AIAA A98-35670

AIAA-98-3967

INTERNAL FLOW ANALYSIS OF ATECHNOLOGY DEMONSTRATOR ROCKETMOTOR WITH NEW CFD CODE

Dr. Erland OrbekkRaufoss Technology ASRaufoss, Norway

34th AIAA/ASME/SAE/ASEEJoint Propulsion Conference & Exhibit

July 13-15,1998/Cleveland, OH

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 20191

INTERNAL FLOW ANALYSIS OF A TECHNOLOGYDEMONSTRATOR ROCKET MOTOR

WITH NEW CFD CODE

Dr. Erland Orbekk,*Raufoss Technology AS

Abbreviations:

AP Ammonium PerchlorateB/KNO3 Boron-Potassium NitrateCFD Computational Fluid DynamicEPDM Ethylene-Propylene-Diene MonomerFW Flight WeightHTPB Hydroxy-Terminated PolybutadieneHW Heavy WallRATEC Raufoss Technology ASSiPh Silica Phenolic

Abstract

This paper presents an updated version of theCFD code at Raufoss Technology AS (RATEC)and its applications on the internal flow ballisticsof a Technology Demonstrator Rocket Motor.

The updated CFD code, including chemicalreactions, boundary conditions for burning ofsolid propellants and particle flow models hasbeen developed and adapted for flow fieldcalculations of solid grain rocket motors.

The numerical method for solving the presentedEuler or Navier-Stokes equations is based on animplicit preconditioned time-accurate integrationwith upwind biased 3rd order accurate finite

volume flux formulation. The chemical reactionsare defined through curve fits of the Jensen andJones reaction rate coefficients. The flow domainis represented by structured grids of multi-blocktype. Turbulence models are of k-e type.

The transport equations are solved for eachspecie including the solid aluminum oxideparticles. The code can be used in equilibrium-,frozen- or in non equilibrium mode.

1 Introduction

Raufoss Technology AS (RATEC) has positiveexperience in using Computational FluidDynamics (CFD) for the evaluation of the internalflow path design in solid propellant rocket motors.

The calculated internal flow field on the selectedtechnology demonstrator test motor is presented.

The gas phase in the motor chamber is definedwith an appropriate set of chemical reactionsdescribing burning aluminized HTPB propellant.

The most critical internal flow field domains arelocalized and the motor performance iscalculated. The results are compared withmeasurements and with post-inspection views offired rocket motors.

* Section Manager, Analysis Group, Rocket Motor Development Department

Copyright ©1998 The American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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The internal flow field defines valuable boundaryconditions for the prediction of thermal loads,structural loads and erosive loads on theinsulation. In addition the non equilibriumchemical reaction sets, including transportequations for the solid particles, defines animproved prediction of nozzle performance. Thelatter is an important input to computer codes forthe prediction of overall ballistic rocket motorperformance.

2 The CFD code

The new CFD code can simulate 2D and 3Dreacting rocket motor flows, containing anarbitrary number of solid particle groups. Thenew code has options for chemical equilibrium,chemical non-equilibrium, or frozen chemistryflows. Furthermore, it can be applied to inviscidor viscous flows, in the latter case the standardk-e turbulence model is utilized.

Equations:

The Navier-Stokes equations that constitute theconservation of mass, momentum and energyare:

and solid particles

d

—(pUj)P+-—(pujUi)P=r

dt dx ,

are added to the above Navier-Stokes equations.The gas and particle phase is coupled throughthe particle drag force and the particle thermalexchange of heat.

The finite volume formulation of L.-E. Eriksson,[1], has been applied.

The above equations are closed by a caloricequation of state, which relates the energy to thetemperature:

where h is the specific enthalpy

Thermodnamic Properties:

The NASA polynomials of Gordon and McBride[2] yield empirical fits of the thermodynamicproperties of various gases in the temperaturerange 300-5000 K. The specific heat at constantpressure for any species s is obtained from:

Additional equations for turbulence

dt dXj ak dXjThe specific enthalpy is obtained by integratingthe equation for specific heat over a temperaturerange:

dx, dx: 7C dXj

, chemistry (conservation of mass)

d d d— ( p s )+ —— (psu : )--—— (psv . )+G)sat dX: dx:

h.(T) = —— (' M

The enthalpy is solved using the Newton-Raphson iteration for temperature:

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n+[ —

which converges to the desired accuracy within afew cycles. The specific heat at constant volumefor the mixture is obtained from:

r — r —K

——M

where the mixture cp is computed similar to theenthalpy. R is the universal gas constant and Mis the average molecular weight of the mixture.

Chemical reactions

The chemical reactions related to species s areconsidered in order to determine the massproduction rate, co, which appears in the speciesconservation equation.

These reactions proceeds (forward and reverse)proportionally to the product of the molarconcentrations of the reactants each raised to apower equal to its stoichiometric coefficient in thereaction equation.

In a general case of nr reactions involving nsspecies, the net rate of change of species s willbe:

where asr is the stoichiometric coefficientinvolving species s in reaction r, in either forward(') or backward (b) direction and

where 6 denotes the activation temperature, athe temperature coefficient and C, the rateconstant at a temperature 7".

The backward rate is derived from theequilibrium constant and the forward rateconstant:

K.

The equilibrium constant is also a function oftemperature and is given by curve fits or iscalculated from the equilibrium composition usingGibbs free energy.

Boundary Conditions

For many solid propellants it is possible toapproximate the burning rate, at least over alimited range, as a function of the chamberpressure. The burning rate versus pressure isexpressed by the formula of Saint Robert Vieille:

'REF\PREF

-r

where the burn rate r is calculated at a pressurep using the reference values of rREF, pPEF and thepressure exponent n.

At the burning propellant grain surface thepressure and density were obtained byextrapolation from the interior flow domain,whereas the velocity normal to the boundary wascalculated from the above empirical expression:

M,'REF\

PREF

where sf equals the number of reactants and sbthe number of products. Kf

r and Kbr denote, the

pertinent forward and backward reaction rateconstant for the arbitrary reaction r, respectively.

Arrhenius (1899) proposed the followingequation for the dependence of the forwardchemical reaction rate K:

K=CTaea<-e/T>

The chemical composition is estimated from theequilibrium composition for the given propellantat the designed chamber pressure andtemperature.

The nozzle exit velocity is supersonic and allvariables are extrapolated from the interior flowdomain. The walls are for the presented analysisassumed to be adiabatic. In the viscous andinviscid case, respectively, no-slip condition andtangential flow were imposed.

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Viscous Effects:

A standard k-e type turbulence model has beenused. The effect of temperature on viscosity isapproximated using the Maxwell relation:

Numerical Integration:

The numerical method for solving the presentedEuler or Navier-Stokes equations is based on animplicit preconditioned time-accurate integrationwith upwind biased 3rd order accurate finitevolume flux formulation.

where, n is defined as 0.67.

Particles

The drag coefficient of the particles,condensed/solid phase, is based upon theformula of Crowe [3] and modified by Hermsen[4].

M—

exp( _ Re/ 2M ) + 2

where

and

and

1 + 11.278 Re

M+I24

CM=—n + 0.

CM is the drag coefficient for incompressible flow.

The heat transfer between the exhaust gas andthe solid particles is calculated from theincompressible value of the Nusselt number, Mv0,correcting for compressible effects using theequation by Scaff, et al. [5].

»*•——^1 + 3.42- Nu

whereRePr

= 2.0 + 0.6Rel/2Prl/3

3 Rocket Motor Design

The rocket motor considered in the analysis is aHeavy Wall (HW) type, with propellant grain asshown in figure 3.1.

The test motor consists of a thick walled steelmotor case with an internal diameter ofapproximately 140 mm and a length of 1600 mm.

The aft- closure, blast pipe and nozzle arerepresentative for Flight Weight (FW) design.The nozzle exit to throat area ratio is 7.5.

The propellant grain is radial burning, casebonded HTPB composite propellant. The bore iscylinder shaped in the forward end with oneradial slot and star shaped in the aft end. Thethrust profile is of boost-sustain type.

The igniter is a pyrotechnical type steel tube filledwith B/KNO3 pellets and inftiated with a Holexinitiator.

The inner surface of the motor case is coveredwith EPDM- Aramide rubber, with extra insulationthickness in the slot region and in the aft end starregion.

The blast pipe consists of an outer steel tubewith an internal SiPh insulation.

The exit cone consists of an outer steel shell ofdecreasing thickness from front to aft. SiPhinsulation is bonded directly to the inside of theshell during molding. The nozzle contour isoptimized by the method of characteristics.

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Figure 3.1: Heavy Wall Rocket Motor

4 Propellant Properties

The composite HTPB propellant has a solidloading of 87%, of which 5% is aluminum, witha theoretical reference specific impulse of 2435Ns/kg, assuming gas expanding from 7.5 MPato atmospheric pressure.

The ballistic propellant properties weremeasured by using 2" model motors. Theresulting burn rate at 10 MPa and 21 °C was9.7 [mm/s] with a Pressure exponent of 0.50.

Gas Composition:

The gas composition in the rocket motorchamber has been defined by using thechemical equilibrium program, CET93/PC [2],for the given propellant at the designedchamber pressure and temperature. The mainspecies in the chamber, equilibrium gascomposition, is shown in table 4.1.

The following 14 reactions, table 4.2, havebeen treated for these 18 species.

ReactionH+H+M <=> H2+MH+CL+M <=> HCL+MH+OH+M <=> HaO+MCO+O+M <=> CO2+MALCL+CL+M <=> ALCU+MH2+OH <=> H2O+HCO+OH <=> CO2+HHCL+OH <=> H2O+CLAL+HCL <=> ALCL+HALO+HCL <=> ALOCL+HALCL+OH <=> ALOCL+HALOH+OH <=> H+ALO2HALCL2+H <=> ALCL+HCLN2+M <=> N+N+M

CoefficientsCf

1.09E+181.45E+223.22E+222.54E+153.00E+161.14E+091.69E+071.30E+135.00E+1 11.00E+111.00E+111.00E+111.00E+112.00E+14

a-1.00-2.00-2.000.00

-0.501.301.300.000.500.500.500.500.500.00

e000

21980

1824-33010502854285428262830903

113200Table 4.2 The treated chemical reactions

speciesHOOHH2H2OC02CONN2AL203(L)

% (mol)0.00890.00050.00990.11170.34020.06710.16870.00000.08960.0232

speciesCLALALCLALCL2

ALOALOCLALOHALO2HHCL

% (mol)0.00900.00000.00020.00020.00000.00030.00000.00020.1686

Table 4.1 Gas composition in chamber

The chemical reactions related to the above 18species are considered. The rate constantsinvolved in these chemical reactions are eitherprovided by experimental measurements ordetermined empirically and are typicallypresented in a curve-fit format [6].

Particle Sizes:

The definition of particle size within a rocketmotor is of great importance with respect to theaccuracy of the performance predictions.

Models of particle growth in the rocket motorchamber came from measurements made onparticles collected from the exhaust gas. Thecorrelation's are basically empirical, and thepresented is based on the same correlation asused in the SPP computer program [7]:

Z>43 =where

= mean particle diameter [|im]= nozzle throat diameter [in.]= average chamber pressure [psia]

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= average chamber residencetime[ms]= AI2O3 concentration in the chamber[g-mol/100 g]

It should be noted that the term edrops out for larger motors.

•o.oooei63ept

If more than one particle group is requested,the particles are distributed using log normaldistribution for each particle group. Threegroups are used in the present analysis. Theseare summarized in table 4.3.

Group123

Diameter [|im]2.194.067.56

Fraction1/31/31/3

Table 4.3 List of particle groups

5 Application on the Test Motor

The ability to accurately predict theperformance of a solid propellant rocket motorrequires an precise definition of the differentloss mechanisms.

The different losses are presented for the testmotor configuration at a motor pressure of 12.5MPa.

The losses are presented in the same form asin the SPP computer program [7]. This in orderto have the possibility to compare with thedifferent loss mechanisms and to evaluate theirindividual importance.

Grid Model:

Periodic boundary conditions are utilized forthe presented geometry. The grid is dividedinto 5 blocks with a total number of pointsequal to 94.955.

A periodic view of the aft- end of the propellantsurface (unburned) is shown in figure 5.1, whilethe aft closure, blast pipe and nozzle wallsurface is shown in figure 5.2.

star shapedaft- end

grainaft-end

Figure 5.1 3D view of propellant surface,seen from aft

aft-closure

- blastpipe

Figure 5.2 3D view of aft closure blast pipeand nozzle

Boundary layer loss:

The boundary layer loss is defined as thedecrement in performance due to viscousforces adjacent to the nozzle/blast pipe wall.

The boundary layer loss, r|m, is defined by thethrust difference of an Euler and a Navier-Stokes calculation.

The approximate boundary layer loss for thepresented case is 0.6% which defines anefficiency of.

77™ =0.994

Chemical kinetics loss calculation:

This loss is due to incomplete transfer of latentheat to sensible heat caused by the finite timerequired for a gas phase chemical reaction tooccur.

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Results are presented for frozen, equilibriumand the non equilibrium gas compositions.

The integrated pressure force inside the nozzlecontour is shown in figure 5.3. Figure 5.4-5.7

£ 4000.0

| 3500.0

•~jj JUUU.U

z 2000.0 •

| 1500.0 •

500.0

^

^ /

/v^-

.

•/

^^̂ .̂**^

^^^^~~-

—̂— non eqi

• - • frozen—— nozzle (

-=8=??^

~~- ——— "

libriumum

xxitour —

0.050

0.040 E.

35

• 0.030 SID

0.020 z

0.010

0.00 0.02 0.04 0.06 0.08 0.10Nozzle Axis [mj

Figure 5.3 Integrated nozzle wall thrust

0.275

0.27-

.20.265 •

1J0.26-

0.25-

-0

Figure0.000!

0.0004!

0.000<

_0.0003!

g o.ooo;20.0002J

1 0.000!s

0.0001 £

0.0001

O.OOOOE

C

— -frozen• • • equilibrium—— noneQUil

H2O /

Nozzle Contout

bnum HCL

H20 -

^

yt£- -—

H

-̂ -s>-—

^^

=L \

^^

1 -0.05 0 0.05 0Nozzle- axis [m]

5.5 Concentration of HCL and H2O

\ -

•

0

\

H

C

V

~~ \̂\"~^~- ^"

-0.1 -0.05

x^

™~ "frozen- - - equilibrium—— non equilibrium

\S^^<^ ̂ 'N-^JTv--...

^^EMUoniour

0 0.05Nozzle- axis [m]

0

0.08

10.06 3

0.04

0.02

01

0.12

0.1

0.08

e,0.06 3

••5at

0.04

0.02

01

presents a comparison of frozen, equilibriumand non equilibrium specie composition alongthe nozzle axis. The main components arepresented.

Nozzle- axis [m]

Figure 5.4 Concentration of CO and CO2

0.014 -

0.012 -

0.01

— -frozen— • - equilibrium—— non equilibrium

1 .fo.008 •

"0.006-

0.002 -

^r

0.12

0.1

0.08

0.06 =1

0.04

He zzle Contour

-0.1 -0.05 0 0.05 0.1Nozzle- axis [m]

Figure 5.6 Concentration of OH and H2

Figure 5.7 Concentration of O and H

The integrated thrust loss for the analyzedcase is approximately 75 [N], which defines anapproximate kinetics efficiency of:

T]Km= 0.996

Equilibrium flow corresponds to the upper limitof the chemical reaction kinetics where thereaction rates are infinite. The frozen flowcorresponds to the lower limit where the

reaction rates are zero. For an actual gas flowhaving finite reaction rates, the magnitudes ofthe rates are between the rates for the twolimiting cases.

For the presented gas flow expansion, there ismore or less no change in the masscomposition for equilibrium-flow and non-equilibrium-flow in the subsonic portion of thenozzle.

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At the nozzle throat, the species begin torecombine rapidly, and their mass fractionsdecrease/increase throughout in the nozzle.

Note that the blast pipe is characterized by aMach number of about 0.48. This results in anoffset between the frozen flow composition andthe equilibrium/non-equilibrium flowcompositions.

Particle loss calculation:

The major thrust loss in solid rocket motors isgenerated by the two-phase flow through thenozzle. This loss is induced by the difference infinite velocity and temperature between the gasand condensed phase (AI2O3 (I) or AL,O3 (s)).

The two- phase flow loss is calculated bycomparing the specific vacuum impulse ratioof the flow solutions, for the cases with andwithout solid particles present in the flow field.

= °-964

The velocities at nozzle exit, motor axis, aretabulated below.

Simulation

Gas velocity, no particlesGas velocity, with particlesAverage particle group velocity

Velocityalong motor

axis2378 [m/s]2280 [m/s]2093 [m/s]

Table 5.1 Exhaust velocities

Plots of particle stream traces are shown infigure 5.8, 5.9 and 5.10 with particle diametergroups as defined in table 4.3. The particlemomentum is increasing with increasing size,resulting in a more straightforward trace withincreasing diameter. The velocity lag,[(°au -VPARTICLE )/VGAS]> between the particlephase and the gas phase is shown as iso-contour lines.

Figure 5.8 Particle traces and velocity lagcontours for the small particles.

Figure 5.9 Particle traces and velocity lagcontours for the medium particles.

Figure 5.10 Particle traces and velocity lagcontours for the large particles.

Nozzle divergence loss:

The divergence loss has been analyzed bycomparing the thrust result of an Eulercalculation with an isentropic expansion.

nw= 0-991

Total loss:

The total predicted efficiency is defined by theproduct of the above quantities:

- 0.946

The total measured efficiency is within anaccuracy of 0.5%. The total efficiency, basedupon the performed motor firings is:

V MEASURED = °'948

The calculated performance is in goodagreement with the measured performance.

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Loads on aft- closure and blast pipe inlet:

The particles tend to impinge at the blast pipeinlet, resulting in heavy mechanical loads onthe insulation at the inlet.

Figure 5.11 shows relative particle density atthe aft closure/blast pipe inlet. The particleconcentration has increased with a factor ofabout 10 compared to a homogenous particleconcentration. The increase in particleconcentration results in a local mass flowincrease of about 2 at the blast pipe inlet. Thetotal density increase, [(pPART1CLE PHASE +PQAS)/PGAS],is shown in figure 5.12. The plot is a periodic3D view, seen from grain aft end and throughthe blast-pipe/nozzle. The periodicity, at eachedge, is defined at the center of the starvalleys. The left side on the plots representsthe aft closure while the right side representsthe nozzle exit.

The local erosion at the blast pipe inlet is about1.8 times higher than the local upstream anddownstream erosion. The mechanical erosioneffects are of importance in this region, and thelocal mass flow increase defines valuable inputfor erosion calculations.

Figure 5.11 Relative particle density

Figure 5.11 Total density increase

5 Conclusion

The present work is performed as a preliminaryvalidation of our new Navier-Stokes CFD codeincluding chemical reactions and two-phaseflow models.

The code is adapted for simulation of solidrocket motors related flow problems.

The calculated results seem to be in excellentagreements with other theoretical models andthe measured motor performance.

The velocity lag and particle loss calculationhas been compared to other models and is ingood agreement with those.

The calculated kinetics loss is in goodagreement with other presented work, and thegas composition at nozzle exit or downstreamin plume can be specified.

The presented CFD model is of general typeand can be applied for any type of rocket motorconfiguration as well as the presented one.

The code defines valuable input with respect tothe dimensioning of insulation. However,further work has to be done in order tocorrelate with mechanical erosion.

Acknowledgements:

This work has been financed by ourparticipation in the Norwegian PropulsionTechnology Development Program, initiated in1997.

Dr. Ivar J. 0ye, CFD norway as, has beeninvolved in the program development of thenew CFD code.

References

[1] Eriksson, L.-E., "A Third Order AccurateUpwind-Biased Scheme for UnsteadyCompressible Viscous Flow," VFA Report9370-154, VAC, Sweden, 1993.

[2] B. McBride, S. Gordon, M. Reno,CETPC/93, " Chemical Equilibrium with

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Transport Properties, 1993", COSMICProgram # LEW-16017, Lewis ResearchCenter, Cleveland, Ohio.

[3] Crowe, C. T., "Drag Coefficient ofParticles in a Rocket Nozzle", AIAAJournal, 5, 1021-1022, 1967.

[4] Hermsen, R. W., "Review of Particle DragModels," JANNAF PerformanceStandardization Subcommittee, 12th

Meeting Minutes, January 1979.

[5] Schaff, S., P. Chambre, "Flow of rarefiedGases," in Fundamentals of GasDynamics, Princeton Series, Vol. Ill,Princeton University Press, 1958.

[6] Jensen, D.E., and Jones, G.A., "ReactionRate Coefficients for Flame Calculations",Combustion and Flame, 32, 1978.

[7] SPP, A Computer Program for thePredictions of Solid Propellant RocketMotor Performance, Software andEngineering Associates Inc., Carson City,Nevada

[8] I. J. 0ye, "On the AerothermodynamicEffects on Space Vehicles," Dr. ing.-thesis, Dept. of Applied Mechanics,Thermo- and Fluid Dynamics, TheNorwegian Institute of Technology,Trondheim, 1996"

[9] Sutton, "Rocket Propulsion Elements",ISBN 0-471-52938-9

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