Post on 29-Jan-2021
transcript
CFD SIMULATION OF LIQUID ROCKET ENGINE INJECTORS
Richard Farmer & Gary Cheng
SECA, Inc.
Yen-Sen Chen
ESI, inc,
INTRODUCTION
Detailed design issues associated with liquid rocket engine injectors and combustion chamber
operation require CFD methodology which simulates highly three-dimensional, turbulent, vaporizing,
and combusting flows. The primary utility of such simulations involves predicting multi-dimensional
effects caused by specific injector configurations. SECA, Inc. and Engineering Sciences, Inc. have
been developing appropriate computational methodology for NASA/MSFC for the past decade. CFD
tools and computers have improved dramatically during this time period; however, the physical
submodels used in these analyses must still remain relatively simple in order to produce useful results.
Simulations of clustered coaxial and impinger injector elements for hydrogen and hydrocarbon fuels,
which account for real fluid properties, is the immediate goal of this research. The spray combustion
codes are based on the FDNS CFD code _ and are structured to represent homogeneous and
heterogeneous spray combustion. The homogeneous spray model treats the flow as a continuum of
multi-phase, multicomponent fluids which move without thermal or velocity lags between the phases.
Two heterogeneous models were developed: (1) a volume-of-fluid (VOF) model which represents
the liquid core of coaxial or impinger jets and their atomization and vaporization, and (2) a Blob
model which represents the injected streams as a cloud of droplets the size of the injector orifice
which subsequently exhibit particle interaction, vaporization, and combustion. All of these spray
models are computationally intensive, but this is unavoidable to accurately account for the complex
physics and coml_ustion which is to be predicted. Work is currently in progress to parallelize these
codes to improve" their computational efficiency.
These spray combustion codes were used to simulate the three test cases which are the
subject of the 2nd International Workshop 0n Rocket Combustion Modeling. Such test cases are
considered by these investigators to be very valuable for code validation because combustion kinetics,
turbulence models and atomization models based on low pressure experiments of hydrogen air
combustion do not adequately verify analytical or CFD submodels which are necessary to simulate
rocket engine combustion.
We wish to emphasize that the simulations which we prepared for this meeting are meant to
test the accuracy of the approximations used in our general purpose spray combustion models, rather
than represent a definitive analysis of each of the experiments which were conducted. Our goal is to
accurately predict local temperatures and mixture ratios in rocket engines; hence predicting individual
experiments is used only for code validation. To replace the conventional JANNAF standard
axisymmetric finite-rate (TDK) computer code 2 for performance prediction with CFD cases, such
codes must posses two features. Firstly, they must be as easy to use and of comparable run times for
conventional performance predictions. Secondly, they must provide more detailed predictions of the
flowfieldsnearthe injectorface. Specifically,theymustaccuratelypredicttheconvectivemixingofinjectedliquid propellantsin termsof the injectorelementconfigurations.
METHODOLOGY
Homogeneous Spray Combustion Model
The homogeneous spray combustion CFD codes utilize very general thermodynamics in a
conventional CFD code. The heterogeneous codes use tabulated properties for the liquid phase and
ideal gas properties for the vapor phase. Thermal and caloric equations of state, vapor pressure, heat
of vaporization, surface tension, and transport properties are modeled with the equations of state
proposed by Hirshfelder, et al3'4 (we term these the HBMS equations of state) and with conventional
correlations, _ for the other properties. The property correlations used were not chosen for their
absolute accuracy, but for their validity over a _de range of temperatures and pressures and for
requiring a minimum of data to describe a particular species. These correlations are explicit in density
and temperature..
HBMS thermal equation of state:4 6
P - Z T_-2 E Bi.iP_ j--1 i=l
t-2 T pPr ;Tr= n ;pr --
Tc Pc
HBMS caloric equation of state:
HRH0_z¢?[ P ((gP'_q .: Po p_T,
These equations are based on the "theorem of corresponding states" for real fluids, which essentially
means that the p-v-T relations for all species are similar if these variables are normalized with their
values at the critical point,i.e, if reduced values are used. The reduced values in these equations are
indicated with a sfibscript r. Ho is the ideal gas species enthalpy. Zc is the compressibility for a given
species at the critical point. The HBMS equations are attractive to use because arbitrary correlations
for vapor pressure, heat of vaporization, and liquid densities can be used. Since multi-component
fluid/vapor mixtures may be present in the flowfield, the mixture properties are calculated by the
additive volume method. This means that mu!tiphase mixtures are treated as ideal solutions. For
H2/O2 propellants under conditions where the species become ideal gases, the thermodynamic data
from the CEC code 6 were used.
The combustion reactions used in the simulations reported herein are shown in Table 1. Not
all of the reactions were used in all of the combustion simulations. Elementary rate data for these
reactions are reported by Gardner, et al 7'8. Such data are empirical and were obtained for
hydrogen/air combustion, under conditions far different from those encountered in rocket engines.
21
Table 1. Combustion Model for H2/O2 Reaction
Chain initiation:
H2 + 02 -- 2OH
1.86 142 + 02 = 1.645 H20 + 0.067 O + 0.142 H + 0.288 OH
Chain Branching:
I42 + OH- H20 + H
2 OH = H20 + O
H2+O=H+OH
O2+H-O+OH
Chain termination:
O+H+M=OH+M
20 + M = 02 + M
2H+M=H2+M
OH+H+M=H20 +M
The CFD solver used was the Finite-Difference Navier-Stokes code with provision for using
real fluid properties, the FDNS-RFV codel This code is pressure based; it differs from an ideal gas
code in the methodology used to relate the pressure correction to the continuity equation and of
course in the properties subroutines used. The pressure correction (p_) equation used in the FDNS-
RFV code is:
3p p' • nA*(uil3pp' ) - Ae(P*DpA p') = -A*(p*tli) P -13
A T At
p.+l=p_ +p, ; 13p=)'/a 2 ; ui = -Dp Ap'
where the superscripts * and n denote the value at the intermediate and previous time steps,
respectively. Dp is the inverse of the matrix gfthe coefficients of the convective terms in the finite-
difference form of the inviscid equations of motion. This is not an obvious definition, but is one
which has made the FDNS-RFVcode a useful solver. The sound speed used in the pressure
correction equation is that calculated for the real fluid multi-component mixture.
In all cases simulated, a k-e turbulence model was used to close the mass averaged
transport equations solved by the code. Our experience is that this incompressible turbulence
model overestimates the mixing in a combusting fiowfield. However, since the liquid propellants
are also mixed by this model, we concluded that there are currently insufficient data to better tune
the turbulence model. The homogeneous spray model has been used to simulate: (1) a single
element like-on-like (LOL) impinger injector element and a single element unlike impinger
element for the configuration and flow conditions used in the cold-flow experiments; (2) an
ensemble of injector elements in the Fastrac engine; and (3) several configurations of the vortex
engine currently being developed. 9
3
Heterogeneous Spray Combustion Model
Simulations of shear coaxial injector combustion may include models that characterize the
breakup or atomization of the round liquid jet, subsequent droplet secondary breakup, turbulence
dispersion, droplet evaporation and gas-phase mixing and combustion. The primary atomization rate
of the liquid jet ismodeled following the work of Reitz and Diwakar l0 Applications of this model
to shear coaxial injector test cases, with a volume-of-fluid equation to model the liquid fuel/oxidizer
jets, were presented by Chen, et al. _1. For the present application, since the liquid core length and
the initial droplet size are specified, the primary atomization model is therefore ignored.
Particulate Two-Phase Flow Model
The two-phase interactions are important throughout the life history of the droplets. In the
initial phase of injection, momentum and energy exchanges through the drag forces and heat transfer
are dominating. These inter-phase transfer terms appear in the Navier-Stokes equations that are
solved using the present CFD flow solver. Mass transfer occurs as the particles are heated through
the surrounding hot gas. Mean gas-phase properties and turbulence eddy properties are used for the
statistical droplet tracking calculations.
Droplet Secondary Breakup ModelThe TAB (Taylor Analogy Breakup) model of O'Rouke and Amsden _2 is based on an
analogy between an oscillating and distorting droplet and a spring-mass system. The restoring force
of the spring is analogous to the surface tension forces on the droplet surface. The external force on
the mass is analogous to the gas aerodynamic force. The damping forces due to liquid viscosity are
introduced also based on this model.
Droplet-Turbulence Interaction
A two-equation turbulence model is used to characterize the flowfield turbulence quantities,
such as turbulence fluctuations, eddy life time and length scale. TUrbulent effects on particles are
modeled by asstiming the influence of velocity fluctuations on the particles creates statistical
dispersion of the particles. The velocity fluctuations, which are calculated from the solutions of the
turbulence kinetic energy, are assumed to follow a Gaussian distribution with standard deviation
proportional to the square root of turbulence kinetic energy. This magnitude of this statistical particle
dispersion is then transported following the trajectory of the particles with their radii of influence
within which coupling effects (also follow the Gaussian distribution) between two phases occur. This
method is classified as the parcel PDF (cloud) model, by Shang 13, for turbulent particle dispersion.
As oppose to the stochastic, separated flow (SSF) model, the number of computational particles
required is drastically reduced for the same statistical representation of the spray. This provides great
savings in computational effort in performing the spray combustion computations.
Droplet Evaporation Model
The droplet evaporation rates and the droplet heat-up rates are determined using the general
evaporation model of Schuman 14, which is continuously valid from subcritical to supercritical
conditions. This vaporization model was extended from the classical approach _5, by neglecting the
effects of solubility of the surrounding gas into the droplet. However, this approach satisfies the
global transient film continuity equation for the drop vapor and the ambient gas to obtain the
expressions consistent for the molar flow rates .....
Chemical Reaction Model
A finite-rate chemistry model with point-implicit integration method is employed in the
present study. A 9-reaction kinetics model of Anon 16is used for modeling the Hz-Oz combustion.
The initiation reaction used produced OH. This chemistry model is listed in Table 1.
SIMULATIONS OF THE RCM-1 EXPERIMENTS
The LN2 cases, RCM- 1-A and -B, were simulated with the homogeneous spray model. The
flow predicted resembles a dense fluid jet with strong density gradients in the shear layer. Such a
flow has been observed in a similar super-critical nitrogen jet experiment reported by Chehroudi, et
al _7. These predictions should compare well to the DLR experimental data. If the comparisons are
not good, adjustment of the parameters in the two-equation k-e or the initial turbulence level
parameters could be made for a better fit of the data. Such tuning has not previously been made since
appropriate test data were not available. For a definitive analysis of the experiments, conjugate heat
transfer to the injector hardware and consideration of the duration of the experiment should be made.
The jet is discharging into a gaseous nitrogen environment, the recirculated gas should become slowly
cooled until a steady state is reached. Since the temporal variation of the recirculating gas
temperature was not reported, the time thaft_/e_'YD simulation should be terminated can not be
determined. Since the measurements were made very close to the injector exit, good simulation ofthe gas temperature might not be crucially important.
The injector configuration and flow conditions for the cryogenic nitrogen jet of the RCM-1
test cases are illustrated in Fig. 1. It can be seen that the chamber pressure for both cases is above
the critical pressure of nitrogen. A 10 lx 1 l-mesh system was used to discretize the injector section,
while the chamber section was modeled by a 30lxl01-mesh system for Case RCM-1-A.. The same
grid system was used to simulate both RCM-!'A and RCM-1-B test cases. The numerical result of
RCM-I-A test case at the locations specified by _CM was plotted as shown in Figures 2-6.
Notice the temperature profiles in Figure 4. These two cold flow cases are not steady-state, although
the simulations assumed this to be the situation, The simulations presented represent a time-slice at
some arbitrary time. Figure 7 shows the flowfieldd near the injector tip. A finer grid system (101x15,
and 301x141) was employed to simulate the RCM-1-B. The numerical results of RCM-1-B test case
are plotted in Figures 8-12. The flowfield is 15resented in Fig. 13. Notice that only a small segment
of the chamber is shown so that gradients in the flowfield may be clearly seen.
5
View A-A
122 mm
800 turn -q
i i i,, ii i i i,!iliiii,,iii,, ii ii iiiiij ,,i::,i i _iiiiiiii!iii!iiii iii it2.2 rnm LN_
Faceplate
View A-A
Case A Case B
Chamber Pressure 3.g7 MPa 5.g8 MPa
Temperature 128.9 °K 128.7 °K
Mass Flow Rate O.oogg5 kg/s 0.01069 kg/s
,o_,TKE o.oo3u'_, o.oo3-u_
Cd/Ical Pressure of N_:3.4 MPa
Critical Temperalure of N_: 126.2 °K
U,,_.Injection Veloclly ol
Figure 1 Configuration of RCM-1 Test Case
(a) 8treamwise Velocity
1.1
l.O
0.9
0.8
E 0.7
8 o.6
_5 0.5
_ 0.4el-
0.3
0.2
0.1
O.C
O.B
E 0.7
0.6
_ 0.5N
0.4
0.3
(b) Density
I.I
1.0
0.9
0.2
0.1_-
0._5' '
i
-,I,I,I , I , I , I , I l I I I L i i I
! 2 3 4 5 6 7 460 465U (m/sec) Den_t7 _g/rn 9)
(c) Turbulence Kinetic Energy
I.I
0.05 0.! 0.15 0.2
TKE [m_/sec _)
Figure 2 Flow Properties at the Injector Exit ofRCM-1-A
6w
45O
4OO
35O
3O0
-_ 250
t_c 2008.)o
150
tO0
X = 5rnrn
× = 15ram
....... X = 25turn
X = 35ram
.......... X = 45ram
X = 55ram
50
0 Hi,l,ilnl0 1 2 3 4 5 6 7 8 9 10
Radial Distance (mr-n)
Figure 3 Density Profiles at Various Streamwise Locations of RCM-1-A
300
250
200
t---
150
- ,t / I'_ ,.,,,'" ..,,,.,'"
I "' "#" /J'/" """ "' /
- I J i / ,,'"- I I .i / .../ t""
! _ .s / .. /"_ _ i / ,,.. i- I i / / ." -/
I i ! / //'-
- ! _ ! / ..i/i- [ # ! I ..t _ X=Smm
- .......- _.*" -_-- -- -_ X = 35rnm
__ X= 55rnm
tO00 1 2 3 4 5 6 7 8 9 10
Radial Distance (mrn)
Figure 4 Temperature Profiles at Various Streamwise Locations ofRCM-1-A
1
7
6
4
"" 3E
v
2
F
- X = 5ram
.........__: - x= 15mm- -"_-._ ....... X = 25ram
.__, ..... X = 35turn
-_ _ __ .......... X= 45ram
0 1 2 3 4 5 6 7 8 g 10Radial Distance (mm)
Figure 5 Axial Velocity Profiles at Various Streamwise Locations ofRCM-I-A
CD
Ev
uJxd
Figure 6 Turbulent Kinetic Energy Profiles at Various Streamwise Locations ofRCM-1-A
LO
o o __ o _ _ o,_ o o o o "_ o o
!_i_i!!!iii!__i!iii_ii_!_i:_iiiiiiiiii_iiiiii"_!_i: ::":
(a} Streamwise Velocity (b) Density
I.I
1.0
0.9
0.8
,,_ O.7
_-0.6
_5 0.5
0.4
0.3
0.7
0.1
0.0
1.1
1.0
0.9
0.8
E 0.7
8 o.e
_ 0.5
O'4 i
0.3
0.2 J
_'2
:, I ,I t I , I i I , i II 2 3 4 5 6 7
U (m_c)
, I , I , I , I I
0_I0 513 516 519 522 525
Density [kg/m s)
(c) Turbulence Kinetic Energy
1.1_
1.o-
0.9-
o.e-
0.7--
_ o.e-Lm 0.5-E___0.4-
0.3-
0.2L
0.1-
I Jl
0.O(_ 0.05 O. 1 0.15 0.2
TKE (rnZ/sec 2)
Figure 8 Flow Properties at the Injector Exit of RCM-1-B
550
500
450
4O0
350
v
:,, 300
r-
m 250£3
20O
X = 51Tlffl
X= 15ram
....... X = 25turn................. X = 35ram
.......... X = 45ramX = 55ram
150
100
50 0 1 2 3 4 5 6 7 8 g
Radial Distance (rnrn)
lO
Figure 9 Density Profiles at Various Streamwise Locations of RCM-I-B
10
300
25O
,,¢'R...,
(1)
zooo_r',E05
I--
150
X = 5mm
X = 15ram
....... X = 25ram
X = 35mm
.......... X = 45ram
.....................X=55mm
1000 1 2 3 4 5 6 7 8 9 10
Radial Distance (mm )
Figure l 0 Temperature Profiles at Various Streamwise Locations of RCM- I-B
o
E
X= 5rnm
X = 15turn
....... X=25mrn
X = 35ram
.......... X=45mrn
X = 55ram
-10 I 2 :3 4 5 e 7 8 9 10
Radial Distance (turn)
Figure l l Axial Velocity Profiles at Various Streamwise Locations ofRCM-I-B
11
1.0
Figure 12 Turbulent Kinetic Energy Profiles at Various Streamwise Locations of RCM-1-B
12
c:.
c:.
0
c:.0'
LQ
o.C),
O
C)
C),
0'
_ _.-- _- ,,_-*.m ,_n_,_ _ ,L'W,L'W_ _ ----
=======================================================================I_iiii!ICiii:,iH!iiiiliii!i',lii!i:_i:,iiiilli_iiti::iiiii:_l_i!iiiM/Eiiiiilili:,!l;:i;ii;i;itiiiiiill;iiil_Cilliiiiiiliil;iitili,;ili_.:W!
Figure 1] Flow t)ropertiesNear the Injector of'RCM-1-B
13
SIMULATIONS OF THE RCM-2 EXPERIMENTS
The sub-critical combustion case, RCM-2, was simulated with both the heterogeneous and
the homogeneous spray combustion models. The MASCOTTE test data should be better than any
which have been previously used to tune the several parameters in these models. It is unreasonable
to expect that spray flames, even of hydrogen and oxygen, can be accurately predicted without
extensive model validation with test data representative of the conditions which exists in rocket
engine combustion chambers. Even global data like chamber pressure and thrust have not been
obtained for single coaxial element combustor flows. The IWRCM data provide a good starting
point, but no CFD model tuning has yet been attempted for such experiments. Direct comparisons
of predictions to test data at this point will not establish which of several modeling techniques is best.
The MASCOTTE single injector test chamber was used in a series of experimental programs
for subcritical and/or supercritical H2-O2 combustion. In the subcritical spray combustion test case
(RCM-2), the designed chamber pressure is 10 bar (or 9.87 atm). The injector orifice diameter for
the liquid oxygen (LOX) injection is 5 mm surrounded by an annular gaseous hydrogen jet with
channel width of 6.4 mm. The overall O/F ratio for this case is 2.11 (see the test conditions given in
Table 2).
Table 2. RCM-2 Test Case Operati
Conditions H2 02
Pressure 1 MPa 1 MPa
Mass flow rate
Temperature
Density
Cp
Velocity
Viscosity
Surface Tension
ng Conditions
23.7 g/s
287 K
0.84 kg/m3
14300 J/kg]K
319 m/s
8.6E-6 kg/m/s
50 g/S85 K
1170 kg/m 3
1690 J/kg/K
2.18 m/s
1.94E-4 kg/m/s
1.44E-2 N/m
The computational model includes the injector geometry, the combustion chamber and the
nozzle section. A 10-block structured mesh is generated (the total number of grid points equals
14,444) for the two-phase flow computation. Relative high grid density (about 10 micron spacing)is
packed in the injector lip region for the purpose of better flow resolution and flame holding in the
expected area. The LOX core length of 7.8 mm is assumed, which serves as the particle injection
boundary with the fixed particle size (82 microns), velocity (10 m/s) and angle distributions given in
the problem specification. Fixed mass-flow boundary conditions are used at the inlet while all flow
properties are extrapolated at the nozzle exit. Supersonic exit flow develops as part of the solution.
The computation starts with a cold flow with inlet and chamber pressure specified. The two-
phase flow particle breakup and evaporation model models are activated from the beginning. The
time step size of the time-marching solution method is 1 I.tsec. After 1000 time steps of cold flow
run, a heat source is introduced in the lip region between and oxygen and hydrogen streams where
a recirculation zone is established. At the same time, the finite-rate chemistry model is turned on to
start the flame spreading throughout the chamber. The chamber pressure drops at the beginning until
the flame fills up the entire chamber. Then, the pressure started to build up to the expected level
14
whentheinletandexit flowsshowsatisfactorymassconservationcondition.Thecalculatedaveragedchamber pressure is around 9.96 atm. The majority of the LOX particles do not survive very far
downstream of the injector exit. Some particles along the chamber axis do survive up to 70 mm
downstream of the injector.
The time-averaged temperature, temperature standard deviation, species mass-fraction
contours and temperature profiles at specified locations are plotted in the following figures. These
data are prepared as requested for data comparison purpose.
Figure 14 shows the mean temperature and standard deviation through the entire length of
the combustion chamber. A close up view of the nozzle tip region is also shown in this figure. Figure
15 shows the OH and 02 and Figure 16 the 1-I2and 1-120 concentration profiles, respectively, in this
same region. Figures 17-25 show radial temperature and standard deviation profiles at various axial
locations. Figures 26-30 show the axial temperature profiles at various radial locations. Figure 30
shows this profile at the near wall location. The flame predicted with this model is long and narrow.
The recirculation zone is very long.
The RCM-2 experiment was also simulated with the homogeneous spray combustion model.
The volume upstream of the injector element tip was neglected for this simulation. The grid use for
the internal element flow was 61 X 43; for the chamber it was 301 X 101. The nozzle was not
simulated. This grid system had a minimum grid spacing of 60 microns in the wake behind the lip
separating the LOX and hydrogen streams. The boundary conditions used are shown in Figure 31.
An equilibrium and several finite rate solutions were obtained for this configuration. The rate of the
global initiation reaction was set fast enough to stabilize the flame near the start of the shear layer.
This rate also essentially eliminated the waviness in the shear layer separating the LOX and hydrogen
streams, without averaging the solution. The stoichiometric coefficients in the global rate expression
were determined by an equilibrium calculation for a stoichiometric flame at the expected chamber
pressure. Such a practice produces temperatures with one rate expression which are very close to
those resulting from using a more detailed reaction mechanism.
The equilibrium solution at the interface between the internal element flow and the flow at the
nozzle tip are shown in Figure 32. The temperature profiles in the radial and axial directions are
shown in Figures 33 and 34, respectively. The temperature and oxygen and OH concentration
profiles are shown in Figure 35. The wall temperature profile is shown in Figure 36. All of these
figures are for the equilibrium solution. The finite rate solutions for the single global reaction and for
the global plus the elementary reactions of Table 1 were also obtained. As expected, the finite rate
solutions were slightly cooler than the equilibrium solutions. The predictions are very similar in all
results to those just shown. To emphasize this point the wall temperature profiles for all three cases
are shown in Figure 36. Even though the global rate was set fast enough to stabilize the flame with
this grid system, it was not so fast that equilibrium conditions were obtained.
Comparing the heterogeneous and homogeneous solutions, the former produced a longer,
thinner flame than the latter. Parameters in the spray combustion model could have been set such that
the solutions matched very closely, or so that both could match test data. Such a step cannot be made
until the RCM test data are published and the CFD models tuned. An optimum rocket engine spray
combustion model cannot be determined until this next validation step is undertaken.
15
. - 3-7290,_';C'Z.... ...... • .......
7.ZS6_OZ .... ...................
• . ,: -_.:---- ...........................4. _ F;-,i,_ _I.:.........................
_,_z,_+t'..z.... ..... ' ................. .....
I.OOoo_-_......... : .....i i ii i i iii ii i
(b) Temperature Standard Deviation (K)
Figure 14 Time-Averaged Temperature and Temperature Standard Deviation of RCM-2
16
DATA _5 ' : " : .............................. " .....
mmr+_s:,o.,i_-o__ii-;-i.i i.i ; i :-i +:.-?-i .i.i-i-i-:+ ? :.-I i :.-; : .+._.:-:.: .:-:.:._-: .:-:.:II
+! :o+rJ+_.,.+:.+rJ......... " ' " - " . ..................: : . : : - : : : : : : : : : : : : : ; ; : : ; : : : : : : : : : ; : : . : : : : : : :
" " o " "t .......... '. " ....................
(a) Time-Averaged OH Mass-Fraction Contours for X up to 150 mm
: : : : - : - : :: : : : : : : : :; ;; ;: : ; ; ; + : ; : :: :; : ; : ; : : ; :: :: ; : . : : : : ; :: ::
.......................... ? ...........................
DATA _5 . .+ .... ... ......... , ..+.. ..... . . '. ...... . ..........:. : :.:9._,_39e,01:. :.. :.:: ::.: .: :..:..:,. :. :+:-:-:.: :.:.:..:. :. :.::.::.: : • .:. :. :. :.::+::.::.:.:.:..'..
._ i+:i.}t',._,,.'+..O.. .;. --. +............;.. :.:........., .......+i;.. '.......
: : : : : : : :: :: : : : : : : : :: :: :: : : : : : • . :: : : : : . : :: ;; : : : : : : :; ::
(b) Time-Averaged 02 Mass-Fraction Contours for X up to 150 mm
Figure 15 Time-Averaged OH and O2 Mass Fractions of RCM-2
17
;o_-_Ai.,i_:.i_.•_...i-;.-i--:.-i_:_i-:--:--:-_-_._.-:-_._.-_-:--:---_.-:-:-_--_:--:--:_...i---.
_'._;0'.'..ii:_ :.iii_II. • :.:_:_-_ ...._i..:.i..:....:..-. .iiii:;:ii..i.-II..-.
(b) Time-Averaged H20 Mass-Fraction Contours for X up to 150 mm
Figure 16 Time-Averaged Hz and H20 Mass Fractions of RCM-2
18
35OO
cO
_3000
¢-,i"1o 2500
'10c_20006"J
1500,,i,,,.i
e,lE _ooo
E
_ 5O0
Radial Profile at X/D1 = 2
............... Mean TomperatureStandard Dm/ia_lan
n-/ , • IV
0 3O
i' i jJJ......................................
, , "- _...... r'---i l , I , I I ,I0 20
Y (mm)
Figure 17 Radial Profiles of Mean Temperature and Standard Deviation at X/D = 2 of RCM-2
35OO
EO'_3000
>
13"1o 2500
"1oE
2000
3 t500
(llt'lE
E
1000
5OO
Radial Profile at X/D1 -- I0
\\
10
Y (mm)
..................... Mean TemperatureStandard Deviation/\
I \i
i \t,. t
! .
!
,,.. / \\,I z
-/iJ1
-jO" ' l J I I I 1 I I I
0 20 30
Figure 18 Radial Profiles of Mean Temperature and Standard Deviation at X/D = 10 of RCM-2
::::z :1:77
:19
Figure 19
Figure 20
cO4-m
tU
Oa"ID
g:
t/J
m"
G.E
#-K:
3500
3000
2500
2000
1500
I000
500
Radial Profile at X/D1 = 16
/ -\/J \
/i \
i \t
t
i-/:i
1
.....................Mean Tsmpomtum
................ Standard Dovlatlon
0 I J _ J |0 30
\\\
\\
/ \\\
I I I ;x. :_:" _--r ...... L I , i
10 20
Y (mm)
Radial Profiles of Mean Temperature and Standard Deviation at X/D = 16 of RCM-2
3500 - Radial Profile at X/D1 = 20CO
'_ 3000
"S
O"0 2500
"0c+._[2000O3
= 1500+,.i
G.E 1ooo
t-500
/\/ \J \
i/, \/
/ \i I1 t
_/ \%\\\
"x
\\, .-*"
Mean Temperature............... Standard Devladon
\\
\\
0 , , I , "'r-- _, ...... .1 ___l__ I0 20 30
Y (mm)
/ \\
\
\, I
10
Radial Profiles of Mean Temperature and Standard Deviation at X/D = 20 of RCM-2
20
Figure 21
cO
¢11D
t-
11,.
.-I
¢UIb-
¢11O.E
¢-
3500 -
3000
2500
2000
1500
1000
5OO
Radial Profile at X/D1 = 36
• "N.\\\
\\
\
Mean TemperatureStandard Dmha_an
\\
\
_...
I "_1 I I I I ---'1.... r'" "* .... I.... "-- ' ' ' I00 lO 20 30
Y (ram)
Radial Profiles of Mean Temperature and Standard Deviation at X/D = 36 of RCM-2
Figure 22
35OO
C0
"_ 3000
r_•1_ 2500
c2OOO
t,B
3 1500
(3.E iooo
c5OO
- Radial Profileat XlDI = 40i......\
\.
\
'\\
x
...................Mean Temperature
.... Standard Deviation
0 ..... r .....i i i 1 , ;"_q-_m--I----l- J ..... t.. , , I0 10 20 30
Y(mm)
Radial Profiles of Mean Temperature and Standard Deviation at X/D = 40 of RCM-2
21
Figure 23
3000"5
a,._ 2500
c2000
15oo
Q.E 1ooo
500
i
_-.... ._._ ".\
\\'\
\
Radial Profile at X/D1 = 43
\
\
Mean TemperatureStandard Deviation
\"-\
0 --1" , , i I ,"-"r---,.- 4.... 1 _, ...... _-- , _ I0 10 20 30
Y (ram)
Radial Profiles of Mean Temperature and Standard Deviation at X/D = 43 of RCM-2
t-
350O
0':m 3000
>
02500
"0c_2000t,B
1500
O.E _o00
¢c
05OO
Radial Profile at XlD1 = 50
.............. Mean Temperature
........ Standard Devimion
0 , , , , l-T" _c_.._:..+- --I'--"1-- -'l" "--,I--7-- I I l0 10 20 30
Y (ram)
Figure 24 Radial Profiles of Mean Temperature and Standard Deviation at X/D = 50 of RCM-2
22
Figure 25
cO
O
lb.
t--
--i
e'lE
c
3500
3OOO
2500
2000
1500
1000
Radial Profile at X/D1 = 60
...................Mean Tgmporatum
........ Standard Dovladon
5OO
0- = I , = I i -i'"--i -- r-.---_ -.-, .....__0 10 20
Y (ram)
, , I
30
Radial Profiles of Mean Temperature and Standard Deviation at X/D = 60 of RCM-2
35OO
3OOO
2500
2000nE
I-- 1500c
1ooo
5OO
Figure 26
Axial Profile at Y/DI = I
//
//
//
\\\
\,\
!/
:/-/
Mean Tamper'alum
, , , , I , J , _ I , , i l I , , l I IO0 100 200 300 400
X (mm)
Axial Profiles of the Mean Temperature at Y/D = 1 of RCM-2
23
35o0- Axial Profile at YID1 = 2
3OOO
2500.e
2OO0
EQ
I- 1500E
1000
5OO
00
//-'//
i/
//
\ I. .,,_._..,.1
Mo_ Tompemtum
_ i i i I i i l ,_ I I 1 l I I I I I I I I100 200 300 400
X (ram)
Figure 27 Axial Profiles of the Mean Temperature at Y/D = 2 of RCM-2
3500 - Axial Profile at Y/D1 = 3
3OOO
25OO
• 2000
E
I-- 1500E
I000
5OO
00
Mean Temperature
.,,.-"J
/
/i
/
i w l i I w i f _ I m l l I I l l i _ I l100 200 300 400
ii_X (mm)
Figure 28 Axial Profiles of the Mean Temperature at Y/D = 3 of RCM-2
24
35OO
3000
25OO
_.2000
E
I-- 1500C
_E1000
500
00
Axial Profile at Y/D1 = 4
MoanTemperature
....-
/."
_ ...- 1"_
I i I I I i l_±_l _ i i I I I i i I I I100 200 300 400
X (mm)
Figure 29 Axial Profiles of the Mean Temperature at Y/D = 4 of RCM-2
3500
3OO0
2500
_2000Q.E
I-- 1500C¢w
1000
5OO
00
- Axial Profile Near Outer Wall
MeanTomparatura
i
F
, l l i I , , l l ! I I l I I , l , , I ,loo 200 3o0 400
X (ram)
Figure 30 Axial Profiles of the Mean Temperature Near the Outer Wall of RCM-2
25
View A-A
t50 mm
I
_iiiii}iiiiiiiiiiiiiiiiiiii{i!ili!ii_i}il/--i.1_:;::iii:;!_!_ii!_!iii::iiiii:(:iiiii:;::ii!_:_::i_i!i_i_!!_::i}i::i{i::iiiii_i::i::i::_ii::_
GH 2
HIHII ",H ................................
5.6 mrn5 mm LOX--_4D,-
GH=
iiiiiiiii!iiiiiliiiiiiiiii!iiiiiiiiii!
Faceplate
T12 rnm
View A-A
400 mrn
LOX GH2
Crilical Pressure 5.04 MPa 1.29 MPa
Critical Temperature 154.6 *K 33 °K
InlelTemperature 85 *K 287 *K
Mass Row Rate 0.05 kg/s 0.0237 kg/s
Chamber Pressure = 1 MPa
Inlet Turbulent Kinetic Energy = 0.00375 U_.i
U_: Propellant Injection speed
Figure 31 Configuration of the RCM,2 Case (Homogeneous Spray Model)
(a) Axial Velocity (b} Density (c) Temperature6 8 l 6--
4E..,EO
_3
4E.EE8
_3
_ I t i l Ii] i I I I I I I I I t I I I I I I l I I I t I
100 200 300 400 0_ 400 800 i 200 100 200 300
U (m/sec) Density (kgkn 8) Temperature _'K)
Figure 32 Flow Properties at the Injector Exit of RCM-2 (Homogeneous Spray Model)
26
O.)i,,._
13)
EO3,
I--c"
O9
3500
3O0O
25OO
2000
1500
1000
50O
I I 1 [ I
00 5 10 15
Radial Distance (rnm)
Figure 33 Radial Profiles of the Mean Temperature at Various Axial Locations of RCM-2
3500
300O
25OO
Eft
O.),- 2000
(13
O9
E 1500(33
I--
I000
500
!ii'//ii i!t" ,.i- ---,..__.... "--........................
{ I '" t j ...................... T.:::':.__.,-=.,=.,---.,---,----,_--''"•]l t .....................!_t J .....
i I_/ /, ]
I 1 I • I 1 I II , = I _ I _ , i i I0 0 100 200 300 400
Distance from the injector (ram)
Figure 34 Axial Profiles of the Mean Temperature at Various Radial Locations of RCM-2
27
Figure 35 Temperature and Species Concentrations Near the Injector of RCM-2
28
1900
17OO
1500
.,,13001..,..
4--,
t,.,.
Q.t,
o_ 1100Eo)
I---
900
700
• • • • #"-_ •
#._'' ..... Single Global Kinetics
j. _. Single Global + Elementary Kinetics
, , I , I , , ....J .......J__ I I , , , I ,___J_____500 0 100 200 300 400
Distance from the injector (rnrn)
Figure 36 Near Wall Temperature Distributions for Various Chemistry Models of RCM-2
29
SIMULATIONS OF THE RCM-3 EXPERIMENT
The super-critical combustion case, RCM-3, was simulated with the homogeneous spray
combustion model. Any drops present will be highly unstable; therefore, this model should represent
the flow rather well. Local equilibrium and simplified finite-rate combustion submodels were used
and the results for the two simulations compared well. More detailed combustion submodels were
attempted, but proved to behave too poorly for successful simulations.
The preponderance of super-critical spray combustion models which have been reported have
been extensions of sub-critical models. Such models encounter a basic problem in over emphasizing
the role of surface tension. Since surface tension is zero for super-critical conditions, drops should
not exist. Although such drops can be observed experimentally, they are extremely unstable and do
not survive very long. The homogeneous CFD model was developed to account for the major
physical effects which do exist. Namely, the large density and momentum differences which exist in
multi-phase super-critical flows. Such a model allows one to accurately relate the inlet conditions
at the injector face to boundary conditions for the CFD simulation. This relationship is essential to
predicting the effects &injector element configuration and inlet momentum vector on the convective
mixing and cross winds which occur in practical rocket engines. Otherwise, one is forced to use the
historical method of creating costly experimental data bases from which to choose designs.
The injector configuration and flow conditions for the supercritical combustion of the
RCM-3 test case are presented in Fig. 37. This is uni-element shear coaxial injector with LOX
and GH2 propellants. The numerical simulation was conducted with some simplification because,
initially, detailed information was unavailable; such as: (1) the flare of LOX injector near the exit
was neglected; (2) the injector was flush at the chamber head-end instead of protruding into the
chamber because the outer diameter of hydrogen tube and distance between the chamber head-
end and the injector exit were not known; (3) the nozzle was not included because of insufficient
information about the chamber tail-end and nozzle geometry; and (4) the coolant (later found to
be helium) for the chamber wall was not included because its flow rate and properties were not
specified. As can been seen, the chamber pressure (60 bar) is well above the critical pressure "of
oxygen; hence, the homogeneous real-fluid model was used to simulate this test case. A two-
zone mesh system (61x39 and 301xI01) was Used to model the injector section and the
combustion chamber.
The combustion reactions in this high pressure experiment are expected to be in local
thermodynamic equilibrium and were simulated as such. To demonstrate the methodology, two
finite-rate simulations were also made with _ubset of the reactions in Table 1. The single global
reaction which produces radicals as well as water provides a good estimate of the temperature field.
Its rate was set to attach the flame near the_jector tip. Since the radicals are not rigorously
simulated with the single reaction, a second finit_rate simulation was made with the 2-body reactions.
Backward reaction rates are determined wlth equifibrium constants. For high pressure cases such
combustion modeling is essential to keep the computation stable.
The chemistry and turbulence modeisu-sedln our simulations do not make use of probability
density functions (PDFs) because most of the s_-ear iayers formed by the injector element should be
continuum. The only regions for which this might not be the case are the intermittent edges of the
30
shearlayers.Pope8termstheseregionsthe"viscoussuperlayer".inverselyproportionalto theReynoldsnumberto the0.75power.theyshouldbeverythin.
Thethicknessof theselayersareFor these high speed coaxial jets,
The flow predicted at the injector tip is shown in Figure 38. The radial temperature profiles
predicted at several axial stations are shown in Figure 39. The axial profiles at several radial locations
are shown in Figure 40. The temperature and oxygen and OH concentration profile fields are shown
in Figure 41. The combustion models used do not predict chemiluminescent OH, which might be
observed in the experiments. These results are shown for the equilibrium combustion model. Results
for the two finite-rate combustion simulations are very similar, hence they are not shown. The wall
temperature distributions for all three cases are compared in Figure 42, and as noted the results are
very similar.
400 niFrl
t50mm
1
Faceplale
10ram
View A-A
LOX GH 2
Critical Pressure 5.04 MPa 1.29 MPa
Critical Temperature 154.6 °K 33 °K
Inlet Ternpefature 85 °K 287 °K
Mass Row Bale 0.1 kg/s 0.07 kg/s
Chamber Pressure = 6 MPa
Inlet Turbulent Kinetic Energy = 0.00375 U_.i
U_: Propellant Injection speed
Figure 37 Configuration of the RCM-3 Case (Homogeneous Spray Model)
(a) Axial Velocity (b) Density (c) Temperature5 5 5-
4 4
10(3' 200 300
U (m/see)
2
Figure 38 Flow Properties at the Injector Exit oERCM-3 (Homogeneous Spray Model)
32
3500
30O0
::K9..., 250O
@3
_ 20OO
E
b- 1500
1000
X/D= 10
X/D = 20
X/D= 30
X/D= 40
X/D= 50
X/D = 60
500
O0 5 10 15 20 25
Radial Distance (ram)
Figure 39 Radial Profiles of Mean Temperature at Various Axial Locations of RCM-3
35O0
3000
1000
0 100 200 300 400
Distance from the injector (ram)
Figure 40 Axial Profiles of Mean Temperature at Various Radial Locations of RCM-3
33
'7" _ d d d1_, i m
Figure 41
Odddddddddddddd
Temperature and Species Concentrations Near the Injector of RCM-3
34
1500
14O0
1300
,.,_,.1200
e._
,,- 1100
(1)o_ 1000E8.)I--
9OO
8OO
7OO
/Equilibrium Chemistry
Single Global Kinetics
Single Global + Elementary Kinetics
600 = = = a I = T i = I = = ] e I = , , ,0 100 200 300 4-00
Distance from the injector (ram)
Figure 42 Near Wall Temperature Distributions for Various Chemistry Model of RCM-3
35
CONCLUSIONS
The following conclusions were drawn from performing CFD simulations of the three RCM
test cases for the 2nd IWRCM.
. A homogeneous and a heterogeneous spray combustion CFD model have bee developed to
simulate combustion in rocket engines. Since neither of these models is expected to be accurate
until critical parameters are evaluated from test data, simulation comparisons to the MASCOTTE
type experiments are needed.
2. The utility of either CFD model cannot be determined until values of critical parameters are
determined and efforts to optimize the computational efficiency of the models are performed.
. Although the CFD rocket engine models pro_de much more detailed information concerning the
vaporization, mixing, and combustion process, their place in the design process is yet to be
identified. Older more approximate rocket "performance" models are difficult to displace.
Furthermore, every physical process thought to be present in the engine does not have to be
modeled to create a useful design code. There are more knobs to adjust in the code than there
are experimental data to justify their turning.
. The experiments conducted in preparation for the 2nd IWRCM appear to be a significant first step
in providing test data valuable to CFD modelers. However, blind comparisons of CFD model
predictions to such data are premature. The CFD modelers have not previously had sufficient test
data properly specify the many assumptions which are necessary to simulate such complex flows.
So Better communication between analysts and experimenters needs to be accomplished. Can the
modeler simulate the experiments which are being performed? Can the data obtained from the
experiment critically test the model?
ACKNOWLEDGEMENTS
The authors wish to express their appreciation to Mr. Robert Garcia and Dr. Bill Anderson
for their encouragement and support. This work was performed under NAS8-00162 for the Marshall
Space Flight Center of the National Aeronautics and Space Administration.
36