PFC/RR-81-26DOE UC-20 C, D, E
AN EVALUATION OF
ACCIDENTAL WATER-REACTIONS WITH LITHIUM
COMPOUNDS IN FUSION REACTOR BLANKETS
P. J. KraneM. S. Kazimi
July 1981
Plasma Fusion Center
and the
Department of Nuclear Engineering
Massachusetts Institute of TechnologyCambridge, Massachusetts 02139
E.G. & G. Idaho, Inc.
and
The U.S. Department of EnergyIdaho Operations Office
under
DOE Contract #DE-AP07-79ID00019
PUBLICATIONS UNDER CONTRACT #K-1702ON FUSION SAFETY
1. M. S. Kazimi et al., "Aspects of Environmental Safety Analysis ofFusion Reactors," MITNE-212, Dept. of Nuclear Engineering, M.I.T.,October 1977.
2. R. W. Sawdye, J. A. Sefcik, M. S. Kazimi, "Reliability Requirementsfor Admissible Radiological Hazards from Fusion Reactors," Trans.Am. Nucl. Soc. 27, 65-66, November 1977.
3. D. A. Dube, M. S. Kazimi and L. M. Lidsky, "Thermal Response ofFusion Reactor Containment to Lithium Fire," 3rd Top. Meeting inFusion Reactor Technology, May 1978.
4. R. W. Sawdye and M. S. Kazimi, "Application of Probabilistic ConsequenceAnalysis to the Assessment of Potential Radiological Hazards of Poten-tial Hazards of Fusion Reactors," MITNE-220, Dept. of Nuclear Engi-neering, M.I.T., July 1978.
5. D. A. Dube and M. S. Kazimi, "Analysis of Design Strategies forMitigating the Consequences of Lithium Fire within Containment ofControlled Thermonuclear Reactors," MITNE-219, Dept. of NuclearEngineering, M.I.T., July 1978.
6. R. W. Sawdye and M. S. Kazimi, "Fusion Reactor Reliability RequirementsDetermined by Consideration of Radiological Hazards," Trans. Am. Nucl.Soc. 32, 66, June 1979.
7. R. W. Green and M. S. Kazimi, "Safety Considerations in the Design ofTokamak Toroidal Magnet Systems," Trans. ANS 32, 69, June 1979.
8. R. W. Green and M. S. Kazimi, "Aspects of Tokamak Toroidal MagnetProtection," PFC/TR-79-6, Plasma Fusion Center, M.I.T., July 1979.
9. S. J. Piet and M. S. Kazimi, "Uncertainties in Modeling of Consequencesof Tritium Release from Fusion Reactors," PFC/TR-79-5, Plasma FusionCenter, M.I.T., July 1979.
10. M. J. Young and S. J. Piet, "Revisions to AIRDOS-II," PFC/TR-79-8,Contract #K-1702, Plasma Fusion Center, M.I.T., August 1979.
11. S. J. Piet and M. S. Kazimi, "Implications of Uncertainties inModeling of Tritium Releases from Fusion Reactors," Proc. TritiumTechnology in Fission, Fusion and Isotopic Applications, April 1980.
12. M. S. Tillack and M. S. Kazimi, "Development and Verification of theLITFIRE Code for Predicting the Effects of Lithium Spills in FusionReactor Containments," PFC/RR-80-ll, Plasma Fusion Center, M.I.T.,July 1980.
Publications Under Contract #K-1702 (continued)
13. M. S. Kazimi and R. W. Sawdye, "Radiological Aspects of Fusion ReactorSafety: Risk Constraints in Severe Accidents," J. of Fusion Energy,Vol. 1, No. 1, pp. 87-101, January 1981.
14. P. J. Krane and M. S. Kazimi, "An Evaluation of Accidental Water-Reactions with Lithium Compounds in Fusion Reactor Blankets,"PFC/RR-81-26, Plasma Fusion Center, M.I.T., July 1981.
15. D. R. Hanchar and M. S. Kazimi, "Tritium Permeation Modelling of aConceptual Fusion Reactor Design," PFC/RR-81-27, Plasma Fusion Center,M.I.T., July 1981.
AN EVALUATION OF ACCIDENTAL WATER-REACTIONS
WITH LITHIUM COMPOUNDS IN FUSION REACTOR BLANKETS
ABSTRACT
Efforts to mitigate potential problems of lithium-based blanketsfor fusion reactors include the use of lithium compounds for breedingpurposes. This report investigates the safety aspects of these alloys -relative to the use of pure lithium in a water-cooled blanket. Includedin the study is a modification of the LITFIRE computer code to predictthe thermal response of an internal blanket breeder-water interaction.
For the problem analyzed, results indicate that some of thelithium-lead alloys may pose safety problems approximate to thoseassociated with the use of liquid lithium. Li20 is shown to besignificantly safer than liquid lithium, while results using LiAl aresimilar to those of the lithium-lead alloys.
In addition, the study provides an overview of this safety question,signaling areas that require further development.
-3-
ACKNOWLEDGEMENTS
Many people helped bring this effort to conclusion. In particular,
Mark Tillack and Steve Piet, and Rachel Morton provided the needed hints
to run LITFIRE and locate material properties.
Gail Jacobson transformed the written notes into a typed manuscript.
This report is based on a thesis submitted by the first author as
part of the requirements for the degree of M.S. in Nuclear Engineering.
-4-
TABLE OF CONTENTS
Abstract .......................................................
Acknowledgements ...............................................
List of Figures ................................................
List of Tables .................................................
page
2
3
6
7
CHAPTER 1.
CHAPTER 2.
CHAPTER 3.
CHAPTER 4.
INTRODUCTION .......................................
BLANKET DESIGN BASIS DESCRIPTION ...................
2.1 Introduction ..................................
2.2 Breeding Material .............................
2.2.1 Lithium-Lead Alloys ....................2.2.2 Alternative Breeders ................
2.3 Coolant .......................................
2.4 NUWMAK Blanket Design .........................
2.4.1 Structural Materials....................2.4.2 Mechanical Design ......................2.4.3 Summary of Important Parameters ........
EQUILIBRIUM Tf CALCULATION .........................
3.1 Introduction ..................................
3.2 Assumptions and Methodology ...................
3.3 Results and Discussion ........................
DYNAMIC CALCULATIONS USING LITFIRE .................
4.1 Introduction ..................................
4.2 LITFIRE Description ...........................
4.3 Internal Blanket Accident Option ..............
4.3.1 Assumptions and Structural Model .......
-5-
Table of Contents (continued)
4.3.2 Heat Transfer Mechanisms ................
A. Heat of Reaction ....................B. Sensible Heat Addition to Reactants .C. Forced Convective Cooling ...........D. Conduction ..........................E. Free Convection .....................F. Radiation ...........................
4.3.3 The Numerical Scheme ....................
4.4 Results and Discussion ........................
CHAPTER 5.
References
Appendix A.
Appendix B.
Appendix C.
Appendix D.
CONCLUSIONS AND RECOMMENDATIONS .....................
.....................................................
Physical Properties Data ...........................
Complete Listing of LITFIRE ........................
Sample Input to LITFIRE ............................
Sample Output of LITFIRE ...........................
page
49
495152535354
55
56
67
69
70
74
115
118
-6-
LIST OF FIGURES
No. page
1.1 LITFIRE Predictions for Consequences of LithiumSpill in UWMAK III Containment ........................... 10
2.1 Cross-Sectional View of NUWMAK ........................... 13
2.2 Top View of NUWMAK ....................................... 14
2.3 Pb-Li Phase Diagram ...................................... 16
2.4 Effects of Lithium Concentration in a Lithium-LeadBreeder on Shielding Requirement and Tritium Breeding .... 18
2.5 Estimated Tritium Inventory in Alternative BreederBlankets for 3000 MWth Reactor ........................... 19
2.6 Phase Diagram for LiAl System ............................ 23
2.7 Impact of Structural Material Content (316 StainlessSteel) on Tritium Breeding ............................... 27
2.8 Cross-sectional View of NUWMAK Blanket ................... 32
2.9 Schematic of the Blanket and Shield for NUWMAK ........... 34
3.1 Equilibrium Final Temperature Profiles for VariousBreeders in Static Calculation ........................... 41
4.1 Internal Blanket Accident Option Heat Flow Diagram ....... 44
4.2 Internal Blanket Accident Option Node Structure .......... 48
4.3 Lithium Breeder Thermal Response to Water Interactions ... 57
4.4 Li7Pb2 Breeder Thermal Response to Water Interactions .... 58
4.5 LiPb4 Breeder-Thermal Response to Water Interactions ..... 59
4.6 LiAl Breeder Thermal Response to Water Interactions........60
4.7 Li2O Breeder Thermal Response to Water Interactions ...... 61
4.8 Comparison of Reaction Zone Temperature Profilesof the Various Breeders .................................. 64
4.9 Comparison of First Breeder Element TemperatureProfiles of the Various Breeders ......................... 66
-7-
LIST OF TABLES
No page
2.1 Reactions of Li-Pb Alloys and Lithium with Water ....... 20
2.2 Summary of Favorable and Unfavorable Features ofLithium-Lead Breeders .................................. 22
2.3 Summary of Favorable and Unfavorable Features ofthe Water-Cooled Blanket Concept ....................... 28
2.4 Summary of Structural Material Assessment for theWater-Cooled Blanket Concept ........................... 29
2.5 Physical Properties of Ti-6-4 .......................... 31
2.6 Major Features of NUWMAK Design ........................ 35
2.7 Summary of Important Blanket Parameters ................ 36
4.1 Breeder - Coolant Reactions of Interest ................ 50
-8-
CHAPTER 1. INTRODUCTION
Advancements in plasma physics research, together with a growing
concern for the risks of energy production in the public sector, has
led to an increasing number of detailed fusion safety studies. Topics,
including routine and accidental releases of tritium, activation of
structural material by neutron bombardment, and the consequences of
lithium fires, are currently under various degrees of investigation.
The findings of these studies are incorporated in subsequent fusion
reactor designs, answering some questions and creating still more.
This work is the product of a research program whose objective is
to minimize the potential problems of a lithium-based blanket for fusion
reactors. Such a blanket is practically forced upon us by the choice of
a D-T fuel mixture for first generation fusion power plants [1]. The
needed tritium is bred via the reactions:
6Li (n,T) 4He + 4.8 MeV
7Li (n,n'T) 4He - 2.5 MeV.
Initially, natural lithium (92.58% 7Li, the rest 6Li), a liquid at
operating blanket tenperatures, was the primary candidate for blanket
breeder and/or coolant materials, due to its excellent breeding and heat
transfer qualities, effectiveness in neutron moderation and relatively
low pumping power need as compared to other liquid metals [2]. However,
with time and study, serious disadvantages in the use of liquid lithium
emerged.
-9-
Pure lithium is highly reactive with air, water and concrete; all
materials that will be in abundant supply in the reactor environment.
Experimentation at the Hanford Engineering Development Laboratory (HEDL)
and computer modelling studies at MIT using the computer code LITFIRE
(to be discussed in more detail later in this report) indicate that
temperatures and pressures in the reactor containment area, in the event
of a sizable lithium spill, can attain critically high values [3].
Figure 1.1 shows such a possibility. Such an event could provide a pathway
for release of tritium or structural activation products, providing a
hazard to plant personnel or the outside world.
This problem and others, including corrosion, difficulties in tritium
recovery, and magnetohydrodynamic instabilities [4], have led designers
to consider alternative materials for fusion blankets. Among such
considerations are lithium-lead alloys.
This report will provide a preliminary analysis of lithium-lead
alloys for use as breeding materials from the safety point of view. While
it is thought that these materials provide less of a hazard than the use
of liquid lithium, little has been demonstrated. Thus, there is the need
to formulate some framework for a comparison.
Before actual calculations can be made, a basis must be established.
The NUWMAK reactor design by the University of Wisconsin (1978) was chosen
for this purpose, due to its use of Li62Pb38 eutectic as the tritium
breeder. The primary hazard here involves interaction between the lithium-
lead alloy breeder and the boiling water coolant, inside the blanket.
Specifics of this design are further discussed in Chapter 2.
-10-
1250-
1000 Pool
750-
CelIGas
0750
250
Stee
Li .e
0 2 4 6 8 10 12
TIME (10 3 sec)
Figure 1 .1 LITFIRE predictions for consequences of lithiumspill in UWOAK III containment (Reference 3) .
-11-
Using this basis, two separate. studies are performed. The first is
a static calculation: the breeder and coolant are allowed to interact
immediately and the subsequent equilibrium final temperature of the blanket
materials is determined. This is presented in Chapter 3. The second
study is a dynamic calculation, using LITFIRE, of the temperature
histories at various points in the blanket, if some accident allows breeder
and coolant to come into contact. This is presented in Chapter 4. It
should be stressed that in both studies, the values obtained are not
sufficient evidence in themselves. Rather, these values must be compared
with similar calculations employing the use of pure lithium. In this
way, a measure of the relative hazards of the alternate breeders can be
assessed.
-12-
CHAPTER 2. BLANKET DESIGN BASIS DESCRIPTION
2.1 Introduction
NUWMAK, a conceptual thermonuclear reactor designed by the Fusion
Engineering Program of the University of Wisconsin in March 1979, is one
of a number of second generation studies aimed at maximizing the strengths
of fusion while minimizing the weaknesses. This work builds upon the
findings of a number of first generation designs aimed at identifying
the important problems of fusion power.
The design philosophy of this study was to search for an "end
product that has the potential to be reliable, maintainable, environmentally
acceptable, and reasonably economic [4]." To do this, a number of changes
were made to the preceeding reactor concept, UWMAK III, including: an
increase in the magnetic field to increase power density, a simplification
of design to facilitate maintainence (as well as eliminate large cost
items), the selection of structural materials to minimize resource
requirements and costs, and a change in blanket breeder and coolant
materials to reduce thermal fatigue and thereby increase reliability.
The resulting structure is shown in Figures 2.1 and 2.2
The new elements in blanket breeder and coolant materials are of
particular interest to those concerned with fusion safety studies.
Utilized in NUWMAK are: (a) Li62Pb38 eutectic for the breeding material,
used because its melting point is very near the blanket operational
temperature and thus, the latent heat of melting can provide energy
storage, and (b) boiling water for the coolant, the "perfect choice,"
discarded previously with the presence of pure lithium as the breeder.
-13-
I-
U,0:
_jCL L)
'TC ..
U)IL
a.
m0j
Ix ..... .
00J
-14-
TOP VIEW OF NUWMAK
INNER SUPERCONDUCTIVEBLANKET OH COILS
TUNGSTEN
EDDY ZONECURRENTSHIELD
- NORMAL COPPEROUTER .TF TRIMMING COILSBLANKET
CENTRALSTRUCTURALCYLINDER -.RF CAVITY
-L GRAPHITE- -REFLECTOR
- / FIXED SHIELD
VACUUM-
REMOVABLE SHIELD
SUPERCONDUCTIVE D MOU- TABL CRYOGENICTF COILS
Figure 2(Reference 4 )
-15-
A preliminary survey of the hazards of lithium-lead alloys indicates
that interaction with water is by far the more severe problem, as these
materials are relatively inert in air. NUWMAK, in addition to its use
of Li62Pb38, provides an opportunity for the breeder and coolant to come
into contact, specifically a breach in the cooling system inside the
blanket. Thus, NUWMAK is the logical first choice for a basis for an
investigation of the relative safety of the lithium-lead alloys.
2.2 Breeding Materials
2.2.1 Lithium-lead alloys
The lithium compound selected as the tritium breeding material must
satisfy many requirements. It must have desirable neutronic and irradia-
tion characteristics, chemical stability at blanket operating temperatures,
and be compatible with other blanket materials. More importantly, the
compound must breed and release tritium at sufficient rates to fuel the
reactor, yet limit the tritium inventory in the blanket to reasonable
1 'vels.
Lithium-lead compounds are interesting materials. Figure 2.3 shows
the phase diagram of a Li-Pb two component mixture. However, beyond Li7Pb2'considered the most attractive lithium-lead alloy for breeding purposes,
little else on the subject of Li-Pb physical properties is certain.- -An
accumulation of data relevant to this study through a literature search
and "data synthesis" is presented in Appendix A.
Two neutronic characteristics of the lithium-leads, breeding cabability
and long-lived activation products, have been studied. In the latter only205 Pb presents any problem in the long term unless significant amounts of
impurities exist. This is not expected to be serious [4]. Breeding
-16-
IU Pb2
7260C IG
LiPb
48 2 C C 4
- - 177 0 C
-IF
20 40ATOM
PHASE
60-% Li
80
K
100
DIAGRAM
Figure 2.3
(Reference 4)
800
700
C.)
2
LLII"
60c
50C
40C
300
200
l000
Pb - Li
I i I
-17-
capability depends on the amount of lead present.
Li7Pb2 has been examined in detail and exhibits an excellent breeding
property. This is due to the presence of lead, which acts as a neutron
multiplier. Figure 2.4 shows the effect of lithium concentration in the
lithium-lead breeder on the total breeding ratio. The total bulk shield
thickness required to protect toroidal field coils is shown for reference.
It is evident that a reduction of the lithium concentration will cause a
substantial loss of fuel multiplication. However, the reduction of lithium
also tends to enhance magnet protection by virtue of more effective nuclear
radiation shielding by the added lead [5].
A diffusion study by Wiswall [6] shows that the soluability of tritium
in Li-Pb is much lower than that in pure lithium, as the activity of lithium
is very low due to the presence of lead. Thus, the tritium inventories can
be much smaller, tritium diffusivities relatively higher, and tritium
recovery much easier. Specifically, Fig. 2.5 shows that Li7Pb2 has the
lowest inventory of any of a number of proposed breeders. A problem here
could be the fact that Li7Pb2 becomes a "chunk" at high temperature. This
would increase the diffusion path of tritium and make recovery difficult [4].
A more serious problem of the lithium-leads involves their compati-
bility with the blanket environment. All react to some extent with water.
Table 2.1 shows the results of experimentation to investigate this at
Argonne National Laboratory. It can be seen that Li-Pb alloys can react
vigorously with water, more so at elevated temperatures. However, a
significant result is that Li17Pb83 exhibited only moderate reaction with
water. Also, insufficient hydrogen was evolved by the alloy reactions
to attain ignition conditions, unlike the case with liquid lithium.
-18-
S1M1 3
0 1-- 0 i
'10) j) 0)09 6103a 05
04
03
02
Of
00 10 20 30 40 so 60 70 60 10 1O
L:ITMIU CONCENTIOATI0,. %
Figure 2.4 Effects of lithium concentration in a lithium-lead breeder on shielding requirement andtritium breeding (Reference 5).
I
U
2
p
ft
U
-19-
650 600 550
TEM. *C
500 450 4003.5
3.01
0 2.5F-
wz- 2.0
CD1.5
0
1.0
0.5I.C
I 1 .1 I I
-
~~~~1
0
0Li20 LI.Pb2
L.At
0
C
1.1 1.2 1.3 1.4 1.5 1.6
10 K/T
Figure 2.5 Estimated tritium inventory in alternativebreeder blankets for a 3000 1lth reactor(Reference 9).
300I I
-20-
TABLE 2.1
Reactions of Li-Pb Alloys and Lithium
with Water
(Reference 7)a Injected under water
Sample
WaterCase Composition State Temp/*K Ter-p/*K Reaction
1 Li7fpb2 s 773 298 Modest
2 Li7Pb2 s 773 369 Vigorous
3 Li7Pb2 s 873 368 Vigorous
4 Li7Pb2 L 1103 36S Very Vigorous
5 Lio. 62 Pbo. 3 8 L 773 368 Vigorous
6 Li0 .17Pb0 .8 3 z 773 368 Very modest
7 Li z 773 368 H2 Detonation
8 Lia Z 773 368 Detonation
-21-
In all reactions, LiOH (melting point at 470 'C) is formed. Liquid
LiOH is an extremely corrosive substance and would degrade the integrity
of the activated structural materials [7]. Fortunately, Li-Pb is relatively
inert in air. It was reported [8] that "LiPb (50-50 mixture) resembles Pb
in every respect except density. LiPb would not ignite, even when exposed
to the flame of a gas-air torch." Therefore, though a Li-Pb - H20. reaction
could be very serious, it is not expected to be as severe as an accident
involving pure lithium. Table 2.2 provides a summary of the advantages
and disadvantages of the lithium-lead alloys.
2.2.2 Alternative Breeders
For completeness, LiAl and Li20, also candidates for the tritium
breeding material, will be analyzed with regard to safety in this study.
Other strong candidates, specifically Li2SiO 3 and LiAl0 2, have been ignored
in this study since they have no appreciable reaction with water.
LiAl is in many ways akin to Li7Pb2, such as a similarity in reactivity
with water. However, the latter material is preferred by designers due
to a superior tritium breeding capability. This is because there is a
lower lithium-atom density in LiAl and no neutron multiplier, with the
absence of Pb. Tritium extraction characteristics are also poorer than
that of Li7Pb2 [9]. The primary activation product is 26Al, more of a
problem than 205Pb. Physical properties of this breeder are also
unexplored and are discussed in Appendix A. The phase diagram is shown
in Fig. 2.6.
Li20 has a marked advantage over the lithium-lead alloys in the matter
of reaction with water. Because it is in oxide form, this compound does
not evolve hydrogen upon reaction and produces less heat [9]. It is
-22-
TABLE 2.2
Summary of Favorable and Unfavorable Features of
Lithium-Lead Breeders
Lithium-Lead Alloys
Advantages
1. High breeding ratioattainable
2. Probably less reactivewith water than liquid Li
3. Tritium recovery appearsfeasible with low-pressurehelium
4. Lead helps shield magnets
Disadvantages
1. Poor technology base:high degree of uncertaintyin properties
2. Reactive with water coolant
3. High blanket weight
4. Uncertain radiation damageeffects
5. Uncertain tritium releasemechanism
6. Requires blanket changeoutduring reactor life
7. Activation product: 205Pb
-23-
800
700
600
So-So
400
300
S2} 456 8
- S
0. or (At
7/
I
---
.17 _1001____ ___
0At.
.0 20
WEIGHT PER CENT LITHIUU1', 2A 25 30 40 5 0 7D BO 90
* REF 5
o*Y. *
601
t
3D 40 50 60 70 SO s 10D30 iC PE E5 H0 __:_ss_____s
ATOMIC PER CENT LITHIUM L.
Figure 2.6 Phase Diagram for LiAl System.(Reference 9)
2
-24-
therefore expected that the use of this breeder will not pose a major safety
problem. However, Li20 has fallen into disfavor because it has a high
lithium-atom density. This, combined with a poor diffusion rate, leads to
excessive tritium inventories. Physical properties of this breeder are
also discussed in Appendix A.
2.3 Coolant
Many -factors affect the choice of coolant. Unique in power production
to fusion is the interrupted burn cycle of the plasma. This produces
the problem of thermal fatigue in the first wall and blanket, caused by the
fluctuating temperature of these structures with the plasma burn cycle.
The temperature change is a combination of three effects:
1. Coolant temperatures rise, Tcout-Tcin
2. Film temperature drop, Twall - Tc (=Q/h)
3. Temperature difference across the first wall, AT= Q X/k [4].
While the third effect depends on structural materials, the first two can
be greatly reduced by choice of the proper coolant, one which has a small
coolant temperature rise that simultaneously provides a large heat transfer
coefficient. This describes a boiling liquid and the first logical
choice is boiling water.
A considerable technology has been developed through the years for
the use of water as a coolant in energy production. There exist many
advantages. Water is an excellent heat-transfer fluid, costs little and
is readily available. It is easy to pump and is non-corrosive with
conventional structural materials.
-25-
It is interesting to note, however, that up to this point, few
designers have considered water for the primary coolant. There exist a
number of concerns and questions including neutronics, tritium, and safety
considerations. In addition, the use of a boiling water or steam coolant
will require high pressure containment. The NUWMAK design calls for
cooling water at 300 *C and 8.6 MPa (1250 psi). This poses additional
design and safety problems.
The safety concerns of a water-cooled blanket have been discussed.
It should be noted that this problem effectively prohibited the use of
water as a coolant until alternative breeders to lithium were suggested.
Even so, current designs using water stress the use of strong cladding
materials for coolant channels.
High-integrity cladding is also the prescription to minimize
tritium diffusion into the cooling water. Tritiated water is a safety
hazard and recovery of the tritium is difficult and expensive. However,
recent studies using permeation rates for stainless steel cooling tubes
show tritium losses could be less and 1 Ci/day, assuming the formation of
oxide films inside the tubes [9]. Irregardless, it is obvious that the
coolant loop cannot be used for tritium recovery, necessitating some
recirculation of the breeder.
The necessity of avoiding contact between breeding materials and
coolant tends inherently, to increase structural material content in the
blanket. From a neutronics point of view, this increase tends to degrade
the tritium breeding ability, due to increased parasitic neutron
absorption. However, the strong neutron slowing-down power of water
improves breeding performance by increasing the 6Li (n,T) 4He reaction
rate for low energy neutrons. This decreases parasitic absorption by
-26-
the structural materials [5]. Therefore, proper design and choice of
materials can leave the tritium breeding capability of a water-cooled
blanket virtually unchanged.
Figure 2.7 shows this phenomenon for various breeders, with 316
stainless steel used as structural material. It is important to note
that the addition of water significantly improves the breeding ratio in
the Li7Pb2 , more so than the other breeders. This is due to reduced
parasitic absorption in lead as well as the stainless steel.
Table 2.3 summarizes the advantages and disadvantages of the
water-cooled blanket concept. Chief among the assets is the use of
available technology in its construction. The major liabilities appear
to be the safety problem and limited choices in compatible breeding and
structural materials. Further study in both areas is necessary before
a final decision can be made.
2.4 NUWMAK Blanket Design
2.4.1 Structural Materials
Many structural materials have been considered for a water-cooled
blanket design, including: austenitic stainless steel, high nickel alloys
and selected titanium, vanadium and niobium alloys [9]. Table 2.4
summarizes an assessment of these candidates with regard to properties
associated with the blanket environment.
One of the liabilities of the water-cooled design is apparent. The
vanadium and niobium materials, which respond well to neutron bombardment,
are eliminated due to water corrosion problems. Also noted is a general
lack of data regarding the compatibility of these structural materials
with the lithium-lead alloys. Since decomposition of these alloys is not
-27-
1.8
1.7 - WITHOUT W.TER15 v/a Hs IN LI Pb2 a LizO
LIP ---- WITH WATER (10-15 v/o)1.6 0-5 v/o He IN LiTpz IN
BREEDER BLANKz-T: 0.8 m1.1 50 %SS+- 50 % SC SHIEL.D: 0.2
.0 1.0 to5 15 20
STAINLESS-STEEL VOLUME. %
Figure 2.7 Impact of Structural Material Content C316 SS)on Tritium Breeding (Reference 6).
-28-
TABLE
Summary of Favorable and
the Water-Cooled
2.3
Unfavorable Features of
Blanket Concept
Water Coolant
Advantages
Excellent heat-transferfluid
Well-developed technologybase
Low cost and readilyavailable
Relatively low temperature(-.320 *C) operation
Compatible with conventionalstructural materials
Low pumping power need
Enha'nces tritium production
Liquid at room temperature
1.
2.
3.
4.
5.
6.
7.
Disadvantages
Highly reactive with candidatebreeding materials
Reaction product (LiOH) is verycorrosive
Requires high-pressurecontainment
Cannot be used for tritiumrecovery
Expensive to remove tritium fromH20 (safety)
Water tends to be a sink fortritium
Nb and V, candidate structurematerials are incompatable
1.
2.
3.
4.
5.
6.
7.
8.
-29-
TABLE 2.4
Summary of Structural Material Assessment for the
Water-Cooled Blanket Concept
Rating numbers defined as follows:
Compares favorably with other candidate structural materials.
Limits operating life but probably acceptable under certainconditions. -
Little data available but may be a libit4in factor.
Probably not viable for conditions of interest.
Rat ing
Property Requirement Fe Ni Ti V Nb
Bulk Radiation Effects 2 2 ? 1 1
Compatibility with H20 1 1 1 4 4
Compatibility with Liquid Li 3 5 3 1 1
Compatibility with SolidLi20 and Li 7Pb2 3 3 3 3 3
Compatibility with H(DT)Environment 1 1 3 -1 .1
*
1.
2.
3.
4.
I
-30-
desirable, this question should be studied.
The NUWMAK design utilizes Ti-6Al-4V alloy for the first wall and
coolant tube material due to its high strength-to-weight-ratio, good
fatigue resistance, fabricaility, low long term residual activity and
well established industry [4]. Physical properties of this alloy are
shown in Table 2.5. The NUWMAK shield is more conventional, primarily
B4C.
2.4.2 Mechanical Design
The blanket of NUWMAK is shown in Fig. 2.8. The blanket structure
is Ti-4A1-4V which operates at a temperature of approximately 350 *C.
The coolant is boiling water at 300 *C.and 1250 psi. The breeder is
Li62Pb38 eutectic, operating at approximately 400 *C. The design life
for each blanket module is two years.
The blanket is divided into eight modules in the reactor. Each
module is fed and discharged coolant and breeding materials separately.
There are two blanket units- in each module; the inner blanket near the
machine axis and the outer blanket, as seen in Fig. 2.8. These two units
are completely separate from each other.
The first wall consists of a continuous bank of tubes running in the
vertical direction. Beyond this, the blanket is cooled with rows of
vertical tubes on a triangular pitch. The spacing between rows of tubes
is progressively increased towards the back of the blanket to account for
the radially decreasing nuclear heating [4]. Radial struts are spaced at
20 cm intervals, reinforcing the first wall against the hydrostatic
pressure of the breeding material, which fills the space between the
coolant tubes.
-31-
TABLE 2.5
Physical Properties of Ti-6-4
Atomic Weight
Melting Point
Mass Density
Yield Strength
Modulus of Elasticity
Yield-to Weight Ratio
Thermal Condcutivity
Coefficient of Thermal Expansion
Heat Capacity
45.9
1668 *C
4.4 g/cm3
530 MPa
85 GPa
120 N-m/g
.12 W/cm-K
10 x 10-6/OC668.8 J/kg-K
T BREEDING MINLET
Al
NNERBLANKE
BREEDINGMATERIALOUTLET COOLANT
OUTLET
T
,---FIRST WALLCOOLING TUBES
0
Figure 2.8 Cross-Sectional Viewi of Blanket (Reference 4) .
-32-
COOLANINLET TERIAL
OUTERBLANKET
3 meters2
i
-33-
At the blanket's edge is a thin graphite reflector. Beyond this is
a shield to protect the cryogenic magnet coils. The shield is primarily
B4GC, operating at approximately 150 *C. Figure 2.9 shows a schematic
diagram of this system.
2.4.3 Summary of Important Parameters
The major features of the NUWMAK design are given in Table 2.6. In
addition, important blanket parameters pertinent to this study are given
in Table 2.7. These values are used where appropriate in subsequent
calculations.
-34-
SCHEMATIC OF THE BLANKET ANDFOR NUWMAK
SHIELD
SHIELD
-JBREEDG
D .A IG
2 1 13.75 5 9 102.9 3.35 3.95 6.4 6.9 7.95
COLD HOT BREEDING GRAPHITESHIELD SHIELD ZONE REFLECTOR SHI
3.5%Ti alloy 4%Ti alloy 5.7%Ti alloy 3.5%Ti.alloy 3.5%
95.25% B4C 93% W 89.4% Pb Li 95.25% C 95.250%
1% H 2 0 2% H20 3.7% H20 1% H2 0 1%
0.25% Pb I % Pb 1.2% Pb 0.25% Pb 0.25%
meters
ELD
ri alloyB4C
Pb
Figure 2.9(Reference 4)
6k-
41-
2k
I I
-35-
TABLE 2.6
Major Features of NUWMAK Design
Power
Total Thermal PowerNet Electric Power
Plasma
Major RadiusMinor RadiusPlasma Height to Width Ratio (b/a)Plasma CurrentToroidal Beta
neTE
q(a)
2283 MWth660 MWe
5.13 m1.13 m1.647.2 MA6%
2 x 101 4 cm- 3-sec
2.64
Magnet
On-Axis Toroidal FieldToroidal Field at NbTi ConductorStabilizerNumber of Toroidal Field CoilsNumber of Cu Trim Coils
6.05 Tesla11.5 TeslaAl uminum816
Blanket
Structural MaterialCoolantBreeding Material
Average Neutron Wall Loading
Titanium AlloyBoiling WaterLi62Pb384.34 MW/m2
-36-
TABLE 2.7
Summary of Important Blanket Parameters
Plasma Burn TimePlasma Down Time
225 sec20 sec
Coolant TemperatureCoolant PressureTotal Coolant Flow RateTotal Coolant Tube
Surface Area
Heat Transfer Coefficientof Boiling Water
Coolant Tube ODCoolant Tube IDN. Tubes in Outer BlanketModule
Pitch Length
Space for Breeder inOutside Blanket Module
Breeder TemperatureShield Temperature
300 *C8.6 MPa1500 kg/sec
4350 m2
20000 Btu/hr-ft2- OF
1.3 cm1.0 cm
475
12 cm
17.72 m3
400 *C150 *C
-37-
CHAPTER 3. EQUILIBRIUM Tf CALCULATION
3.1 Introduction
Lithium-lead alloys are considered less of a safety hazard due to
the presence of lead, which is thought to slow down the water reaction,
decrease the heat of reaction and help absorb what heat is released.
However, a number of physical properties are altered with the addition
of lead. Since most of these properties have direct bearing on an
interaction with water, the consequences of such an interaction are not
directly predictable.
For this reason, a preliminary analysis of the Li-Pb - H20 reaction is
performed using a static calculation. In this case, the breeder inside
one blanket module is allowed to interact completely with varying amounts
of the water available to that module. Assuming the heat of reaction is
contained within the blanket, the equilibrium temperature of the reaction
products, unreacted breeder and blanket structural materials is then
determined.
Such a scenario is unrealistic, but this calculation is important
for two reasons. First, it serves as a reference for further study.
Second, with its assumptions, such a calculation may indicate the
maximum attainable bianket temperature in a particular module in the case
of an internal blanket water interaction.
3.2 Assumptions and Methodology
The outer blanket section of an individual module is chosen for
consideration. The inner blanket section contains only a nominal amount
of breeder and the consequences of an accident in that section do not
-38-
appear as severe. Data from the NUWMAK design (Table 7.H.2) indicates
that an outer blanket module contains 38.4 tonnes of titanium structural
material, 106.0 tonnes of graphite and 17.7 m3 of space to contain the
breeder. Therefore, the amount of breeder present can be determined with
knowledge of the density.
The initial temperature of breeder and graphite is 400 *C. The
structural materials are at a temperature of 350 *C and the coolant is
at 300 *C and 1250 psi. The reaction between breeder and coolant is
assumed to be immediate and complete at 400 *C, the heat of reaction
helping to raise the water temperature to that point. The heat of reaction
can be determined using:
AHr = AH 5 + ZAHprod - EAHreact, cal/g breeder (3.1)
where AH2 5 is the standard heat of hydrolysis at 25 'C and AHprod and
AHreact are the enthalpy changes of reaction products and reactants,
respectively, as they are heated from 25 *C to 400 *C.
The amount of coolant water available to the outer blanket module
can be determined by analysis of NUWMAK's steam generating unit. In this
respect, NUWMAK is very much like a fission boiling water reactor [4].
Examination of the Dresden BWR reveals that the total coolant volume in
the 3411 MW th plant's cooling system is 11,695 ft3 [10]. Scaling this
down to NUWMAK's 2283 MWth output and assuming the average density of
water in the coolant loop to be 62.37 lb/ft 3 (an overestimate), it can be
shown that approximately 15,260 pounds of water are available to
interact with the breeder in one module.
---------- -
-39-
It is assumed that a fixed percentage of this -cooling water interacts
with the breeder. Thereafter, no loss of heat is allowed from the
blanket. The resulting final equilibrium temperature can be calculated
using the expression
T f= T 0 + R (3.2)(Ms~s + Mb'b + ZMRi Ri
where Tf = final equilibrium blanket temperature
T = initial blanket temperature
QR = reduced heat of reaction
Ms = structural mass
Mb = remaining breeder mass after reaction
MR = reaction product mass after reaction
C = mean specific heat for each component
Reaction products include hydrogen gas, LiOH and the alloy element.
A proper evaluation of the M C. terms in the above equation varies
with each component. For example, LiOH is evaluated above its melting
point as
M LiOH [s(T mel t- To)+ AHmel t L(Tf-Tmelt) (MLiOH LiOH T T (3.3)
where Cs = mean solid specific heat of LiOH
CL = mean liquid specific heat of LiOH at 470 *C
AHmelt = heat of melting for LiOH at 470 'C
Tmelt = melting point of LiOH (470 *C)
-40-
Similar expressions can be written for the other components.
The reduced heat of reaction can be written as
QR = xMc [ao AHR ~c (T - T )] - MTi CTi (To - T i), (3.4)
where Mc = mass of total available- coolant
M = mass of titanium structural material
Cc = mean specific heat of coolant
CTi mean specific heat of titanium structural material
Tc = coolant temperature
TTi = titanium structural material temperature
x = fraction of available coolant reacting
ao = reaction stoichiometric combination constant
This is done to raise the coolant and titanium alloy structure to the
initial blanket temperature of 400 *C.
3.3 Results and Discussion
Figure 3.1 shows the resulting equilibrium blanket temperatures for
the various breeders under consideration, plotted against the reacting
percentage of available water. A number of interesting results are noted.
First, as expected, the pure lithium breeding blanket reached the
highest temperature upon reaction with water. The dotted line signifies
that with a high percentage of available water reacting, some of the
unreacted lithium will begin to vaporize at a temperature also close to
the melting point of steel. This indicates a potential for further
problems if a steel blanket liner is used.
-41-
TEMPERA
URE
C
±1450
1300
1±50
1000
700
550
400
0.25 0.50 0.75 1.00
PERCENTAGE OF AVAILABLE H20 .REACTING
Figure 3.1 Equilibrium Final Temperature Profiles forVarious Breeders in the Static Calculation.
Li
LiAl
Li Pb
-.- - Li2
- -
-42-
Li7Pb2 and LiAl are very much alike. Though lower equilibrium
temperatures are exhibited than those of the pure lithium breeder, the
difference is not very large to be significant. At low percentages of
reacting available water, there is no difference.
Li20 and LiPb4, on the other hand, appear to be significantly "cooler"
than the pure lithium case. In the case of Li20, the key difference is a
very low heat of reaction with water. LiPb4 , with a relatively high
density, is the only case in which there exists more available water
than breeder. Thus, a limited heat of reaction and large residue of
lead leads to reduced equilibrium temperatures.
I- -I
-43-
CHAPTER 4. DYNAMIC CALCULATION USING LITFIRE
4.1 Introduction
Though valuable as a reference, the calculations of Chapter 3 have
little to do with a plausible internal blanket breeder-coolant interaction.
It is incorrect to assume that these materials will react instantly at a
constant temperature; it is imprudent to declare that the flow of cooling
water will cease and that all heat will be retained within the blanket
perimeter. Clearly, a dynamic formulation is needed.
To this end, the LITFIRE computer code is modified to estimate the
thermal response of the NUWMAK blanket to possible accidents. In this
modification, called the internal blanket accident option, the breeder and
water react in a zone located in the middle of the breeder mass. The
leakage of water into this "reaction zone" is determined by the number of
broken coolant tubes, set small enough to justify the assumption that
this is the limiting effect on the reaction rate. The heat of reaction
is transferred to the breeder mass by conduction and free convection, to
the blanket liner and shield by further conduction, and out of the
blanket via forced convective cooling by unbroken coolant tubes. Figure
4.1 shows the heat flow diagram for this system.
It is hoped this model presents a truer picture of what will happen
within the blanket in the event of a cooling system leak. Again, due to
uncertainties concerning data and some assumptions, this study can only
provide a measure of relativt safety, compared with the trials
utilizing liquid lithium.
-44-
7Heatof REACTION ZONE ;G4onvec ve
Reaction Cooling
Free Convection Conduction
FIRST BREEDER ELEMENT CoolingCooling
- Conduction
BREEDER SECOND BREEDER ELEMENT ) ConvectiveZONE C Cooling
4'Conduction
FINAL BREEDER ELEMENT ConvectiveCooling
Conduction
LINER
Conduction
SHIELD
Figure 4.1 Internal Blanket Accident Option Heat FlowDiagram.
-45-
4.2 LITFIRE Description
LITFIRE is a computer code developed at MIT [11] to predict the
consequences of a hypothetical lithium spill in a fusion reactor
containment. It was first written in 1977 as a mofidication of the
Argonne National Laboratory code SPOOLFIRE, used to model the conse-
quences of sodium fires. LITFIRE was later modified and improved in
1980 [3], utilizing the experimental results of small-scale lithium
spill tests performed at the Hanford Engineering Development Laboratory.
In this code, the flow of heat is traced from the lithium reaction
zone source to reactor containment components, and eventually out to
the ambient. This system is simulated by a nodal network in which
each node has a heat capacity and temperature equal to that of its
physical counterpart. Heat flows between nodes are calculated using
standard heat transfer correlations.
To provide the reactor containment thermal and pressure response,
LITFIRE solves a set of coupled heat and mass transfer equations.
This is done by using the method of finite differences for the spacial
dimensions, and either Simpson's rule or a Runge-Kutta method in the
time domain [3]. Properties are computed at each time step from the
integral equation
t
Y(t) = Y(t0 ) + dt' dY/dt',
where the rates of change dY/dt are given for each node by finite
difference solution of the heat transfer relations.
-46-
4.3 Internal Blanket Accident Option
4.3.1 Assumptions and Structural Model
The internal blanket accident option models an accidental inter-
action of coolant water and lithium-based breeder in the center of an
outside blanket module. This interaction is caused by a breach of
several neighboring coolant tubes, while the reactor as a whole undergoes
normal operation.
It is assumed that this event is undetected, thus assuring
continuance of the plasma burn and coolant recirculation. It is felt
that the three monitored parameters relevant to an accident of this
type, namely bulk breeding material temperature, coolant temperature,
and coolant flow rate, will not change appreciably until later stages
of the accident.
The reaction rate is immediate and limited by the leakage of water
into the breeding material. The leakage rate, dictated by the number of
broken coolant tubes, is set very low, 0.6 kg/sec (three broken tubes),
to make this assumption reasonable. Although there is a suspicion
that the water reaction rate of the lithium-lead alloys is slow at low
temperatures, no data exists. It is also assumed that the reaction
zone pressure at high temperatures does not significantly retard the
leakage rate of water into the zone.
The reaction zone is very difficult to characterize. However,
certain assumptions can be made. First, the zone can be considered
spherical, as boiling water at 8.6 MPa will disperse equally in all
directions upon tube rupture. The reaction zone must be large enough
to accomodate the influx of breeder and coolant, thus the zone radius
-47-
should be large compared to the coolant tube pitch length. However, to
accomodate the assumption that the water reiction is instantaneous, the
reaction zone volume should be small, compared to that of the blanket
module.
The initial radius of the reaction zone for three ruptured coolant
tubes is set at one foot. This is over six times the characteristic
distance separating the three coolant tubes in question. The volume
of this zone is less than 2% of the total blanket volume. This seems
reasonable for the small leakage rate. Further research in this area
would aid the accuracy of the model.
The reaction products (LiOH and alloy element, if any) remain in the
reaction zone, thus increasing the radius of this zone with time. The
heat capacity of this expanded zone is calculated summing the products
of the individual heat capacity of each component multiplied by the
weight percent.
The nodal structure of this system is shown in Figure 4.2. It can
be seen that the reaction zone and breeder mass a.re broken into a number
of sections. This is to more accurately account for heat transfer by
conduction. The number of sections in each zone is selected so as to
keep the element widths to approximately 6 inches. These elements
increase and decrease in width with time in the reaction zone and
breeder zone, respectively, as the reaction zone expands.
The blanket elements are spherical, like the reaction zone, to
facilitate computation. The outer element is therefore irregularly
shaped to account for the NUWMAK geometry. This is not expected to
create any difficulty, as it is doubtful that much heat will be
-48-
-a--.
N
"S
N'
REACTIONa *
ZONE L-' ,i1
'S
-'p..
7,
'5-
N, *.
'.5' *\'S .5
\ 5.
'~ *\~) . . . 0 0I
/ i/
I /5, I
5/ . S
//
5-
//
/
I
7/'
BREEDER ZONE
SHIELD
,L IN ER
Figure 4.2 Internal Blanket Accident OptionNode Structure.
-49-
transferred to this region. For completeness, the steel liner and
B4C shield are also monitored in the code. The conduction of heat is
assumed to stop at the far edge of the shield.
The heat of reaction is distributed evenly throughout the reaction
zone, heating the reactants and reaction products. Heat is removed by
conduction and free convection to the breeder zone, and via forced
convection by unbroken coolant tubes as shown in Fig. 4.1. The surface
area of cooling tubes in each element is calculated as a volume
percentage of the total.
Finally, it should be noted that the densities and thermal
conductivities of the lithium-lead alloys and other alternate breeders
are held constant with temperature in this analysis. As discussed in
the appendix, this data has only been determined at one temperature.
Rather than increase uncertainties with various correlations, the values
are unaltered.
4.3.2 Heat Transfer Mechanisms
A. Heat of Reaction
All of the alternate breeders considered in this study react to
some extent with water. Table 4.1 shows the reactions of interest.
Other reactions also take place, such as the production of Li202, but
are discarded as they play a very minor role. For exampl.e, the peroxide
is unstable above 250 'C [11] and is not produced above that temperature.
Reaction occurs at the reaction zone temperature Tcz' The heat
of reaction can be calculated using
AHR H25 + AHrod - EAHreact ,e Btu/lb breeder (4.1)
-50-
TABLE 4.1
Breeder-Coolant Reactions of Interest
AHhyd
(kJ/g-atom of Li)
Li + H20 - LiOH + 1/2 H2 205
1/7 Li7Pb2+ H20 + LiOH+ 1/2 H2 + 2/7 Pb 200
LiPb4 + H20 + LiOH + 1/2 H2 + 4Pb 170
LiAl + H20 LiOH +1/2 H2 + Al 200
Li20 + H20 + 2LiOH 64
-51-
where HO5 is the standard heat of hydrolysis at 25 C and AHprod and
AHreact are the enthalpy changes of the reaction products and reactants,
respectively, as they are heated from 25 *C to Tcz'
Since the reaction is immediate, limited by the leakage of water
into the reaction zone, the reaction rate is the leakage rate. This
can be written as
R = NT lb H20/sec (4.2)
where m is the mass flow rate of water through one tube and NT is the
number of ruptured tubes. Thus, the total heat generation rate inside
the reaction zone can be given by
Q = a0 AHR m NT BTU/sec (4.3)
where a is the stoichiometric combination constant for the breeder
and water in the given reaction.
B. Sensible Heat Addition to Reactants in the Reaction Zone
A portion of the heat of reaction is used to heat the inflowing
coolant water and breeder to the reaction zone temperature. This can
be written as
Qs =NTi w cw (Tcz- Tc) + rb cb (Tcz- T ) BTU/sec (4.4)
where m w is the mass flow rate of water in a coolant tube
c w is the mean specific heat of the coolant
-52-
m b is the mass influx of breeder to the reaction zone
Cb is the mean specific heat of the breeder
Tc is the coolant temperature
TL is the bulk breeder temperature.
In this case. the influx of breeder into the reaction zone is
considered equal to the leakage rate of the coolant into the zone, as
reaction is immediate . This mass transfer is further discussed in
the free convection section.
C. Forced Convective Cooling
Forced convection, due to the continued coolant recirculation
through undamaged tubes, is an important heat transfer mechanism.
Because only a small number of the 475 coolant tubes in an outside
blanket module are damaged, cooling will take place in both the
breeding and reaction zones. The cooling tube surface area in each
element can be determined as a volume percentage of the blanket as
a whole. For example, the initial reaction zone, approximately 2%
of the blanket by volume, comes into contact with roughly 2% of the
total cooling tube surface area. This total area can be determined
using the information in Table 2.7.
This total heat flow can be computed for each element using
Qc + (T - Tc) BTU/sec (4.5)k TiAso hA J
where 6 is the coolant tube thickness
kTi is the thermal conductivity of the titanium alloy
-53-
A s is the outer coolant tube surface area
AsI is the inner coolant tube surface area
h is the boiling water heat transfer coefficient
T. is the bulk temperature of the element in question.
D. Conduction
Conduction plays a major role in the transfer of heat from the
reaction zone to the breeder mass. The heat conduction term between
two elements can be expressed'as
Qcondij = Ai (Ti - Tj)/d 1 j BTU/sec (4.6)
where A is the inner element surface area
k is the inner element thermal conductivity
k is the outer element thermal conductivity
T is the inner element bulk temperature
T is the outer element bulk temperature
di. is the separation distance between the elements.
The surface area assigned to each element is at its outer
perimeter. In the above expression, it is assumed that the inner
element is at a higFier temperature, as is the case at all times in
the LITFIRE option.
E. Free Convection
A preliminary order of magnitude analysis indicates that the
free convective enhancement to conduction is Pr Gr 1 /2, where Pr and
Gr are the Prandl and Grashof numbers. For a 400 'C temperature
-54-
difference between the reaction and breeder zones in the lithium case,
this enhancement is better than a factor of ten. Thus, free convection
is an important mode of heat transfer in the model.
As mentioned before, there will be mass transfer in the breeding
zone due to the influx of this material into the reaction zone. It is
this movement that allows convective cooling of the reaction zone by
the first breeder zone element.
Given the spherical shape of the reaction zone, the semi-empiracle
relation
Fi = 2.0 + 0.60 Gr1/4 Pr1/3 (4.7)
is useful to find the average heat transfer coefficient for Grl/2
Prl/ 3 < 200. NIII is the average Nusselt number and is related to theaverage heat transfer coefficient him by
Nu =h m L/k (4.8)
where L, the characteristic distance, is in this case the reaction zone
diameter.
Thus, the heat flow due to free convection can be described by
Q'c AczDkb (2.0 + 0.60 Gr1/4 PrT/3 )( T 4.9)D cz- L sec
where Acz is the reaction zone surface area and kb is the bulk breeder
thermal conductivity. Gr = D3p2gaAT and Pr - C2 k are applicable to
-55-
the fluid breeders.
F. Radiation
Using an order of magnitude analysis, the radiative heat flow is
related to the conductive heat flow by
grad T3L Q (4.10)
where a is the Stefan-Boltzmann constant. At 1500 OF, this radiative
heat flow is a factor of ten less than that of conduction in a lithium
breeder. Therefore, radiation is neglected in the model.
4.3.3 The Numerical Scheme
The temperature of a thermal element may be found from the solution
to
mc t = q+ + q3 + ... , T = T0 at t = to, (4.11)
where mc is the element's heat capacity and ql, q2' q3 ... are heat
flows into the element, shown in Fig. 4.1. This may also be expressed
as
T ( +q 2 + q 3 + ... ) dt +T. (4.12)
t0
In LITFIRE, this is expressed as
T = INTGRL (T , dt/dt). (4.13)
-56-
A set of sub-routines is used to perform the integrutions using
either Simpson's Rule or a Runge-Kutta method.
For example, heat flows into the reaction zone are the heat of
reaction, sensible heat addition to the reactants, conduction, free
convection and forced convective cooling. Therefore, the temperature
of the reaction zone at time t can be determined in LITFIRE by using
Eq. (4.13) and
dT lQQ Q- Q1 (4.14)dtQ - Qs ~ QcR ~ condRL
where the subscript R'denotes the reaction zone and Li denotes the
first breeder element. Q, Qs' QcR' QcondRL1, and Q can be determined
using Equations (4.3), (4.4), (4.5), (4.6), and (4.9), respectively.
Similar equations can be written for each thermal element in the model.
4.4. Results and Discussion
Figure 4.3 shows the thermal response of the reaction zone (TCZ),
first breeder element (TLIl) and middle breeder element (TLI4) over the
first 1000 seconds for a lithium breeder accident, as described earlier
in this chapter. Similar graphs are plotted in Figures 4.4 through 4.7
for Li7Pb2, LiPb 4, LiAl and Li20 breeders, respectively. A number of
interesting points are noted.
First, the general shapes of the curves in each case are similar,
although different maximum temperatures are attained. A change of time
step shows no appreciable difference. The reaction zone ri.ses rapidly,
reaching a maximum value within the first two minutes of the coolant
tube breaks. Thereafter, the temperature decreases monotonically,
-57-
TCZ
- T L I4
100 200 300 400 SO 6ee 7ee see goo e0eTIME (SECONDS)
Figure 4.3 Lithium Breeder Thermal Response to WaterInteraction.
aiee
1900
1700TEM IseePER 1300ATU 1.±00R
E 00
700
see
300
-58-
19ee
1700
T 1500EMP 1300ERAT 1100URE 900
F
700
500
300
T C Z ~
T L 11TL14
100 200 300 400 500 600 700 800 900 1000
TIME (SECONDS)
Figure 4.4 Li Pb Breeder Thermal Response to HaterInter ction.
I
-59-
TEMPERATURE
1700
1500
1300
1100
900
'- 700
see
300
100 200 300 400 500 600 700 800 90 1000
TIME (SECONDS)
Figure 4.5 LiPb4 Breeder Thermal Response to L'aterInteraction.
TCZ
TLIl
- TL14
I
-60-
1700 - -
Ti'ee
EMP 1300 TCZER
1100
URE 90 ___ TITLIl
700 - L14
see --
300
100 200 300 400 500 600 700 800 900 1000
TIME (SECONDS)
Figure 4.6 Li,'.1 Breeder Thermal Response to VaterInteraction.
-61-
1300
T.E 1100MPERA goo
URE 700
500
300
100 200 300 400 500 600 700 800 900 1000
TIME (SECONDS)
Figure 4.7 Li C Breeder Thermal !esponse to UaterInteraction.
TCZ
TL14- TLI4 -
- -I I I I I I I I
-62-
more gradually as time progresses. The first blanket element exhibits
similar behavior, but at lower temperatures and lagging over a minute
behind. The middle blanket element is relatively unchanged, slowly
increasing 50 OF in the lithium case and nearly constant in the
alternate breeders.
This behavior may be due to different characteristic times for the
various heat transfer processes. The heat of reaction in the reaction
zone is instantaneous and relatively large compared to the conductive
and convective flows, thus a rapid initial rise. Eventually, as the
temperature difference between the reaction zone and first breeder
element increases, so do the conductive and convective flows and the
temperature profile flattens and decreases. Thereafter, as this
temperature difference decreases, the reaction zone temperature decreases
more gradually. This continues until the breeder (or water, in the LiPb 4case) is depleted, eliminating the heat of reaction. Thereafter, all
zones are eventually recooled to 752 *F. The first 1000 seconds are
shown as the entire process takes upwards to 11 hours (4 x 104 seconds).
The relatively small volume of the reaction zone (less than 2% of
the blanket module volume) may account for both the high temperatures
attained in the reaction zone and the large temperature difference
between this zone and the first breeder element (approximately 1000 *F
in the lithium run). A small volume implies a small mass and surface
area. The small mass is very sensitive to the heat of reaction and the
small surface area impedes conductive and convective flows out. As
the reaction zone expands, this effect is diminished.
-63-
The blanket liner, shield and other breeder elements were also
monitored. All zones outside of the fourth breeder element showed
no significant change. Thus, the accident appears to be effectively
localized. The second and third breeder elements showed similar
behavior as the first, with progressively shorter time lags.
Figure 4.8 presents a comparison of the reaction zone temperature
profiles for the various breeders. As expected, the liquid lithium
breeder produces the highest temperatures. Also expected, using the
results of Chapter 3 as reference, is that the Li20 breeder temperatures
are significantly less. This breeder has a definite safety advantage
compared to pure lithium.
The same can not be said, however, of the lithium-lead breeders
and LiAl. Though less, the resulting temperatures are well within the
range of the lithium case, as close as 70 OF (Li 7Pb 2 ) and not further
apart than 250 OF (LiPb4). These differences are insignificant at a
base temperature of 1950 *F.
This result was surprising in the case of LiPb 4. Equation (4.14)
indicates that the temperature rate of change in the reaction zone is
inversely proportional to the reaction zone mass. Since the reaction
zone volume is initially fixed and there is a factor of 20 increase
in the density of LiPb4 over that of Li (at 400 *C, the density of Li
3 3is 0.51 g/cm ; the density of LiPb 4 is 9.9 g/cm ), it was felt that the
temperature rise would be proportionally decreased.
However, a closer look at Eq. (4.14) indicates that the temperature
rate of change is also inversely proportional to the reaction zone
specific heat. In this case, the specific heat of LiPb4 , approximately
-64-
200 300
TIME (SECONDS)
400 500
Figure 4.8 Comparison of Rleactor Zone Temperature Profilesof the Various Breeders
21ee
iee
1700
Isee
1300
1100
TEMPERATURE
F
Li
-LiAl Li Ph 2
Li 0
-. I
900
700
-65-
that of Pb, i-s nearly a factor of 20 less than that of pure lithium
(at 400 *C, the specific heat of lithium is 1.01 cal/g- *F; that of
LiPb4 is 0.041 cal/g - 'F). Thus, the terms in the denominator of
Eq. (4.14) effectively cancel each other out and the slightly different
reaction zone temperature profiles of Li and LiPb4 are simply a
reflection of the slightly different heats of reaction of the two
breeders with water.
A comparison of the thermal responses of the first breeder elements
for the various breeders, shown in Fig. 4.9, is also interesting.
Again, the lithium case produces the highest temperatures and the Li2O
case produces the lowest. The lithium-lead alloy and LiAl results are
again similar. Here the Li7Pb2 element is cooler overall due to a very
low thermal conductivity, experienced in the lithium-lead system at
a 20% lithium atom percentage [13]. However, in this comparison, the
differences between these alloys and the lithium case are more pronounced.
This indicates that the use of liquid lithium.will produce more wide-
spread accidental consequences.
-66-
1109
ieeeTEMPER SeeATURE
F 800
700
100 200 300 400 500 600 700 800 s00 1000
TIME (SECONDS)
Figure 4.9 Comparison of First Breeder Element TemperatureProfiles of the '!arious Breeders.
Li 2
I I I * I I I
-67-
CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS
Results indicate that the lithium-lead alloys may not be signifi-
cantly safer than pure lithium as a fusion reactor breeding material,
utilizing the NUWMAK geometry. In both calculations, short term
temperatures resulting from interaction of Li7Pb2 and LiPb4 with water,
though lower, are within a few hundred degrees of those associated with
the use of liquid lithium.
However, a proper conclusion to this study is that a conclusion
cannot yet be made. The calculations of Chapters 3 and 4 provide an
overview of the safety question, raising some interesting observations
and determining areas that need to be explored in more detail.
First, the lithium-lead alloys and LiAl can pose safety problems
approximate to those of liquid lithium, as noted above. This can be
quite serious, as shown in Chapter 3, with temperatures reaching to
the melting point of steel in a water-cooled blanket. For this reason
alone, further study of these alternate breeders is required.
Results of. Chapter 4 indicate that such an interaction could go
undetected, as a continuance in coolant recirculation may keep the
consequences localized. Measurable quantities, like bulk breeder
temperature and coolant temperature and flow rate a're practically
unperturbed. Thus, further design work might include features to
mitigate this problem.
Uncertainties in characterizing the reaction zone in the dynamic
model render the resulting temperature profiles less meaningful. Further
work in this area, perhaps experimental, would make the model more
accurate.
-68-
Finally, better physical properties data on the alternate breeders
is required. In particular, an understanding of the water reaction
rates is central to the study of these materials. If it can be proved,
as surmized, that these rates are significantly lower than those of
liquid lithium, a significant reduction in safety hazards may be
assured.
-69-
REFERENCES
1. A. J. Impink, Jr. and W. G. Homeyer, "Tritium Regeneration inProposed Fusion Power Reactors," Transactions of the AmericanNuclear Society, S(l): 100, June 1962.
2. J. L. Ballif, et al., "Lithium Literature Review: Lithium'sProperties and Interactions," HEDL report TC-1000, January, 1978.
3. Mark S. Tillack, "Development and Verification of the LITFIRE Modelfor Predicting the Effects of Lithium Spills in Fusion ReactorContainments," Master's Thesis, MIT, June 1980.
4. B. Badger, et al., "NUWMAK", University of Wisconsin, UWFDM-330,March 1979.
5. "Special Purpose Materials - Annual Progress Report," DOE/ET-0095,May 1979.
6. R. H. Wiswall and E. Wirsing, "Tritium Recovery from Fusion BlanketsUsing Solid Lithium Compounds," Radiation Effects and TritiumTechnology for Fusion Reactors Conference, Gatlinburg, Tenn., 1975.
7. R. G. Clemmer, et al., "Assessment of Solid Breeding Blanket Ophonsfor Commercial Tokamak Reactors," ANL-CEN/205, 1980.
8. N. A. Frigerio and L. L. LaVoy, "The Preparation and Properties ofLiPb, A Novel Material for Shields and Collimators," NuclearTechnology, 10, 322, 1971.
9. D. L. Smith, et al., "Fusion Reactor Blanket/Shield Design Study,"ANL/FPP-79-1, July 1979.
10. "Dresden Nuclear Power Station Units 2 and 3, Safety Analysis Report,"Commonwealth Edison Company, 1968.
11. D. A. Dube and M. S. Kazimi, "Analysis of Design Strategies forMitigating the Consequences of Lithium Fire within Containment ofControlled Thermonuclear Reactors," MITNE-219, July 1978.
12. R. Bird, W. Stewart and E. Lightfoot, Transport Phenomenon, JohnWiley & Sons, Inc., 1960.
13. Marie-Louis Sabourgi, et al., "Thermodynamic Properties of aQuasi-ionic Alloy from Electromotive Force Measurements: The Li-PbSystem," The Journal of Chemical Physics, 68, 4, February 15, 1978.
14. John H. Perry, et al., Chemical Engineers' Handbook, McGraw-HillBook Company, Inc., 1963.
-70-
APPENDIX A
Physical Property Data
-71-
Table A.1 summarizes the important physical property data of the
various alternate breeders analyzed in this report. Except as indicated,
all of these values are gathered from the previously identified
references. It is important to realize that, aside from the lithium
and melting point data, all numbers are estimates at best.
For reasons detailed earlier, only the physical properties of the
lithium breeder are allowed to vary with temperature in calculations
of Chapters 3 and 4. The correlations used are:
p = 0.5368 - 1.0208 x 10~ 4T (g/cm3 )k = 10.48 + 4.98 x 10- 3 (T- 180.6) -0.58x10- 6 (T-180.6) 2
(cal/sec-m-*C)
c = 1.0037 - 0.01063x + 0.00564x2 - 0.001279x3 (cal/g *C)
where x = .004938T - 6.20741
Here, p = density of lithium
k = thermal conductivity of lithium
cp = specific heat of lithium
T = lithium temperature in *C
The latent heats of melting for the alloy breeders are determined
using the correlation
Hmelt/Tmel t " 2.2
This is an average value for metallic alloys [14].
-72-
The thermal conductivity of LiPb4 is estimated with the correlation
km = k1w1 + k2w2 - 0.72(k 2 - k1)(w w2)
This is appropriate for a binary liquid mixture. Here, the weight
fraction w2 refers to the component having the larger value of k [14].
The specific heat data of the alloy breeders is determined using
the relation
C, Xi c +XcACalloy Li CLi + XA CPA
where XLi = weight fraction of lithium
XA = weight fraction of the alloy element
cpA = specific heat of the alloy element
c =Li specific heat of lithium
The specific heat values for the alloy elements, lead and aluminum,
can be found in the literature.
-73-
TABLE A.1
Summary of Physical Properties of Candidate
Breeding Materials at Standard Conditions
Lithium Li7Pb2LiPb 4 LiAl Li20
Properties
Melting Point, *K
AHmelt, cal/g mole
Density, g/cm 3
Li atom density, g/cm3
Thermal conductivityw/m-k
Specific Heat cal/g OK
Heat of Reactionwith Water
g-atom Li
Atomic weight
453
722.4
0.51
0.51
50
1.01
245
7
999
2200 a
4.59
0.49
\20
0.14b
200
463
508
1120a
9.9
0.08
,'35 a
973
2140 a
1.76
0.37
30
0. 04 1b 0.44b
170c
835
200
1970
2.01
0.93
1.73
0.35
64
34 30
correlation
interpolated value
~estimated
a.
b.
c.
-74-
APPENDIX B
Complete.Listing of LITFIRE
-75-
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