(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. A01-34296 AIAA 2001 -3584 Modeling the Gas Dynamics Environment in a Subscale Solid Rocket Test Motor Andrew M. Eaton, Mark E. Ewing and Kirk M. Bailey ATK Thiokol Propulsion Corp. 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit July 8-11,2001 Salt Palace Convention Center Salt Lake City, Utah For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics, 1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.
Transcript
(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.
A01-34296
AIAA 2001 -3584
Modeling the Gas Dynamics Environmentin a Subscale Solid Rocket Test Motor
Andrew M. Eaton, Mark E. Ewing and Kirk M. BaileyATK Thiokol Propulsion Corp.
37th AIAA/ASME/SAE/ASEEJoint Propulsion Conference and Exhibit
July 8-11,2001Salt Palace Convention Center
Salt Lake City, UtahFor permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,
1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.
(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.
AIAA 2001-3584
MODELING THE GAS DYNAMICS ENVIRONMENT IN A SUBSCALE SOLIDROCKET TEST MOTOR
Andrew M. Eaton/ Mark E. Ewing* and Kirk M. Bailey*ATK Thiokol Propulsion Corp.
Brigham City, Utah
ABSTRACTSubscale test motors are often used for the evaluation ofsolid rocket motor component materials such as internalinsulation. These motors are useful for characterizinginsulation performance behavior, screening insulationmaterial candidates and obtaining material thermal andablative property design data. One of the primarychallenges associated with using subscale motorshowever, is the uncertainty involved whenextrapolating the results to full-scale motor conditions.These uncertainties are related to differences in suchphenomena as turbulent flow behavior and boundarylayer development, propellant particle interactions withthe wall, insulation off-gas mixing and thermochemialreactions with the bulk flow, radiation levels, materialresponse to the local environment, and other anomalousflow conditions. In addition to the need for betterunderstanding of physical mechanisms, there is also aneed to better understand how to best simulate thesephenomena using numerical modeling approaches suchas computational fluid dynamics (CFD).
To better understand and model interactions betweenmajor phenomena in a subscale test motor, a numericalstudy of the internal flow environment of arepresentative motor was performed. Simulation of theenvironment included not only gas dynamics, but two-phase flow modeling of entrained alumina particles likethose found in an aluminized propellant, and off-gassing from wall surfaces similar to an ablatinginsulation material.
This work represents a starting point for establishingthe internal environment of a subscale test motor usingcomprehensive modeling techniques, and lays thegroundwork for improving the understanding of theapplicability of subscale test data to full-scale motors.It was found that grid resolution, and inclusion ofphenomena in addition to gas dynamics, such as two-phase and multi-component gas composition are all
important factors that can effect the overall flow fieldpredictions.
INTRODUCTIONSubscale test motors are often used for the evaluation ofsolid rocket motor component materials such as internalinsulation. An example of one such motor is referred toas a Seventy Pound Charge or 'SPC motor, the nameoriginating from the propellant weight originally usedin an early design of the motor. These motors are usefulfor characterizing insulation performance behavior,screening insulation material candidates and obtainingmaterial thermal and ablative property design data.
One of the primary challenges associated with usingsubscale motors is the uncertainty involved whenextrapolating the results to full-scale motor conditions.For example, insulation erosion in the SPC char motormay be quite different than observed in a full-scalemotor for what were thought to be similar Machnumbers. The uncertainties are typically the result of aninadequate understanding of the local aerothermalenvironment of the subscale motor compared with thefull-scale. These uncertainties can be attributed to any,or a combination of any of the following:
1) Turbulent flow behavior and boundary layerdevelopment may be much different.
2) Metallized propellant particle interactions withthe wall may not be representative of particleinteractions in certain regions of full-scalemotors.
3) Pyrolysis gas products leaving the surface ofthe insulator may have higher relativeconcentration levels that could lead todifferences in material ablation behavior.
4) Radiation levels may be lower than those infull-scale motors due to the small scale andassociated optical thickness.
5) Non-uniform erosion behavior in multiplesamples may result in anomalous flowconditions.
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6) Uncertainties in the how the material responseis related to the local environment.
In addition to the need for understanding these physicalmechanisms, there is also a need to better understandhow to best simulate these phenomena using numericalmodeling approaches such as computational fluiddynamics (CFD). Of particular interest are the use of'comprehensive' codes that employ fully-coupledsolutions of the gas dynamics with two-phase flow andmulti-component gases. CFD-related tools can provideinsights into the interplay of the various mechanisms ofinterest and also serve as a scaling tool for comparingsmall motor and large motor environments if theappropriate modeling approaches can be identified.These approaches are related to areas such asturbulence modeling and the associated wall-boundarycondition approach, and how fine the computationalgrid must be to accurately capture the flow details ofinterest.
To help address these issues, a numerical study of theinternal flow environment of an SPC motor wasperformed. The objective of this study was to assess thesensitivity of the internal aerothermal environmentpredictions of the SPC test motor to grid fineness andassociated wall boundary condition approach.Simulation of the environment included not only gasdynamics, but two-phase flow modeling of entrainedalumina particles like those found in an aluminizedpropellant, and off-gassing from wall surfaces similar toan ablating insulation material
DESCRIPTION OF CFD SIMULATIONSTo achieve the objectives of this study, a series of SPCflow predictions were done for both a relatively coarseand a finely meshed computational grid. Given the twogrids, three different kinds of flow situations wereconsidered: assuming all the propellant combustionproducts flow as a single-phase gas flow, assuming atwo-phase mix of propellant gas combustion productsand entrained alumina particles, and single-phase gasflow with two gaseous components (propellantcombustion products and insulation charring-ablationoff-gas).
GeometryA sketch of the geometry of the SPC motor consideredin this study is shown in Fig. 1. When testing insulationmaterials in this motor, performance can becharacterized over a wide range of operating conditionsby varying the bore diameter in the three flow regionsof the motor designated as the low, medium and highvelocity sections. In these regions, flow diameters canvary from as large as 20 to as small as 3.2-cm, withcorresponding Mach numbers ranging from 0.0027 to
0.08 and gas velocities ranging from 3.5 to 110-m/secrespectively. A typical test motor pressure can be ashigh as 5.5-6.5-MPa.
General Assumptions and Operating ConditionsIn modeling the SPC internal flow field, all of thepredictions of the internal environment were made withthe commercially available Fluent® CFD code, and thefollowing general assumptions and operating conditionswere used:
which has demonstrated improved predictionscompared with the standard k-£ model u.
• Steady-state flow.• Constant wall boundary temperature (2500K)
for the areas of the motor corresponding toinsulation samples, adiabatic walls elsewhere.
• Propellant gas properties with molecularweight = 28.44, dynamic viscosity = 9.65x10-5 kg/m-s, Specific heat = 2000 J/kg andthermal conductivity = 0.38 W/m-K.
• Total propellant mass flow rate of 0.49 kg/s, ata total pressure of 6.2 MPa and a totaltemperature of 3400K.
Gridding and turbulence modelingGiven the general operating conditions andassumptions, the primary objective of this study was toassess the sensitivity of the flow field predictions togrid resolution. Of particular interest was the wall heattransfer. In turbulent flow modeling however, thecreation of the grid is closely coupled with the choice ofthe wall boundary condition approach. A review ofturbulent flow models and the options available fordefining wall boundary conditions has been performedby several investigators, such as Wilcox3, Pope4 andEaton, et al5. Based on these reviews, two cases werechosen as representative to assess the effects of gridresolution and the related wall boundary conditionapproach on the wall heat transfer:
1. A relatively coarse grid (10,000 cells) and awall function boundary condition.
2. A relatively fine grid (100,000 cells) and atwo-layer zonal boundary condition.
Coarse grid case. Launder and Spalding6'7 firstproposed the standard wall function boundary conditionfor CFD-related predictions using a two-equationturbulence model. This boundary condition is based onthe assumption that a universal velocity andtemperature profile exists between the wall node centerof the fluid cell adjacent to the wall. The velocity andtemperature profiles can be described in non-dimensional coordinates as
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AIAA 2001-3584
U*=-ln(Ey*)K
wherel /4 i 1/2> K
JT*== V w
and
y* = -V
£7 and T are the velocity and temperature at the nodecenter of the fluid cell adjacent to the wall, y is thedistance from the wall to the node center, and k is theturbulent kinetic energy. C^, K, and E are empiricalconstants, Cp, p, and v are the local fluid properties ofspecific heat, density and kinematic viscosityrespectively, and iw is the local wall shear stress. Theseexpressions for £/*, 7*, and v* are the same asexpressions for universal log-law in terms of U*, T*,and y+ described in references such as Kays andCrawford8, given the relationships
U*=aU+
T* = aT+
y* = ay+
where a is defined by the ratioy^l/47 1/2
a =•
The ratio a is a measure of the development of theboundary layer. In a developing boundary layer, it isless than 1, in a fully-developed boundary layer it isabout equal to 1, and boundary layers with high free-stream turbulence, such as a wall jet, it is greater than 1.Given a cell velocity, the log-wall relationships relatesthe local shear stress imposed by the wall on the flowwith the neighboring cell velocity.
When creating a grid for a prediction that will employ awall function boundary condition, the main controllingparameter driving the grid resolution is the magnitudeof ;y* for the fluid cell adjacent to the wall. To keepthis wall function in its range of applicability, the y*value should ideally be in the range of 30-100.Following this criterion for the SPC motor resulted in agrid with 10,000 cells.
Fine grid case. For the fine grid case, the two-layerzonal boundary condition presented by Rodi9, Chen and
Patel10 and Kim and Choudhury11 was employed, whichhas been shown to be more robust and provide betterperformance than alternative low-Reynolds k-eturbulence models. In contrast with the wall functionapproach, the two-layer zonal boundary conditionapproach makes no assumption about the velocityprofile, but calculates it directly based on the local gridspacing. It does this by dividing the flow field into twomain parts, a region along the wall dominated byviscous effects, and a region away from the wallcorresponding to fully-turbulent flow. In the near-wallregion, a one-equation turbulence model is employed,and the high-Reynolds number RNG-model is used inthe fully-turbulent region. This approach thereforerequires grid resolution that extends into the viscoussublayer of the flow, which corresponds to y+ values inthe neighborhood of 1. Given this kind of gridresolution, the two-layer model accounts for thechanges in turbulent kinetic energy and dissipation inthe near-wall region of the flow field. For the SPCmotor, following the requirements for the two-layerwall boundary condition resulted in a grid with about120,000 cells.
Particle transportIn additional to the single-phase gas flow cases, for thetwo computational grids described above, fully-coupledtwo-phase predictions were made to characterize theparticle transport. The particle size distribution andloading were similar to those described by Whitesideset al12 for RSRM propellant. The size distribution wasdivided into 8 separate sizes with a minimum diameterof 10 microns, a maximum diameter of 600 microns, amean diameter of 93.7 microns and a spread factor of1.157. For the particles, the density was assumed to be100 kg/m3, the specific heat 1760 J/kg and aconductivity of 10.5 W/m-K.
The loading of the particles corresponded to about 8%of the total mass flow rate of the propellant (0.0395kg/s), which is representative of the amount of aluminaparticle in the propellant gas with diameters equal to orgreater than about 10 microns.
Insulation Off-gassingIn addition to the single and two-phase calculations, forthe two computational grids described above, theoff-gassing of the ablating insulators into the propellantgas was modeled as an in-flow boundary condition.These were modeled as gas-only flows, but theinsulation off-gas representing the charring/ablationproducts was modeled with one composition, and thepropellant gas as another composition. The compositionof the off-gas was assumed to correspond to theelemental composition of the insulation, which is a mixof carbon, ethylene, propylene, and neoprene. This
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mixture was calculated to have an equivalent molecularweight of 26.38. No reactions were assumed and themixing was driven by diffusion and turbulencetransport. The mass flow rates assumed for each of thesections was base on typical insulation erosion rates,which are as follows:
• Low velocity section = 0.0054 kg/s• Medium velocity section = 0.0039 kg/s• High velocity section = 0.0073 kg/s
RESULTS OF THE PREDICTIONSThe results of the predictions for all the cases aresummarized in Figures 2-10. While the full-motor wasanalyzed, figures with contour images have beenmagnified in areas where the insulation sections wouldbe located.
Figure 2 is a comparison of velocity and streamfunction predictions for the single-phase gas flow cases.As seen in these figures, very different flow fields arepredicted for the two cases. The fine grid case predictsgreater mass flow along the walls than in the coarsegrid case. There is a corresponding higher heat flux ratein the fine grid case, which is evident in the lower gastemperature for the fine grid case shown in thecomparisons in Figure 3. The values for the wall heatflux are between the two cases are compared in Figure4.
Figure 5 is a comparison of velocity and temperaturefor the two-phase flow cases. In these predictions, thedifferences between the coarse and fine grid predictionsare not as great as the single-phase gas predictions. Oneof the reasons for this is shown in Figure 6, whichcompares coarse and fine grid particle concentrations.Both predict that the particles entering the medium andhigh velocity section of the motor tend to concentratealong the centerline of the motor rather than staying in auniform distribution. As a result the differences in gastemperature, shown in Figure 5, and the heat flux,shown in Figure 4, are also not as great as in the single-phase cases. There is enough of a difference in the flowfield predictions however, to alter the level of particleconcentrations along the wall. These comparisons areshown in Figure 7. Much higher particle concentrationsare predicted for the fine grid case than the coarse gridcase.
Figure 8 compares contour images of the insulation off-gas fraction for the two-component gas flowpredictions. The gas fraction values along the wall areshown in Figure 9. These comparisons show that thegrid resolution does not significantly affect theprediction of off-gas fraction along the wall. In relatingthis parameter to the corresponding effect on insulationerosion, it is useful to calculate how the insulation off-
gas fraction affects the value of ft , which is defined byMcDonald and Headman13 as
where MWe is the molecular weight of the gas at the
edge of the boundary layer, MWAl o is the molecularweight of the alumina in the entrained particles, andXj is the mole fraction of the species 7. f t can beshown to be the ratio of char oxidation rate to the rate atwhich oxidizing species from the boundary layer edgecan diffuse to the wall. The presence of upstream off-gas can therefore dilute the oxidizing species andattenuate char oxidation. To determine the relationshipbetween off-gas fraction and ft , a series of mixingcalculations were made with the NASA-Lewis code.This relationship is shown in Figure 10. As an exampleof the effect of off-gas, a value of 0.04, which isrepresentative of the value in the medium and high-velocity sections of the char motor, f t is reduced from0.1 to 0.04, which would be a 40% reduction in the charrate. The mixing of the off-gas with the propellant cantherefore have a noticeable affect on downstreamerosion.
CONCLUSIONSThis work is the starting point for establishing theinternal environment of a subscale test motor, and laysthe groundwork for improving the understanding of theapplicability of subscale test data to full-scale motors.The results may also give insights into the appropriatedesign of improved subscale testbeds, and providevaluable information for improved modeling techniquesfor internal insulation.
Grid resolution and the related wall boundary conditionapproach used in the simulations was demonstrated tobe an important factor in prediction results. If we followthe standard assumption that increasing grid resolutionincreases the accuracy of the prediction, then the finegrid predictions best represent the flow field andsuggest that wall function approaches may not providethe needed accuracy. The comparison with the two-phase simulations indicate however, that the affects ofgrid spacing and wall boundary condition are attenuatedby the addition of a the discrete phase.
Coupling of the gas dynamics with entrained particlesin the two-phase predictions was also found to have anmajor effect on the flow field predictions, although thedifference was not as great for the coarse grid case as
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the fine grid case. The change in particle concentrationswhen flowing into regions where there are significantchanges in geometry, like the transition from the low-velocity to high velocity sections of the motor can havea dramatic effects on the resulting overall gas flowdistribution. These results suggest the need for two-phase flow predictions to accurately characterize thedynamics of the flow field.
From the multi-component predictions, it can beconcluded that the local environment needs to beproperly characterized in order to fully understand localcomponent behavior. For example, upstream insulationerosion has the potential to affect downstream erosionbecause of changes introduced in the local environment.
As an overall conslusion from this study, there is adefinite need to apply more comprehensive modelingapproaches in studying the internal flow of solid rocketmotors. This need is as great in obtaining accuratepredictions as the need for adequate grid resolution.The changes in flow field predictions that result whenmore complex physics is included in the predictionhave underscored this need, as well as illustrating howthe differences in local environment in comprehensivemodel predictions may have significant effects on thelocal material response.
REFERENCES1. Yakhot, V. and Qrzsag, S.A. Renormalization
group analysis of turbulence: I. Basic Theory. J.Scientific Computing. 1(1): 1, 1986.
2. Choi, D., J.S. Sabnis and TJ. Barber. Applicationof an RNG k-epsilon turbulence model tocompressible turbulent shear layers. AIAA 94-0188.
3. Wilcox, D.C. Turbulence modeling for CFD. LaCanada, CA: DCW Industries, Inc., 1998.Pope, S.B. Turbulent Flows. Cambridge.Cambridge University Press. 2000.Eaton, A.M., Smoot, L.D., Hill, S.C. and Eatough,C.N. Components, formulations, solutions,evaluation, and application of comprehensivecombustion models. Prog. Energy CombustionScience. 7999; 25:387.Launder, B.E. and Spalding, D.B. Lectures inmathematical models of turbulence. New York:Academic Press, 1972.Launder, B.E. and Spalding, D.B. The numericalcomputation of turbulent flows. Computer Methodsin Applied Mechanics and Engineering, 3:269,1974.Kays, W.M. and Crawford, M.E. Convective Heatand Mass Transfer. New York, McGraw Hill,1980.Rodi, W. Experience with 2-layer modelscombining the k-e model with 1-equation modelnear the wall. AIAA Paper 91-0216. 1991.Chen, H.C. and Patel, V.C. Near-wall turbulencemodels for complex flows including separation.AIAA J. 26(6):641, 1988.Kim, S., and Choudhury, D. Computations ofcomplex turbulent flows and heat transfer usingtwo-layer based wall functions. ASME HTD-Vol.311. 1995 National Heat Transfer Conference. 9.169. 1995.
12. Whitesides, R.H. Dill, R.A. and Purinton, D.C.Application of two-phase CFD analysis to theevaluation of asbestos-free insulation in the RSRM.AIAA-97-2861. 1991.McDonald, A. J. and Hedman, P.O. Erosion of
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13.graphite in solid-proOpellant combustion gases and
PhenolicTransitionSection Nozzle
st~ ->Gas Flow
/Propellant
Low-VelocitySpecimen
Medium-VelocitySpecimen
High-VelocitySpecimen
Figure 1. Sketch of the SPC char motor
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AIAA 2001-3584
I1.0004-02
9.0064-01
a 0064-01
7.00&4-01
6.0004-01
5.0004-01
4.0004-01
3.0004-01
20004-01
1.0004-01
0.0004-00
1.30e+ 02
1 1704-02
1.0404-02
9.1004-01
78004-01
6.5004-01
5.2004-01
39004-01
2.8004-01
3 1.3004-01
00004-00iContours of Velocity Magnitude (m/s) May 21. 2001 Contours of Velocity Magnitude (m/s)
FLUENT 5.6 (axi, segregated, rngke)May 22,2001
FLUE NT 5.6 (axi, segregated, rngke)
i7.886-02
7.096-02
8.300-02
5.516-02
4.736-02
3.940-02
3.156-02
2366-02
1.580-02
7.880-03
0.0004-00
iS.OOe-02
7200-02
6.400-02
5.800-02
4800-02
4000-02
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00004-00
Contours of Stream Function fkg/s) May 21,2001FLUENT5 6 (axi. segregated, mgke)
Contoursof Stream Function (kg/s) May 22. 2001FLUE NT 5.6 (axi, segregated, rngke)
a. Coarse grid with wall function b. Fine grid with two-layer zonalFigure 2. Comparison of single-phase gas velocity magnitude and stream function.
i3.4004-03
3.310+-03
3.2204-03
3.1304-03
3.0404-03
29504-03
28604-03
27704-03
26804-03
25904-03
25004-03
3.4004-03
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32204-03
31304-03
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Contoursof Static Temperature (k) May 21, 2001 Cortoursof Static Temperature (k)FLUENT 5.6 (axi, segregated, rngke)
May 22. 2001FLUENT5.6 (axi, segregated, rngke)
a. Coarse grid b. Fine gridFigure 3. Comparison of single-phase gas temperatures.
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