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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

https://ntrs.nasa.gov/search.jsp?R=20010037826 2018-07-19T08:30:23+00:00Z

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: ::":<::::::;:::::;;::::::::::::::::::::::::_:

Figure 7 Flow Properties Near the Injector of RCM-1-A

9

(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.Thecalculatedaveraged

chamber 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

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Figure 19

Figure 20

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3500

3000

2500

2000

1500

I000

500


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\\\

\\

/ \\\

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


20

Figure 21

cO

¢11D

t-

11,.

.-I

¢UIb-

¢11O.E

¢-

3500 -

3000

2500

2000

1500

1000

5OO


• "N.\\\

\\

\

Mean TemperatureStandard Dmha_an

\\

\

_...

I "_1 I I I I ---'1.... r'" "* .... I.... "-- ' ' ' I00 lO 20 30

Y (ram)


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)


21

Figure 23

3000"5

a,._ 2500

c2000

15oo

Q.E 1ooo

500

i

_-.... ._._ ".\

\\'\

\


\

\

Mean TemperatureStandard Deviation

\"-\

0 --1" , , i I ,"-"r---,.- 4.... 1 _, ...... _-- , _ I0 10 20 30

Y (ram)


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)


22

Figure 25

cO

O

lb.

t--

--i

e'lE

c

3500

3OOO

2500

2000

1500

1000


...................Mean Tgmporatum

........ Standard Dovladon

5OO

0- = I , = I i -i'"--i -- r-.---_ -.-, .....__0 10 20

Y (ram)

, , I

30


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)


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)


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

.,,<.0%...o_>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


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


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

REFERENCES

1. Chen, Y.S., "Compressible and Incompressible Flow Computations with a Pressure Based

Method," AIAA Paper 89-0286, 1989.

2. Nickerson, G.R., et ai, "Two-Dimensional Kinetics (TDK) Nozzle Performance Computer

Program," Vols. I-III, Rpt. No. SN91, Software and Engineering Associates, Inc., mar. 1989.

3. Hirschfelder, J.O., et al, "Generalized Equations of State for Gases and Liquids," IE____C_C,50,

pp.375-385, 1958.

4. Hirschfelder, J.O., et al, "Generalized Excess Functions for Gases and Liquids," IE___CC,50, pp.386-

390, 1958.

5. Reid, R.C., et al, The Properties of Gases & Liquids, 4th ed, McGraw-Hill, 1987.

6. Gordon, S., and B.J. McBride, "Computer Program for Calculation of Complex Chemical

Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-

Jouget Detonations," NASA-SP-273, 197I.

7. Gardiner, W.C., Jr., Combustion Chemistry., Springer-Verlag, 1984.

8. Gardiner, W.C., Jr., Ed., Gas-Phase Combustion Chemistry, Springer, 1999.

9. Farmer, R.C, G. Cheng, H. Trinh, and K. Tucker, "A Design Tool for Liquid Rocket Engine

Injectors," AIAA 2000-3499, 2000.

10. Reitz, R. D., and Diwakar, R., "Structure of High-Pressure Fuel Sprays," SAE Paper 860469,1986.

11. Chen, Y. S., Shang, H. M., and Liaw, P., "A Fast Algorithm for Transient All-Speed Flows and

Finite-Rate Chemistry," AIAA Paper 96-4445, 1996 AIAA Space Programs and Technologies

Conference, September 24-26, 1996, Huntsville, AL.

12. O'Rourke, P. J., and Amsden, A. A., "The TAB Method for Numerical Calculation of Spray

Droplet Breakup," SAE Paper 872089, 1987.

13. Shang, H. M., "Numerical Studies of Spray Combustion in Liquid-Fueled Engines," Ph.D. Thesis,

University of Alabama in Huntsville, 1992.

14. Schuman, M. D., "General Evaporation Model," CDR-88-054, Rockwell International Corp.,Feb. 1988.

15. Abramzon, B., and Sirignano, W. A., "Droplet Vaporization Model for Spray Combustion

Calculations," AIAA Paper 88-0636, 1988.

16. Anon, "Spray Combustion of Synthetic Fuels, Phase II - Spray Combustion Phenomena,"

DOE/PC40276-5, SAI, Inc., Chatsworth, CA, May 1983.

17. Chehroudi, B., et al, "Initial Growth Rate and Visual Characteristics of a Round Jet into a Sub-

to Supercritical Environment of Relevance to Rocket, Gas Turbine, and Diesel Engines," AIAA

99-0206, 1999.

18. Pope, S.B., Turbulent Flows, Cam b.r.idge, 2000.

37

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