to temperature x ( = B, bottom;= L, layer; = T, top)
Rate of change of heat flux to the axial surface with
respect to surface temperature
Aerosol particle size rangea
Time.step
Maximum timestep
Minimum timestep
Error in geometric standard deviation for aerosolparticle size distribution
Area of the edge of each layer exposed to atmosphere orcoolant
Energy loss to the concrete ablation products
Emissivity
Emissivity of metallic phase
Emissivity of melt surface exposed to atmosphere
Emissivity of the above-pool surroundings
Error in the natural logarithm of the aerosol particle sizedistribution
Emissivity of oxidic phase
Emissivity of atmosphere surroundings
Emissivity of ablating concrete surfaw
Mass of coolant added during timestep
Gas flOW nite
Mass of gas transported in film during timeatep
Mass of gas transformed by oxidelatmosphere reactionduring timestep
Mass of gas transported as bubbles during timestep
Surface area of the top melt layer, used in aerosolcalculations
145
W/m2-K
Wlm2-K
W/m2-K
W/m2-K
~m
s
s
s
Mz
w
kg
kgls
kg
kg
kg
cm2
NuREG/cR-5843
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description Units
FLMANG (J)
FMCI
FMM (N)
FMMRER (1)
FMO (N)
FMS (N,I)
FMSAV
FMTRN
FOTRN
FPATWT (I)
G (I,K)
GDPMWT
GFCP (J)
GFKOND (J)
GFLINT (L)
GFLMFL (J)
GFMWT (J)
GFPR (J)
GFRHO (J)
GFVISC (J)
GMET
GMOL
GMWINT (L)
GOXD
GRAV
GSD
--
. .
. .
. .
. .
. .
. .
. .
. .
8
. .
Average slope of the gas film over a Taylor cell radkM
Initial mass of coolant
Metallic phase splashout rate
Mass fraction composition of rebar
Oxidic phase splaahout rate
Specified rate of additions to pool
Maas of reinforming steel ablated by the light oxide layerduring timeatep
Mass of metal rising or sinking in the pool during thetimestep
Mass of oxide rising or sinking in the pool during thetimestep
Fission product atomic weights
Free energy of species I involving element K
Molecular weight of gaseous products of concreteablation
Gas film specific heat
Gas film thermal conductivity
Mass of flow of gas at interface
Mass flow of gas in the film
Gas film molecular weight
Gas film Prandtl number
Gas film density
Gas film dynamic viscosity
Quantity of gas sparging the through the metal, used inaerosol calculations
Total quantity of gas sparging through the metal duringthe timestep, used in aerosol calculations
Molecular weight of gas at interface
Quantity of gas sparging through the oxide, used inaerosol calculations
Gravitational acceleration
Geometric standard deviation of aerosol particle sizedistribution
rad
kg
kgls
kgls
kgls
kg
kg
kg
glg-mol
Callmol
gig-mol
J/kg-K
W/m-K
kgls
kg/8
g/g-mol
kglm
kglm-a
g-molts
g-molts
glg-mol
g-molls
In/s
NUREG/CR-5843 146
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN AlgebraicSymhd symbol Deau’iption units
HANGL (J)
HBB
HBC
HC
HCINTB (L)
HCINTI’ (L)
HCN
HCON (J)
HCSIDE (L)
HEATUP
HFCT
HTCTRN
HTGFLM
HTGSAV
HTGTRN
HTHAT (L)
HTM (L)
HTMAX
HTMELT
HTMIN
HTMSAV
HTMTRN
HTo (L)
. .
h~
h.
h
h
. .
. .
. .
. .
. .
Negative of cavity surface inclination angle
Concrete cmcible base thickness, Figure 4.3
Concrete crucible dimension, top to center ofhemisphere, Figure 4.2
Concrete crucible dimension, top to start of hemisphere,Figure 4.2
Heat transfer cdficient, bulk to bottom
Heat transfer coefficient, bulk to top
Heat tmnsfer coefficient across gas film
Gas film heat transfer coefficient
Heat transfer coefficient, bubble agitation
Heat to concrete decomposition products duringtimestep; converted to rate ~ in EDIT
Latent heat of fusion for concrete
Concrete cmcible depth, Figure 4.3
Total enthalpy of coolant added during timeatep
Total enthalpy of gas transported in film during timestep
Total enthalpy of gas transformed by oxide/atmospherereaction during timestep
Total enthalpy of gas transported as bubbles during thetimestep
Total enthalpy of new layer mass at old temperature
Enthalpy of the metal in the layer
Maximum allowed melt thickness for the timedependentmelt radius (entered in cm; used internally in m)
Thickness of the melt layer (timedependent melt radius)
Minimum allowed melt thickness for the timedependentmelt radius (entered in cm, used internally in m)
Total enthalpy of reinforcing steel ablated by the lightoxide layer during the timestep
Total enthalpy of metal rising or sinking in pool duringtimedep
Enthalpy of the oxide in the layer
d
m
m
m
W/m2-K
W/m2-K
W/m2-K
W/m2-K
W/m2-K
J
J/kg
m
J
J
J
J
J
J
m
m
m
J
J
J’
147 NUREG/CR-5S43
Coding Information
Table 5.7 Dictionary of principal variablea in CORCON (continued)
FORTRAN Algebraic
symbol symbol Description units
HTOT (L)
H-rm
HYSPR
IABL
IAOPAC
IATM
ICHEM
ICLN
ICOK
ICON
ICOOL
IDMF
IFILMB
IFILMS
IFLOR
IFP
IFVAN
IGAS
IGEOM
IHMX
IHOX
ILMX
ILOX
ILYR
IMASTR (N)
IMAXR
IMAXZ
IMET
IMrx
IMOD (J)
IMOV
NuREG/cR-5843
. .
--
--
.-
. .
.-
. .
. .
. .
.-
Total enthalpy
Total enthalpy of oxide rising or sinking in pool duringtimestep
Hydrogen/steam pressure mtio
Surroundings ablation index
Aerosol opacity index
Index of top surface of the pool, including coolant
Flag for condensed phase chemistry and coking options
Index of the coolant layer
Switch for coking reaction
Concrete composition index
Coolant layer flag
DiffMion mechanism flag for aerosol calculations
Flag for gas film on pool bottom
Flag for gas film on pool side
Index for cavity top ray
Decay heat power index
Switch for using the VANESA aerosol model
Gas phase index
Cavity geometry index
Index for heavy mixed layer
Index for heavy oxide layer
Index for light mixed layer
Index for light oxide layer
Melt layer configuration index
Master list of fission product groups
Body point at maximum cavity radius
Body point at maximum cavity depth
Index for metal layer
Flag for calculating entrainment and deentrainment
Heat transfer model number
Cavity shape plot index
148
J
J
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraic
symbol symbol Description units
IMPF
IOD
IPG
IPINC
IPNT (r)
IR31 (L)
IRAD
IRE
IRSTRT
ISPNAM
ISRABL
IT
ITANG
ITIMR
ITITL
ITOPR
IUSER
JBODY
KATIS
I(RY
LA
LAYER (L)
LYR
MO
NAMSP
NB
1
.-
. .
—
. .
. .
La
. .
Mo
Nb
Impaction mechanism flag for aerosol calculations
Quantity of iodine (I) in the fission product inventoly
Time plot index
Print incmnent, number of timesteps
Position of Itb species in the CORCON msster list
Number of iterations required in MLTREA for
convergence
Flag for calls to TRADII (timedependent melt radius)
Identifying number of chemical reaction
Restwt option index
CHARACTER*8 name of master-list species
Atmosphere surroundings ablation index
Iteration (timestep) number
Number of the body point constmined to move verticallyat the limit of a flat bottom
Flag for time-dependent melt radius option
CHARACTER*8O run identification
Index of the top interface of the melt
Flag enabling user flexibility options
Index of body point
Flag to signal use of Kataoka and Ishii, and Azbelmodels for mechauiud release of aerosols
Quantity of lanthanum (La), ytterbium (Y),praseodymium (Pr), samarium (Sin) and neodymium(Nd) in the fission product inventory
Quantity of lanthanum (1A) in the fission productinventory
Numbers (l-7) of occupied layers
Index of current melt layer
Quantity of molyMenum (Me) in the fission productinventory
CHARACTER*8 name of input species
Quantity of niobium (Nb) in the fission productinventory
149
gad
. .
g-ml
g-mol
g-ml
. .
g-mol
NUREG/CR-5843
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description unita
NBO
NBOT
NCL
NCORN
...ND
NDECM
NDECO
NEM
NEO
NFPEL
NG1
NG2
N(HW
NINP
NLAY
NLAYER
NMASTR
NMP (I)
NMSI
NM1
NM2
N03
NORAD
NOSC
NRAYS
NS
NuREG/cR-5843
Nd
--
--
. .
--
-.
. .
.-
.-
--
. .
-.
--
. .
.-
-.
.-
Quantity of niobium oxide (NbO) in the fission productinvento~
Number of body points on the flat bottom of cavity,including the center line and tangency point
Master list number of coolant species
Number of body points defining a cavity comer, notincluding tangency points
Quantity of neodymium (Nd) in the fission product
inventory
Number of points in metallic phase power input table
Number of points in oxidic phase power input table
Number of points in metallic phase emissivity table
Number of points in metallic phase emissivity table
Number of fission product elements
LOeation of first gas in master species list
Location of last gas in master species list
Number of groups of fission product elements
Number of concrete species input
Total number of layers allowed (includes coolant and
atmosphere)
“rohlnumber of occupied layers
Maximum number of species containing a fissionproduct element
Number of points in the input mass addition tables
Number of metallic species input
Location of the first metal in the master species list
Location of the last metal in the master species list
Location of the last oxide in the master specie-s list
Maximum number of entries in the table of times andmelt radii
Number of sections in the aerosol particle sizedistribution
Number of rays
Number of points in surroundings emissivity table
I50
g-mol
g-mol
. .
. .
Coding Information
Table 5.7 Dictionary of principal variablea in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description units
NSIDE
NSP1
NSP2
NSPG
NSR (N)
NTP
NUMELE
NUMSPE
OMEGA
OXMOL
P (I,K)
PA
PAT (N)
PATM
PD
PI
PIM (N)
PINT (L)
PIO (N)
PI02
PI03
PLAY (L)
PMETP
POXP
PR
PRESS
PTBB
PTDIA
. .
. .
M
T
P=
--
P
U12
$?13
P
. .
Pr
.-
Number of body points defining the side of thecylindrical cavity
Number of xnetallic species in the aplaahout tablm
Number of oxidic species in the aplaahout tables
Number of species in surroundings
Species number of species in fission product inveatory
Number of points in mmmmdings tempemtum table
Maximum number of elements
Maximum number of chemical species
Implicitness fraction (= 1)
Total quantity of oxides
Partial presswe of species K involving element I
Initial gas pressure
Gas (atmosphere) pressure
Atmospheric pressure
Quantity of palladium (Pal) in the fission productinventory
Pi
Metallic phase input power
Interface pressure
Oxidic phase input power
Pi12
Pi13
Average pressure
Volume of metallic phase
Volume of oxidic phase
Quantity of praseodymium (Pr) in the fission productinventory
Ambient (atmospheric) pressure for aerosol calculations
Number of particles per bubble, for aerosol calculations
Mean particle size for aerosol produced by mechanicalprocesses
g-mol
Pa
Pa
Pa
Pa
g-mol
w
Pa
w
Pa
cmy
cd
g-ml
atm
m
151 NuREG/cR-5843
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description unitsPu
PVAR
QABL (L)
QCONV
QDCY (L)
QINT (L)
QMETP
QOXP
QPOOL (L)
QRAD
QREAC (L)
QSIDE (L)
QSN
QSNP1
QZEROR (L)
QZEROZ (L)
R (J)
WC
RADLEN
RADT
RADTIM (N)
RB
RBR
Pu
. .
%lv
--
. .
--
%d-
. .
qR
aQ+’
--
r
. .
--
L
.-
, Rb
Quantity of plutonium (P@ in the fission productinventory
Average pressure in the coolant pool for aerosolcalculations
Rate of change in enthalpy due to heat 10SSto concrete
Convective heat flux across gas film
Internal heat source rate
Interface heat flow rate (positive up)
Molar density of metallic phase for aerosol calculations
Molar density of oxidic phase for aerosol calculations
Rate of change in enthalpy due to heat from adjacentlayers
Net radiative heat flux across the gas film
Heat source rate from chemical reactions
Radial heat flux
Surface heat flux at the start of the timestep
Surface heat flux at the end of the timestep
Radial heat flux to the gas film, extrapolated to asurface temperature equal to the layer tempemture
Axial heat flux to the gas film, extrapolated to a surfacetemperature equal to the layer temperature
Radial coordinate
Concrete crucible radius, Figure 4.3
Concrete cmcible comer radius, Figure 4.3
Characteristic path length for aerosol opacity
Current melt radius (timedependent melt radius)
Melt radius at time TIMRAD (N) in the table of timesand radii (timedependent melt radius)
Quantity of rubidium (Rb) in the fission productinventory
Mass fraction of reinforcing steel in concrete
g-mol
atm
w
Wlm2
w
w
g-mol/cm3
g-mol/cm3
w
Wlm2
w
W/mz
W/mz
W/mz
w
w
m
m
m
m
m
m
g-mol
NuREG/cR-5843 152
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraic
symbol symbol Description units
RDROP (L)
RELERH
RELERM
REYNLD (J)
RH
RHoc
RHOLAY (L)
RHOM (L)
RHoo (L)
RHOPCT
RI
IUNT (I)
RMAX
RNOT
RO
RS
RSIZ (N)
RTANG
RTM
RTO
RU
RVM
RVO
RW
SAREA
SB
Re
Rh
L%
.-
. .
. .
RO
Ru
Sb
Radius of entrained or deentrained drops
Relative numerical error in energy conservation
Relative numerical error in mass conservation
Gas film Reynolds number
Quantity of rhodium (R@ in the fission productinventory
Concrete density
Average density
Density of metal phase
Density of oxide phase
Partial density of concrete in reinforced concrete
Interface radius in EDIT; also @ as R (J) elsewhere
Interface radius
Maximum radius of concrete cavity
Universal gas constant
Radial location of ray origin ( = O)
Concrete crucible radius, Figure 4.2
Characteristic aerosol particle size in range N
Radius of flat bottom of concrete crucible
Bubble rise time in the metal phase for aeroaolcalculations
Bubble rise time in the oxide phase for aerosol
calculations
Quantity of mthenium (Ru) in the fission productinvento3y
Bubble rise velocity in the metal phase for aerosolcalculations
Bubble rise velocity in the oxide phase for aerosolcalculations
Outer radius of mncrete crucible, Figures 4.24.4
Surface area of the cavity
Quantity of antimony (Sb) in the fission productinventory
m
g-mol
kglm3
kglm3
kglm3
kg/m3
kglm3
m
m
m
J/g-mol K
m
m
pm
m
s
s
g-mol
C3331S
Cmls
m
m3
g-mol
153 IWJREG/cR-5843
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description uNts
SCALRG
SCALRM
SDOT (J)
S1
SIGEFF
SIGLAY (L)
SIGM (L)
SIGMA
SIGO (L)
SIZ
SM
SMCTRN
SMETP
SMGATM (I)
SMGFLM (I)
SMGGEN (I)
SMGSAV (I)
SMGTRN (I)
SMMET (I,L)
SUMMHO
SMMSAV (I)
SMMTRN (1)
SMOTRN (I)
SMOXY (I,L)
. .
ii
u~F
u~
u~
. .
.-
. .
Sm
. .
. .
. .
. .
-.
Free energy divided by ROT for chemical system
Total moles in gas phase of chemical system
Concrete recession rate
Mass fraction of concrete decomposing into gas; silicon
Stefan-Boltzmamz constant times shape factor
Surface tension
Surface tension for metal phase
Stefan-Boltzmann constant
Surface tension for oxide phase
Aerosol particle size
Mass fraction of concrete species; mole fraction ofgaseous species; quantity of samarium (Sin) in the
fission product inventory
Mass of coolant species added during timestep
Total quantity of metal phase in aerosol calculations
Mass of gas in atmosphere
Mass of gas transported in the gas film during thetimestep
Cumulative mass of gases species generated
Mass of gas transformed by oxidelatmosphere reactionduring timestep
Maaa of gas transported as bubbles during timestep
Maaa of metallic species
Total enthslpy of new pool msas for old temperaturesand melting ranges
Mass of metallic products of oxide/atmosphere reactionduring time.step
Maas of metal rising or sinking in the PI duringtimestep
Maaa of oxide rising or sinking in the pool during thetimestep
Mass of oxidic species
g-mol -
2221S
W/mZ-K’
N/m
N/m
W/mZ-K’
N/m
pm
g-mol
kg
g-mol
kg
kg
kg
kg
kg
kg
J
kg
kg
kg
kg
NUREG/CR-5843 154
coding Inhmation
Table 5.7 Dictionary of principal variablea in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description units
SN
SOXPSPEMW (I)
SR
ST2
STM
STO
SXMP (I,K)
TA
TC
TCI
TCIR
TE
TEDIT
TEMP
TEMPA (J)
TEMPx
TGFL
TGSV
TGTR
THET (J)
THKLAY (L)
THKM (L)
THKO (L)
TIC
Sn
Sr
. .
T.
Tc
. .
--
Te
. .
. .
Quantity of tin (Sri) in the fission product inventory
Total quantity of oxide phase in aerosol calculations
Molecular weight
Quantity of strontium (Sr) in the fission productinventory
Timestep in aerosol calculations
Surface tension of the metal phaae in aerosolcalculations
Surface tension of the oxide phase in aerosolcalculations
Cumulative quantity of chemical species
Initial gas (atmosphere) temperature
Quantity of technetium (Tc) in the fission productinventory
Initial coolant tempature
Temperature of coolant added
Quantity of tellurium (T’e) in the fission productinventory
Time when next edit will be generated
Average coolant pool temperature used in aerosolcalculations
Temperature of pool/film interface at Z(J)
Flag for emissivity table for x ( = M, metal; = O,oxide; = S, surroundings); tme if independent variable
is temperature rater than time
Tempemture of gas transported through the film
Temperature of gas transformed by theoxide/atmosphere reaction
Temperature of gas transported as bubbles
Ray angle
Thermal conductivity
Thermal conductivity of metal phase
Thermal conductivity of oxide phase
Initial concrete temperature
g-ad
g-mol
glg-mol
g-mol
s
dynelcm
g-ml
K
g-ml
K
K
g-ml
s
K
K
K
K
K
K
d
W/m-K
W/m-K
W/m-K
K
155 NuREG/cR-5843
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description Utits
TIM(N)
TIME
TIMECR
TIMEND
TIMEO
TIMESD
TIMRAD (N)
TINT (L)
TIO (N)
TLAY (L)
TLCNTR (L)
TLCNTZ (L)
TLIQCT
TLIQLA (L)
TLIQM (L)
TLIQO (L)
TMET
TMI
TMM (N)
TMO (N)
TMPS (N)
TMs (N,I)
TMsv
TMTR
TOI
TORT1 (M or N)
NuREG/cR-5843
t
TI
. .
T~
?,,
T,*
T:
T[
. .
. .
.-
. .
--
.-
--
. .
Times in metal phase input power table
Cwreat time
Time at which the layer crusts are thick eaough to stop
melt spreading (timedependent melt radius)
End time for calculation
Start time for calculation
Tkne at which the spreading melt layer contacts the sideof the concrete cavity
Time at which the melt has radius IWDTIM (N) in thetable of times and radii (timedependent melt radius)
Interfaw temperature
Times in oxide phase input power table
Average (bulk) tempxsture
Average liquid temperature, radial
Average liquid temperature, axial
Concrete liquidus temperature
Liquidus temperature
Metal phase liquidus
Oxide phase liquidus
Mass -averaged metal phase temperature used in aerosolcalculations
Initial temperature of metallic phase
Times for metallic phase splashout table
Times for metallic phase splashout table
Temperature of surroundings
Time in mass addition table
Temperature of metallic products of oxide/atmospherereaction
Temperature of metal rising of sinking in the pool
Initial temperature of the oxidic phase
Time or temperature for oxidic phase emissivity table
156
s
s
s
s
s
s
s
K
s
K
K
K
K
K
K
K
K
K
s
s
K
s
K
K
K
sor K
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description Units
TORT2 (M or N)
TORT6 (M or 7:)
TOTALH
TOTALM
TOTR
TOXD
TPA (N)
TPRIN
TSAT
TSIDE (L)
TSN
TSNP1
TSOL~
TSOLID (L)
TSOLLA (L)
TSOLM (L)
TSOLO (L)
TSTART (L)
‘lTA
‘l-m(N)
‘w
UBUB (L)
URO
VA
VAPOR
VISLAY (L)
VISLIQ (L)
VISM (L)
VISMET
.-
T:
.-
-.
Tw
u’
--
. .
P{
-.
Time or temperature for metallic phase emissivity talde
Time or temperature for surroundings emissivity table
Total pool enthalpy required by energy conservation
Total pool mass required by mass conservation
Temperature of oxide rising or sinking in the pool
Mass-averaged oxide phase temperature used in aerosolcalculations
Time in gas (atmosphere) pressure table
Time for start of diagnostic print
Side (radial) boundary temperature
Surface temperature at the start of the time.step
Surface temperature at the end of the time.step
Concrete solidus temperature
Solidification temperature
Solidus temperature
Metal phase solidus
Oxide phase solidus
Temperature at the start of a timestep
Current layer temperature
Time in surroundings temperature table
Concrete ablation temperature
Bubble rise velocity
Unit round off error
Initial gas volume
The concentration of aerosol particles generated byvaporktion
Dynamic viscosity
Dynamic viscosity of liquid
Dynamic viscosity of the metal phase
Mass-averaged dynamic viscosity of the metal phase,used in aerosol calculations
157
sor K
sor K
J
kg
K
K
s
s
K
K
K
K
K
K
K
K
K
K
s
K
kglm-s
kglm-s
kglm-s
glcm-s
NUREG/CR-5843
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symtwl Description unit8VISO (L)
VISOXD
VMET
VOL (J)
VOLM (L)
VOLO (L)
VOLRAT (I)
VOXD
VROVR
VSGINT (L)
WF (I)
WFRBR
X (J)
XEN
XL (I, K)
XM (I, K)
XMAS
XMTU
XM~H
XN (I,K)
Y
YKG (I,N)
z (j)
ZB
ZINT (L)
. .
. .
.-
.-
--
.-
--
--
. .
. .
.-
--
--
--
--
.-
Y
--
z
Dynamic viscosity of the oxide phase
Mass-averaged dynamic viscosity of the oxide phase,used in aerosol calculations
Superficial gas velocity through the metal, used inaerosol calculations
Cumulative cnvity volume
Volume of the metal phase in attainment calculations
Volume of the oxide phase in entrainment calculations
Exponential volatization rate of fission products
Superficial gas velocity through the oxide, used inaerosol calculations
Velocity ratio for aerosol calculations
Superficial gas velocity
Weight fraction of concrete constituents
Weight fraction of rebar in concrete
Path length in the film
Quantity of ruthenium (Ru), technetium (T’c), rhodium
(Rh), and palladium (Pal) in the fission prtiuctinventory
Quantity of fission product inventory speeies
Quantity of fission product inventory species
Aerosol generation rate
Core size, metric tonnes of uranium
Core operating power (thermal)
Array containing the molecular weights for species K ofelement I
Quantity of ytterbium (Y) in the fission productinventory
Array containing the quantities of fission product in kg
Axial coordinate (positive down)
Axial coordinate of the bottom of the concrete crucible
Interface location
kglm-s
gicm-s
Crnls
m3
m3
m3
S’
Cmls
n’lls
--
m
g-mol ~
kg
g-mol
gls
Mg
MW
glg-mol
g-mol
kg
m
m
m
NUREG/CR-5843 158
Coding Information
Table 5.7 Dictionary of principal variables in CORCON (continued)
FORTRAN Algebraicsymbol symbol Description Units
ZMAX .- Axial coordinate of deepeat point in the cavity m
Zo .. Axial coordinate of ray origin m
ZT Axial coordinate of tbe topof the concrete crucible, m
Fimme 4.3
I59
6.0 Sample Problems
To illustmte the use of CORCON-Mod3, and to verifythe correct functioning of the code following itsinstallation, we have provided a set of sample problems.The input decks for these samples should providevaluable help to the new user in assembling correct inputdecks. The sample problems also demonstrate thecapabilities of the code.
No one problem utilizes all the capabilities of CORCON-
Mod3. The CORCON standard problem exercises themore commonly used capabilities of CORCON; theadditional sample problem exercises some of the newerfeatures in the code.
6.1 The CORCON Standard Problem
The CORCON standard problem describes deposition ofessentially the entire core of a typical large (3400 MWt)PWR into a reactor cavity formed of limestoneaggregate/common sand concrete. Deposition takes placethree hours after reactor SCRAM, at which time thezirconium cladding is assumed to be approximately 50percent oxidized. The melt also includes a significantamount of steel, from the upper internals and thebreached lower head; the steel is assumed to be 5 percentoxidized. The initial water inventory of 60 metric tomesrepresents the contents of the accumulators of a typicalPWR. The cavity radius is taken as 3.0 meters, and doesnot include the area of the keyway in a plant such asZion or Indian Point. Containment pressure is assumedto rise linearly from 1.5 bars at deposition time to 3.0
bars 3 hours later. The effects of aerosol opacity are
included with the characteristic path length taken as a
nominal 1.0 m.
This problem does not model any particular plant oraccident sequence. It is intended merely to provide atypical problem to exercise the basic capabilities of
CORCON.
The calculation assumes that the core melt is initiallystratified. It remains stratified because the interlayermixing models are not activated (ILYR < 10).Condensed phase chemistry is not calculated and thecoking reaction is disabled (ICHEM = O). Slag heattransfer is assumed at the bottom surface, while gas filmheat transfer is assumed at the side surface (IFILM = 1).A full VANESA calculation is performed (IFVAN = 1),
and the VANESA fission product composition isdetermined from the CORCON composition (IVANFP =O). The effects of aerosol in the cavity atmosphere isincluded in the calculation of radiative heat transfer(IAOPAC = 1).
NUREG/CR-5843
The release calculation is performed assuming idealchemhy (IDEAL = 1).
The data cards used for this problem are shown in Table6.1. This input follows the input description of Section4.1.
A partial output listing for time 16200 seconds (270 tin)for this calculation is shown in Table 6.2. Plots of the
output are shown in Figures 6.1 through 6.9.
In the Standard Problem calculation, the melt remainsstratified in a three layer configuration with the heavyoxide layer on the bottom, a metal layer in the middle,and a light oxide on the top. Unlike the calculations withearlier versions of CORCON, no layer flip is calculatedduring the three hours of the interaction.
Because the heavy oxide layer remains on the bottom ofthe melt, axial (downward) ablation is rather slow. Thisis true because an oxide crust exists at the interface withthe concrete. The crust remains throughout thecalculation and grows to a quasi-steady thickness ofapproximately 4 centimeters. As the crust grows, theablation rate decreases to a nearly constant value of 2cm/hr.
Figure 6.2 shows the maximum axial and radial ablationdistances calculated by the code. Note that the hotmetallic layer ablates concrete at a fairly rapid rateduring the first hour of the calculation. After about onehour, the lower oxide layer has grown such that themaximum radial ablation location is adjacent to the oxidelayer rather than the metal layer. This is true until 80minutes later. At this time, the maximum radial ablationlocation is adjacent to the metal phase, and the maximumradial ablation distance again increases rapidly.
The calculated layer temperatures are shown in Figure6.3. The three layer temperatures drzrease during thefirst 100 minutes of the interaction. At approximately,110 minutes after the start of the interaction, theoverlying coolant pool boils off, and the layers begin toincrease in temperature. By the end of the calculation,the layers have reached a new quasi-steady temperaturelevels of between 2100 and 2200 K.
Figures 6.4 and 6.5 show the cumulative amount of gasentering the cavity atmosphere, and the rate of gas
generation. As expected, the early gas generation isdominated by the steam from coolant boiling. (Note thatthe steam production is initially low because the coolantpool is subcooled. When the coolant is subcooled, steamis assumed to condense before reaching the pool surface.)Boiloff of the coolant is shown clearly in Figure 6.5 at
160
Sample Problems
about 295 minutes, where the steam generation rateabruptly decrease-s.
Figure 6.6 shows the calculated rates of energygeneration and energy loss. Energy generation occurs byradionuclide decay and by chemical reactions. Energylosses include heat losses to the concrete and to theoverlying wak’ pool, atmosphere, and structures. Inaddition, euergy lost from the melt in beating theincoming ablation products is included. This term isusually small, as is the case here. In cases where theablation rate is extremely rapid, this term is larger.
Heat transfer to the coolant is initially quite high.During the first 15 minutes of the interaction, the coolantheat flux is greater than 1 MW/m2 over theapproximately 32 m2 surface area. After 110 minutes,however, the coolant heat flux has decreased to0.5 MW/m2. Boiloff of the coolant occurs at this time,and the surface heat flux drops rapidly. Late in the
calculation, the heat flux due to thermal radiation isapproximately 0.3 MWlmz.
In this sample calculation, energy ge33eration fromchemical reactions is much smaller than that fromradionuclide decay, This is true because the ablation rateand consequently gas generation rates are relatively low.In calculations with higher ablation rates, the energygeneration from chemical reactions can greatly exceedthe contribution from radionuclide decay.
Figures 6.7 through 6.9 show the calculated aerosolwncentration and aerosol generation rate for theCORCON Standard Problem. The general trend of theaerosol concentration and aerosol generation curvesfollows that of the gas generation and melt temperature
curves. ‘he aerosol concentration is greatest early in thecalculation, with a maximum value of approximately 200g/m3 at STP, but declines rapidly to a quasi-steady level
of approximately 30 to 40 g/d. Similarly, the aerosolgeneration rate is highest at the onset of the interaction
(at > 150 g/s), but quickly reaches a nearly constantvalue of 20 gls.
Another important safety consideration is the magnitudeof radionuclide release from the core debris. Thecalculated release fractions for sevend of the importantrefractory radionuclides are shown below:
ReleaseRadionuclide E!W@!
Tellurium 0.3s9
Molytxkmum 1.30 x 1(Y
Uranium 5.24 X 10sBarium 3.49 x 10’
Strontium 4.34 x 103
Cerium 1.13 x 103Lanthanum 8.53 X 10s
It should be noted that these releases are for only the firstthree hours of the interaction. Though the bulk of therelease occurs during this period, radionuclides will
continue to be released for several hours. It should alsobe noted that these are releases from the melt surfacerather than into the cavity atmosphere. A significant
fraction of the released radionuclides is trapped withinthe overlying water pool. Currently, this material iseffectively lost from the problem once it becomestrapped. It is not returned to the core debris if the waterpool evaporates completely. Also, the code does nottreat decay power generation in the water pool from thetrapped radionuclides.
6.2 Additional Sample Problem
A second sample problem is provided to illustrate someof the new features of CORCON-Mod3. This problemsimulates an accident at a typical BWR plant. The core-concrete interaction is assumed to begin three hours afterreactor shutdown. Initially, approximately one-third ofthe core is deposited into the reactor cavity. Thezirconium included in the initial pour is assumed to be 20percent oxidized. During the next 3 hours of the
calculation, the second third of the core is assumed to
enter the cavity. The reactor cavity is assumed to beconstructed from basaltic concrete and is assumed to havea diameter of 3.2 meters. Water is added after one hourof the interaction. The water addition rate of 20 leg/s
(approximately 300 galhnin) is sufficient to fill the5 meter deep cavity in approximately 2 hours. Thepressure in the cavity atmosphere is assumed to rise from1.5 bars to 2.5 bars during the 3 hours of the calculation.
The core melt is assumed to be well-mixed initially, andthe interlayer mixing models are enabled (ILYR = 13).Condensed phase chemistry is
161 NUREG/CR-5843
Sample Problems
calculated and coking is disabled (ICHEM = 1). Slagfilm heat transfer is assumed at both the bottom and sidesurfaces (IFILM = O). A complete VANESAcalculation is performed (IFVAN = 1), and theVANESA fission product composition is determined fromthe CORCON composition (IVANFP = O). The releasecalculation is performed assuming ideal chemistry(IDEAL = 1). The effects of aerosols on thermalradiation is included (IAOPAC = 1), and a mean pathlength of 3.0 meters is assumed. The optional userflexibility input is provided (IUSER = 1), with the
following user modifications specified:
1) the thermal conductivity for the metal phase ismultiplied by 0.5,
2) the viscosity of the oxide phase is multiplied by5.0,
3) the oxide phase solidus temperature is assumed todecrease to the concrete solidus at 20 mole percentconcrete oxides.
The input for this sample problem is shown in Table 6.3.A partial listing of the output for time = 16200 s (270rnin) from the calculation is provided in Table 6.4. ofthe calculated results are provided in Figures 6.10through 6.18.
The melt is assumed to be well-mixed at the start of theinteraction. After 10minutes, themeltiscalculated tobe a dense oxide layer and a mixture of dense oxides andmetal. In this sample calculation, a mixture of denseoxides and metals is calculated to form (i.e., an HMXlayer). (The oxides are denser than the metals becausefiel oxides are being continuously added to the melt.)
Immediately, this layer begins to stratifi, with the denseoxides settling out of the mixture. The evolution of thelayering configuration is shown clearly in the layertemperature plot of Figure 6.12.
Figures 6.10 and 6.11 show the calculated axial ablationrate, and axial and radial ablation distances for the BWRsample problem. Because the heavy oxide layer is on thebottom of the melt during most of the calculation, theablation rate is slow due to the existence of a oxide crustat the interface with the concrete. The spike in ablationrate seen at 9 minutes arises from the changes in layerconfiguration Occurnngatthistime.Thecrustreachesaquasi-steady thickness of 2.5 cm prior to water addition.After water addition, the crust is calculated to shrink asconcrete oxides mix with the fuel oxides lowering themixture scdidus temperature. By the end of thecalculation the crust thickness is 0.2 cm. Thinning of the
crust is not accompanied by an increase in the ablationrate because the oxide temperature has fallen to 1865K.
Figure 6.12 shows the rapid decline in the melttemperature during the first hour of the calculation. Atthis point, water is added onto the melt. After wateraddition, the melt temperature decreases at a slightlyfaster rate. Approximately 100 minutes after wateraddition, energy generation from radionuclide decay andchemical reactions exceeds losses to the coolant and theconcrete, and the temperature of the melt begins toincrease slightly.
Figures 6.13 and 6.14 show the cumulative gasgeneration and the gas generation rate calculated for theBWR sample problem. Production of HZO and COZ issuppressed. The code predicts that gas reactions with theHMX mixture produce methane (CHJ and otherhydrocarbons at the expense of steam and carbon dioxide
production. The steam releaseseenat270minutesis,ofcourse, the steam produced by boiling of the coolant.
The calculatul energy generation and energy loss termsare shown in Figure 6.15. The decay power is calculatedto increase from 7 MW to 11 MW as core debris entersthe cavity. Energy generation from chemical reactions iscomparable to the decay power during the first hour ofthe calculation. The spike in chemical energy generationat 8 to 10 minutes occurs when the core debris becomesfully mixed and all of the oxides, metals, and gases aresuddenly assumed to react chemically. When water isaddedat240minutes,heatlossthroughthemeltsurfacequicklyincreasesto20 MW (0.65 MW/m~, and thendeclines to a level that almost exactly balances the decaypower.
Figures 6.16 through 6.18 show the calculated aerosolconcentration and aerosol generation rate for the BWRsample problem. The high concentration and generationrates seen during the first 10 minutes of interaction arise
from the relatively high melt temperatures and the gasgeneration rate spikes seen in Figures 6.12 and 6.14respectively. The gas generation spike occurred duringthe rapid melt layer configuration changes. This couldalso influence the chemistry driving release. After thefirst 10 minutes the high hydrogen to steam ratio (i.e.,low oxygen potential) in the gas stream promotes thereduction of refractory oxides to more volatile species.This enhances the release of both oxides from theconcrete such as silica and fission product oxides such asBaO and I+OJ. The aerosol generation rate andconcentration increase to about 200 gls and 250 g/m3(STP). At water addition at 240 minutes, the aerosolrelease shows a distinct drop corresponding to the melttemperature decrease. The increasing generation rate and
NUREG/CR-5843 162
Sample Problems
concentration during the last 1 1/2 hours of theconcentration can be attributed to the slight increase in Radionuclidemelt temperature and to the release of concrete oxidessuch as Na02 and K02, which comprise nearly 3/4 of the Telluriumaerosol mass at the end of the calculation. Molybdenum
UraniumBarium
The following are the release fractions calculated for Strontiumsome of the more important radionuclides: Cerium
Lanthanum
ReleaseFraction
0.1556.28 X 1096.23 X 1050.1100.1870.05132.26 X 103
New Results(2.281
0.135.8 X 1095.65 X 10S9.92 X 1021.89 X 10’4.48 X 1021.83 X 103
Note that these releases are relative to the total mass ofcore debris in the reactor cavity (i.e., two-thirds of thetotal core mass). To determine release fractions relativeto the total core inventory, multiply the above values by2/3.
163 NUREG/CR-5843
&:w
10
9
8
7
6
5
4
3
2
1
0
I 1 I I l“’’I’’ ’’1’ ’’’1 ’’’’1’’” l“’’1 ’’’{1’’”:
r 1 1 1 I II, ,11, t, lll!llllllllllll Ii lllllllllllll=
180 200 220 240 260 280 300 320 340 360
Time (rein)
Figure 6.1 Axial ablation rate calculated for the CORCON standard problem
50
45
40
35
30
25
c 20
10
5
0
,-.
I I I Il“’’I’’ ’’1’ ’’’1 ’’’’1’’” l“’’1 ’’’’11’”:
‘.
.“#.-
●.”.“
.“.“
.“,0
.“,0 ‘
,,
--------- -’- - -- . . . . . . . . . . - - - - - - -
.“-------”---,...-
.“. ..“
.“.“
●*.’
.’,0
,0 Axial,“,’,’ ---------- Radial*’
●’,0●*,0*’a“
●’**
—,’a,r
180 200 220 240 260 280 300 320 340 360
Time (rein)C/lm3
-a_CD
Figure 6.2 Axial and radial ablation distance calculated for the CORCON standard pmbla
2600
2500
2400g
a)5~ 2300cl)
E
z 2200
2100
I I 1 Il“’’I’’ ’1 1’’’ ’1 ’’’’1’’” 1“’’1’’’’1’’”-
— HOXb
‘\
- - - - - - - -- - - - - - - -- - .
------ .—-—-— -—.—. -
2000 I I 1 1 11111111111111111111111111111 ‘1’’’’ 1’’”1180 200 220 240 260 280 300 320 340 360
Time (rein)
gl
3u-0
‘w3
f
Figure 6.3 Layer temperatures calculated for the CORCON standard problem
104
103
102
10’
10°
10’
102
II I Il“’’I’’ ’’1’ ’’’1 ’’’’1’’” l“’’I’’’’1 ’’1’:
-_.—-- -—-—-— -—..—-— -—-—.— .—.—.-------------.4-./--
. ./-H.0
,//
!
. /.
—
[
!
1--------------------------
!. --------------- - - ---------------------------------------$s
I.a-
.“---9
! /=- — co
! /-“y’ ------ H2
J –-–-–. H20jY,, ,1, ,,, l,, ,,1, ,,, l,, ,,l ,,, ,1,,,,1,,,,1,,,,-
180 200 220 240 260 280 300 320 340 360
Time (rein) !fuir
Figure 6.4 Cumulative gas generation calculated for the CORCON standard problem
104
103
102
10’
10°
10’
I 1 I I I I I I
‘r------------ -_i -—.—.—-_._-= *i!I-8!!
!
=i - \,---------I \ ----- ----- - ________ ___---i
co-------- C02------ H2–-–-–. H20
-
-.---------- ----------
i
~ I ------- ----<------------! j
---------.-- ------- -.----- -- .------ ---------------
! ●-----------~-_-H-
L~*’-,‘t. .
180 200 220 240 260 280 300 320 340 360
Time (rein)
Figure 6.5 Gas generation rate calculated for the CORCON standard problem
50
40
30
20
10
0
) I I Il“’’I’’ ’’1’ ’’’1 1’ ’’1’’” I“’’l ’’’’ l’”i
— Decay Heat
--”----------Chemical Rxn
-------- Loss to Concrete
------ LosstoSurface
–-–-–. Ablation Products-\\ \ \ \ %\\
~ ----.
-- ----------
-----9III
~. t-------- --. * It
------ ------ ------ ----
8------- -------‘-- -- -. - - - -. - ---- -1 --------------%......................... -------------............................-.............................................................................-”” ----------
180 200 220 240 260 280 300 320 340 360
Time (rein)
Figure 6.6 Enemy terms calculated for the CORCON standard problem
100
90
80
70
60
50
40
30
20
10
0
I I I I [1’ ’’1’ ’’’1 [’’’ 1’’’ ’1’1”1 1’{’ 1’ ’’’1’’”:
1
1 1 1 I 1,, , ,1,,,,1,1,,1,,,,1,,,,1 ,,, lllllil, lM~*
180 200 220 240 260 280 300 320 340 360Time(min)
figure 6.7 Aerosol concentration (wbientconditiom) calculat4for the CORCONstindard prohkn
-1
200
180
160
140
120
100
80
60
40
20
0
\ 1 1 I l“’’I’’ ’’1’ ’’’1 ’’’’1’’” l“’’I’’’’I”” J
1 I I I 1,, , ,1,,,,1,,,,1,,,,1,,,, 1 ,1,,1,,,,1,,,,=
180 200 220 240 260 280 300 320 340 360Time (rein)
Figure 6.8 Aerosol concentration (STP) calculated for the CORCON standard problem
250
200
0
\ I I I l“’’I’’ ’’1’ ’’’1 ’’’’1’’” l“’’1 ’’’’1’’”-
} I I 1 1,, ,,1,,,,1,,,,1,,,111,,,1 ,,, ,1! 1,11,,,11
180 200 220 240 260 280 300 320 340 360Time(min)
Figure 6.9 Aerosol generation rate calculated for the CORCONstandard prohlem
In
o
u)
‘e
m
0 I 1 I I I I I 1
180 200 220 240 200 280 300 320 340 360Time (rein)
$=_(D
Figure 6.10 Axial ablation rate calculated for the BWR sample problem
2
0m
mm
10
0
.84t----------------------- ------- ----- ------- ------ ---tt
t8t------ ----------8t
It
It1I8 E AxialII ------- RadialfIIIIItIo#II —
II
I 1 I 1 i 1 I 1
180 200 220 240 260 280 300 320 340 360Time (rein)
Figure 6.11 Axial and radial ablation distances calculated for the BWR sample problem
00a
o0-
I
I
z 180 200 220 240 260 280 300 320 340 360
Time (rein)
Figure 6.12 Layer temperature calculated for the BWR sample problem
73
--, . . .
“ . . 0
1’ “ “ l“” “’ I “ ‘ ““ I ‘ “ 1’”” ”1”””” l“””” 1””””
180 200 220 240 260 280 300 320 340 360Time (rein)
Figure 6.13 Cumulative gas generation calculated for the BWR sample problem
●O
.‘o< --,---,
& *
- 180 200 220 240 260 280 300 320, 340 360Time (rein)
Figure 6.14 Gas generation rate calculated for the BWR sample problem
m’5:
w_t-b
.
~ Decoy Heat~ Chemical Reaction——I+—Loss to Concrete~ Loss to Surface~ Ablation Product
180 200 220 240 260 280 300 320 340 360Time (rein)
Figuk 6.15 Energy terms calculated for the BWR sample problem
0:
0
180 200 220 240 260 280 300 320 340 360Time (rein)
Figure 6.16 Aerosol concentration (ambient conditions) calculated for the BWR sample problem
000
010 200 220 240 260 280 300 320 340 360
Time (rein)
Figure 6.17 Aerosol concentration (STP) calculated for the BWR sample problem
o0m
o0
I I I I I I I I0180 200 220 240 260 280 300 320 340 360
Time (rein)
Figure 6.18 Aerosol generation rate calculated for the BWR sample problem
Sample Problems
Table 6.1 Input listing for the CORCON standard problem
70000.
CORCON STANDARD PROBLEM (slightly different from Ifodl/Mod2 problem)
$$ user flags
$ *lLYR (stratified, mixing off)
$: *ICHEM (condensed phase chemistry off, coking off)A *IFIU4 (slag\film)
:A *IMoV (movies)
220010 0180 1 0 1 1 0 1$ ad~itio;al user flags$ *I~AN (do VANEsA calculation)&oloo$$ time information
30,0 10800. 21600.$$ ray system information
60 0.0 1.5$$ geometry information - rt. circular cylinder 3.2 m radius
0.0 3.0 5.00 0.1 4.0 2.0 10 6$$ concrete specifications - abl temp - 1650 K
300.0 1650. .6 .135$$ initial debris composition and temperature (T - 2500 K)
34 2500. 2500.U02 1.OE5ZR02 1.4E4FEO 6.0E3ZR 1.0E4FE 4.0E4CR 1.0E4NI 6.0E3$$ core MTU and operating power
90. 3400. 0$$ initial water inventory and temperature - 60000 kg. subcooled
322.H20 6.0E4$$ cavity atmosphere conditions and composition
5.0E4 0.0 380. 2H2 0.5H20 0.5$$ pressure in cavity vs. time (Pa)
210800.0 1.5E5 21600.0 3.0E5
NUREG/CR-5843182
SampleProblems
Table 6.1 Input listing for the CORCON standard problem (continued)
$$ temperatureof surfaces above
210800.0 400.0 21600.0
s
melt
800.0
$ emissivities VS. time - oxides, metals,TIMETIMETIME
1110.0 0.80.0 0.60.0 0.6
mean beam length for atmospheric3.0
VANESA inputuser options
opacity
surroundings
calculation (m)
* IDEAL-1, run with Ideal chemistry turned on1111
pool scrubbing parameters20 - 2.3 1 1 1.0 l.O
183 NUREG/CR-5843
Table 6.2 Output listing forthe CORCON standard problem
z m
ss
gUoo
2.
3.
5.
6.
7.
%?
8.9.
10.11.12.13.14.15.
16.
17.18.
19.20.21.
22.
IMAGES IN INPUT FILE (TAPE5) wCORCON STANOARD PROBLEM (slightly different fmn Modl/%d2 problem)$
8~
$ user flare ~s ●lLYR ~stratified, mixing off) G1
$“ ●ICHEM (condensed phase chemistry off, coking off)$’ . *l FILF! (stag/film)
01220010 0180 1 0 0 1 0 1$ additiona[ user flags
*I FVAN (do VANESA calculation):0100$S time information
30.0 10800. 21600. 70000.s$ ray system information
60 0.0 1.5s$ geometry information - rt. citcular cytinder 3.2 m radius
0.0 3.0 5.00 0.1 4.0 2.0$$ concrete specifications - abl tap = 1650 K
300.0 1650. .6 .135$$ initia[ debris composition and temperature (T = 2500 K)
34 2500. 2500.U02 1. 0E5ZR02 1.4E4FEO 6.0E3ZR 1.0E4FE 4. 0E4CR 1. OE4N] 6.0E3sS core MTU and operating pwer
90. 3400. 0$S initial uater inventory and temperature - 60000 kg. subcooled
322.li20 6.0E4$S cavity atmosphere conditions and ccmmsition
5.0E4 “ 0.0 380. 2 “H2 0.5H20 0.5sS pressure in cavity vs. time (Pa)
2
10 6
TabIe 6.2 Output listing forthe CORCONstandard problem (continued)
23.
24.25.
26.27.28.
%
31.
32.
33.
wU
s$
$s
10800.0 1.5E5 21600.0 3.0E5
temperature of surfaces above mtt2
10800.0 400.0 21600.0 800.0
emissivitiesTIMETIMETIME
110.00.00.0
s
vs. time - oxides, meta(s, surroundings
0.80.60.6
S mean beam length for atmospheric opacity calculation (m)3.0
sS VANESA irputS user options
111sS pool scrubbing parameters
20 2.3 1 1 1.0 1.0
Table 6.2 Output listingfor the CORCON standard problem (continued)
z mKs
3g
3F
c1 CORCON STANOARO PROBLEM (s( ight (y different fran Modl/Mod2 probtem)6
***ILYR = O ICOOL = 1ICHEM = O 1FP =0lSPLSH= O lPINC =**IMOV = o IPG = 1ITIMR = O I FVAN = 1
TIMESTEP CONTROL. DTMIN(l )30.000
EDIT CONTROL. DEDIT(I)5400.000
***INPUT***
FLAGS ● **[ GEOM = 2 I CON ❑ 2ISUR = 1 IABL =0IFILM = 1 IRSTRT = OISRAEL = O I AOPAC = 1IVANFP = O IUSER = O
DTMAX( I ) T] MOT(I)30.000 1.OOOE+1O
TED IT(I)1.OOOE+1O
RAY CENTER COORDINATES
RO = O. 0000 OOE+OO Zo =
CONCRETE CAVITY GEOMETRY
RIGHT CYLINDER
1.50000
NRAYS - NUMBER OF RAYS = 60
ZT - Z- COOROI NATE OF TOP = O. 0000 OOE+OO
RAO - CYLINOER RADIUS (M) = 3.00000
HIT - CYLINDER HEIGHT (H) = 5.00000
RADC - CORNER RAOIUS (M) = 0.100000
NBOT - NL04BER OF BOTTOM POINTS = 10
NCORN = NUt4BER OF CORNER POINTS = 6
*** CONTROL PARAMETERSTIMEO = 10800.00 (SEC)TIMEND = 21600.00 (SEC)DPRIN = 0.00 (SEC)
~G=~
● **
DELTIM = 30.0000 (SEC)
TPRIN = 70000.00 (SEC)
Table 6.2 Output listing for tbe CORCON standard problem (ctmtinued)
● ☛ ☛ CONCRETE spEC1 F1cATIONs ● ● *
L 1MESTONE AGGREGATE - COMMONSAND CONCRETE
RliOC RBR s] TSOL TL1O TIC(KG/M3)
TU DELH EU(KG/KG C) (-) (K) (K) (K) (K) (J/KG) (-)
2.340000E+03 1.350000E-01 2.585400E-01 1.420000E+03 1.670000E+03 3.000000E+02 1.650000E+03 3. 118502E+06 6.0000 OOE-01
SPECIES NAME MASS FR. (KG/KG C) MOLECULAR UT.
S102 0.3580 60.0843TI02 0.0018 79.8988MNO 0.0003 70.9374MGO 0.0048 40.3044CAO 0.3130 56.0794NA20 0.0008 61.9790K20 0.0122 94.1960FE203 0.0144 159.6922AL203 0.0360 101.9613CR203 0.0001 151.9902C02 0.2115 44.0098H20EVAP 0.0270 18.0152H20CHEM 0.0200 18.0152
MELT FISSION PRODUCT INVENTORYBASEO ON 9. 0000 OE+O1 METRIC TON URAN 1UPl CORE OPERATEO AT 3 .40000E+03 MU(THERMAL )
MELT CONTAINS 8.81390E+01 METRIC TONS URANIUM, CORRESPONDING TO 97.93 PERCENT OF CORE
ELEMENTS, RETAINEO FRACTIONS (**DENOTES USER INPUT, OTHERS FROM WASH 1400), ANO GRAM-ATOMS IN MELT
MO (0.970) 1.8885E+03 TC (0.970) 4.8318E+02 RU (0.970) 1. 1976E+03 RH (0.970) 2.1821E+02SB (0.850) 6.5124E+O0 TE (0.850) 1.6880E+02 SR (0.900) 6.3021E+02 BA (0.900) 5.5260E+022R (0.990) 2.3563E+03 CE (0.990) 1.2329E+03 NP (0.990) 1.2203E+02 CM (0.990) 5.0995E+O0NB (0.990) 3.6129E+01 PU (0.990) 2.2541E+03 AM (0.990) 1.6241E+01 Y (0.990) 3.5403E+02LA (0.990) 5.3006E+02 PR (0.990) 4.60&$E+02 ND (0.990) 1.4801E+03 S#! (0.990) 1.7342E+02EU (0.990) 5.1556E+01 RB (0.190) 5.0434E+01 CS (O. 190) 2.2933E+02 BR (O. 100) 1. 7078E+O01 (0.100) 1.O1O9E+O1
FISSION PRCOUCTS GRWPED AS 4 PSEUDO-SPECIES
3 .96277E+03 GRAM-ATOMS OF FPM UITH ATOMIC FRACTIONS
: MO 4.76552E-01 TC 1.21930E-01 RU 3.02216E-01 RH 5.50639E-02
z TE 4 .25953E -02mC)
6whmAw
SB 1.64339E-03
Table 6.2 Output listing for the CORCON standard problem (continued)
z K
s 3Q
3_m
CJ 1.02555E+04 GRAM-ATCBIS OF FPOX WITH ATOMIC FRACTIONS6
‘u
zSR 6.14511E-02 BA 5. 38829E -02 ZR 2.29756E-01 CE 1.20214E-01 NP 1.18992E-02 3CM 4 .97248E -04 NE 3.52284E-03
&lPU 2.19792E-01 AM 1.58367E -03 Y 3.45213E-02 ~
w LA 5.16855E-02 PR 4.49355E-02 NO 1.44321E-01 SM 1.69103E-O2a
EU 5.02712E-03 ;w
2.79767E+02 GRAM-ATCU4S OF FPALKMET UITH ATOMIC FRACTIONSRB 1.80272E-01 CS 8.19728E-01
1.18168E+01 GRA14-ATOMS OF FPHALOGN WITH ATOMIC FRACT IONSBR 1.44524E-01 1 8.55476E-01
INITIAL POWER AT START OF CORCON, 1.08000E+04 SEC AFTER SCRAM 1S 2.06797E+07 WATTSREPRESENTING 0.62 PERCENT OF OPERATING POUER OF FRACTION OF CORE IN MELT
INITIAL CORE MASSES (KG) OF CONSTITUENTS ANO TEMPERATURES
OXIDES SPEFUJ CONINP METALS SPEMIJ CONINP
FEO 7. 1846397E+01 6.0000000E+03 FE 5. 5847000E+01 4.0000000E+04U02 2. 7002780E+02 1.0000000E+05 CR 5. 1995998E+01 1.0000000E+04ZR02 1.2321880E+02 1.4000000E+04 NI 5 .8709999E+01 6. 0000000E+03FPOX 1.4748473E+02 1.5125297E+03 ZR 9.1220001 E+O1 1. 0000000E+04
a FPALKHET 1. 2435149E+02 3.4789448E+01 FPM 9.9529678E+01 3.9441333E+02U3 FPHALOGN 1.201 1028E+02 1.4193141E+O0
INITIAL TEMPERATURE (TO) IN DEGREES K = 2.5000000E+03
INITIAL TEMPERATURE (TM) IN OEGREES K = 2. 5000000E+03
INITIAL MASS OF OX1OES = 1.2154874E+05
INITIAL MASS OF METALS = 6.6394414E+04CWILANT IS H20
INITIAL MASS OF CCOLANT = 6.0000000E+04
INITIAL TEMPERATURE OF COOLANT = 3 .2200000E+02
* ● ● REAcTINfj GAs MIXTURE * * ●
● ** ATMOSPHERIC PRESSURE SPECIFIED AS OF TIME ***T lME 1.0800E+04 2. 1600E+04
PRESSURE 1. 5000E+05 3. OOOOE+05
VA(m) (%2) (D; K)
5.0000000E+04 1.5000000E+05 3. 8000000E+02
Table 6.2 Output listing for the CORCON standard problem (continued)
GAS INPUT
SPECIES NAME HOLE FR. (-)
H2 0.5000H20 0.5000
● ** MELT INTERNAL CONDITIONS ● **
● ** BOUNOARY CONO1T IONS - SURROUNOINGS ABOVE MELT ***
●** SURFACE TEMPERATURE VARIAT 10N WITH T I14E ● **
*** TS(OEG K) INPUT AS TABLES .VS. TIME ***
T] ME(SEC) TS(OEG K)1 .0800E+06 4. 0000E+022. 1600E+04 8.0000E+02
●** SURROUNDINGS MATERIAL MELTING OR ABLATION OURING INTERACTION
●** ABLAT 10N OF SURRCUNO I NGS 1S CONPUTEO IN PROGRAM ***
00 ●** BCUNDARY CONDl T IONS - RADIATIVE HEAT TRANSFER ● **a
MOLECULAR UT.
2.015818.0152
●**
● ** SURFACE EMISSIVITIES .VS. TIME OR TEMP. ● **
TIME 0.0000E+OOEO 8.0000E-01
T lHE 0.0000E+OOEM 6.0000E-01
T IHE O. OOOOE+OOES 6.0000E-01
●** AEROSOL OPACITY INCLUDED IN ATMOSPHERE ●**CHARACTER I ST 1C PATH LENGTH (H) = 3.0000E+OO
“:* NO MELT/CtXILANT SPLASH~T ● **
●** NO TIME -DEPENDENT MELT RADIUS USEO ● **
zc%J *** pLoTS ~RE NoT spEC1 F I ED , IMV = omo
IS BEING PERFORHEO USING THE DEFAULT CDRCON NCOELS
Table 6.2 Output listing for the CORCON standard problem (continued)
zc
gEl
g u_● ● ● vA~E~A[NW● ● ●
06 -u~ ~
~%3 #& BUBBLE DIAMETER IS CALCULATED
PART I CLE DIAMETER = 1.00 MICROMETERSPART I CLES/BUBBLE 1S CALCULATED
FECRFEOCR203NIHoRUSNSETEAGMNCAOAL203SI02U02ZR02CS20BAO ‘SROLA203CE02NBOCs IZR
INITIAL MELT COMPOSITIONG-NOLES716242.6 40000.:0192322.5 10000.00083511.5 6000.000
0.00010219::! 6000.000
1888.7 181.1981899.3 191.%6
0.0 0.0006.5 0.793
168.8 21.5380.0 0.0000.0 0.0000.0 0.0000.0 0.0000.0 0.000
370372.0 100000.000113619.0 14000.000
.134.0 37.755552.8 84.772630.3 65.310
1524.8 496.8135976.6 1028.693
36.1 3.93511.8 3.070
109625.1 10000.000
*** WATER POOL OECONTAMINATION ● **INITIAL BUBBLE SIZE(CM)= 1.00SIZE SEGMENTS IN OISTRIBUTICN = 20ALL SCAVENGING HECHANISUS ARE OPERATINGIHPACTION BASE ON V(REL)/V(RISE)= 1.00
GEONETRIC STANOARO DEVIAT1(M OF INPUT SIZE DJSTRIBUIU= 2.30
● ☛☛ ENO OF INPUT ● **
Table 6.2 Output listing for tbe CORCON standard problem (continued)
TINE = 16200.00 COIN3M STANDARD PR08LEM (s[ightly different fran hdl/Ma12 probtem) IT. NO. = 180● ***GENERAL SUMMARY****
HELT ANO CIMANT LAYERS●
NIMBER OF LAYERS, NLYR = 4CONFIGtJRATION, lLYR = 4COOLANT PRESENT, lCOOL = 1
EXTREHE CAVITY DIMENS1ONS, UITH LOCATIONS
RADIALNAXINUM CAVITY RADIUS (M) = 3.34555OUTSIDE RADIUS OF CONCRETE (H) = 4.00000REMAINING THICKNESS (n) = 0.65465CORRESPONDING BODY POINT 24
( SEE MANUAL FOR EXPLANAT 10N ANO CA&ATS)
INTERNAL (OECAY) SUJRCE (u) = 1.813E+07CHEMICAL REACT 10N S(XJRCE (U) = 3.591E+06
a HEAT LOSS TO CONCRETE (u) = 6.680E+06HEATUP OF ABLAT ION PRmUCTS (U) = 1.243E+06HEAT LOSS FRIM SURFACE (u) = 1. 592E+07
(TO COOLANT)
CHANGE IN POOL ENTHALPY (U) = -2.126E+06(SUMMATION OF WIWDT)
NUXER I CAL CHECKS ON MASS ANO ENERGY CONSERVATIW
RELATIVE ERROR lW MASS = 9.41753E-tM
CHECK ~ RECESSION CALCULATION (00/DS SHOULD BE -LE. 1 )
llAXINiM DD/DS = 0.01143
AXIALOEEPEST POINT IN CAVITY (N) = 5.05129NAXINUX DEPTH OF CONCRETE (m) = 7,00000REHAINING THICKNESS (m) = 1.94871CORRESPOND] NG BCOY POINT . 1 APPROXIMATE OVERALL ENERGY BUOGET FOR OEBRIS
RELATIVE ERROR IN ENTHALPY = 9.41753E-06
Table 6.2 Output listing for the CORCON standard problem (continued)
z~ ~m(3
6 TIME = 16200.00mL!aaw
GAS EXITING POOL
SPECIESC(G)CH4coC02C2H2C2H4C2H6HH2H20NNH3N2o02OHCuoCH20CR03(G)FPM02(G)FPH03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)OALOH(G)AL02(G)
CORCON VERS1ON 2.26CORCON STANOARO PR08LEH (s[ ight ly different from Modl/f40d2 problem)
● ***GAs GENERATION*** *
( I NCLUOES FILM ANO COOLANT)
2.08918E-089.92945E-038. 88729E+O01. 33536E+O0O. 0000OE+OO1. 76372E-035. 62896E-072. 02445E-024. 79748E+O04. 23213E+020.0000OE+OOO. 0000OE+OO0. OOOOOE+OO1.19961E-108.47086E-163.86864E-088.50161E-065. 22054E-064.38516E-215.51032E-162.45928E-20O. OOOOOE+OO0.0000OE+OO0.0000OE+OO0.0000OE+OOO. 0000OE+OO0.0000OE+OO0.0000OE+OO
GENERATION RATE CUMLILAT IVE RELEASEMASS (KG/S) MOLES (1/S) MASS (KG) MOLES (-)2.50932E-101. 59294E-042 .48936E-015.87681E-020.0000OE+OO4.94777E-051.69260E-082.04044E-059.67077E-037.62427E+O0O. OOOOOE+OOO. OWOOE+OO0.0000OE+OO1.91931E-122.71057E-176.57951E-102.46702E-071. 56753E-074.38491E-227.18199E-173.59882E-21O. OOOOOE+OO0.0000OE+OO0.0000OE+OO0.0000OE+OO0.0000OE+OOO. OOOOOE+OOO. OOOOOE+OO
5. 72707E -064.06591E-011.80765E+032. 26163E+02O. 0000 OE+OO9.37977E-022 .69389E -053.34079E-017.01920E+015.01489E+04O. 0000OE+OOO. 0000OE+OO0.0000OE+OO4.64784E-072.96563 E- 114 .25586E -052. 58788E-039.59070E-041.39577E-157.19931E-111.07032E- 140.0000 OE+OO0.0000OE+OOO. OOOOOE+OO0.0000OE+OOO. 0000OE+OO0.0000OE+OOO. OOOOOE+OO
4.76819E-042.53444E+016.45349E+045. 13892E+030.0000 OE+OO3. 34359E+O08.95890E-043.31460E+023 .48209E+042. 78370E+06O. OOOOOE+OO0.0000OE+OOO. 0000 OE+OO2.90501E-059. 26793 E- 102.50237E-038.91811E-023.19411E-021.39586E-145.52361E-107.31408E-140.0000 OE+OO0.0000 OE+OO0.0000OE+OO0.0000OE+OO0.0000OE+OOO. 0000OE+OOO. 0000OE+OO
SPECIESC(G)CH4coC02C2H2C2H4C2H6HH2H20NNH3N2o02OHCHOCH20CR03(G)FPM02(G)FPM03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)OALOH(G)AL02(G)
IT. NO. = 180
Table 6.2 Output listing for the CORCON standard problem (continued)
TIME = 16200.00
BODYPOINT
:3456789
101112131415
a 16u 17
18192021222324
25
262728.
2930
z 3132333435363738
RCODRO1NATE
(M)
0.0000000.3269440.6538880.9808321.3077751.6347201.9616632.2886072.6155512.9000002.9361592.9529882.9685812.9824522.99.42963.0031363.0087633.0109523.0119583.0119813.0149173.0854553.2164983.3455533.3450363.1132243.0329573.0248103.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.000000
CORCON VERSION 2.26CORCON STANDARO PROBLEM (s1ight [y different f mm !40dl /Fh3d2 woblem)
zCODRDI NATE
(M)
5.0512855.0512855.0512855.0512855.0512855.0512855.0512855.0512855.0512855.0512855.0436405.0342815.0199695.0017854.9810814.9584044.9351174.9124124.7964224.6793144.5651634.5168934.51W364.5110014.5103414.2142414.1117134.0758573.9666673.8500003.7333343.6986153.6166673.5000003.3833333.2666673.1500003.0333342.9166672.8000002.6833332.566667
STREAMLENGTH
(n)
0.0000000.3269440.6538880.9808321.3077751.6347201.9616632.2886072.6155512.9000002.9369582.9562152.9773803.0002503.0241023.0484423. 0723W3.0952093.2112043.3283123.4425003.5279733.6590513.788416
oX1OE /METAL /
4.295512OXIDE /
4.4442564.5609234.677589COOLANT /4.7942564.9109235.0275905.1442575.2609235.3775905.4942575.61W245.7275915.844257
****-GE-OMETR y****
BODYANGLE(DEG)
0.0000.0000.0000.0000.0000.0000.0000.0000.0000.000
20.50835.81347.60656.44564.46672.56080.45386. W789.74689.25861.45616.527
1.31566.009
METAL INTERFACEOXIOE INTERFACE
115.429COOLANT 1NT ERFACE
96.40190.00090.000
ATMSPHRE INTERFACE90.00090.00090.00090.00090.00090.00090.00090.00090.00090.000
RAYANGLE(DEG)
0.0005.260
10.43315.44020.21624.71728.91532.80036.372
0.00039.64439.88040.14340.42140.70140.97041.21541.42442.41843.45244.52745.64446.80548.013
49.268
50.57251.92753.334
54.79556.31057.880S9.50761.18962.92864.72266.57168.47470.427
VOLUME
(M3)
0.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.204530.459450.853611.359381.940242.580903.241923.888117.19277
10.5303913.7869215.1978415.1029015.40512
28.17427
32.3205935.6192638.91792
42.2166045.5152748.8139452.1126155.4112958.7099562.0086365.3073068.6059771.90464
SURFACEAREA(M2)
0.000000.335811.343253.022315.372W8.39531
12.0892316.4548021.4919726.4208027.0984227.4546927.8484328.2760128.7238729.1824729.6349430.0663132.2611234.4773636.6394038.2774840.8725943.53947
53.70102
56.5201858.7192960.91840
63.1175265.3166467.5157569.7148771 .913W74.1131076.3122278.5113380.7104582.90956
IT. NO. = 180
VOIDFRACTION
(-)
0.016280.016280.016280.016280.016280.016280.016280.016280.016280.016280.016270.016220.016120.016040.015960.015910.015870.015860.015850.015850.015840.015410.014680.01402
0.01573
0.017440.006590.00659
1.000001.000001.000001.000001.000001.000001.000001.000001.000001.00000
Table 6.2 Output listing for the CORCON standard problem (continued)
z:
g~
g39
3P
4041
dam 42.Pw 43
4445464748495051525354555657585960
3.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.0000003.oomoo3.0000003.0000003.0000003.0000003.0000003.0000003.000000
2.4500002.3333332.2166672.1000001.9833331.8M6671 .=00001.6333331.5166671.4000001.2833331.1666671.0500000.9333330.8166670.7000000.5833330.4666670.3500000.2333340.1166670.000000
5.9609246.0775916.1942586.31W256.4275916.5442586.6609256.7775926.8942587.0109257.1275927.2442597.3609267.4775927.5962597.7109267.8275927.9442598.0609268.1775938.2942608.41W27
90.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.000
72.42974.47676.56478.69C80.84883.03285.23687.45589.68291 .9W94.13196.34098.531
100.697102.832104.931106.991lW.006110.973112.891114.755116.565
75.2033278.5019881.8006685.0993388.3980091.6966794.9953598.29601
101.59269104.89136108.19003111.48870114.78737118.08604121.38472124.68338127.98206131.28073134.57941137.87807141.17674144.47542
85.1086887.3077989.5069191.7060293.9051496.1042698.30338
100.50249102.70161104.90072107. OW841W. 29895111.49806113.69718115.89630118.09541120.29453122.49365124.69277126.89188129. W1OO131.29012
~m
1.00000 w1.00000 21.00000 0-
1.0000067
1.00000:
1.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.00000
Table 6.2 Output listing for the CORCON standard problem (continued)
TINE =
80DYPOINT
;3456789
101112131415161718192021222324
25
262728
16200.00
A81AT IONRATE(n/s)
7.512E-067.512E-067.512E-067.512E-067.512E-067.512E-D67.512E-067.512E-067.512E-067.512E-066. 742E -065.502E-064.048E-062.979E-062. I14E-061.413E-069.544E-077.712E-077.5 D8E-077.517E-072.414E-067.07DE-067.217E-061.933E-06
3.815E-05
0.000E+OOO. 000E+OOO. 000E+OO
CORCON STANDARO● ***
FILM FILHTHICKNESS FLOU
(H)
1. OOOE-101. OOOE-101. OOOE-101. OOOE-101.OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101.OOOE-101.237E-D41.647E-041.81 OE-O41.903E-041 .947E-D41.973E-041.993E-042.136E-042.265E-D42.491E-043.476E-041.619E-039.172E-04
1.363E-03
1.964E-031 .948E-031 .948E-03
(XXCON VERSION 2.26PROBLEM (s1 ightly different fran Modl/Hod2 problem)HEAT TRANSFER RESULTS****
FILM REYNOLOSVELOCITY NUM8ER
(KG/S) (m/s) (-)
0.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1810.000E+OO 0.000E+OO 0.1624.573E-04 1.752E+O0 0.4271.542E-03 4.414E+O0 1.3902.414E-03 6.262E+O0 2.1663.077E-03 7.559E+00 2.7503.547E-03 8.492E+O0 3.1603.858E-03 9.098E+O0 3.4314.074E-03 9.505E+00 3.6205.044E-03 1. W7E+01 4.4816. O1lE-03 1.233E+01 5.3408.004E-03 1.492E+01 7.1031.258E-02 1.641E+01 10.9062.344E-02 6.301E+O0 19.4983.063E-02 1.397E+01 24.497
OX1OE / METAL INTERFACEMETAL / OXIDE INTERFACE
4.194E-01 1.420E+02 369.984OXIDE / COOLANT INTERFACE
4.349E-01 1.033E+02 387.9204.349E-01 1. D42E+02 387.9204.349E-01 1.042E+02 387.920
COOLANT / ATMSPHRE INTERFACE
REGIME HT TRANSCOEF F
(U/M2-K)
SLG.BUB. 1.000E+03SLG. BUB. 1.000E+03SLG. BUB. 1.000E+03SLG. BUB. 1.000E+03SLG.BUB. 1.000E+03SLG. BUB. 1.000E+03SLG. BUB. 1.000E+03SLG. BUB. 1.000E+03SLG. BUB. 1.000E+03SLG. BLIB. 1.000E+03SLG. BUB. 1.000E+03TRN. BUB. 1.537E+03LAM. FLM. 1 198E+03LAH. FLM. 1.090E+03LAM. FLM. 1.037E+03LAN. FLM. 1.013E+03LAM. FLM. 1.000E+03LAM. FLH. 9.901E+02LA1l. FLM. 9.236E+02LAM. FLN. 8.712E+02LAM. FLM. 7.920E+02LAN. FLH. 5.676E+02LAM. FLM. 1.219E+02LAX. FLM. 2.151E+02
TRN. FLH. 4.278E+02
TRN. FLN. 3.039E+02TRN. FLH. 3. D65E+02TRN. FLH. 3.065E+02
lNTERFACETEMPERATURE
(K)
1702.61702.61702.61702.61702.61702.61702.61702.61702.61702.61697.21669.01666.31662.81659.41656.41654.41653.51653.61653.71662.71694.21723.31667.9
1895.2
397.1397.1397.1
CONVECTIVEFLUX
(u/H2)
5. 262E+OL5. 262E+065. 262E+04
5. 262E+045. 262E+045. 262E+045. 262E+045. 262E+045. 262E+045. 262E+ 044. 723E+042.925E+041. 955E+041.398E+049.761E+036.481E+034. 359E+033.511E+033.334E+033.266E+031. 007E+042. 508E+048.932E+033.857E+03
1. 049E+C15
0.000E+OD.0.000E+OO0.000E+OO
IT. NO. = 180
RAOI AT IVEFLUX
(u/M2)
O. OOOE+OO0.000E+OO0.000E+OO0.000E+OOO. OOOE+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO9.285E+038.806E+036.894E+035. 047E+033.419E+032.326E+031.891E+031.925E+032.000E+036.837E+032.445E+04Q.163E+049.686E+03
1.624E+05
0.000E+OO0.000E+OOD.000E+OO
Table 6.2 Output listing forthe CORCONstandard problein (continued)
zc
m
P~5-0z
:CORCON VERS1ON 2.26
wTIME = 16200.00 CORCON STANOARD PROBLEM (slight(y different fran Modl/Mod2 prob(ein)
A● * * ● BULK ~ETAL,GAS REACTION D“RING T, HESTEp ● ~ ● +
00e
OX1OESSPECIES
NAMES
FEOMNOAL203U02ZR02CR203NIOFPM02FPM03FE304MN304SI02U308CAO
aa
REACTANTS(MOLS)
PROOUCTS(MOLS)
O. OOOOE+OOO. OOOOE+OO0.0000E+OOO. 0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OOO. 0000E+OO0.0000E+OO0.0000E+OO
1.4685E-03O. 0000E+OO0.0000E+OO0.0000E+OO4.9949E+OI5.2261E-101.6783E-060.0000E+OO9.6365E-181.6218E-190.0000E+OOO. OOOOE+OO0.0000E+OO0.0000E+OO
METALSSPECIES
NAMES
FECRNIZRFPMMNc(c)ALuS1UAL3UAL2CAx
REACTANTS(MOLS)
7.5115E+051.9232E+051.0219E+056.0012E+043.9344E+030.0000E+OO0.0000E+OO0.0000E+OOO. OOOOE+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO
PRODUCTS(MOLS)
7.5115E+051.9232E+051.0219E+055 .9962E+043.9344E+030.0000E+OOO. OOOOE+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO
NO. OF ITERATIONS = 36
IT. NO. = 180
$
GASESSPECIES
NAMES
C(G)CH4coC02C2H2C2H4C2H6HH2H20NNH3N2o02OHCHOCH20CR03(G)FPM02(G)FPM03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)OALOH(G)AL02(G)
REACTANTS(MOLS)
0.0000E+OO0.0000E+OO0.0000E+OO6.4719E+010.0000E+OOO. OOOOE+OO0.0000E+OOO. OOOOE+OO0.0000E+OO3.5127E+01O. OOOOE+OOO. OOOOE+OO0.0000E+OOO. 0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OOO. 0000E+OOO. 0000E+OOO. 0000E+OOO.0000E+OOO. 0000E+OOO.0000E+OO0.0000E+OO
PRODUCTS(FIOLS)
1.9405E-074.3962E-026.4663E+012.5253E-040.0000E+OO5. 7203E -031.5751E-061.7938E-013.4937E+OI6.8712E-04O. 0000E+OO0.0000E+OOO. 0000E+OO1.6306E-091.3711E-144.5300E-077.0703E-053. 7694E -057.9216E-208.8495E-154.4033E-19O. 0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO
Table 6.2 Output listing for the CORCON standard problem (continued)
CORCON VERS1ON 2.26TIME = 16200.00 CORCON STANDARO PROBLEM (s1ight 1y different f ran Modl/t40d2 probtein) IT. NO. = 180
* ● ● * FILM METAL/GAS REAcTI~N ouR]NG’ TIREsTEp * * ● ●
OXIDESSPECIES
NAMES
FEOMNOAL203U02ZR02CR203NIOFPM02FPM03FE304MN304S102U308CAO
REACTANTS(MOLS)
O. 0000E+OOO. 0000E+OD0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OOO. OOOOE+OO0.0000E+OO0.0000E+OOO. 0000E+OOO. OOOOE+OO0.0000E+OO0.0000E+OO
PR~UCTS(MOLS)
3.2491E-030.0000E+OO0.0000E+OO0.0000E+OO1. 5623E+029.1865E-103.6791E-060.0000E+OO8.9785E-181.2365E-19O. 0000E+OOO. OOOOE+OOO. 0000E+OOO. 0000E+OO
METALSSPECIES
NAMES
FECRN]ZRFPMMNc(c)ALuSIUAL3UAL2CAx
REACTANTS(MOLS)
7.5115E+051.9232E+051.0219E+055.9962E+043.9344E+030.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OOO. OOOOE+OO0.0000E+OO0.0000E+OO0.0000E+OO
PRODUCTS(MOLS)
7.5115E+051.9232E+051.0219E+055 .9806E+043.9344E+030.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO
GASESSPECIES
NAMES
C(G)CH4coC02C2H2C2H4C2H6HH2H20NNti3N2o02OHCHOCH20CR03(G)FPM02(G)FPM03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)OALOH(G)AL02(G)
REACTANTS PRCOUCTS(MOLS) (MOLS)
0.0000E+OO 4.3271E-070.0000E+OO 2.5392E-010.0000E+OO 2. 0196E+022. 0230E+02 5. 7203E-040.0000E+OO0.0000E+OO0.0000E+OOO. 0000E+OO0.0000E+OO1.0981E+02O. 0000E+OOO. OOOOE+OOO. OOOOE+OOO. OOOOE+OO0.0000E+OO0.0000E+OOO. 0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO
O. 0000E+OO4.7191E-021.5312E-054.2796E-011. 0899E+021. 5092E -030.0000E+OOO. 0000E+OOO. OOOOE+OO1.9682E-091.1701E-147.0759E-071.8434E -041.1892E-045.2339E-207.6814E-152.9745E-19O. 0000E+OOO. 0000E+OO0.0000E+OOO. 0000E+OO0.0000E+OOO. 0000E+OO0.0000E+OO
NO. OF ITERATIONS = 36
Table 6.2 Output Ming for tbe CORCON standard problem (continual)
z~
WJg
Mc)
GJ
MASS OF LAYER
XASS OF SPECIESS1021102FEOIwoMooCAoNA20K20FE203AL203IX)2ZR02CR203NIOFPU02FPM13FPOXFPALKMETFPNALOGNFE3MFECRN)ZRFPHH20CLN
CORCON VERS1ON 2.26COR~ STANOARO PR06LEN (s1 ight [y different f ran Hodl/ld2 probletn) IT. NO. = 180
● ***p OoL C OPPOSITION****
OXIOE
1. 2424E+05
1.3383E+036.7653E+O05.9750E+031. 1275E+O01.8040E+011. 1764E+034.4579E-011.3185E+015.4122E+011.352C!JM29.9997E+041.4000E+045.2406E-010.0000E+OO0.0000E+OO0.0000E+OO1.5109E+O31.1119E+014.3336E-010.0000E+OO
METAL OXIOE COOLANT
6.3804E+04 1.3990E+04 9.9014E+03
3.830%+031 .9338E+OI1.6931E-013. 2230E+O05. 1567E+013 .3626E+031.2506E+O03.8901E+011.5471E+023 .8672E+020.0000E+OO6.1388E+031 .4996E+O02.3492E-044.0894E-343.a946E-14O. 0000E+OO0.0000E+OO0.0000E+OO1.6749E-15
4.1958E+041. 0000E+045 .9995E+035.4555E+033.9049E+02
SI021102FEOUNOHGOCAoNA20K20FE203AL203U02ZR02CR203NIOFPM02FPM03FPOXFPALKMETFPilALOGNFE304FECRNIZRFPH
9.9014E+03 H20CLN
Table 6.2 Output listing for the CORCON standard problem (continued)
CORCONVERS1ON 2.26TINE = 16200.00 CORCON STANDARD PR08LEM (s1 ight 1y different f ran Modl/Mcx!2 problan) IT. NO. = 180
● *** LAy ER PROPERTIES****
OX10E METAL OXIDE CIXILANTMAss (KG) 1.2J%24E+05 6.3804E+04 1.3990E+04 9.9014E+03DENSITY (KG/M3 ) 8. 1834E+03 6.8386E+03 3 .3051E+03 9.3454E+02THERMAL EXPANSIVITY
AVERAGE TEMPERATUREINTERFACE TEMPERATUREEOGE TEMPERATURESOL IOUS TEMPERATUREL IQU1OUS TEMPERATURESPECIFIC ENTHALPY
(l/K) 3.5134E-05 2.7389E-05 6.5698E-05 3.6279E-04
(K) 2.1751E+03 2. 1677E+03 2.1408E+03 3.9714E+02(K) 1. 7026E+03 2.1745E+03 2. 1603E+03 1. 7061E+03 3 .9726E+02(K) 1 .6678E+03 2. 1228E+03 1.8937E+03 3.9714E+02(K) 2. 1663E+03 1 .7357E+03 1.5616E+03 2.6821E+02(K) 2 .7594E+03 1.7481E+03 2.3464E+03 2.7821E+02
(J/KG) -4. 1876E+06 1.5372E+06 -9.2276E+06 -1. 5462E+07TOTAL ENTHALPY (j) -5.2026E+11 9.8082E+1O -1.290%+11 - 1.5309E+11SPECIFIC HEAT (J/KG K) 5.6732E+02 7.3921E+02 1.0475E+03 4. 2723E+03
VI SWSITY (KG/M S) 1 .7888E+02 4.961 OE-O3 9.6411E-02 2.2203E-04THERMAL CONOUCTIVI TY (U/M K) 2.8134E+O0 4.9019E+01 4. 1632E+O0 6.0000E-01THERNAL DI FFUSIVI TY (!42/s) 6.0599E-07 9. 6969E - 06 1.2026E-06 1.5028E-07SURFACE TENS ION (N/M) 4.8896E-01 1. 7679E+O0 5.0125E-01 7.3000E-02
z EUISSIVITYw (-) 8.0000E-01 6.0000E-01 8.0000E-01 1.0000E+OO
SUPERFICIAL GAS VEL (M/S) 6.0021E-03 8.2516E-03 8.9130E-03 9.1706E-!J3BUBBLE RADIUS
1.7271E-03(N) 1.7714E-03 1.8421E-03 1 .8657E-03 1.0702E-03
BUBBLE VELOCITY (M/s) 4.6921E-04 4.1037E-O1 3.2474E-01 2.9782E-01VOIO FRACTION (-) 1.5844E-02 1.4711E-02 1.6500E-02 9.8439E-03
BOT CRUST THICKNESS (M) 4.0531E-02 O.0000E+OO O. 0000E+OO O. 0000E+OOHT COEFF, LIQ TO BOT (U/N2 K) 4.8306E+02 7.1721E+04 2 .8838E+04 1. 0386E+03Z-AVE LIQ TEMPERATURE (K) 2. W06E+03 2. 1677E+03 2. 1408E+03 3.9714E+02HT COEFF, LIQ TO TOP (U/N2 K) 3. 0639E+04 7.5815E+04 1. 2956E+03 2.7328E+04TOP CRUST THICKNESS (N) 0.0000E+OO O. 0000E+OO 0.0000E+OO 0.0000E+OO
R-AVE lIQ TEMPERATURE (K) 2.=25E+03 2. 1677E+03 2. 14082+03 3.9714E+02HT COEFF, LIQ TO SID (u/N2 K) 7. O1O2E+O1 1.3018E+04 1. 0882E+03 1. OOOOE-10SIDE CRUST THICKNESS (N) 2.8749E-01 0. 0000E+OO O. 0000E+OO O. OOOOE+OO
OECAY HEAT (u) 1.6045E+07 2.0809E+06 1.4077E-10HEAT TO CONCRETE
0.0000E+OO(u) 1 .8039E+06 4 .0124E+06 8.6398E+05 0.0000E+OO
z HEAT OF REACT ION (u) 0.0000E+OO 3.5914E+06 O.0000E+OO 0.0000E+OOc [NTERLAYER HEAT FLW (u) 1.4246E+07 1 .6236s+07w
1. 5925E+07 -9.5822E+04
mo
sw&waw.
Table 6.2 Output listing for the CORCON standard problem (continued)
ldi
s CORCON VERSION 2.26
?JTINE = 16200.00 CORCON STANDARD PROBLEM (s1 ight i y different f ran Hodl/Nod2 problem)
da ● **** VA NE SAOUTPU T*****coe TEMPERATURE OF METAL (K) 2. 1677E+03
TEMPERATURE OF OXIDE (K) 2.1724E+03AEROSOL - AMBIENT CONDITIONS (G/CC)AER~OL - STANDARO STATE CONOIT 10NS (G/CC)
( 298.15 (K) ANO 1 ATM. )GAS (G-MOLES/S)AEROSOL RATE ( GRAMS/S)AEROSOL DENSITY (G/CM3)PARTICLE SIZE (MICROMETERS)BUBBLE OIAMETER FOR THE METAL PHASE (CM)BUBBLE DIAMETER FOR THE OXIDE PHASE (CM)MECHANI CAL RELEASES FRCU THE AZBEL ANO THE
I
234
E;
789
10
:;131415161718
::21222324
2:;
FECRNIHoRUSNSBTEAGMNCAOAL203NA20K20SI02U02ZR02CS20BAOSROLA203CE02NBOCs 1FEO
1.6011E-054.5203E-05
1. 5768E+011. 7439E+012.1587E+O05.1680E-013.7568E-013.6322E-01
ISH I I ANO KATAOKA CORRELAT IONS ARE CALCULATED.
AEROSOL COMPOSIT ION MELT CWPOSI TION LOSS (MOLES)
302 CR203CARBON IN MELTZIRCONIUM IN MELT
(WEIGHT %)
1.3288E-014.2230E-051.3939E-070.0000E+OO5.1569E-022. 1472E+000.0000E+OOO. 0000E+OO7.1594E-026.9456E-038.4035E+O08.0945E+OI1. 2329E+O01.4891E+O04.96672-023. 2348E+O04.0843E-024.3326E-031.8584E-032.7688E-028.1685E-054.8073E-011.6795E+O08. 7870E -05
(KG)4. 1957E+041.0000E+045. 9995E+031.8118E+021.9193E+02O. 0000E+OO3.5001E-011.6951E+010.0000E+OO0.0000E+OO4.5390E+035. 2200E+021.6966E+O05.2091E+015. 1692E+039. W86E+042.0139E+041. 1987E+018.4491E+016.5023E+014.9684E+021.0293E+033.9345E+O09.3738E-015.9752E+032.0237E+O0O. 0000E+OO5.4555E+03
1.1841E-022.3028E-067.2155E-09O. 0000E+OO2.2160E-038.8038E -020. 0000E+OOO. 0000E+OO6.6791E-033. 5638E-047.0935E-014 .4954E+O01.0735E-012.8854E-022.1088E-O36.0052E-021.3935E-032.1875E-042.9841E-058.4160E-043.9241E-069.6804E-031.2230E-013 .0246E -06
RELEASE FRACT ION
1.1475E-041.5092E -074.6916E-090.0000E+OO5.5855E-012.1298E-010.0000E+OO0.0000E+OO3.1164E-051.3888E-048.5309E-017.0141E-014.2576E-033.2393E-057.2723E-076.8164E-012.8717E-034. 2697E -036.4637S-051.0986E-033.6349E-056.9467E-014.1655E-042.1690E-07
IT. NO. = 180
Table 6.2 Output listing for the CORCON standard problem (continued)
—.
I GAS CO+4POSI T 10N RELEASE RATE(UEIGHT %) (GRAf4S/SECOND )
H20: H23 H4 OH5 06 027 C028 co
4.6914E+O03.0311E+011.6385E-013.4767E-031. 2898E-058.5013E-071.9020E+D06. 2928E+01
1.3327E+019.6350E+O02 .6042E -029.3238E-D33. 2529E-054.289 ftE-061.3199E+012. 7794E+02
Table 6.2 Output listing for the CORCON standard problem (concluded)
ij
ti(36 CORCON VERSION 2.26
%J TINE = 16200.00 CORCtM STANDARD PR08LER (s I ight 1y di f fersnt f ran Modl/ModZ problem)
J1 ● *****POOL SCRUBBING***** ●
00aw INFORMATION SUPPLIED BY VANESA
MEAN PARTICLE SIZE (UM)AEROSOL RATE (GRAMS/S)AEROSOL OENSI TY (G/CM3)POOL OEPTH (CM)PooL TEMPERATURE (K)AMBIENT PRESSURE (ATM)
SIZERANGE
0.000- 0.1310.131- 0.1780.178- 0.2180.218- 0.2560.256- 0.2950.295- 0.3340.334- 0.3750.375- 0.4180.418- 0.4650.465- 0.s170.517- 0.5740.574- 0.6380.638- 0.7120.712- 0.8000.800- 0.9060.906- 1.0421.042- 1.2251.225- 1.5031.503- 2.0342.034.***
CNARACTER 1ST [CSIZE
0.1010.1560.1980.2370.2750.3140.3540.3%0.4410.4910.5450.6050.6740.7540.8500.9701.1261.3471.7142.644
UAssIN RANGE
7.7D98E-017.9560E-018.0501E-018.1029E-O18.1357E-018.1557E-018.1663E-018.1689E-018.1637E-018.1503E-018.1278E-018.0942E-D18.0463E-017.9T92E-017.8844E-017.7472E-017.5389E-017.1949E-016.5287E-014.5833E-01
. ---------------------- . . . . . . . . ..- --------
5.1680E-011. 7439E+012. 1587E+O03.861 OE+O13.9708E+022.2516E+O0
OECONTANINATIONFACTOR
1. 131 OE+OO1.0960E+O01. D831E+O01.0761E+O01 .0718E+O01.D691E+D01. 0677E+O01.0674E+O01.0681E+O01 .D698E+O01. 0728E+II01.0773E+O01 .D837E+O01 .0928E+O01. 1059E+OO1. 1255E+O01. 1566E+D01.2119E+O01 .3356E+CI01 .9024E+W
. . . . . . . ..- ----OVERALL OECONT#MINATItM FACTOR 1.1289MASS CUT 1 .54484E+01
FIT OF OECONTANINATEO AEROSOL TO LOG NORMALNEU NEAN PARTICLE SIZE (WI) 0.488RANGE (W 0.485 - 0.491NEW GEOMETRIC STANOARD OEVIATION 2.183RANGE (IM) 2.208- 2.158
LINEAR WRRELATIW COEFFICIENT 0.999763
IT. NO. = 180
n~~● COOLANT OEPLETED AT TIME = 1.7S200E+04 *
Sample Problems
Table 6.3 Input listing for the BWR sumple problem
BWR ACCIDENT - WATER ADDED AFTER 1 HOUR
s$ user flags
s *ILYR(mixed, mixing on)
$“ *ICHEM (condensed phase them on, coking off)
s“ . *IFILM (slag/film)13 0 2 1 1 0 1 0 0 180 0 0011
1
s$ additional user flags
$ *IFVAN (do VANESA calculation)
$ a *IUSER (include user flexibility input)&o 101
$$ time information
30.0 10800. 21600. 70000.
s$ ray system information
60
sS geometry
0.0
sS concrete
300.0$.
0.0 1.5
information - rt. circular cylinder 3.2 m radiue3.2 5.00 0.1 4.438 3.05 10 6
specifications - abl temp = 1630 K1630. .6 .135
S initial debris composition and temperature (T = 2500 K)
34 2500. 2500.U02 53133.ZR02 10997.FEO 1000.ZR 13690.FE 23387.CR 3700.NI 2055.
s$ core MTU and operating power
140.1 3293. 0
sS cavity atmosphere conditions and composition
4505. 0. 380. 3C02 0.17H2 0.13N2 0.70
sS preeeure in cavity atmosphere vs. time
210800.0 1.5E5 21600.0 2.5E5
203 NUREG/CR-5843
Sample Woblemti
Table 6.3 Input listing for the BWR sample problem (continued)
s$ temperature of aurfacea above the melt
210800.0 500.0 21600.0 1000.0
sS time-dependent mass additionS species added
80U02ZR02FEOFE
CR
NI
ZR
H20CLN
s$ time and flow rate information
222222 2610800. 4.920 21600. 4.92010800. 1.018 21600. 1.01810800. .0926 21600. 0.092610800. 0.926 21600. 0.92610800. .3426 21600. 0.342610800. .1902 21600. 0.190210800. 1.267 21600. 1.26710800. 0. 14400. 0. 14430. 20.00 18030. 20.0018060. 0. 21600. 0.
s$ temperature of added material - oxides, metals, coolant
22210800. 2300. 80000. 2300.10800. 2300. 80000. 2300.10800. 320. 80000. 320.
s$ emissivities vs. time - oxides, metals, surroundingsTIMETIMETIME
1110.0 0.80.0 0.60.0 0.6
s$ mean beam length
3.0
s$ user flexibility input
000000 000000 010010000 011
NUREG/CR-5843 204
Sample Problems
Table 6.3 Input listing for the BWR sample problem (continued)
s$
$$
$$
$$
$$
ss
ss
—
temperature dependent metal phase thermal conductivity multiplier1
0. 0.5
temperature dependent oxide phase viscosity multiplier.L
o. 5.0
mole fraction concrete oxides at which oxide solidus = concrete solidus
0.2
cutoff for inclusion in chemistry solution - ZILCH0.01
VANESA inputuser options
* IDEAL=l, run with ideal chemistry on1111
pool scrubbing parameters20 2.3 1 1 1.0 1.0
205 NuREG/cR-5843
Table 6.4 Output listing for the BWR sample problem
z gcz 3g
3r
L> CARD IMAGES IN INPUT FILE (TAPE5)6
-0
Z1. BUR ACCIDENT - MATER ADDED AFTER 1 HOUR ~
2.
3.
4.
5.
6.
s$ user flagss ●lLYR(mixed, mixing cm)$A ●ICHEN (condensed phase them on, coking off)s’ A ●IFILII (s~ag/film)
130211010 0180 0 0 0 1 1 1sS additional user flagss ●I FVAN (do VANESA calculation)s . ●lUSER (include user flexibility input)&ololsS time information
30.0 10800. 21600. 70000.sS ray system i nf ormat icm
60 0.0 1.5sS geometry information - rt. circular cylinder 3.2 m radius
0.0 3.2 5.00 0.1 4.438s
3.05 10 6
100 S concrete specifications - abl tarp = 1630 K0! 7. 300.0 1630. .6 .135
s
8.9.
10.11.12.13.14.15.
16.
17.18.19.20.
21.
S initial debris conqmsition and temperature (T = 2500 K)34 2500. 2500.
U02 53133.ZR02 1W7.FEO 1000.ZR 13690.FE 23387.CR 3700.N1 2055.sS core HTU and operating fxuer
140.1 3293. 0sS cavity ataxxphere condi t ims
4505. 0. 380.and ccqxxition
3Co2 0.17H2 0.13N2 0.70sS pressure in cavity atmos~ere vs. time
2
Table 6.4 Output Wing for the BWR sample problem (continued)
22.
23.24.
25.26.27.28.29.30.31.32.33.
34.
N 35.0+
%38.39.40.41.42.43.
.44.45.46.47.
48.49.50.51.52.
53.
108OO.O 1. 5E5 21600.0sS teqxwature of surfaces above
lLO.O 500.0 21600.0sS time-dependmt mass tiititiS species added
80
2R02FEOFECRNIZRH20CLNs
2.5E5
the melt
1000.0
S time and ftou rate infortmaticm2222222610800. 4.920 21600. 4.92010800. 1.018 21600. 1.018108OO. .0926 21600. 0. W26108OO. 0.926 21600. 0.926108OO. .3426 21600. 0.3426108OO. .1902 21600. 0.190210800. 1.267 21600. 1.26710800. 14400. 0. 14430. 20.00 18030.18060. ::
20.0021600. 0.
sS teqmrature of added material - oxides, metals, coolant
2 210800? z$oo. 80000. 23W.10800. 2300. 80000. =00.108OO. 320. 80000. 320.
sS emissivities vs. time - oxides, metals, surrotadingsTIIQETINETIME
1 10.: 0.80.00.0 :::
sS mean be- length
3.0s
Table 6.4 Output listing for the BWR sample problem(continued)
z gc 3
Euz
bi
6wLw* 54.w 55.
56.57.
58.59.
60.
61.
w 62.000
63.
s
s
“ss
ss
ss
s
Q
azuser flexibility input
00000000 0000010 g01000001 1
temperature dependent metal phase thermal conductivity rndtipl ier1
0. 0.5
temperature depetxlent oxide phase viscosity rrdt ipl i er1
0. 5.0
mole fraction concrete oxides at uhich oxide0.2
cutoff for inc(usion in chemistry solution -0.01
solidus = concrete sol idus
ZILCH
S VANESA i noutS user opt ikss ● 10EAL=1, run ~ith ideal chemistry cm
1111sS pol scrubbing parameters
20 2.3 1 1 1.0 1.0
Table 6.4 Output listing for the BWR sample problem (continued)
BUR ACCIDENT - WATER ADDED AFTER 1 HOUR
***INPUT***.
● ** FLAGS *** *** CONTROL PARAMETERS ● **
ILYR = 3 lcmL = o IGE134 = 2 ICON = 1 TIMEO = 10800.00 (SEC) DELTI14 = 30.0000 (SEC)ICHEM = 1 I FP =0 ISUR = 1 IABL =0 TIHENO = 21600.00 (SEC)ISPLSH= O IPINC =** [FILM = O lRSTRT = O OPRIN = 0.00 (SEC) TPRIN = 70000.00 (SEC)IHOV = O I PG 1 ISRABL = 1 IAOPAC = 1lTIMR = o IFVAN ~ 1 IVANFP = O IUSER = 1
TIMESTEP CONTROL. DTMIN(I) DTMAX(I) TINDT(I)30.000 30.000 1.OOOE+1O
EDIT CONTROL. DEDIT(l) TEDIT(1)5400.000 1.OOOE+1O
RAY CENTER C~DINATES
RO = o. Zo = 1.50000
CONCRETE CAVITY GEOMETRY
RIGHT CYLINDER
NRAYS - NUNBER OF RAYS = 60
ZT - Z-COORDINATE OF TOP = o.
RAD - CYLINDER RADIUS (H) = 3.20000
HIT - CYLINDER HEIGHT (M) = 5.00000
RADC - CORNER RADIUS (M) = 0.1 ODooo
NBOT - NUNBER OF BOTTOM POINTS = 10
NCORN = NUMBER OF CORNER POINTS = 6
Table 6.4 Output Iisting forthe BWRsample problem (continued)
:g33
~ v
RHOC(KG/IQ)
2 .340000E+03
o0-
● ● ● CONCRETE sPECIFICATIONS * ● ● F~
BASALTIC AGGREGATE CONCRETE
RBR TSOL TLIQ TIC(:;
TU(KG/KG C)
DELH(K) (K) (K) (K) (J/KG) (:;
1.350000E-01 7.360000E-02 1.350000E+03 1.650000E+03 3.000000E+02 1.630000E+03 2.339836E+06 6.0000OOE-01
SPECIES NAME KASS FR. (KG/KG C) MOLECULAR UT.
S102T102MOCAoNA20K20FE203AL203C02H20EVAPH20CHEM
0.54840.01050.06160.08820.01800.05390.06260.08320.01500.03860.0200
60.084379.898840.304456.079461.979094.1960
159.6922101.9613
44.009818.015218.0152
MELT FISSI(M PRCWCT INVENTORYEASEO ON 1.401 OOE+O2 METRIC TON URANIIM CORE OPERATEO AT 3.29300E+03 IW(THERMAL)
MELT CONTAINS 4.68309E+01 NETRIC TONS URANIUN, CORRESPONDING TO 33.63 PERCENT OF CORE
ELEFIENTS, RETAINEO FRACTIONS (**OENOTES USER INPUT, OTHERS FROM WASH 1600), ANO GRAH-ATU4S IN KIELT
MO (0.970) 6.2430E+D2 TC (0.970) 1.5973E+02SB (0.850) 2.1529E+O0 TE (0.850) 5.5801E+01ZR (0.990) 7.7894E+02 CE (0.990) 4.0756E+02NB (0.990) 1.1944E+01 PU (0.990) 7.4516E+02LA (0.990) 1.7523E+02 PR (0.990) 1.5235E+02EU (0.990) 1.7043E+01 RB (0.190) 1.6673E+01I (0.100) 3.3419E+O0
F I SS1 ON PRmUCTS GROUPED
RU (0.970) 3.9591E+02 RH (0.970) 7.2135E+01SR (0.900) 2.0834E+02 BA (0.900) 1.8268E+02NP (0.990) 4.0342E+01 CM (0.990) 1.6858E+O0AM (0.990) 5.3691E+O0 Y (0.990) 1.1704E+02ND (0.990) 4.8929E+02 SM (0.990) 5.7331E+01CS (0.190) 7.5814E+01 BR (0.100) 5.6457E-01
AS 4 PSEIJDO-SPECI ES
1.31OO3E+O3 GRAM-AT~S OF FPH WITH AT~IC FRACTIONSHO 4.76552E-01 TC 1.21930E-01 RU 3.02216E-01 RH 5.50639E-02 SB 1.64339E-03TE 4.25953E-02
3.39030E+03 GRAN-ATCPIS OF FPOX WITH ATOMIC FRACTIONSSR 6.14511E-02 BA 5.38829E-02 ZR 2.297%E-01 CE 1.20214E-01 NP 1.18992E-02cm 4.97248E-04 NB 3.52284E-03 PU 2.19792E-01 M 1 .58367E-03 Y 3.45213E-02LA 5.16855E-02 PR 4 .49356E - 02 NO 1.44321E-01 SM 1.69103E-O2 EU 5 .02713E-03
Table 6.4 Output listing for the BWR sample problem (continued)
9. 24864E+OI GRAX-AT(XIS OF FPALKMET WITH AT(BI1 C FRACTIONSRB 1.8D272E-01 CS 8.19728E-01
3.9U643E+O0 GRAN-ATCMS OF FPHALOGN WITH ATOMIC FRACTIONSBR 1.44524E-01 1 8.55476E-01
INITIAL PCAIER AT START OF CORCON, 1.D8000E+D4 SEC AFTER SCRAM 1S 6.86111E+06 UATTSREPRESENTING 0.62 PERCENT OF OPERATING P(MER OF FRACTION OF CORE IN F4ELT
INITIAL CORE MASSES (KG) OF CONSTITUENTS AND TEMPERATURES
OX1OES SPEXU CON1NP METALS SPEXLI CONINP
FEO 7.1846397E+01 1. 0000000E+03 FE 5.5847000E+01 2. 3387000E+04UD2 2. 700278DE+02 5. 3133000E+04 CR 5. 1995998E+01 3. 7000000E+03ZR02 1.2321880E+02 1. D997000E+04 NIFPOX
5 .8709999E+01 2. 0550000E+031.4748474E+02 5. 0001773E+02 ZR 9.1220001E+01 1. 3690000E+04
FPALKMET 1.2435149s+02 1. 1500827E+01 FP# 9. 9529694E+01 1.30386&E+02FPHALOGN 1 .2011028E+O2 4.6920219E-01
M INITIAL TEMPERATURE (TO) IN DEGREES K = 2. 5000000E+03
INITIAL TEMPERATURE (TM) IN OEGREES K = 2.5000000E+03
INITIAL MASS OF OXIOES = 6.5641984E+04
INITIAL UASS OF METALS = 4. 2962387E+04
● ● ● RWcT]NG ms MIxTmE * ● ●
- ATXOSPHERIC PRESSURE SPECIFIED AS OF TIME e
TIME 1.08DOE+04 2.1600E+04PRESWRE 1.5000E+05 2.5000E+05
PA(U) (N/N2)
4.5D50DOOE+03 1 .5000000s+05
GAS INPUT
SPECIES NAME MOLE FR. (-)
Co2 0.1700H2 0.1300N2 O.m
TA(OEG K)
3.80000DOE+02
HDLECULAR UT.
44.00982.0158
28.0134
,
Table 6.4 Output listing for the BWR sample problan (continued)
; ~
● ☛☛
● ☛☛
MELT INTERNAL CONDITIONS ● **
BOUNDARY CONDIT IONS - SURRWND I NGS ABOVE MELT ● **
*** SURFACE TEMPERATURE VARIAT ION W TH TIME ● **
*** TS(DEG K) INPUT AS TABLES .VS. TIME ● **
TIHE(SEC) TS(DEG K)1. 0800E+04 5.0000E+022.160 DE+04 1.0000E+03
*** SURRC4JNDINGS MATERIAL MELTING OR ABLAT ION DURING INTERACT ION
●** ABLAT 10N OF SURRWND INGS IS COMPUTED
●** MASS FLOU RATES OF METALS AND OXIDES
SPECIES TIHE(SEC)
U02
ZR02
FEO
FE
CR
1. D800E+D42. 1600E+04
1. 0800E+042. 1600E+04
1.D8DOE+042.1600E+04
1. 0800E+D42. 1600E+04
1.0800E+042.1600E+D4
FLON RATE(KG/S)
4.9200E+O04.9200E+O0
1.018DE+O01 .0180E+O0
9. 2600E -029. 2600E -02
9.2600E-019.2600E-01
3.4260E-013.4260E-01
IN PROGRAM ***
INTO POOL SPECI F IEO
***
AS 1NWT ●**
Table 6.4 Output listing for the BWR sample problem (continued)
NJ1.0800E+04 1.9020E-012. 1600E+04 1.9020E-01
ZR1.0800E+04 1. 2670E+O02. 1600E+06 1. 2670E+O0
H20CLN1. 0800E+04 0.0000E+OO1.4400E+04 0.0000E+OO1. 4430E+04 2.0000E+O11. 8030E+04 2.0000E+O11. 8060E+04 O. OOOOE+OO2.1600E+04 0.0000E+OO
●** F. P. COMPOSITION NOT SPECIFIEO. - UILL ASSUME SAME RELATIVE C(MPOS1TION AS INITIAL MELT. ● **
● ☛☛ T(OEG K) INPUT AS TABLES .VS. TIME
TIME(SEC) TMET(OEG K)1. 0800E+06 2.3000E+038.0000E+04 2.3000E+03
TIME(SEC) TOX(OEG K)1. 0800E+04 2.3000E+038.0000E+04 2.3000E+03
TIME(SEC) TCLN(OEG K)1. 0800E+04 3.2000E+028.0000E+04 3. 2000E+02
●** BOUNOARY CONO1TIONS - RADIATIVE HEAT TRANSFER
●** SURFACE
T lHE 0.0000E+OOEO 8.0000E-01
T 1ME O. 0000E+OOEN 6.0000E-01
T I HE O.0000E+OOES 6.0000E-01
● ☛☛
● ☛☛
EHISSIVITIES .VS. TINE OR TEMP. ●**
Table 6.4 Output listing for the BWR sample problem (continued)
z zs 3m ~
(n
**
● ☛☛
AEROSOL OPACITY INCLUDED IN ATMOSPHERE ● **CHARACTERISTIC PATH LENGTH (U) = 3 .0000E+OO
NO HELT/C03LANT SPLASHUIT ***
NO TIME-DEPENDENT UELT RAD lUS USED ●**
●** PLOTS UERE NOT SPECIFIED, IROV = O
-* ~ol T lONAL usER ~ppLIEO ~EL ]NpljTs ●**
m THE USER HAS CHOSEN TO NODl FY SCME CORCON ltIX)ELS AND PARAF4ETERS
Ixm= 1THE USER HAS CHOSEN TO SUPPLY TEMPERATURE-OEPENDENT MULT lPL I ERSFOR THE CALCULATE METAL 141XTURE THERMAL CONDUCTIVITY
NE TEHP(K) HULTIPLIER
0.0000E+OO 5.0000E-01
IVSO = 1THE USER HAS CHOSEN TO SUPPLY TEMPERATURE -DEPENDENT NULT IPL IERSFOR THE CALCULATED OXIDE MIXTURE V] SCOSI TY
TEMP(K) MULTIPLIER
O.0000E+OO 5. DDOOE+OO
lPHO = 1THE USER HAS CHOSEN TO ~1 FY THE OX1OE PHASE OIAGRAN
THE OX1OE SDLIOUS TEMPERATURE EQUALS THE CONCRETE SOL lDUS AT X(CONCRETE) = 2.0000E-01
IZIP = 1THE USER HAS CHOSEN TO SUPPLY THE VALUE FOR ZILCH USEO IN MLTREA
ZILCH = 1.0000E-02
Table 6.4 Output listing for the BWR sample problem (continued)
● ● ● VANEsA IN~T ● ● ●
BUB8LE DIAMETER IS CALCULATEDPARTICLE DIANETER = 1.DO MICROMETERS
PART I CLES/8UBBLE IS CAIWLATEDIDEAL CHEMISTRY IS ASSWED
FECRFEOCR203N1MDRUSNSBTEAGMNCAoAL203S102
ZR02CS20BAoSRo
CE02NBOCSI2A
INITIAL MELTG-MDLES418769.1
71159.313918.6
3500;::624.4627.9
0.02.2
55.80.00.00.00.00.0
1%789.889247.7
44.3182.82D8.4504.1
1975.811.9
3.9150076.7
COMPOSITI(M
Z387.EO3700.0001000.DOO
205::E59.90163.461
0.0000.2627.120O.DDOO. ODDO.0000.000o.mo
53133.0001D997.DDD
12.48128.02421 .59a
164.238340.M9
1.3011.015
13690.ODO
~ WATER POOL DEWNTAMINATI~ =
zINITIAL BUBBLE s12E(~)= l.~
cSIZE SEUOWIS IN DISTRIBLJT1m = 20
~ ALL SCAVENGINGMECHANISMS ARE DPERATINGIMPACTION MS m V(RELMKRW= 1.00
0z EIXTRIC sTMm DEVIATIW OF INPUT SIZE DISTRIWIm= 2.30zh00*w. ● ** END OF IWLJT ● **
Table 6.4 Output listing for the BWR sample problem (continued)
z m
s 5~
uz
CORCON VERSION 2.28TIME = 10800.00 BUR ACCIDENT - WATER AOOED AFTER 1 HOUR IT. NO. = O
● ***GENERAL SUMMARY****
MELT ANO COOLANT LAYERS
NUMBER OF LAYERS, NLYR = 1CONFIGURATION, lLYR = 2NO CWLANT PRESENT, lCCXIL = O
EXTREME CAVITY D1F!ENS1ONS, UITH LOCATIONS
RADIALHAXIMJH CAVITY RADIUS (M) = 3.20000OUTSIDE RADIUS OF CONCRETE (H) = 4.43800REMAINING THICKNESS (M) = 1.23800CORRESPONDING BCQY POINT . 18
APPROXIMATE OVERALL ENERGY BUDGET FOR OEBRIS(SEE MANUAL FOR EXPLANAT 10N ANO CAVEATS)
AXIALOEEPEST POINT IN CAVITY (m) = 5.00000MAXIMUN OEPTH OF CONCRETE (M) = 8.05000REMAINING THICKNESS (M) = 3.05000CORRESPOND 1NG BWY POINT = 1
INTERNAL (DECAY) SIllRCE (u) = 6.848E+06CHE141CAL REACT 10N SCURCE (u) = 0.000E+OO
HEAT LOSS TO CONCRETE (u) = 1 .6B6E+07HEATUP OF ABLAT ION PRODUCTS (U) = 0.000E+OOHEAT LOSS FRCP4 SURFACE (u) = 1. 756E+07
(TO SURROUNDINGS)
CHANGE 1N PU)L ENTHALPY(SUNMAT ION OF M*DH/OT )
(u) = 0.000E+OO
NUNER I CAL CHECKS ON NASS AND ENERGY CONSERVATION
RELATIVE ERROR 1N MASS = O. 0000OE+OO RELATIVE ERROR IN ENTHALPY = 0.0000OE+OO
CHECK ON RECESSION CALCULATION (DO/DS SHOULO BE .LE. 1)
MAXIMJM DD/DS = 0.00000
Table 6.4 Output listing for the BWR sample problem (continued)
CORCON VERSION 2.28TIHE = 10800.00 BUR ACCIDENT - UATER ADDED AFTER 1 WLIR
● ***GAs GENERATION*** ●
GAS EXITING POOL ( INCLUDES FILM AND CCOLANT)
GENERAT ION RATE CUF4ULAT IVE RELEASESPECIESC(G)CH4coC02C2H2C2H4C2H6HH2H20NNH3N2o02OHCHOCH20CR03(G)FPU02(G)FPM03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)Q4LOH(G)AL02(G)
MASS (KG/S)O. OOOOOE+OOO. OOOOOE+OO0.0000OE+OOO. OOOOOE+OOO. OOOOOE+OOO. OOOOOE+OOO. OOOOOE+OOO. OOOOOE+OOO. OOOOOE+OOO. OOOOOE+OO0.0000 OE+OOO. OOOOOE+OO0.0000OE+OOO. OOOOOE+OOO. OOOOOE+OOO. OOOOOE+OO0.0000 OE+OOO. OOOOOE+OO0.0000 OE+OOO. OOOOOE+OO0.0000 OE+OO0.0000 OE+OO0.0000OE+OOO. 0000OE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OOO. OOOOOE+OO
HOLES (1/S)0.0000 OE+OO0.0000OE+OO0.0000OE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OO0.0000OE+OO0.0000OE+OOO. 0000 OE+OOO. OOOOOE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OOO. OOOOOE+OO0.0000 OE+OO0.0000OE+OO0.0000OE+OO0.0000 OE+OOO. ODOOOE+OOO. OOOOOE+OOO. OOOOOE+OOO. OOOOOE+OOO. 0000OE+OOO. 0000OE+OOO. 0000OE+OOO. OOOOOE+OOO. OOOOOE+OOO. 0000OE+OO
MASS (KG)0.0000 OE+OO0.0000 OE+OO0.0000OE+OO0.0000OE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OOO. OOOOOE+OOO. OOOOOE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OO0.0000OE+OO0.0000OE+OO0.0000 OE+OO0.0000 OE+OOO. 0000OE+OOO. OOOOOE+OOO. 0000 OE+OOO. 0000OE+OO0.0000OE+OO0.0000OE+OO0.0000 OE+OOO. 0000 OE+OOO. 0000OE+OO
MOLES (-)O. OOOOOE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OOO. OOOOOE+OOO. 0000OE+OOO. OOOOOE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OO0.0000 OE+OOO. OOOOOE+OOO. 0000 OE+OO0.0000 OE+OOO. OOOOOE+OO0.0000 OE+OO0.0000OE+OO0.0000OE+OOO. 0000 OE+OOO.0000OE+OO0.0000 OE+OOO. OOOOOE+OOO. OOOOOE+OOO. 0000OE+OOO. OOOOOE+OOO. 0000OE+OOO. 0000 OE+OOO. 0000OE+OO
IT. NO. = O
SPECIESC(G)CH4coC02C2H2C2H4C2H6HH2H20NNH3N2o02OHCHOCH20CR03(G)FPM02(G)FPM03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)OALOH(G)AL02(G)
Table 6.4 Output listing for the BWR sample problem (continued)
~ VIw
iiwa TINE = loBoo. 00w
BCOYPOINT
1
:456789
1011121314151617181920
2122232425262728293031323334
:3738
RCOORDINATE
(H)
0.0000000.3444440.6888891.0333331.3777781.7222222.0666672.4111112.7555563.1000003.1000003.1222523.1433893.1623693.1781833.190W73.1974933.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003 .2000m3.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.200000
BUR ACC1OENT - UATER
zCOORDINATE
(HI
5.0000005.0000005.0000005.0000005.0000005.0000005.0000005.0000005.0000005.0000005 .oomoo4.9974934.9900976.9781834 .%23494.9633884.922252.$.900000.$.7833336.6666674.5505314.5500004.4333334.3166674.2000004.0833333.9666673.8500003.7333343.6166673.5000003.3833333.2666673.1500003.0333332.9166672.8000D02.6833332.566667
STREAMLENGTH
(H)
0.0000000.344444o.&88891.0333331.3777781.7222222.0666672.4111112.7555563.1000003.1000003.1223933.1447863.1671793.1895723.2119653.2343573.2567503.3734173.490083MIXTURE /3.6067503.7234173.8400843.9567504.0734174.1900844.3067504.4234174.5400844.6567514.7734174.8900845.0067515.1234185.2400855.3567515.4734185.590085
CDRCON VERS1ON 2.28ADOEO AFTER 1 HOUR● ***GEoHET
BCOYANGLE(DEG)
0.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000
12.85725.71438.57251.42964.28677.14386.78690.00090.000
ATMSPHRE 1NTERFACE90.00090.00090.00090.000w. 00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.000!TF.00090.00090.000
IT. NO. = OR.y~***
RAYANGLE(OEG)
0.0005.621
11.13516.44921.48726.20030.56134.56338.21341.532
0.00041.75642.00842.27742.55042.81343.05543.26444.26445.300
46.37547.69048.64549.84451.08652.37453.70755.08856.51757.99559.52161.09862.72364.39866.12167.89169.70671.565
VOLIJNE
(M3)
0.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.076260.304280.676341.176301.780232.457553.172836.92599
10.67914
14.4323018.1854621.9386225.6917729.4449333.1980936.9512440.7043944.4575548.2107151.9638655.7170159.4701763.2233366.9764870.7296374.4827978.23594
SURFACEAREA(M2)
0.000000.372721.490903.354525.963609.31812
13.4180918.2635123.8543930.1907130.1907130.6284431.0692231.5128331.9588932.4068932.8562533.3063135.6520337.W775
40.3434842.6892045.0349347.3806449.7263752.0720954.4178256.7635359.1092661.454W63.8007066.146-$268.4921570.8378873.1835975.5293177.8750480.22076
VOIOFRACT ION
(-)
0.000000.000000 .Ooooc0.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.00000
1.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.00000
Table 6.4 Output listing for the BWR sample prdlem (continued)
3940414243444546474849505152535455565758
M 59
G 60
3.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.200000
2.4500002.3333332.2166672.1000001.9833331.8666671.7500001.6333331.5166671.4000001.2833331.1666671.0500000.9333330.8166670.7000000.5833330.4666670.3500000.233334o.ll&i670.000000
5.7067525.8234195.9400856.0567526.1734196.2900866.4067536.5234196.6400866.7567536.8734206.9900877.1067537.2234207.3400877.4567537.5734207.6900877.8067547.9234208.0400878.156754
90.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.000
73.46575.40377.37679.38081.41183.46385.53387.61489.70291.79093.87395.94798.005
100.042102.054104.036105.985107.896IW.767111.595113.378115.115
81.9891085.7422589.4954193.2485697.00172
100. 7S487104.50803108.26118112.01434115.76749119.52065123.27380127.02695130.78011134.53326138.28641142.03957145.79272149.54588153.29903157.05219160.80534
82.5664884.9122087.2579389.6036591.9493794.2950996.6408298.98653
101.33226103.67798106.02370108.36942110.71514113.06087115.40659117.75231120.09804122.44376124.78949127.13521129.48093131.82664
1.000001.000001.000001.000001.00000\.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.00000
Table 6.4 Output listing for the BWR sample problem (continutxl)
g
TIME = 10800.00
BODYPOINT
;3456
1!
1:1112131415161718
E
ABLATIONRATE(u/s)
7.389E-057.389E-057. 389E -057. 389E -057.389E-057. 389E-057.389E-057.389E-057. 389E -057. 389E -057.389E-057.565E-058.024E-058.61 OE-O59.173E-059.616E-059.893E-059.981E-059.987E-059. 987E -05
CORCON VERS1ON 2.28BUR ACCIDENT - WATER ADOED AFTER 1 HOUR
● ***HEAT TRANSFER
FILMTHICKNESS
(m)
1. OOOE-101. OOOE-101.000E-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-10
FILMFLOU
(KG/S)
0.000E+OOO. 000E+OO0.000E+OOO. OOOE+OO0.000E+OO0.000E+OOO. 000E+OO0.000E+OOO. OOOE+OOO. 000E+OO0.000E+OO0.000E+OO2.941E-044.664E-031.123E-021.819E-022. 544E-023.283E-027.155E-021.103E-O1
FILMVELOCITY
(m/s)
O. OOOE+OO0.000E+OOO. OOOE+OO0.000E+OOO. 000E+OO0.000E+OOO. OOOE+OO0.000E+OO0.000E+OOO. 000E+OOO. 000E+OOO. 000E+OO0.000E+OOO. 000E+OOO. 000E+OO0.000E+OO0.000E+OOO. 000E+OOO. 000E+OO0.000E+OO
REYNOLDSNUMBER
(-)
0.7480.7480.7480.7480.7480.7480.7480.7480.7480.7480.7480.7660.8223.9469.452
15.25621.28627.45259.82792.212
Ml XTURE / ATMSPHRE 1NTERFACE
IT. NO. = ORESULTS****
REGIME HT TRANSCOEFF
(U/M2-K)
SLG. BUB . 1. 000E+03SLG. BUB . 1. 000E+03SLG. BUB . 1. 000E+03SLG. BUB . 1. 000E+03SLG. BUB . 1. 000E+03SLG. BUB . 1. 000E+03SLG. BUB . 1. OOOE+03SLG .BUB . 1. 000E+03SLG .8UB . 1. 000E+03SLG .BUB . 1. 000E+03SLG .BUB . 1. 000E+03SLG. BUB . 1. 000E+03TRN .BUB. 1. 000E+03SLG . FLM. 1. 000E+03SLG. FLM. 1.000E+03SLG . FLM. 1.000E+03SLG. FLM. 1.000E+03SLG. FLM. 1.000E+03SLG. FLH. 1.000E+03SLG . FLH. 1.000E+03
INTERFACETEMPERATURE
(K)
2018.42018.42018.42018.42018.42018.42018.42018.42018.42018.42018.42027.62051.72082.52112.12135.42150.02154.62154.92154.9
CONVECT IVE RAOI AT lVEFLUX FLUX
(u/M2 ) (u/M2 )
3. 884E+053.884E+053. 884E+053. 884E+053 .884E+053. 884E+053. 884E+053. 884E+053. 884E+053. 884E+053. 884E+053.976E+054.217E+054. 525E+054.821E+055. 054E+055. 200E+055. 246E+055. 249E+055. 249E+05
0.000E+OOO. 000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OO
IQIQ
Table 6.4 Output listing for the BWR sample problem (continued)
TIME ❑ 10800.00
MASS OF LAYER
MASS OF SPECIESFEOU02ZR02FPOXFPALKMETFPHALOGNFECRN]ZRFPM
CORCON VERSION 2.28BUR ACCIOENT - UATER AOOEO AFTER 1 HWR
● ***poo L COMPOSITION*** ●
MIXTURE
1. 0860E+05
1. 0000E+035.3133E+041. 0997E+045. 0002E+021.1501E+014.6920E-012. 3387E+043. 7000E+032.0550E+031.3690E+041. 3039E+02
FEOU02ZR02FPOXFPALKNETFPHALOGNFECRNIZRFPM
IT. NO. = O
Table 6.4 Output listing for the BWR sample problem (continued)
u
zw&m TINE =
CORCONVERS1ON 2.2810800.00 BUN ACC1OENT - WATER ADOEO AFTER 1 HOUR
e ● *** LAy ER Properties****
MIXTUREMAss (KG) 1.0860E+05DENSITY (KG/M3) 7.5340E+03THERMAL EXPANSIVITY (l/K) 2.6364E-05
AVERAGE TEMPERATUREINTERFACE TEMPERATuRE [;;
2 .5000E+032. 0184E+03 2. 1392E+03
EDGE TEMPERATURE (K) 2. 15@E+03SOLIDUS TEMPERATURE (K) 1.7575E+03LIQUIDUS TEMPERATURE (K) 2.8522E+03SPECIFIC ENTHALPY (J/KG) -1.8419E+06TOTAL ENTHALPY (J) -2.0004E+11SPECIFIC HEAT ( J/KG K) 5 .8900E+02
vIscosITY (KG/M S) 4.8300E-01IQ THERMAL CONOUCTIVI TY (lJ/N K) 1.1414E+01
s THERMAL DIFFUSIVITY (w/.$) 2.5722E-06SURFACE TENSION (N/N) 9.7989E-01ENISSIVITY (-) 7.0832E-01
SUPERFICIAL GAS VEL (~~) 5.4636E-02 5 .4636E-0281J8BLE RAOI US 2.6460E-03SU88LE VELOCITY (m/s) 2.8072E-01VOID FRACTION (-) O. 0000E+OO
80T CRUSTHT COEFF,Z-AVE LIQNT COEFF,TOP CRUST
R-AVE LIQNT C(IEFF.
THICKNESSL1O TO 80T (UM] K)
0.0000E+OO8. 0640E+02
TEMPERATURE (K) 2.5000E+03LIQ TO TOP (U/NZ K) 1.5127S+03THICKNESS (m) 0.0000E+OO
TEMPERATURE (K) 2. 5007E+03LIQ TO SID (U/R2 K) 1.5195E+03
IT. NO. = O
SIDE CRtkT THICKNESS (M) 1.2881E-03
DECAY HEAT (u) 6.8481E+06HEAT TO CONCRETE (u) 1.6855E+07HEAT OF REACTION (u) 0.0000E+OOlNTERLAYER HEAT FLW (u) 1.7557E+07
Table 6.4 Output Iistkg for the BWR sample problem (CtNItiIIU~J
CORCON VERSION 2.28TINE = 10800.00 8UR ACCIOENT - UATER AODEO AFTER 1 HOUR
● ***l MT ERLA yERHIx]M6*~ ● *
LCUER MIXTURE LAYER
PHASE HASSES (KG)PHASE OENS1 TIES (KG/M3)LIW1OUS TEMPERATURE (K)SOL IOUS TEMPERATURE (K)PHASE ENTHALPIES (J)MASS ENTRAINEO (KG)MASS OE-ENTRAINEO (KG)
OX10E
6. 5642E+048.4080E+032.4432E+032.8522E+03
-2.6854E+11O. 0000E+OOO. 0000E+OO
MLTREA REWIRED 111 ITERATIONSMLTREA REWIREO 51 ITERATIONS
MNw
*-******m*— —***W***
* LAYER ORIENTATION CNANGE AT TIME = 1.08300E+04 ●
● LAYER NKK BECOMES A NEU MET IAYER ●
—* —-*
HLTREA REQIJIREO 111 1TERAT 10NSHLTREA REQUIREO 51 lTERATICNS
~*● LAYER ORIENTATICM CHANGEAT TIME = 1.0MOOE+04 ●
● LAYERS LOX ANOMET _IllEO TO FORMA NEM HMX LAYER ●
zc*~ MLTREA REWIREO 1% ITERATIONS
6%&00$.
NETAL
4. 2962E+046. 5014E+031.7575E+031. 7675E+036.8492E+1OO.0000E+OOO. OOOOE+OO
IT. NO. = O
Table 6.4 Output listing for the BWR sample problem (continued)
zc
g
wm
..~
C)
sw
~3
***** ***** ********************************************* g
& ● LAYER ORIENTATION CHANGE AT TIME = 1. 11900E+04 ●=
Q ● LAYER I(MX BECONES A NEU LMX LAYER ●.7.
***** ***** *********************************************
MLTREA REWIREO 94 ITERATIONSMLTREA REWIREO 53 ITERAT IONS
***** ***** ********************************************** LAYER ORIEUTAT 10N CHANGE AT TIME = 1. 12200E+OG ●
● LAYER LMX BECC#4ES A NEU LOX LAYER ●
***** *************************************************
Ng
● ******************************************
* LMX LAYER CREATEO AT TIME = 1. 12500E+04 ●
●******************************************
HLTREA REWIREO 116 ITERATIONSMLTREA REWIREO 51 ITERATIONS
***** ***** *********************************************● LAYER ORIENTATION CHANGE AT TIME = 1. 131 OOE+O6 *
● LAYER HOX BECONES A NEW LOX LAYER ****** ***** *********************************************
HLTREA REWIREO 51 ITERATIONS
***** ***** *********************************************● LAYER OR1ENTATION CHANGE AT T lHE = 1. 13400E+04 *
● LAYERS LMX ANO LOX CC@!BINEO TO FORM A NEW LOX LAYER ****** ***** *********************************************
IQIQm
Table 6.4 Output listing for the BWR sample problem (continued)
***** ***** *********************************************● LAYER ORIENTATION CHANGE AT TIME = 1. 13400E+06 ●
* LAYERS LOX ANO MET CCMBI NED TO FORH A NEU HMX LAYER ●
***** ***** *********************************************
MLTREA REQUIRED 94 ITERATIONSMLTREA REQUIRED 51 ITERATIONSINITOS ETA MAY BE T(XI SMALLINITDS ETA MAY BE TOO SHALLINITDS ETA MAY BE TLXJ SMALLlNITDS ETA MAY BE TOO SMALL14LTREA REWIRED 52 ITERATIONSMLTREA REIJUIREO 51 ITERATIONS
Table 6.4 Output listing for the BWR sampleproblem(continued)
3
TIME =CORCON VERSION 2.28
16200.00 SMR ACCIDENT - UATER ADDED AFTER 1 HOUR IT. NO. = 180● ***GENERAL SUiiHARY****
MELT AND COOLANT LAYERS
~ER OF LAYERS, NLYR = 3CONFIGURATION, ILYR = ONO COOLANT PRESENT, ICOOL = O
EXTRENE CAVITY DIMENSIONS, UITH LOCATIONS
RADIALMAXIM CAVITY RADIUS (N) = 3.40992~SIDE RADIUS OF CONCRETE (H) = 4.43800REMAINING THICKNESS (M) = 1.0280sCORRESPONDINGS(XW POINT . 22
APPROXIMATE OVERALL ENERGY ~GET F(M DE8R1S(SEE NANUAL FOR EXPLANATION AND CAVEATS)
INTERNAL (DECAY) SOURCE (u) = 8.780EwCHEMICAL REACTION SUJRCE (U) = 2.674E+Ob
HEAT LOSS TO CONCRETE (u) = 3.107E+O6HEATUP OF A8LATIDN PRODUCTS (U) = -1.212E+06HEAT LOSS FROM SURFACE (u) = 1.344E+07
(TO SURRWNDIUGS)
CHANGEIN POOL ENTHALPY (u) = -1.372E+1O(mT1ox OF ~H/DT)
NIMERICAL CHECKS CU MASS AND ENERGY CUNSERVATIm
RELATIVE ERR~ IN MASS = -2.264982-06
CHECK ON RECESSION CALCULATION (DO/DS SHOULD BE .LE. 1)
MAXIM OD/DS = 0.02083
AXIALDEEPEST POINT IN CAVITY (m) = 5. 063WHA.KIMM DEPTH OF ~CRETE (M) = 8.05000REKAINING THICKNESS (M) = 2.98601CORRESPONDING SODY PoINT = 1
RELATIVE ERROR IN ENTHALPY = -1.07288E-06
Table 6.4 Output Iii for the BWR sampleproblen (continued)
CCRCUNUERSION 2.28TI18E = 16200.00 SW ACCIDENT - UATER ADDED AFTER 1 NOUR
•*~*GAs GENER
GAS EXITING POOL (IIICLUIES FILM AND LXMLANT)
SPECIESC(G)CN4a)Co2C2H2(X4C2N6HHzH20uNN3112002ONCNoCH20CR03(G)FPM02(G)FPtUi3(G)M202(G)M20(G)ALO(G)(MM(G)ALON(G)mON(G)M02(G)
GENERATION RATEMASS (KG/S)2.45Q79E-133.763142-033.43%6E-038. O2764E-10
1.389222-034.%181E-fM9.58165E-077.63946E-033.42554E+O0
MOLES (1/S)2.04045E-112.34572E-011.227922-011.82btN5E-080.0000OE+OO4.95214E-021.643472-049.5 D654E-043.78979E+O01.901472+02
oioooOE+ooo.ooWoE+oo1.2D597E-166.92543E-235.71401E-131 .07627E-W5.515532-W5.502182-291.28187E-226.046%2-282.906WE-151.39218E-077.87894E-131.om-141.51476E-084.21=-141.11161E-21
O. ODOOOE+OOo.ooWOE+m7.53760E-152.16428E-213.35974E-113.70892E-081.83691E-075.50250E-289.83506E-224.13222E-272.07S7SE-141.98989E-lM1.83312E-112.44025E-133.44351E-077.03026E-131.88471E-20
AT ION****
CIMJLATIVE RELEASERASS (KG)
4.61357E-079.1 1339E+O01.30867E+021.752482-020.00D0OE+OO3.04785E+O07.74307E-031.71173E-011.021 DOE+D28.81155E+D3o.0000DE+oo0.0000OE+OO0.00D0OE+OO1.68767E-071.29229E-111.33089E-051.738202-041.55793E-D43.56293E-161.63%32-112.406532-15S.zmm-w1.33456E-024.93128E-W2. Z3683E-081.855S2E-031.335822-071.939182-12
MOLES (-)3.84112E-055 .68D74E+024 .67209E+033.98202E-010.00D0OE+oO1 .08646E+022.57507E-011.69832E+025 .064982+044.8911724050. 0000OE+OO0.0000OE+OOo. OoDOoE+oo1.05483E-05b.03857E-lo7.825402-045.9W01E-035.18856E-033.56314E-151.25799E-101.64452E-143.73991 E-0111.90754E-011.147322-046.221642-074.21815E-022.22681E-063.287832-11
SPECIESC(G)CH4coC02C2H2C2H4C2H6HH2H20NUH3N2o02OHCHOCH20CR03(G)FP19J2(G)FPlt03(G)AL202(G)AL20(G)ALO(G)WIH(G)ALOH(G)MLOH(G)AL02(G) “
IT. NO. = 180
Table 6.4 Output listing for the BWR sample problem (continued)
TINE = 16200.00CORCW VERS1ON 2.28
BNR ACCIDENT - WATER ADDED AFTER 1 NOUR
COO&NATE(H)
0.000ooo0.35071i20.7014831.0522261.4029671.7537092.1044512.4551932.8059343.1000003.1462893.1612093.1764933.1907683.2029733.2122253.2184853.2213353.2294833.3126833.3878693.4099213.3590403.2295803.2215953.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.200000
CO& NATE(H)
5.0639885.0639885.0639885.0639885.0639885.0639885.0639885.0639885.063988s .0639885.0522615.0411345.0268525.0094414.9893524 .%72734.9447206.9226684.8135814.7781774.7290664.6257604.5458984.3427034.3041794.2000004.0833333.9666673.8500003. n33343.6166673.5000003.4192323.3833333.2666673.1500003.0333332.9166672.800000
STREAMLEUGTII
(m)
0.0000000.3507420.7014831.0522261.4029671.7537092.1044512.4551932.8059343.1000003.1477513.1M3633.1872823.2097973.2333023.2572423.2806473.3028823.4122743.5026933.5924983.698131
OXIDE /4.033756MIXTURE /4.1794924.2961594.4128264.5294924.6461594.7628264 .87%93COOLANT /4. W61605.1128265.2294935.3461605.4628275.579494
● ☛☛☛ GEo MET
BmYANGLE(OEG)
0.0000.0000.0000.0000.0000.0000.0000.0000.0000.000
25.46539.88646.85754.68662.W270.87578.%184.18254.39028.10255.551
100.226MIXTURE INTERFACE
112.106COOLANT INTERFACE
95.85590.00090.00090.00090.00090.00090.000
ATWPHRE INTERFACE90.000W.00090.00090.00090.00090.000
RV****
RAYANGLE(DEG)
0.0005.621
11.13516.44921.48726.20030.56134.56338.213
o.mo41.53241.75642.00842.27742.55042.81343.05543.26444.26445.30046.37547.490
48.646
49.84451.08652.37453.70755.08856.51757.995
59.52161.09862.723M .39866.12167.891
VQLIME
(M3)
o.ooOoo0.000000.000000.oOOOO0. OOODO0.000000.000000.000000.0000o0.000000.359350.707021.157581.711982.356973.070643.803134.521398.086709.27686
11.0086914.75801
24.56062
29.1939232.%70736.7002340.4533844.2065447.95%951.71285
55.4660059.2191562.9723166.7254770.6786274.23177
SURPACEAREA(M2)
0.000000.386481.545913.478306.183659.66195
13.9132218.9374424.7345930.1907131.1277431 .4%5531.9130532.3634232.8355733.3180433.7908934.2407436.4576638.3160340.2064542.46235
49.46302
52.4067654.7524857.0982159.4439361.7896564.1353866.48110
68.8268271.1725473.5182675 .863W78. 2W7180.55543
WIDFRACTION
(-)
0.007320.007320.007320. ooz320.007320. oon20.00732o.m7320.007320.00732o.m732o. 00R80.007240.007200.007170.00714o.m7130.007120.007100.006890.006710.00666
0.00710
0.003630.002980.002980.002980.002980.002980.00298
1.000001.000001.000001.000001.000001.00000
IT. W. = 180
Table 6.4 Output li.sting fortbe BWRsample problem (continued)
37383940414243444546476849505152535655565758
E
3.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.200000
2.6833332. 5664%72.4500002.3333332.2166672.1000001.9833331.8666671.7500001.6333331.5166671.4000001.2833331.1666671.0500000.9333330.8166670.7000000.5833330.4666670.3500000.2333340.1166670.000000
5.6%1605.8128275.9294946.0461616.1628276.2794946.3%1616.5128286.6294956.7461616.8628286.9794957.0961627.2128297.32%957.4461627.5628297.67%957.7961627.9128298.0294958.1461628.2628298.3794%
90.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.000
69.70671.56573.46575.40377.37679.38081.61183.46385.53387.61489.70291.79093.87395.94798.005
100.062102.054104.036105.985107.896109.767111.595113.378115.115
77.9849381.7380885.4912489.2643992. W75596.75070
100.50386104.25701108.01017111. ?6332115.51648119.26963123.02279126.77594130.52910734.28226138.03542141.78856145.54172149.29488153.04803156.80118160.55434164.30E0
82.9011585.2468787.5926089.9383292.2840494.6297696.97549W.32121
101.66693104.01265106.35838108.70409111.04982113.39554115.74126118.08698120.43271122. ~3125.12415127.46988129.81560132.16132134.50703136.852~
1.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.00000
w
Table 6.4 Output listing forthe BWRsample problem (continued) )
IT. NO. = 180RESULTS****
16200.00
ABLATl~RATE(m/s)
4.970E-066.970E-064.970E-064.970E-064. 970E -066.970E-D66 .970E-064 .970E-064.970E-D64 .970E - 064.299E-063.456E-062. W4E-D62.4782-061.974E-061.579E-061.305E-061.1872-062.497E-066.163E-062.623E-061.145E-06
7.031E-05
O. 000E+OOO. 000E+OOO.000E+OOO. 000E+OOO. 000E+OOO. 000E+OOO. 000E+OO
CORCONVERS1ON 2.28BUR ACC1OENT - UATER ADOEO AFTER 1 MWR
● ***HEAT TRANSFER
FILU FILM FILM REYNOLDSTHICKNESS FL(XJ VELOCITY NUMBER
(m) (KG/S) (m/s) (-)
1. OOOE-10 0.000E+OO O. OOOE+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0381. OOOE-10 0.000E+OO 0.000E+OO 0.0331. OOW-10 1.398E-04 0.000E+OO 0.1181. OOOE-10 3.619E-04 0.000E+OO 0.3051. OOOE-10 5.6572-04 0.000E+OO 0.4741. OOOE-10 7.395E-04 0.000E+OO 0.6181. OOOE-10 8.813E-04 0.000E+OO 0.7341. OOOE-10 9.940E-04 0.000E+OO 0.8261. OOOE-10 1.087E-03 0.000E+OO 0.9031. OOOE-10 1.764E-03 0.000E+OO 1.4611. OOOE-10 2.790E-03 0.000E+OO 2.2541. OOOE-10 3.821E-03 0.000E+OO 3.0181. OOOE-10 4.487E-03 0.000E+OO 3.521
OX1OE / MIXTURE INTERFAcE1.000E-10 6.284E-02 0.000E+OO 52.079
MIXTURE / COOLANT INTERFACE1. OOOE-10 7.21 OE-O2 0.000E+OO 60.2921. OOOE-10 7.21 OE-O2 0.000E+OO 60.2921. OOOE-10 7.21 OE-O2 0.000E+OO 60.2921. OOOE-10 7.21 OE-O2 0.000E+OO 60.2921. OOOE-10 7.21 OE-O2 0.000E+OO 60.2921. OOOE-10 7.21 OE-O2 0.000E+OO 60.2921. OOOE-10 7.21 OE-O2 0.000E+OO 60.292
COOLANT / ATMSPHRE INTERFACE
REGIHE
SLG. BUB.SLG. BUB.SLG. BUB.SLG. BUB.SLG. BUB.SLG. BUB.SLG. BUB.SLG. BUB.SLG. BUB.SLG.8UB.SLG. BUB.SLG. FIM.SLG. FLM.SLG. FLM.SLG. FLH.SLG. FLM.SLG. FLH.SLG. FLM.SLG. FLM.SLG. FLH.SLG. FLH.SLG. FLM.
SLG. FLH.
SLG. FLH.SLG. FLM.SLG. FLM.SLG. FLH.SLG. FLM.SLG. FLM.SLG. FLM.
NT TRAMSCOEFF
(U/M2-K)
1.000E+031. OOOE+031. OOOE+031.000E+031. 000E+031.000E+031. 000E+031. 000E+031.000E+031. OOOE+031.000E+031.000E+031.000E+031.000E+031.000E+031.000E+031. OOOE+031. OOOE+031. 000E+031. OOOE+031.000E+031.000E+03
2 .532E+03
1. 000E+031. OOOE+031.000E+031. 000E+031. 000E+031. OOOE+031.000E+03
INTERFACETEMPERATURE
(K)
1656.11656.11656.11656.11656.11656.11656.11656.11656.11656.11652.61648.21645.71643.01640.41638.31636.91636.21643.11651.91642.71636.0
1776.0
393.4393.4393.4393.4393.4393.4393.4
CONVECTIVEFLUX
(W2)
2.612E+042.612E+042.612E+042.612E+042.612E+042.612E+042.612E+042.612E+042.612E+042.612E+042 .260E+041 .816E*041.574E+041.302E+041. 038E+048.301E+036. 85 BE+036.2372+031.312E+042.188E+041. 273E+046.017E+03
3.695E+05
0.000E+OO0.000E+OOO. 000E+OOO. 000E+OOO.000E+OOO.000E+OOO. 000E+OO
RAOIATIVEFLUX
(u/M2 )
0.000E+OOO.000E+OOO. 000E+OOO. 000E+OO0.000E+OOO. 000E+OOO. 000E+OOO. 000E+OOO. 000E+OOO. 000E+OOO.000E+OO0.000E+OOO. 000E+OOO. 000E+OOO. 000E+OO0.000E+OO0.000E+OOO. 000E+OOO. 000E+OOO. 000E+OO0.000E+OOO.000E+OO
O. OOOE+OO
O. 000E+OO0.000E+OOO. 000E+OO0.000E+OO0.000E+OOO.000E+OOO. 000E+OO
Table 6.4 Output listing forthe BWRsample problem (continued)
TIME = 16200.00
OXIDESSPECIES REACTANTS
NANES (NOLS)
FEO 1.9766E+01MNOAL203U02ZR02CR203N1OFPX02FPM3FE304MN304SI02U308CAO
0.0000E+OO2.3525E+016.3566E+D27.2761E+021.8154E-103.7869E-062.2580E-361.2690E-163.2003E-18O. 0000E+OO2.5571E+024.8613E-169.7071E+01
CORCON VERSION 2.28BUR ACCIDENT - UATER ADDED AFTER 1 WUR
● ● ● ● WLK HETA1/oxl DE/GAs REACT]oN IN HHx LAyER DURING T[MESTEp ● ● ● ●
PRODUCTS(XOLS)
2.1284E-030.0000E+OO1.0559E+O06. 1182E+021.0718E+032.1527E-111.5396E-06O. 0000E+OO3.7533E-211.1578E-230.0000E+OO2.7372E-023.5876E-219.4947E+OI
METALSSPECIES REACTANTS
NAMES (HOLS)
FECRNIZRFPMMNc(c)ALu.51UAL3UAL2CAx
5.6412E+051.0654E+055. 2389E+045.5457E+041. 9496E+03O. 0000E+OOO. 0000E+OO2. D658E+046. 6506E+021. 1482E+053.6726E-017.0164E+012.3012E+021.8691E+02
PRU)UCTS(MoLS)
5.6414E+051. 0654E+055. 2389E+045.5113E+041.9496E+03O. 0000E+OOO.0000E+OO2 .072 ZE+046.9854E+021. 1508E+052.8939E-016. 0602E+012 .3225E+021.8691E+02
GASESPECIES
NAMES
C(G)CH4coC02C2H2C2H4C2H6H112H20NNH3N2o02onCHOCH20CR03(G)FPM02(G)FPU03(G)AL202(G)AL20(G)ALO(G)OALH(C)A1OH(G)OALOH(G)AL02(G)
[sREACTANTS
(MOLS)
0.0000E+OOO. OOOOE+OOO. OOOOE+OO3.5968E+O00.0000E+OO0.0000E+OO0.0000E+OOO. OOOOE+OOO. OOOOE+OO3.4327w010.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OOO.0000E+OOO. 0000E+OOO. 0000E+OOO. 0000E+OOO. 0000E+OOO. ODOOE+OO0.0000E+OOO. 0000E+OO0.0000E+OOO. 0000E+OO0.0000E+OO0.0000E+OOO.0000E+OO
PROOUCTS(XOLS)
3.6536E-101.3934E+O01. 5769E+O03.0861E-07O. 0000E+OO3.1241E-018. 0338E-041.0871E-023.0907s+012 .3463E-050.0000E+OO0.0000E+OOO. OOOOE+OO1.5328E-135.1498E-205.6%9E-105 .6969E-072.3278E-061.4224E-262.3224E-201.0517E-253.6256E-132.6484E-053.1823E-104.0254E-124.3880E-061.1952E-114.2534E-19
IT. NO. = 180
NO. OF ITERATI~S = 41
Table 6.4 Output listing for tbe BWR sample problem (continued)
‘zm
c 5m
F1 Zc) w
? CORCON VERSIW 2.288
~ TIME = 16200.00 BUR ACCIDENT - UATER ADDED AFTER 1 HOURo-F
UIw*1A
OXIDESSPECIES REACTANTS
NAMES (!401S)
FEOMNOAL203U02ZR02CR203NIOFPU02FPM03FE304HN304S102U3LN3CAO
0 .0000E+OOO.0000E+OOO.0000E+OOO. 0000E+OOO. 0000E+OO0.0000E+OOO. 0000E+OOO. 0000E+OO0.0000E+OOO. 0000E+OOO. 0000E+OOO. 0000E+OO0.0000E+OOo. 0000E+OO
PRODUCTS(MOLS)
* ● ● ● FILM NETAL/GAs REA~Tl~ o~[NG TIMESTEP ● ● + +
3.4646E-050.0000E+OO4.0162E-022.09572+013.4.457E+012.3390E-132.5112E-080.0000E+OO1. Ii156E-233.8678S-26O.0000E+OO6.4176E-042.1627E-233.5951E+O0
METALSSPEC1ES REACTANTS
NAMES (MOLS)
FECRNIZRFPXMNc(c)ALus!UAL3UAL2CAx
5 .6414E+051.0654E+055.2389E+045.5113E+041 .9496-E*O3O. 0000E+OOO. 0000E+OO2.0722E+046.9854E+021. 1508E+052.8939E-016.0602E+012. 3225E+02O. 0000E+OO
NO. OF I TERAT IONS = 45
PRODUCTS(XOLS)
5.6414E+051. 0656E+055.2389E+045.50782+041 .9496E+03O. 0000E+OOO. OOOOE+OO2.0702E+046.6740E+021. 15084E+053.7086E-017.0708E+012. 2865E+020.0000E+OO
GASESSPECIES REACTANTS
NAMES (NOLS)
C(G)CH4coC02C2H2C2H4C2H6HH2H20NNH3N2o02OHCHOCH20CR03(G)FPM02(G)FPno3(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)OALOH(G)AL02(G)
O.0000E+OOO. 0000E+OOO. 0000E+OO1.O1O5E+O1O. 0000E+OOO. 0000E+OOO. 0000E+OOo. 0000E+OO0.0000E+OO9.6442E+01O.0000E+OO0.0000E+OO0.0000E+OOO. OOOOE+OOO. 0000E+OOO. 0000E+OOO. OOOOE+OOO. 0000E+OOO. 0000E+OOO. 00 D0E+OOO.0000E+OOO. 0000E+OOO. 0000E+OOO. 0000E+OOO. 0000E+OOO. 0000E+OO0.0000E+OOo. 00002+00
PRmUCTS(PN)LS)
2.4678E-105. 6438E+O02.1068E+OO2.3861E-070.0000E+OO1. 1732E+O04.1270E-031.7649E-028.2787E+013.4182E-050.0000E+OOO. 0000E+OOO. 0000E+OO7.2847E-141.3430E-204.3823E-105.42992-073.1829E-062.2830E-276.2813E-211.8797E-262.6019E-133.3213E-052.317OE-103.2954E-125.9426E-069.1383E-121.4007E-19
IT. NO. = 180
Table 6.4 Output listing for tbe BWR sample problem (continued)
Nww
TIME = 16200.00
MSS OF LAYER
MASS OF SPECIESSI02T102FEOMGOCAONA20K20FE203AL203
ZR02CR203NIOFPM02FPM03FPOXFPALXMETFPHALOGNFE3D4U308FECRNIZRFPMALus!UAL3UAL2CAH20CLN
CORCON VERSION 2.28BUR ACCIDENT - WATER ADOED AFTER 1 NOUN
O)(IOE
1.2343E+05
1.27490031.6784E+022. 1650E+029.7082E+021 .3m+031.8187E+026. D860E+021 .0006E+032.6908E+027.93365443. 7307E+041.6M6E-071.4285E-031.88102-331. M68E-137.00NE+021.612bE+014.1236E-014.73602-152.6164E-12
•S~~po(jL COMPOSITION****
MIXTURE
4.9660E+04
8.3979E-043.1878E-011.3866E+O01.8680E+O02.7581E+O05.2B67E-011.5946E+O01.9006E+O05.5~-021.5895E+028.3274E+OI1.6502E-125.8346E-08O. 0000E+OO2.7516E-221 .4956E+O03.4400E-021.3637E-031.3425E-241.5169E-213.1539E+045.5501E+033.0815E+03S .0623E+031.9393E+02S. S8S7E+021. S886E+023.2321E+031.18302-012.0646E+019.1644E+O0
COOLANT
2 .6S89E+04
S102T102FEO
CAONA20K20FE203AL203
ZR02CR203N1OFPX02FPM03FPOXFPALKXETFPNALDCXFE304U308FECRN!ZRFPXALu51UAL3UAL2CA
2.6S89E+04 H20CLN
IT. NO. = 180
Table 6.4 Output listing forthe BWRsample problem (continued)
zcv j’mC) F6 ww 3da00aLJ f
IT. NO. = 180CORCONVERSION 2.28
TIME = 16200.00 BIR ACCIDENT - WATER AOOED AFTER 1 WLJR● *** LAy ER PROPERTIES****
OX1OE MIXTUREHASS (KG)
~LANT1. 231i3E+05
DENSITYb.9660E+04 2.6589E+04
(KG/M3) 7.0929E+03 6.02772+03 9.3580E+02THERMAL EXPANSIVITY (l/K) 4 .6053E - 05 2.2891E-05 3.6328E-04
AVERAGE TEMPERATUREINTERFACE TEMPERATURE [{] 1EDGE TEMPERATURE (K)SOLIDUS TEMPERATURE (K)L1OUIDUS TEMPERATURE (K)SPECIFIC ENTHALPY (J/KG)TOTAL ENTHALPY (J)SPECIFIC HEAT (J/KG K)
VISCOSITY (KG/N S)THERNAL CC#DUCTIVITY (lJ/# K)THERNAL OIFFUSIVITY (m2/s)SURFACE TENSION (N/u)EF41SSIVITY (-)
1.87982+03 1.83582+03 3 .9341E+02.6561E+03 1.8544E+03 1.6763E+03 4.0314E+02
1.6360E+03 1. 7760E+03 3.9341E+021. 7838E+03 J .7534E+03 2.6821E+022. 7553E+03 2.7664E+03 2.7821E+02
-5.2045E+06 1.3785E+06 -1 .5478E+07-6.4239E+11 6.8454E+1O -4.1153E+11
6.0514E+02 7.4533E+02 4.2651E+03
7.6446E+02 6.9844E. 03 2.2941E-042.8554E+O0 2.6069E+01 6.0000E-016.6526E-07 5.3574E-06 1.5033E-075.17182-01 1.6444E+O0 7 .3000E-028.0000E-01 6.00862-01 1.0000E+OO
SUPERFICIAL GAS VEL (~~) 2.1406E-03 2.7123E-03 2 .5993E-03 5.7956E-06BUBBLE RAOIUS 1.0211E-02 1.0331E-02 6.1839E-03BUBBLE VELOCITY ()!/s) 3.2471E-03 3.6135E-01 2.7339E-01VO1O FRACTIW (-) 6.%50E-03 5.9156E-03 3.0615E-03
BOT CRUST THICKNESS (H) 1.6761E-02 0.0000E+OO 0.0000E+OOHT CWFF, L19 TO BOT (U/H2 K) 1.7162E+02 1.4%1E+04 7.5858E+02Z-AVE LIQ TEMPERATURE (K) 1. B850E+03 1.8381E+03 3.9341E+02HT COEFF, LIO TO TOP (U/H2 K) 7. W12E+03 4.8941E+03 9.8951E+02TOP CRUST THICKNESS (M) 0.0000E+OO 4.4561E-03 0.0000E+OO
R-AVE LIQ TEMPERATURE (K) 1.8874E+03 1.8358E+03 3.9341E+02HT COEFF, LIQ TO S1O (U/H2 K) 5.6B15E+01 6.1745E+03 1. OOOOE-10SIDE CRUST THICKNESS (m) 7.08B5E-02 O.0000E+OO 0.0000E+OO
DECAY HEAT (W 7.681 OE+O6 1.0987E+06 0.0000E+OOHEAT TO CONCRETE (u) 9.69372+05 2.1375E+06 0.0000E+OOHEAT OF REACTION (u) O. 0000E+OO 2 .6739E+06 O. 0000E+OOINTERLAYER HEAT FLW (u) 8.0071E+06 1.3443E+07 -3.0W3E+05
Table 6.4 Output listing forthe BWRsample problem (continued)
CORCON VERSION 2.28TIME = 16200.00 BUR ACCIOENT - MATER ADOEO AFTER 1 HOUR
● ***l NT ERLA yER#]xlNG** ● *
LOUER MIXTURE LAYER
OXIDE METAL
PHASE MASSES (KG) 2.54172+02 4.9406E+04PHASE DENSITIES (KG/H3) 7.1571E+03 6. 0228E+03L I WIDUS TEMPERATURE (K) 1.9640E+03 1.7534E+03SOL IDUS TEMPERATURE (K) 2.7664E+03 1.7634E+03PHASE ENTIIALPIES (J) -1.3325E+09 6.9787E+1OMASS ENTRAINED (KG) 0.0000E+OO O.0000E+OOMASS DE-ENTRAINEO (KG) 2.5508E+02 0.0000E+OO
Nwm
IT. NO. = 180
IQwm
Table 6.4 Output Ikt.ingfor the BWR sample problem (continued)
E
TINE = 16200.00 BWACCIDENT - UATER● ***
TEMPERATURE OF METAL (K)TEMPERATURE OF OXIDE (K)AEROSOL - AMBIENT CONDITIONS (G/CC)AEROSOL - STANDARD STATE CONDIT IONS (G/CC)
( 29S.15 (K) AND 1 ATH. )GAS (G-mLES/S)AEROSOL RATE (GRAMS/S)AEROSOL DENSITY (G/CM3)PARTICLE SIZE (WICR~ETERS)BUBBLE DIAMETER Fm THE METAL PHASE (CM)BUBBLE DIANETER FOR THE OXIDE PHASE (CM)
CORCW VERS1ON 2.28ADDEO AFTER 1 HOUR● VA NE SA OUTPUT* ● ***
1.8369E+031 .8808E+031.0962E-043.0112E-04
3.9139E+O02.8835E+012. 1826E+O09.8129E-012.07062+002 :0462E+O0
MECHANICAL RELEASES FROM THE AZBEL AND THE ISHII AND KATAOKA C~RELATIONS ARE CALWLATEO.
FECRNIwRUSNSBTEAGMNCAOAL203NA20K20SI02UD2ZR02CS20BAOSROLA203CE02NBOCSIFEOCR203
CARBONIN MELTZIRCONIW IN NELT
AEROSOL COUPOSITIW MELT CCUPOSITION(UEIGHT X) (KG)
3.1511E+04
1.161 OE-O31.79SOE-115.2327E-110.0000E+OO1. ZD69E-047.55082-020.0000E+OOo. 0000E+W6.761 OE-O14.1 OS7E-O21.8041E+012.9598E4015. 1185E+011.0945E-023.%18E-037.2857E-028.27462-021.1093E-O15.9528E-042.53372-022.0713E-073.8499E-023.5513E-026.5855E-09
5.53982+033.0757E+038. W14E+019.5250E+01O.0000E+OO3.851 OE-O18.5732E+O00.0000E+OO0.0000E+OO1.3806E+032.6913E+021.8240E+026.1025E+O21.27WE+037.93392+043. 7360E+041.7913E+013.59172+012. W)4E+OI2.4540E+024.7559E+021.9491E+O08.95182-012.1511E+021.65462-070. 0000E+OO5. 0242E+03
LOSS(F40LES)
1.7107E-O41.6212E-124.47872-120. 0000E+OO8.5~2E-065.1191E-03O.0000E+OOo. 000DE+OO1.0429E-013.48592-032.5181E+O02.71 79E+O07.3693E+O03.50682-042.7814E-042.2365E-034.6681E-039.2608E-031.58D5E-051.2Z$4E-031.6453E-OS1.28192-034.2759E-033.7482E-10
RELEASE FRACT1m
2.2240E-048.3773E-093.37282-080. 0000E+OO2.1320E-021.9793E-01O. 0000E+OOO. 0000E+OO2.3555E-025 .3254E-033.8645E-012.9093E-016.75492-028.301 OE-O53.1543E-065.8427E-021.44372-012.4563E-013.01 D9E-036.8293E-024.2344E-064.1200E-012.3861E-048.4718E-12
IT. No. = 180
Table 6.4 Output listing for the BWR sample problem (continued)
1
noH2Hono02C02co
EM COMPOSITION(WIGHT X)
1.8230E-049.6818E+014.4239E-026.7616E-092.27062-121.8782E-181.4430E-063. 1373E+O0
RELEASE RATE(GRAMS/SECONO)
1.2854E-047.6390E+O01.7453E-03k.487SE-W1.4214E-122.3523E-182.4856E-063. 6395E+O0
Table 6.4 Output listing for the BWR sample problem (continued)
zcw jmn
z
6-
Y CORCONVERS1ON 2.28 3
* TINE = 16200.00 BUR ACCIDENT - WATER AOOEOAFTER 1 HWR~
11. NO. = 180
& ● *****POOL SCRUBBING***** ● $w
INFORMATION SUPPLIED BY VANESA
MEAN PARTICLE SIZE (U?!)AEROSOL RATE (GRAMS/S)AEROSOL OENSITY (G/CM3)POOL DEPTH (CM)POOL TEMPERATURE (K)AMBIENT PRESSURE (ATM)
SIZERANGE
0.000- 0.2490.249- 0.3370.337- 0.4140.414- 0.4870.487- 0.560
N 0.560- 0.6340.634- 0.712
% 0.712- 0.7950.795- 0.8840.884- 0.9810.981- 1.0901.090- 1.2121.212- 1.3531.353- 1.5191.519- 1.7211.721. 1.9781.978- 2.3272.327- 2.8532.853- 3.8623. &j2 .******
CHARACTERISTICSIZE
0.1920.2960.3760.4510.5230.5960.6720.7530.8380.9311.0341.1491.2801.4321.6141.8412.1372.5583.255S.021
MASSIN RANGE
1. 1988E+O01. 2362E+O01.2433E+O01.2407E+O01.2321E+O01.2187E+O01.2007E+O01. 1778E+O01. 1496E+O01.1151E+001. 0734E+001. 0227E+O09.6117s-018.8595E-017.9341E-016.7877E-015.3627s-013.6109E-O11.6050E-018.6443E-03
. ------- . . ------ -------- . . . . . . . . . . . . . . . ..-
9.8129E-012.8835E+012. 1824E+O08.6848s+013 .9336E+022.0500E+O0
OECONTAHINATIONFACTOR
1 .2027E+O01. 1663E+O01. 1596E+O01.1621E+O01. 1702E+O01. 1830E+O01.2008E+O01.2241E+O01.2542E+O01 .Z929E+O01.3432E+O01 .4097E+O01.5000E+O01.6274E+O01 .8172E+O02.1241E+O02.68J35E+O03.9928E+O08.9828E+O01 .6679E+02
. . . . . . . . . . . . --OVERALL DECONTAMINATION FACTORMASS WT
FIT OF OECONTAMINATEO AEROSOL TONEU HEAN PARTICLE SIZE (UM)RANGE (W)NEU GEOMETRIC STANOARD OEVIATIONRANGE (U)!)
LINEAR CORRELATION COEFFICIENT
1.55911.8495E+01
LOG NCWIAL0.726
0.707- 0.7451.829
1.945 - 1.719
0.990469
MLTREA REWIREDMLTREA REWIREDMLTREA REOUIREDMLTREA REWIREDMLTREA REWIREDMLTREA REWIREDHLTREA REWIREDHLTREA REWIREDHLTREA REOUIREDHLTREA REWIREDMLTREA REWIREDMLTREA REWIREDHLTREA REWIRED
53 ITERATIONS53 ITERATIONS55 ITERATIONS61 ITERATIONS53 ITERATIONS53 ITERATIONS53 ITERATIONS53 ITERATIONS53 ITERATIONS51 ITERATIONS51 ITERATIWS51 ITERATIWS51 ITERATIONS
Table 6.4 Output listing for the BWR sample problem (continued)
Table 6.4 Output listing for tbe BWR sample problem (continued)
zc
w$
% ‘a
0z
s~ CORCONVERSION 2.28 $TIME = 21600.00 EUR ACCIDENT
z- WATER ADDED AFTER 1 HCUR
****GENERALz
A SUMMARY****w ;
IT. x0. = 360
MELT AND COOLANTLAYERS
NIMBER OF LAYERS, NLYR = 3CONFIGURATION, ILYR = ONO COOLANT PRESENT, ICOOL = O
EXTREME CAVITY DIMENSICMS, UITH LOCATIONS
RAOlALMAXI~ CAVITY RADIUS (II) = 3.43926OUTSIDE RAOI US OF CONCRETE (N) = 4.6384)0REMAINING THICKNESS (m) = 0.99874CORRES~DING 800Y POINT = 24
AXIALDEEPEST POINT IN CAVITY (M) =“ 5.08486MAXIM OEPTH OF CLMCRETE (M) = 8. 05DO0REMAINING THICKNESS (H) = 2.96514CORRESPWOING 800Y POINT = 1
APPROXIMATE OVERALL ENERGY 8U)GET FOR DEBRIS
~(SEE MANUAL FOR EXPLANATI~ AND CAVEATS)
INTERNAL (DECAY) SOURCE (U) = 1. 103E+O7CHEMICAL REACTION SOURCE (U) = 3.580E+06
HEAT LOSS TO CONCRETE (u) = 3.49%+06HEATUP OF ABLATION PRODUCTS (U) = - 1.687E+06HEAT LOSS FROM SURFACE (u) = 1.058E+07
(TO SURR(lJNDINGS)
CHANGE IN POOL ENTHALPY (u) = -2.164E+1O(mTION OF WOH/DT)
N~ER I CAL CHECKS ON XASS ANO ENERGY CONSERVATION
RELATIVE ERROR IN MASS =
CHECK W RECESS1(M CALCULATION
XAXIXUM DD/OS = 0.00402
-4.05312E-D6 RELATIVE ERR(M IN ENTHALPY = -1.78814E-07
(DD/DS SHOULD BE . LE. 1)
Table 6.4 Output listing for the BWR sample problem (continued)
TIME = 21600.00 BUR ACCIDENT - HATER● **
GAS EXITING POOL (INCLUDES FILM AND COOLANT)
SPECIESc(G)CH4coC02C2H2C2WC2H6HH2H20NNH3N2o02OHCHOCH20CR03(G)FPM02(G)FPM03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)OALOH(G)AL02(G)
GENERAT ION RATEMASS (KG/S)9.69796E-145.24064E-031.85434E -033.28865E-100.0000OE+OO1.61999E-038.171972-M7.31174E-078.23833E-035.25126E+O0O.0000OE+OOo. 0000OE+OOo. 0000OE+OO4.28101E-171.~147E-232.96114E-135.53478E-103.79128E-091.13606E-293.54648E-231.32&34E-281.55346E- 151. OO21OE-O73.88366E-136.32648E-151.156272-082.38082E-143.51935E-22
UOLES (1/S)7.90771E-123.26670E-016.62017E-027.47253E-09O. 0000 OE+OO5.77475E-022.71770E-D47.25443E-D44. G8688E+O02.9149DE+02O.0000OE+OOO. 0000OE+OOO. 0000OE+OO2.67573E-155.47356E-221.7411 OE-111 .90734E-081.26266E-071.13612E-282.72101E-229.05205E-281.10962E-141.43234E -069.03576E-121.43820E- 132.62855E-073.96881E-135.966992-21
CORCONVERS1ON 2.28AOOEO AFTER 1 HOUR● GAS GENERATION****
CUNLILATIVE RELEASEMASS (KG)
4.61905E-073.20791E+011.41OOOE+O21.75267E-020.0000OE+OO1.04995E+014.20700E-021.74762E-011.4001 1E+023.05659E+04O.0000 OE+OOO. 0000OE+OOO. 0000OE+OO1.687672-071.29229E-111.33104E-O51. 76750E-041.74482E-043.56293E-161.63%3E-112.406532-155. 24340E - 091.38175E-024.933272-062. 73988E-081.90972E-031.336972-071.93918E-12
MOLES (-)3.845682-051.99962E+035 .03383E+033.98245E-010.0000OE+OO3.74275E+021.3991OE+OO1.%3392E+026.945682+041.696672+060.0000OE+OOO.0000OE+OOO.000DDE+OO1.05483E-054. O3857E-107.826282-046.090982-035.8I101E-O33.56314E-151.257WE-101.64452E-143.74528E-081 .97499E-011.14778E-046. 22858E-074.341372-022.22872E-063.28783E-11
IT. NO. = 360
SPECIESC(G)CH6co(x32C2H2C2H4C2H6HH2H20NNH3N2o02OHCHOCH20CR03(G)FPM02(G)FPN03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)OALOH(G)AL02(G)
Table 6.4 Output listing for the BWR sample problem (continued)
TIME = 21600.00 BUR ACC1OENT - UATERCORCONVERSION 2.28ADDED AFTER 1 HCUR
BODYPOINT
;365678
1:111213141516
;:19
:!222324
25262728
::3132
;:3536
RCOOROI NATE
(u)
0.0000000.3527960.7055911.0583871.4111821.7639782.1167742.4695692.8223653.1000003.1589843.1726563.1874663.2012793.2132233.2224983.2291423.2324143.2421943.3268013.3989033.4213393.4241393.4392603.4367933.2106263.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.200000
zCOORDINATE
(m)
5.08485$5.08485
5.0848575.0848575.0848575.0848575.0848575.0848575.0848575.0848575.0665965.0539595.0390345.0210015.0005214.9783624.9561284.9344424.8266244.7921494.7395854.6362244.5139534.4018764.3985924.0974804.0833333.9666673.8500003.7333343.6166673.5000003.3833333.26&673.1500003.0333332.9166672.8000002.694737
STREAMLENGTH
(M)
0.0000000.3527960.7055911.0583871.6111821.7639782.1167742.4695692.8223653.1000003.7617463.1803633.2013903.2241053.2478133.2718363.2950413.3169723.4252323.5165943.6058223.7115913.8338943.946985
OXIOE /MIXTURE /4.3453764.4620434.5787104.6953766.8120434.9287105.0453775.1620445.2787105.3953775.5120445.628711COOLANT /
80DYANGLE(OEG)
0.0000.0000.0000.0000.0000.0000.0000.0000.0000.000
29.97343.98348.88656.14963.51870.32677.39283.11853.49329.13156.92383.22185.502
104.613UIXTURE INTERFACECOOLANT INTERFACE
108.45590.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.000
ATMSPHRE INTERFACE
RAYANGLE(DEG)
0.0005.621
11.13516.44921.48726.20030.56134.56338.213
0.00041.53241.75642.00842.27742.55042.81343.05543.26444.26445.30046.37547.49048.64649.844
51.08652.37453.70755.08856.51757.99559.52161.09862.72364.39866.12167.891
VOLUNE
(M3)
0.000000.000000.000000.000000.000000.000000.000000.000000.000000.000000.561870.959741.433922.012012.673833.394684.121534.832648.382479.55094
11.4184715.1946319.6947223.84123
34.8740238.6271842.3803346.1334849.8866453.6398057.3929561.1461064 .8W2668.6526272.4055776.15872
SUR FACEAREA(M2)
0.000000.391021.564073.519166.256289.77543
14.0766319.1598625.0251230.1907131.4048331.7751532.1952832.6511933.1289633.6146534.084W34.5301836.7322538.6176940.5030342.7692745. 3W4847.83797
56.1475458.4932660.8389863.1847065.5304367.8761570.2218772.5673974.9133177.2590479.6047681.95048
IT. NO. = 360
VOIOFRACTION
(-)
0.006400.006400.006400.006400.00640O.ooao0.006400.006400.006400.006400.006400.006360.006330.006300.00627D.006250.006230.006230.006210.006020.005870.005830.005820.00579
0.006300.002600.002600.002600.002600.002600.002600.002600.002600.002600.002600.00260
Table 6.4 Output listing fortbe BWRsample problem (continued)
3738394041424344454647484950
;;
z;55
;!5B5960
3.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003.2000003,2000003.2000003.2000003.2000003.2000003.2000003.200000
0
2.6833332.5666672.4500002.3333332.2166672.1000001.9833331.8666671.7500001.6333331.5166671.4000001.2833331.1666671.0500000.9333330.8166670.7000000. 5B3333o.&$66670.3500000.2333340.1166670.000000
5.7453785.8620445.9787116.0953786.2120456.3287126.4453786.5620456.67B7126.7953796.9120457.0287127.1453797.2620467.3787137.4953797.6120467.7287137.8453797.9620468.0787128.1953798.3120L68.628713
90.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.00090.000w .00090.00090.000
69.70671.56573.46575.40377.37679.38081.41183.46385.53387.61489.70291.79093.87395.94798.005
100.042102.054104.036105.985107.896109.767111.5%113.378115.115
79.9118883. f%50387.4181991.1713494.9245098.67765
102.43081106.18396109.93712113.69027117.44343121.19658124.94974128.70290132.45605136.2W21139.96237143.71552147.46867151.22183154.974W158.72813162.48129166.23445
84.2962086.6419288.9876591.3333793.6790996.0248198.37054
100.71626103.06198105.40770107.7s343110.09914112.44487114.79059117.13631119.48203121.82776124.17348126.51920128.86493131.21065133.55637135.90208138.24780
1.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.000001.00000
z
TIME =
BOOYPOINT
2324
252627282930313233343536
21600.00
ABLATIONRATE(N/s)
3.735E-063. ZZ5E-063.735E-063.735E-063.735E-063.735E-063.735E-063. Z55E-063.735E-063.735E-063.838E -063.937E-063.973E-066.026E-064.075E-064.113E-06Ii.143E-064.158E-066.007E-063.833E-064.032E-064.158E-064.161E-064.164E-06
0.000E+OOO.000E+OOO.000E+OOO.000E+OO0.000E+OO0.000E+OOO.000E+OO0.000E+OOo. 000E+OOO.000E+OOO.000E+OOb.000E+OO
CORCLM VERSION 2.28WA ACCIDENT - UATER AOOEOAFTER 1 HCUR
****HEAT TRANSFER
FILMTHICKNESS
(m)
1. OOOE-101. OOOE-101. OOOE-101. OOOE-101.000E-101. OOOE-101. OOOE-101. OOOE-101.000E-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-10
1. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-101. OOOE-10
FILMFLW
(KG/S)
0.000E+OOO. 000E+OOO. 000E+OOO. 000E+OOO. 000E+OOO. OOOE+OO0.000E+OOO. 000E+OOO. OOOE+OOO. OOOE+OO7.797E-061.930E-044.6782-047.693E-061.089E-031.618E-031 .739E-032.044E-033.531E-036.752E-035 .978E-037.512E-039.321E-031.1 OOE-O2
FILMVELOCITY
(N/S)
0.000E+OO0.000E+OO0.000E+OOO. 000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OOO. 000E+OO0.000E+OO0.000E+OOO. OOOE+OOO. OOOE+OOO. 000E+OOO. OOOE+OOO. 000E+OOO. OOOE+OO0.000E+OO0.000E+OO0.000E+OOO. 000E+OO0.000E+OO0.000E+OO0.000E+OO
REYNOLOSNIB4BER
(“)
0.0280.0280.0280.0280.0280.0280.0280.0280.0280.0280.0310.1630.3930.6430.9071.1771.4411.6922.9143.8224.7065.8757.2848.557
OXIOE / MIXTURE INTERFACEMIXTURE / COOLANT INTERFACE
9.061E-02 0.000E+OO 75.7669.061E-02 0.000E+OO 75.7669.061E-02 0.000E+OO 75.7669.061E-02 0.000E+OO 75.7669.061E-02 0.000E+OO 7s.7669.061E-02 0.000E+OO 75.7669.061E-02 0.000E+OO 7s.7669.061E-02 0.000E+OO 75.7669.061E-02 0.000E+OO 75.7669.061E-02 0.000E+OO 75.7669.061E-02 0.000E+OO 75.7669.061E-02 0.000E+OO 75.766
C~LANT / ATMSPHRE INTERFACE
IT. NO. = 360RESULTS****
REGIME HT TRANSCOEFF
(U/N2-K)
SLG.8UB. 1.000E+03SLG. BU8. 1.000E+03SLG. BUB. 1.000E+03SLG. BUB. 1.000E+03SLG.BUB. 1.000E+03SLG.8UB. 1.000E+03SLG. BUB. 1.000E+03SLG. BUB. 1.000E+03SLG.BUB. 1.000E+03SLG. BUB. 1.000E+03TRN. BUB. 1.000E+03SLG. FLM. 1.000E+03SIG. FLM. 1.000E+03SLG. FLM. 1.000E+03SLG. FLM. 1.000E+03SLG. FLM. 1.000E+03SLG. FLH. 1.000E+03SLG. FLM. 1.000E+03SLG. FLM. 1.000E+03SLG. FLH. 1.000E+03SLG. FLM. 1.000E+03SLG. FLH. 1.000E+03SLG. FLM. 1.000E+03SLG. FLH. 1.000E+03
SLG. FLH. 1.000E+03SLG. FLM. 1.000E+03SLG. FLM. 1.000E+03SLG. FLM. 1.0dOE+03SLG. FLM. 1.000E+03SLG. FLH. 1.000E+03SLG. FLH. 1.000E+03SLG. FLM. 1.000E+03SLG. FLM. 1.000E+03SLG. FLH. 1.000E+03SLG. FLM. 1.000E+03SLG. FLM. 1.000E+03
INTERFACETEMPERATURE
(K)
1649.61649.61649.61649.61649.61649.61649.61649.61649.61649.61650.21650.71650.91651.21651.41651.61651.81651.91651.11650.11651.21651.91651.91651.9
400.6400.6400.6400.6400.6400.6400.6400.6400.6400.6400.6400.6
cNVECTIVEFLUX
(u/M2)
1. 963E+041.%3E+041. 963E+041.%3E+041. %3E+041.963E+041.%3E+041.963E+041.%3E+041.%3E+042.017E+042.069E+042. 088E+042. 116E+042.142E+042.162E+042.177E+042.185E+042.106E+O42.015E+042.119E+042. 185E+042.187E+042. 188E+04
O. 000E+OOO.000E+OO0.000E+OOO.OOOE+OOO.000E+OOO.000E+OO0.000E+OOO.000E+OOO.000E+OO0.000E+OOO.OOOE+OOO.000E+OO
RAOIATIVEFLUX
(WH2)
O. 000E+OOO. 000E+OOO. 000E+OO0.000E+OO0.000E+OO0.000E+OO0.000E+OOO. OOOE+OO0.000E+OOO. OOOE+OO0.000E400O. OOOE+OOO. 000E+OOO. OOOE+OO0.000E+OO0.000E+OOo. OOOE+OO0.000E+OOO. OOOE+OO0.000E+OOO. 000E+OO0.000E+WO. 000E+OOO.000E+OO
O. 000E+OO0.000E+OOO. 000E+OOO. 000E+OO0.000E+OOO. OOOE+OOO.000E+OOo. 000s+00O.000E+OOO. 000E+OOO.000E+OOO.000E+OO
TIME = 21600.00
OXIOESSPECIES REACTANTS
NAMES (MOLS)
FEO 3.0591E+01UNO O.0000E+OOAL203 2.9313E+01U02 1.8896E+03ZR02 2.3107E+O3cR203 3.18172-11M1O 2.5855E-06FP!I02 O.0000E+OOFPM03 3.2519E-21FE304 7.95%E-24IIN304 O.0000E+OOS102 Z.9571E+02U308 4.5309E-21CAo 2 .2009E+02
CORCONVERS1ON 2.28BNR ACCIOENT - WATER AOOEO AFTER 1 HOUR IT. NO. = 360
● ● * ● ~LK HETAL/oxloE/~s REAcT1~ ]N H~ LAYER DuRING TIHEsTEP ● ● ● ●
PRODUCTS(MOLS)
4.1609s-03O. 0000E+OO3.6904E+O01.8614E+032. 7056E+034.1287E-113.3371E-CM0.0000E+OO4.2405E-211.0386E-23o. OWOE+OO7.1775E-025.88392-212.1604E+02
METALSSPECIES REACTANTS
NAMES (MOLS)
FE 6.7418E+05CR 1.4212E+05NI 6. 9884E+04ZR 6. 4534E+04FPN 2.6041E+03MN O. 0000E+OOc(c) O. 0000E+OOAL 2.8315E+04u 8.9135E+02SI 1. 5961E+05UAL3 7.2474E-01UAL2 1.2188E+02CA 2. 19762+02x 4.4415E+02
PRODUCTS(MOLS)
NO. OF ITERATIONS = 43
6.7421E+051.4212s+056.9884E+046.4139E+042.6041E+03O. 0000E+OOo. 0000E+OO2.8396E+049.3450E+021.5971E+055.8642E-011.071 1E+022.2381E+024.4415E+02
GASESSPECIES REACTANTS PRODUCTS
NAMES (HOLS) (MOLS)
C(G)CH4coC02C2H2C2H4C2H6HH2H20NNH3N2o02OHCHOCH20CR03(G)FPM02(G)FPH03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)DALOH(G)AL02(G)
O. 0000E+OO0.0000E+OO0.0000E+OO2.7011E+O0O. 0000E+OOO. OOOOE+OOO.00D0E+OOO. 0000E+OOO. 0000E+OO2.577%+01O.0000E+OOO.0000E+OOO. OOOOE+OO0.0000E+OO0.0000E+OO0.0000E+OOO. OOOOE+OOO. 0000E+OOO. OOOOE+OO0.0000E+OO0.0000E+OOO.0000E+OOO. 0000E+OOO. OOOOE+OO0.0000E+OOO.0000E+OOO.0000E+OOO.0000E+OO
1. O986E-101. 45 Z3E+006.3387E-019.7050E-08O.0000E+OO3.0384E-011.1306s-035.5995E-032.2250E+011. 2858E-05O. 0000E+OOO. 0000E+OOO. ODOOE+OO4.08562-141.04%E-202.1046E-102.2208s-071.1931E-062.4953E-275.15492-211.9350E-261.3909E-131.3048E-051.1243E-101.6815E-122.28262-064.8124E-121.0560E-19
Table 6.4 Output listing for tbe BWR sample problem (continued)
~
TIME = 21600.00
— —
OXIDESSPECIES REACTANTS
NAMES (MOLS)
FEOHNOAL203U02ZR02cR203NIOFPM02FPM03FE304
iii
S102U308CAO
O. OOOOE+OOO. 0000E+OOO. 0000E+OOO. 0000E+OOO. 0000E+OO0.0000E+OOO. ODOOE+OO0.0000E+OOO. 0000E+OOO. OOOOE+OOO. 0000E+OOO. 0000E+OOO.0000E+OOO. 0000E+OO
BUR ACCIDENT - UATER● *** FILH
-.
PROOUCTS(NOLS)
3.3529E-05O. 0000E+OO6.4360E-022.9316E+014.0574E+012.3488E-132.7279E-08O.0000E+OO9..4O48E-241.9863E-260.0000E+OO8.1247E-041.9448E-233.7372E+O0
CORCON VERSION 2.28ADOED AFTER 1 HOURHETAL/GAS REACTION DURING TIHESTEP ● ● ● *
METALSSPECIES REACTANTS
NAMES (MOLS)
FE 6.7421E+05CR 1.4212E+05MI 6.9884E+04ZR 6.4139E+04FPN 2.6041E+03MN 0.0000E+OOc(c) 0.0000E+OOAL 2 .8396E+04u 9. 3450E+02SI 1.5971E+05UAL3 5.8642E-01UAL2 1. 0711E+02CA 2.2381 E+02x O. 0000E+OO
PRCWCTS(!40LS)
NO. OF ITERATIONS = 39
6.7421E+051.4212E+056.9884E+046.40982+042.6041E+030.0000E+OO0.0000E+OO2. 8366E+D48. 9029E+021.5971E+057.2514E-011 .2188E+022. 2007E+02O. OOOOE+OO
GASESSPECIES REACTANTS
NAMES (MOLS)
C(G)CH4coC02C2H2C2H4C2H6HH2H20NNH3N2o02OHCHOCH20CR03(G)FPN02(G)FPM03(G)AL202(G)AL20(G)ALO(G)OALH(G)ALOH(G)OALOH(G)AL02(G)
0.0000E+OO0.0000E+OO0.0000E+OO1. 2566E+010.0000E+OO0.0000E+OO0.0000E+OOO. OOOOE+OOO. OOOOE+OO1. 1993E+02O. OOOOE+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OOO. OOOOE+OO0.0000E+OO0.0000E+OO0.0000E+OO0.0000E+OOO. OOOOE+OOO. OOOOE+OO0.0000E+OO0.0000E+OO0.0000E+OO
PRODUCTS(HOLS)
1.2737E-108.3428E+O01.3522E+O01.2713E-070.0000E+OO1.4286E+O07.0225E-031.6164E-021.0036E+023.3704E-050.0000E+OO0.0000E+OO0.0000E+OO3.9416E-145.9263E-213.1187E-103.5013E-072. 5948E-069.1305E-283.0081E-217.8059E-271.9380E-132. W23E-051.5864E-102.6331E-125.6030E-067.0940E-127.3414E-20
IT. NO. = 360
Table 6.4 Output listing for the BWR sample problem (continued)
TIME = 21600.00
MASS OF LAYER
MASS OF SPECIESSI02T102FEOmmCAoNA20K20FE203AL203U02ZR02CR203NIOFPM02FPN03FPoXFPALKMETFPHALOONFE304U308
:N]ZRFMALuS1UAL3UAL2CAH20CLN
CORCON VERSION 2.28BUR ACCIOENT - UATER ADDED AFTER 1 HWR IT. NO. = 360
OXIOE
1 .6648s+05
2. 2839E+032.3866E+026.2649E+021.3861E+031.9731E+032.6081E+028.8027S+021.4229E+034 .4084E+021 .05472+055.07260041.519ZE-071.4247E-031 .865@ -331.l~E-139.4722E+022.1681E+016.1044E-O14.69772-152.5952E-12
● ***POOL COMPOSITION****
MIXTURE
6.1700E+04
3.4521E-031. 1734E+O02.1 W4E+O06.8839E+O09.7569E+O01.W72E+O05. W39E+O06. W56E+O03.03082-015.21 OOE+O22. 9205E+024. W59E-121.9898E-070.0000E+OO4.9234E-224.8849E+O01.1234E-014.5782E-031.9074E-243.9353E-213.7686E+047.4002E+034.1086E+O35.8851E+032.5907E+027.6536E+022.1191E+024 .4855E+032.3130E-013.5588E+018.8206E+O0
COOLANT
4. 2034E+04
SI027102FEOmooCAoNA20K20FEZ03AL203UD2ZR02CR203NIOFPN02FPN03FPOXFPALKMETFPHALOGNFE304U308FECRNIZRFPMALu.S1UAL3UAL2CA
4. 2034E+04 H20CLN
Table 6.4 Output Ming for the BWR sample problem (continued)
IT. m. = 360
zcN i
Fi Z
6 cWCON VERSION 2.28N TIME = 21600.00 SW ACCIDENT - WATERADDEDAFTER 1 HOUR 3
h ● ***LAYERw
PROPERTIES****
A fw
OXIDE NIXTURE COOLANTMASS (KG) 1 .6648E+05 6. 1700E+04 4. 203.4E+04OENSITY (KG/m3) 6. W15E+03 S.9G8E+03 9.3336E+02THERMAL EXPANSIVI TV (l/K) 4.6773E-05 2.2572E-05 3. 6233E-06
AVERAGE TEMPERATURE (K) 1. 8655E+03 1.81 03E+03 6. 01k2E+02INTERFACE TEMPERATURE (K) 1.6496E+03 1.83~E+03 1 .5077E+03 4.6163E+02EDGE TEMPERATURE (K) 1.65192+03 1.7579E+03 4. 0062E+02SOLIOUS TEMPERATURE (K) 1.6645E+03 1.7@3E+03 2.6821E+02L IQUIDUS TEMPERATURE (K) 2 .7459E+03 2. 7658E+03 2.7821E+02SPECIFIC ENTHALPY (J/KG) -5 .2271E+06 1.3197E+06 -1 .5447E+07TOTAL ENTHALPY (J) -8.7018E+11 8.1424E+I0 -6.4930E+11SPECIFIC HEAT (J/KG K) 6. I128E+02 7.6676E+02 4.2791E+03
VISCOSITY (KG/M S) 8. 19QE+01 7.9704E-03 2.1554E-D4THERMAL CWOUCTIVITY (U/H K) 2.8648E+O0 2.4104E+O1 6.0000E-01THERNAL OIFFUSIVITY (M2/s) 6.7032E-07 5.4306E-06 1.5023E-07
N SURFACE TENSI~ (N/M) 5.16192-01 1 .6219E+O0 7. 3000E - 02A00 ENISSIVITY (-) 8. DOOOE-01 6.0233E-01 1. 0000E+OO
SUPERFICIAL GAS VEL (TR) 1.2638E-03 1.6330E-03 1.4629E-03 3.4032E-04BUBBLE RADJUS 5.1573E-03 5.17532-03 3.1141E-038UBBLE VELWITY (ws) 7.4180E-03 3.2813E-01VOIO FRACTIW
2.4024E-01(-) 6.00402-03 4 .6563E-03 2.7775E-03
BOT CRUST THICKNESS (M) 2.2077E-03 o. 00002+00 O.0000E+OOHT COEFF, LIO TO 801 (U/M2 K) 9.3934E+01 1.2@3E+04 6.0676E+02Z-AVE L IO TEWERATURE (K) 1.8662E+03 1.82 V3E+03 4 .0D62E+02HT COEFF, LIO TO TOP (U/W2 K) 6.7001E+03 4.4003E+03 5.1897E+02TOP CRUST THICKNESS (M) 0.0000E+OO 1.7888E-02 0.0000E+OO
R-AVE LIO TEMPERATURE (K) 1 .8657E+03 1.8103E+03 4.0062E+02HT CCEFF, LIO TO S10 (U/U2 K) 1.08722+02 6. 1330E+03 1. OOOOE-10SIDE CRUST THICKNESS (M) 1.66882-03 0.0000E+OO 0.0000E+OO
OECAYHEAT (u) 9.6270E+06 1 .40422+06 0.0000E+OOHEAT TO CONCRETE (u) 9.6984E+05 2.5290E+06 0.0000E+OOHEAT OF REACTl~ (u) o.omw+oo 3.5801E+06 0.0000E400INTERLAYER HEAT FLW (w) 6.2253E+06 1.0584E+07 -1.0185E+06
Table 6.4 Output listing for tbe BWR sample problem (continued)
CORCON VERSION 2.28TIME = 21600.00 EM ACCIDENT - UATER ADDED AFTER 1 HwR IT. NO. = 360
● ● ● ● ] N T E R L A y E R N I x I N G* •~~
LOWER MIXTURE LAYER
PHASE MASSESPHASE DENSIT [ESL IOUIDUS TEMPERATURESOL IDUS TEMPERATUREPHASE ENTHALPIESMASS ENTRAINEDMASS DE-ENTRAINED
OXIDE
(KG) 8.5336E+02(KG/N3) 7.0653E+03
(K) 1.%57E+03(K) 2. 7658E+03(J) -4.5495E+W(KG) O.0000E+OO(KG) 2.2460E+02
METAL
6.08472+045 .9306E+031.7488E+031. 7S89E+038.5968E+1OO. 0000E+OOO. 0000E+OD
Table 6.4 Output listing for the BWR sample problem (continued)
~ Ca@~
o5wL! TIME = 21600.00 BUR ACCIDENT - WATERmA
****w
TEMPERATURE OF METAL (K)TEMPERATURE OF OXIDE (K)AEROSOL - AMBIENT CONOITIONS (G/CC)AEROSOL - STANOARD STATE CONOIT IONS (G/CC)
( 298.15 (K) AND 1 ATM. )GAS (G-HOLES/S)AEROSOL RATE (GRAMS/S)AEROSOL OENS1 TV (G/CU3)PARTICLE SIZE (MICROMETERS)BUBBLE DIAMETER FOR THE METAL PHASE (CM)BUBBLE OIAMETER FOR THE OXIDE PHASE (CM)
CORCON VERSION 2.28ADDEO AFTER 1 HUJR*V AN ES AOUT, PUT** ***
1.8102E+O31.8651E+032.8787E-046.1913E-04
4. 1562E+O06.2927E+012. 0860E+O01.3765E+O01. 0374E+O01. 0339E+O0
MECHANICAL RELEASES FROM THE AZBEL AND THE ISHI1 ANO KATAOKA CORRELATIONS ARE CALCULATED.
I
6789
10111213
22232425
202
FECRN]HoRUSNSBTEAGHNCAOAL203NA20K20S102U02ZR02CS20BAOSROLA203CE02NBOCs1FEO
302 CR203CARBON IN MELT
AEROSOL C(MPOSITION MELT COMPOSITION
ZIRCONIUN IN MELT
WEIGHT %)
3.7655E-044.2806E-121.2218E-11O. 0000E+OO4.1977E-052.9383E -020 .0000E+OOO. 0000E+OO1. B433E-019.3835E-032.4104E+O15.5831E+011.9569E+013.0218s-031.1493E-031. W79E-012.2645E-023.1240E-021.4953E-046.0783E - 035 .8690E-082.7115E-021.1144E-023.4217E-15
(KG)3. 7659E+047.3899E+036. 1029E+O31.1 W3E+021. 2704E+020.0000E+OO5.1631E-011. 2054E+010.0000E+OO0.0000E+OO1. 9828E+034.4114E+022.6281E+028. B634E+022. 2839E+031.0583E+055. 0987E+042.3895E+014.981 OE+O13.5069E+013.2729E+026.4539E+022.5976E+O01 .3306E+O04.2591E+021.5192E-070.0000E+OO5 .8470E+03
LOSS(MOLES)
1.2108E-O48.4229E-132.2821E-12O. 0000E+OO6.5087E-064.3472E-030.0000E+OO0.0000E+OO6.2050E-021.7373E-037.3418E+O01. 1188E+016. 1420E+O02.1128E-041. 7608E -041.2781E-022.7903E-035.6915E-038.6637E-066.6667E-041.0173E-081. 9702E-032.9281E-034.2500E-16
RELEASE FRACTION
1.6701E-046.281OE-W2.52 B8E-080.0000E+OO1.6227E-021.5452E-01O. 0000E+OO0.0000E+OO1.6844E-023.8163E-033.7452E-012.7860E-015.1632E-026.2333E-052.4342E-065.5371E-021.0961E-011 .B657E-012.26072-035.1273E-023.25 B8E-063.4451E-011.W68E-046.9257E-12
IT. NO. = 360
TabIe 6.4 Output listing forthe BWRsample problen (continued)
I
1 H20Hz
: H4 OH5 06 027 C028 co
GAS COMPOS1TION(WEIGHT X)
2.1330E-049.8371E+013.5088E-025.9564E-091.5731E-121.5013E-188.5647E-071.5936E+O0
RELEASE RATE(GRAMS/SECOND)
1. 5963E-048.2380E+O01.6693E-034.2083E-091.0452E-121. W57E-181.5658E-061.8543E+O0
Table 6.4 Output Ming for the BWR sample problem (cmtinued)
zcN
Hzw ~m VERSIW 2.28b TIME = 21600.00 BkR ACCIDENT - MATER ADDED AFTER 1 HOUR IT. NO. = 36000
elNFnltATIm SUPPLIED BY
MEAN PARTICLE SIZE (W)AEROSOL RATE (GRANS/S)AEROSOL DENSITY (G/CM3)POOL DEPTH (CM)POOL TEMPERATURE (K)AMBIENT PRESSURE (ATM)
SIZERANGE
0.000- 0.3490.349- 0.4730.473- 0.5800.580- o.6a20.682- 0.7840.784- 0.8880.888- 0.997O. W?- 1.1131.113- 1.2381.238- 1.3751.375- 1.5261.526- 1.6971.697- 1.8951.895- 2.1272.127- 2.4112.411- 2.7712.771-3.2593.259-3.W73.W7- 5.4095.409.*****
CHARACT
0:;0.40.50.6
;::0.91.01.11.3
:::
;::2.2
::;3.54.57.0
● *****POOL SCRUBBING***** ●
VANESA
1.3745E+O06.2927E+012.0860E+O01.4079E+024 .0059E+022.5920E+O0
RISTICIE
ItAssIN RANGE
2 .4603E+O02.5011E+O02.4694E+O02.4099E+D02.3309E+O02 .2346E+O02.1214E+O01. W1lE+OO1.8430E+O01.6766E+O01 .4916E4001. 2886E+O01.06%E+O08.3838E-016.0389E-013.8021E-011.8933E-015.8834E-025.3661E-031.0000E-06
DECONTAMINATE1~FACT~
1. 2788E+O01. 2580E+O01. 2742E+O01.3056E+O01.3498E+O01.4080E+O01.4832E+O01.5802E+O01. ?W2E+O01.8766E+O02.1093E+OO2.4417E+O02.9422E+O03. 7529E+O05.2101E+OO8. 2753E+O01.6618E+015.3478E+015 .8632E+022.8603E+06
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .OVERALL OECWTAMINATIW FACT~MASS OUT
2.25032 .7964E+01
FIT OF DECONTAMINATED AEROSOL TO LOG NORNALNEU MEAN PARTICLE SIZE (W) 0.846RANGE (W) 0.805 - 0.888NEU GEONETRIC STANDARO DEVIATION 1.581RANGE (IM) 1.742 - 1.435
LINEAR CORRELATl~ CWFFICIENT 0.%9414
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Greene, G. A., J. C. Chen, and M. T. Conklin,“Bubble-Induced Entrainment Between StratifiedLiquid Layers, ” International Journal of Heat andMaas Transfer, Vol. 34, p. 149, 1990.
Beard, K. V., and H. R. Pmppacher, “ADetermination of the Terminal Velocity and Dragof Small Water Drops by Means of a WindTunnel, ” Journal of Atmomheric Science, Vol. 26,p. 1066, 1969.
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Bottinga, Y., D. F. Weill, and P. Richert,“Thermodynamic Modeling of Silicate Melts, ”Therrnodvnamics of Minerals and Melts, R. C.Newton, A. Navrotaky, and B. J. Wood, eds.,Springer-Verlag, 1981.
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85. Speich, G. R., “Cr-Fe-Ni (Chromium-Iron Nickel),●Metals Handbook, Vol. 8, American Society forMetals, Metals Park, OH, p. 424, 1973.
257 NuREG/cR-5$43
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IRC FORM = U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NuMBERf.ssl‘RCM1102.201.320? BIBLIOGRAPHIC DATA SHEET
-~:zv?ky ‘“”NUREG/CR-5843
I* imtmctims on the Iww=) SAND92-0167
TITLE AND SUSTITLE
CORCON-Mod3: An Integrated Computer Modelfor Analysis of Molten Core-Cbncrete Interactions 3. OATE REPORT PULILISHEO
MONTHI
VEAR
October 1993User’s Manual 4. FIN OR GRANT NUMBER
L1484AUTHOR(S)
D.R. Bradley6. TYPE OF REPORT
D. R. GardnerJ.E. Brockmann Technical
R. 0. Griffith7. PERIOD COVEREO fmrwwwr mrc$l
PERFORMING ORGAN IZ&- ION - NAME AND AOORESS (If NRC. prov#& Owitin. Okeot Rap”on. U.S Nudes RW.btLNV ~,- md m9ilin9 #$ma I
Md mciit17##ddm##: it Conframot. Provi-
Sandia National LaboratoriesAlbuquerque, NM 87185
1.SPONS7. S””~ Z. ORGAN IZATION - NAME AND ADO R ESS (If NRC. IVPC“>mr u ●oou””. if COIWKW. Pmwide NRC Owh,on, Ofkt 01 Rvion. u.S. NUC&U Rwhrorv timmmmn.#no malt... &car*sL/
Division of Systems ResearchOffice of Nuclear Regulatory Research . .U.S. Nuclear Re ulatory Commission
!Washington, DC 0555
0. SUPPLEMENTARY NOTES
1. ABSTRACT (ZOOwti~ O,&u/
The CORCON-Mod3 computer code was developed to mechanistically
model the important core-concrete interaction phenomena, including
those phenomena relevant to the assessment of containment failure
and radionucliderelease. The code can be applled to a wide range
of severe accident scenarios and reactor plants. The code
represents the current state of the art for simulating core debris
interactionswith concrete. This document comprises the user’s
manual and gives a brief descriptionof the models and the
assumptions and limitations in the code. Also discussed are the
input parameters and the code output. Two sample problems are
also given.
2.~EY WCI R DS/DESC R !PTORS (List woti or Ph-ura WMr will Nix -emtin in IWatiw VfI@mPLW: 13. AvAILABILITY STATEM~~T
Core-concrete interaction1
concrete ab ation unlimitedsevere reactoraccidents radionuclid release ld.SECURITY CLASSI$ICA1lO~
severe accident codes “aerosol scrubbingbasemat meltthrough
ITfuaP*IVANESA
debris coolability molten debris unclassified
CORCON{r~~Rebwnl
aerosolgeneration unclassified15.NuMBEROFPAGES
16. PRICE
NRCFORM3351249)
3HISPAWINIEWIIOMA.LLYLEFTB-
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