Combustion'Model of Supersonic Rocket Exhausts in anEntrained Flow Enclosure

Bruce T. Vu t and Justin Oliveira2

NASA Kennedy Space Center, FL 32899

Dimal PateeOrbital Sciences Corporation, Inc., VA 20166

This paper describes the Computational Fluid Dynamics (CFD) model developed tosimulate the supersonic rocket exhaust in an entrained flow cylinder. The model can be usedto study the plume-induced environment due to static firing tests of the Taurus-II launchvehicle. The finite-rate chemistry is used to model the combustion process involving rocketpropellant (RP-l) and liquid oxidizer (LOX). A similar chemical reacting model is also usedto simulate the mixing of rocket plume and ambient air. The model provides detailedinformation on the gas concentration and other flow parameters within the enclosed region,thus allowing different operating scenarios to be examined in an efficient manner. It isshown that the real gas influence is significant and yields better agreement with the theory.

Nomenclature

Ak

C;

DeEAk

j,g,h

rgiK

Kjk

K bk

f-lA-

M;

NTqRRoap

pre-exponential factor for reaction step k

molar concentration of species i

coefficient of diffusivitytotal energy per unit volume

activation energy of reaction step k

fluxes in x, y, z directions

ratio of specific heats

Gibbs free energy of species i

coefficient of thermal conductivityforward rate constant for reaction k

backward rate constant for reaction k

first coefficient of viscosity

second coefficient of viscosity

chemical symbol of species i

exponent of temperature in the rate constant ofreaction k

dependent conservation variable

gas constantuniversal gas constant

turbulence transport quantitiesdensity

t Lead, Fluid Systems Group, Senior Member AIAA.2 Aerospace Engineer, Member AIAA.3 Principle Engineer, Guidance, Navigation, and Control Department.

1American Institute of Aeronautics and Astronautics

https://ntrs.nasa.gov/search.jsp?R=20110016721 2019-08-30T17:43:22+00:00ZCORE Metadata, citation and similar papers at core.ac.uk

Provided by NASA Technical Reports Server

ST'ij

u,v,w

w,

source termstatic temperatureviscous stresses

velocities in x, y, z directions

molecular weight of i

stoichiometric coefficient of i in reactant side of step k

stoichiometric coefficient of i in product side of step k

mass flow rate per unit volume ofproduction of i from reaction k

I. Introduction

NASA awarded to Orbital Sciences Corperation (OSC) a Commercial Orbital Transportation Service (COTS)contract to demonstrate delivery of cargo to the International Space Station. For these COTS missions OSC

intends to use Taurus-II to launch its Cygnus spacecraft. The baseline Taurus-II is a two-stage vehicle, designed tolaunch payloads weighing up to 15,000 lbs into low-Earth orbit (Figure 1). The first stage uses RP-I (kerosene) andliquid oxygen (LOX) as propellants, powering two Aerojet AJ-26-62 main engines. The second stage is a CASTOR30 solid rocket motor, built by Alliant Tech Systems, Inc. (ATK). This paper focuses on the first stage engine only.This engine is previously known as the Russian NK-33 liquid rocket engine, which provides high performance withlight weight design, high chamber pressure, stable combustion, and a LOX rich prebumer1

. Currently OSC isplanning to conduct a series of cold and hot first stage tests at Wallops Flight Facility (WFF). During these tests thetwo main rocket engines will be enclosed in an extended cylinder that resembles the hold-down bay. As shown inFigure 2, there are several vents around the cylinder to allow air entrainment during the hot firing test. Theobjective of this analysis is to solve the flowfield within the enclosed cylinder and to quantify the amount of airentrained during the test. The solutions can also be applied toward the study of the plume-induced environment.The analysis is based on multi-species, chemical reacting simulations. The results at the nozzle exit are compared totheoretical rocket performance data obtained from chemical equilibrium with applications (CEAl A simplified,single-species simulation is also presented here for comparison purposes

II. Modeling ApproachThe analysis pertains to a complex system involving swirling flows, complex chemical reactions and complex

geometry. These complexities provide a significant computational challenge. All modeling reported in this paperwas performed using CFD++ 10.1, a multi-purpose CFD code developed by Metacomp Technologies, Incy,5.

A multi-block, structured mesh is created to model the AJ-26 rocket engines in an enclosed cylinder (Figure 3).There are a total of 321,936 cells for the single-species case and 406,656 cells for the multi-species case. In bothcases a symmetry boundary condition is used to reduce the computational domain by half. The entire domain isinitialized with a small disturbance (V = om mls); this disturbance helps initialize the freestream turbulencequantities in the K-8 model.

The solution is based on compressible, real gas, Reynolds-Average Navier-Stokes (RANS) with a K-8

turbulence model. The simulation starts from the combustion chamber, where the total pressure and temperatureare specified. For single species, ideal gas simulation only total conditions (P = 162 atm and T = 3814 K) arerequired in the combustion chamber and the gas flow in the nozzle is assumed to be air with a constant specific heatratio (r =1.4). For multi-species simulations the fuel-oxidizer reactions in the chamber and mixing reactions

outside of the nozzle are also described in the boundary conditions. The three main chemical molecules that madeup the fuel and oxidizer are carbon, hydrogen and oxygen. Outside of the nozzle, nitrogen is added to make up theambient air. Combustion is handled using II-species, I8-reaction chemistry mechanism solved with a finite-ratekinetics scheme and a constant-pressure combustion model. Standard non-reflecting, interpolated boundaryconditions are imposed at the outflow boundary, as well as no-slip conditions at solid surfaces and symmetryboundary condition at the midplane. Steady-state solutions are obtained using a multi-grid, time-stepping scheme.The solutions are compared between single-species, non-reacting and multi-phase, finite-rate chemical reactingflows. The solutions are also compared against theoretical performance data obtained from CEA.

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III. Governing EquationsThe CFD++ flow solver can be used to provide steady-state or unsteady flowfield solutions by solving the

transport equations such as mass conservation equation, time averaged Navier-Stokes equations, energy equationand other scalar transport equations. The general form of these equations can be written as:

aq + a(fi- Iv) + a(gi-gv) + a(~-hv) =8at ax By az

where the subscripts i and v denote the inviscid and viscous flow terms, respectively. For the Reynolds­averaged Navier-Stokes equations the dependent quantities and the inviscid fluxes can be written as:

e (e+p)u (e+p)v (e+p)w

p pu pv pw

pu pu2+p pvu pwu

pvfi=

puv pv2+phi =

pwvq= gi=

pw2 +ppw puw pvw

PCYI pUCYI PVCYI pWCYI

PCYN pUCYN PVCYN pWCYN

where CYi 'S represent turbulence kinetic energy and ''undamped'' eddy viscosity in the pointwise turbulence

models. Flow with multiple species can also be computed within this framework. The first five rows representterms from the standard Euler equations with the first being the energy equation followed by the continuity and threemomentum equations. The equation of state couples pressure to density and temperature is the perfect gas equationof state ( p = pRT ) which can be written in terms of the conservation variables as follows:

The viscous terms are defined as follows:

aT aT aTK-+UTxx +VTxy + WTxz

K ~+UTxy +VTyy +WTyz K-+UTxz +VTyz +WTzzax az0 0 0

TxxTxy Txz

Txy Tyy Tyz

Iv = Txzgv = Tyz hv= Tzz

D aCYl D BCYI D aCYlp - p - p -ax By Bz

D aCYN D BCYN D aCYNp -- p --ax p -- azBz

where viscous stresses Tij 'S are defined as:

3American Institute of Aeronautics and Astronautics

T = f.J(av + Ow)yz 8z 8y

2where the Stokes theorem for gases is assumed to hold true, thus A =- f.J. The temperature can be related to

3the conservation quantities via the equation of state:

The source terms are written as:

g r\! ... nN)Tz ~~

where gi's are the body forces which can be activated if necessary, and nj,s are the source terms such asproduction and dissipation of turbulence.

IV. Chemistry ModelHydrocarbon rocket fuels such as RP-I consist of at-least 87 identifiable hydrocarbon based compounds6

,7.

Modeling the reaction rates for each of these compounds in addition to the subset of possible intermediatecompounds would result in a very large and, for the present study, unnecessary computational burden. Therefore theapproach taken is to utilize the widely accepted wet-CO (H20 catalyzed) and thermal-NO mechanisms as describedin the following sections, which model the thermophysics associated with conversion of the intermediate statecompounds to their final combustion products. The initial global reaction steps to these intermediate molecularstates are model as irreversible reactions of the RP-l hydrocarbon chains with oxygen. The initial intermediatestates in the combustion chamber are provided by the industry standard complex chemical equilibrium code CEA2

.

In the present study, the finite-rate reactions of hydrogen, oxygen, and carbon are considered for the chemistrymodel in the combustion chamber. This model employs 8 species and 12 elementary reactions. Outside of thenozzle exit, nitrogen molecule is considered for the plume-air mixing reaction, which involves 3 more species and 6more reactions. For a general chemical reaction k:

(1 )

where the rate of production of species i from the reaction step k can be written as follows:

The forward rate constant for each reaction step k is given by Arrhenius kinetics:

4American Institute of Aeronautics and Astronautics

(2)

Any kinetic step, including reactions with third bodies in the product and/or reactant side can be included in the

flow solver through inputs ofV;k' V;~,Ak ,NT,Np,EAk .

The backward rate constant K bk is computed from the equilibrium condition:

where the change in Gibbs free energy for reaction step k is given by:

N NI1Gk =LV;~Wigi - LV;kWigi

i=1 i=1

(3)

A summary of chemical reactions and reaction rates used in the model is given in Table 1. The first 12 reactionsare related to RP-1 and LOX in the combustion chamber and the last 6 reactions describe the exhaust plume mixingwith air outside of the rocket nozzle. These reaction equations are obtained from various sources8

• 9.10.

(-EA J .!.(cm3 t-J(~mol)K jk = AkTNT exp __k Ak NT E

AkRoT s kmol

1 +02.: 0H + 0 1.2xlO"u -0.91 691563802 2+ 0.: OH + H 1.5x10lu 2.00 316248923 + H20': OH + OH 1.5xlO'" 1.14 722569994 H + H2.: H20+ H 1.0x10 1.60 138108715 O+H+M':OH+M 1.0x10 1

' 0.0 06 +0 + M.:02+M 1.0x10"u -1.0 07 +H+M.:H2+M 9.7x101

' -0.6 08 20+M.:H+OH+M 1.6x10"u 0.0 4783752759 O2+ H2.:H+ OH + OH 7.9x10" 0.0 18714751410 ::;0 + OH.: CO2+ H 4Ax10' 1.5 -310242111 ::;0 + 0 + M.: CO2+ M 5.3x10'o 0.0 -1901496712 ::;0 + O2.: CO2+ 0 2.5x101J 0.0 20015754513 +N2.:N+NO 1Ax10 0.0 31411787414 N2+ O2': NO + NO 9Ax10" -2.5 53753844315 1\ 0 + 0 .: N + NO 1.6xlOIl 1.0 16184394716 I\O+M':O+N+M 2.3x10"u -0.5 62322447617 " + OH .: NO + H 4.0x10 1b 0 018 ~02+ N.: CO+ NO 2.0xlO'Q -0.5 33283891

Table 1. Reaction Rate Equations

V. Discussion of ResultsIt is shown that for the non-reacting calculations, if the K-C turbulence model is used, the swirl is predicted to

decay too quickly and therefore recirculation zones are not captured. As a result, the single-species simulationshows a greater air entrainment at the ceiling, whereas in the multi-species simulation the recirculation causes flow

5American Institute of Aeronautics and Astronautics

reversals, thus reducing the entrainment from the top. Figures 4 and 5 show the velocity vectors at the symmetryplane for single-species and multi-species, respectively. Also, particle traces in Figures 6 and 7 indicate that a lowerentrainment rate is detected for the multi-species case, due to recirculation and flow reversals.

Furthermore, the single-species simulation with constant specific heat ratio (r) shows an over-predicted

solution at the nozzle exit plane. Figure 8 shows the Mach contours on the symmetry plane, where M =6.83 at thenozzle exit centerline; which is much higher than the CEA prediction (M =3.667). The simple explanation is thatthe speed of sound is a function of specific heat ratio and molecular weight or singularly local static temperature.What is expected to be occurring in reality is additional energy release from continued exothermic reaction in thenozzle, most notably the re-combination of dissociated molecules of hydrogen and oxygen from the now changingequilibrium conditions as the flow expands and reduces static pressure and temperatures in the nozzle. This isclearly evident in Fig 9 which depicts a sharp increase in total temperature of the flow as the flow expands past thethroat of nozzle for the reacting chemistry case and matches well with CEA predictions.

For single-species, ideal gas simulation, both of these parameters are assumed to be constant, resulting in a lowspeed of sound compared to real gas. Figure 10 shows the speed of sound contours for the ideal gas simulation,where C =384.84 mls at the nozzle exit centerline, compared to C =879.4 mls predicted by CEA. The under­prediction by the ideal gas assumption can also be found from observing other flow parameters, e.g. pressure andtemperature at the nozzle exit centerline are predicted to be 0.0458 atm and 368.13 K, respectively. CEA yields atthe same location a pressure of 0.664 atm and temperature of2041.12 K. Figures 11 and 12 show the pressure andtemperature contours at the symmetry plane. These results are sound in the sense that it correctly predicted theshock structures in the plume flowfield 11, but the under-prediction of pressure magnitude makes the nozzle moreover-expanded that it actually is.

The multi-species simulation with finite-rate chemistry shows a much better agreement with the theory. Figures13-16 show the contours for Mach number, sonic velocity, pressure, and temperature at the symmetry plane. Theconditions at the nozzle exit plane obtained from these simulations match up with CEA within I% of error. Inaddition, Figures 17-21 show the mole fractions of some of the gases that made up the plume and ambient air.Apparently, there are strong recirculation zones between the plumes and in the region between the cylinder andexternal nozzle surface. These behaviors were not captured in the single-phase, ideal gas simulation. Table 2summarizes the nozzle exit plane conditions, predicted by CEA and by real gas simulation. Excellent agreement hasbeen achieved with the current chemistry model.

FLOW VARIABLES Chamber Throat Exit Exit(CEA) (CFD++)

P, atm 162.02 93.541 0.66433 0.65199T,K 3814.03 3617.25 2041.12 2041.24Sonic velocity, mls 1224.2 1182.2 879.4 883.7Mach number 0.0 1.0 3.695 3.669MOLE FRACTIONCO 0.29698 0.28981 0.23532 0.23511CO2 0.16922 0.18276 0.27071 0.27078H 0.02327 0.02030 0.00072 0.00072H2 0.06879 0.06675 0.07650 0.07689H2O 0.34094 0.35551 0.41627 0.415700 0.01191 0.00925 0.00000 0.00000OH 0.06620 0.05660 0.00048 0.0004302 0.02238 0.01885 0.00001 0.00001

Table 2. AJ-26 Combustion Data

VI. ConclusionCalculations were performed on a dual nozzle, RP-1/LOX combustion engine as part of an ongoing effort to

study the plume-induced environment due to stage testing of Taurus-II launch vehicle. It has been shown that thefinite-rate chemistry impacted the computational results. When included in the computational model, the chemicalreaction significantly influences the flowfield. While the non-reacting, single-species simulation can provide

6American Institute of Aeronautics and Astronautics

quantitative results, it cannot capmre all physical features of this particular problem. The plume flowfield obtainedfrom this model can be used to improve the thermal analysis that determines the plume impingement impact onground support equipment.

AcknowledgmentsThe authors would like to acknowledge Mr. John Morin and Ms. Marina Browning from Orbital Sciences

Corporation for their technical insights. Thanks are also due to Mr. Steven Cain and the NASA Commercial CrewPlanning Office for the support ofthis collaboration..

ReferencesI. Lacefield, T.C. and Sprow, W.J., "High Performance Russian NK-33 LOXlkerosene Liquid Rocket Engine," AIAA-1994­

3397, 30th ASME/SAE/ASEE Joint Propulsion Conference, Indianapolis, IN, June 27-29, 1994.

2. McBride, BJ. and Gordon, S., "Computer Program for Calculation of Complex Chemical Equilibrium Compositions andApplications," NASA-RP-1311, Lewis Research Center, Cleveland, Ohio, June 1996.

3. U. Goldberg, O. Peroomian, and S. Chakravarthy and B. Sekar "Validation of CFD++ Code Capability for SupersonicCombuster Flowfields," AIAA-97-3271, Seattle 1997.

4. Chakravarthy, S., Peroomian, 0., "Some Internal Flow Applications of a Unified-Grid CFD Methodology," AIAA-96-2926,32nd AIAAlASME/ASEE Joint Propulsion Conference & Exhibit, Lake Buena Vista, FL, July 1996.

5. Batten, P., Leschziner, M.A., and Goldberg, U.C., "Average-state Jacobians and Implicit Methods for Compressible Viscousand Turbulent Flows," 1. Computational Physics, Vol. 137, pp. 38-78, 1997.

6. Wang, Ten-See, Thermophysics Characterization ofKerosene combustion", Journal of Thermophysics and Heat Transfer,0887-8722 vo1.15 no.2, pp. 140-147,2001

7. Wang, T" Mcconnaughey P., Warsi, S., Chen, Y., "CFD Assessment ofthe Pollutant Environment From RD-170 PropulsionSystem Testing", Aerospace Environmental Technology Conference, p 25-47,1995

8. Gardiner, W.e., "Gas-Phase Combustion Chemistry," second ed., Springer, New York, 2000.

9. Westbrook, C.K., "Chemical Kinetic Modeling of Higher Hydrocarbon Fuels," AIAA Journal, vol. 24, no. 12, pp. 2002­2009,1986.

10. Chen, Y.S., Shang, H.M., and Liaw, P., "A fast Algorithm for Transient All-Speed Flows and Finite-Rate Chemistry,"AIAA-96-4445, Space Programs and Technologies Conference, Huntsville, AL, September 1996.

II. Greenwood, T., Prozan, R., Ratliff, A., and Seymour, D., "Analysis of Liquid Engine Rocket Exhaust Plumes," Journal ofSpacecraft and Rockets, 0022-4650, vol 8, no 2, pp. 123-128, 1971.

7American Institute of Aeronautics and Astronautics

CASTOR 30STAGE 2

STAGE 1RP/LOX2 x AJ..26-62

OPTIONALSTAR48VSTAGE 3

OPTIONALORBITRAISING KIT

Fig. 1 Taurus-II Configuration

8American Institute of Aeronautics and Astronautics

~/vent /

//

Fig. 2 Stage 1 Test Configuration

Fig. 3 Computational Domain

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\\ vent

\

Fig. 4 Velocity vectors, single species Fig. 5 Velocity vectors, multi species

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Fig. 6 Particle traces (single-species)

Fig. 7 Particle traces (multi-species)

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IFig. 8 Mach contours at the symmetry plane (single-species)

Rp·lILOX Nozzle Aow5000 ,......~-,........,--,.......--.,......~-.,......--.......-~-.-~-...,...---r-~.....,..--....,

~::

.. ·.. · ..·~~·~c: . /1 .

/ /:............. .. ;......./.;..~.I.. ~

:",,"" : /.... .; : /: ....... : it'. ...~ . /.

"O-'--~'~'~'~'~~':':"'~':~~"''l'~.,;.:;.-,~«.......... ...;.,..._ .....

:_ ........ ~-_..-:- .

....... .: ~ ~ ~. .... .. . : .

o

4000 ......

--Tt: Auent Equililorlum Chemistry Prediction--Tt: Auent Frozen Chemistry Prediction

o Tt: NASA GLEN CEA Equilibrium Chemistry Prediction- - Ts: Auent Equibllrium Chemistry Prediction- - n: Auent Frozen Chemistry Prediction

C Ts: NASA GLEN CEA Equilibrium Chemistry Predictiono Scaled Nozzle Contour for Reference

.2000 L'::=::e==:C==C:=::::i==:r:==--L_-l__-L__..L_-.J-10 0 10 20 30 40 50 60 70 80 90

Length, in

Fig 9 Total & Static Temperature Predictions Through Nozzle

·1000

g. 3000 ...,

5f! 1000 .

~'"!<l;§~

12American Institute of Aeronautics and Astronautics

Fig 10 Sonic velocity contours at the symmetry plane (multi-species)

4.$ 0\."..-.....

Level P (31m)

97 162.0293 115.6S989 82.607485 58.985381 42.118177 30D74273 21.474369 15;333665 10.948961 7.8179757 5.5823853 3986064Q 2.8462345 2D323341 1.4511737 1D36233 0.73989429 0.52831725 0;37724221 016936717 0.1923413 0.1373399 oD9806635 oD7OO2371 OD5

Fig 11 Pressure contours at the symmetry plane (single-species)

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Fig 12 Temperature contours at the symmetry plane (single-species)

Fig 13 Mach number contours at the symmetry plane (multi-species)

14American Institute of Aeronautics and Astronautics

Fig 14 Sonic velocity contours at the symmetry plane (multi-species)

"'0\1(;1 P (lim)

~7 lfl?.oZ~3 12lL~!

so 101.613S6 8M7!.;$! flUZ8377 50.4688n 39,Q6~Z

69 31.652365 250066$1 19.$51257 15,n-oo53 12.4649 9.S5tl6145 7.003241 6.1S3<11n 4.8g'1~~

33 3,87$1429 3.0712525 2,4322421 U261S17 1.6264113 1.20¢l)39 0.9566866 0.7576361 0.6

Fig 15 Pressure contours at the symmetry plane (multi-species)

15American Institute of Aeronautics and Astronautics

Fig 16 Temperature contours at the symmetry plane (multi-species)

Fig 17 C02 mole fraction at the symmetry plane

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G02 Mole Frac

0.27370.26430.25480.24540.23600.22650.2171

t+ 0.20760.19820.18880.17930.16990.16040.15100.14160.13210.12270.11330.10380.09440.01349

~0.07550.06610.05660.04720.03780.021330.01890.0094

Fig 18 H2 mole fraction at the symmetry plane

Fig 19 H20 mole fraction at the symmetry plane

17American Institute of Aeronautics and Astronautics

H2 MoleFrac

0.08620.08330.08030.07730.07430.07140.06840.06540.06250.05950.05850.05350.05060.04760.04460.04180.03870.03570.03270.02970.02680.02380.02080.01780.01490.01190.00890.00590.0030

H20MoieFrac

0.41600.40170.38730.37300.35860.34430.32990.31560.30120.28690.27260.25820.24390.22950.21520.20030.18650.17210.15780.14340.12910.11430.10040.08610.07170.05740.04300.02370.01430.0000

02 MoleFrac

01095010200.19400.18700.17960.17210.16460.15710.14960.14210.13470.12720.11970.11220.104700973008980082300748006730059900524004490037400299002240.01500.00750.0000

Fig 20 02 mole fraction at the symmetry plane

N2 MoleFrao

0.96670.93330.90000.86670.83330.80000.76670.73330.70000.66670.63330.60000.56670.53330.50000.46670.43330.40000.36670.33330.30000.26670.23330.20000.16670.13330.10000.06670.0333

Fig 21 N2 mole fraction at the symmetry plane

18American Institute of Aeronautics and Astronautics