Modeling of Radiation Heat Transfer in Liquid Rocket Engines

Modeling of Radiation HeatTransfer in Liquid Rocket EnginesM.H. NaraghiDepartment of Mechanical Engineering, Manhattan College,Riverdale, NY 10471S. Dunn and D. CoatsSEA Inc., 1802 North Carson Street, Suite 200 Carson City, NV89701

Motivation• Design of cooling circuits of regenaratively cooled rocketengines both a good physical insight on the workings ofthe engine and a method of calculating the effects ofdesign changes on the heat transfer via conjugatedconvection/conduction/radiation and coolingrequirements of LRE’s• Conjugated convection and conduction models for liquidrocket engines are well established (e.g., TDK-RTEmodel)• Combustion gases in liquid rocket engines consists ofgases at very high temperatures (up to 7000R) withradiatively participating gases, e.g. water vapor, CO,CO 2 and soot.

Previous Works• Hammad, K.J., and Naraghi, M.H.N., “ExchangeFactor Model for Radiative Heat Transfer Analysis in RocketEngines,” AIAA Journal of Thermophysics and Heat Transfer,Vol. 5, No. 3, pp. 327-334, 1991.• Liu, J., and Tiwari, S.N., “Radiative Heat Transfer Effects inChemically Reacting Nozzle Flows,” AIAA Journal ofThermophysics and Heat Transfer, Vol. 10, No. 3, 1996.• Badinand, T. and Fransson, T.H., “Radiative Heat Transfer in FilmCooled LH/LO Rocket Engine Thrust Chamber”, AIAA Journal ofThermophysics and Heat Transfer, Vol. 17, No. 2, pp. 29-34, 2003.• Wang, Tee-See, “Multidimensional Unstructured-Grid Liquid RocketEngine Nozzle Performance and Heat Transfer Analysis,”AIAA paper 2004-4016 presented at the 40th AIAA/ASME/SAE/ASEEJoint Propulsion Conference and Exhibit July 11-14, 2004,Fort Lauderdale, Florida.

Radiation Heat Transfer fromHot-Gases• Combustion Gases consist of several radiativelyparticipating species• These species are: soot, CO, CO 2 , and watervapor• HITRAN and HITEMP database is used toevaluate absorption coefficients• Properties of the radiatively participating speciesare spectral, consisting of a large number ofbands• A Plank-mean approach is be used to evaluateabsorption factors

Exchange Factors betweengas and surface elementsr sirxr gidg ids ir gjr si dg j ds j ψjjijijijjjiddsrdssψτββπψψ∫−−=maxmin2)(coscos2),(rrrrrrjjijiijjjtjiddxdrrkdsgjψβ τπψψ∫−−=maxmin2)(cos2),(rrrrrrjjijijjjjiddsrdgsψτβπψψ∫−−=maxmin2)(cos2),(rrrrrrjjijijjjtjiddxdrrkdggjψτπψψ∫−−=maxmin2)(2),(rrrrrrjik tjierrr(r−−=− )τ

Radiative Nodal PointsNodal points in axialdirection, the sameas stationsNodal points inradial direction

Total Exchange FactorsAccount for wall reflection and gas scatteringDSS[ { [ ] } ]−1−1I − dss + dsgωW I − dggωW dgs ρW dss + dsgωW [ I − dss W ]{−1= ω dgs}α0g0g−1[ I − dggωW ] dgs I − ρW dss + dsgωW [ I − dgg W ]s[ { }] −1-1dgs αDGS = ω0gs0g0g0g0gWall heat flux at station nq2nr+ mm⋅nrr, n= ∑ ws,jDSjSnEs,j+ ∑ wg,jDGjSnEg,j−j=1j=1Es= εσT4n s nEgj=4 (1 ) 4Kt−ωl 0σTgjEs,nThis model is built in the TDK’s radiation module (RAD2005)

0.6Plank-Mean Properties for Water-Vapor0.5Ka/P (cm bar) -10.40.30.2HITEMPHITRAN0.100 500 1000 1500 2000 2500 3000T, K

Plank-Mean Properties for CO 20.40.35ka/P (cm bar) -10.30.250.20.15HITEMPHITRAN0.10.0500 500 1000 1500 2000 2500 3000T, K

Plank-Mean Properties for CO0.040.035Ka/P (cm bar) -10.030.0250.020.015HITEMPHITRAN0.010.00500 500 1000 1500 2000 2500 3000T (K)

Absorption Coefficient of SootWhen engines running with rich hydrocarbon fuels soot is presentin the combustion gases.As of today little is known about the nature of the production,Destruction, shape and size distribution. An approximate valueof soot absorption coefficient can be obtained via:k = 3.72f C T / Ca v 0 2CWhere f v is volume fraction of soot0=( n2−k236+π2)nk2+ 4nC 2 =1.4388 cm K, n and k are real and imaginary part of index ofrefraction2k2

Computer ModelThe properties and computational models(RAD2005) discussed were incorporated inthe TDK-RTE.Naraghi, M.H.N., Dunn, S., and Coats, D., “A Model forDesign and Analysis of Regeneratively Cooled RocketEngines,” AIAA paper 2005-3852, present at the JointPropulsion Conference, Fort Lauderdale, July 2004.

Results for a LH2-LO2 Engine(SSME)The specifications of this engine are:Chamber pressure3027 psiaO/F 6.0Contraction ratio 3.0Expansion ratio 77.5Throat diameter10.3 inchesPropellantLH2-LO2CoolantLH2Total coolant flow rate29.06 lb/sCoolant inlet temperature95RCoolant inlet stagnation pressure 6452 psiaNumber of cooling channels 430

Effects of radiation on the wallheat flux of the SSMEWall Heat Flux (Btu/in 2 s)11010090807060504030No RadiationWith Radiation, HITRANWith Radiation, HITEMP20-15 -10 -5 0 5 10Axial Position (in)

Effects of radiation on the walltemperature of the SSME1600Wall Surface Temperature (R)140012001000800600No RadiationWith Radiation HITRANWith Radiation HITEMP-15 -10 -5 0 5 10Axial Position (in)

Effects of radiation on the coolantstagnation temperature of the SSMECoolant Stagnation Temperature (R)700600500400300200100-15 -10 -5 0 5 10Axial Position (in)No radiationWith Radiation, HITRANWith Radiation, HITEMP

Effects of radiation on coolantstagnation pressure of SSME70006500Coolant Stagnation Pressure (psi)600055005000With Radiation, HITEMPWith Radiation, HITRANNo Radiation45004000-15 -10 -5 0 5 10Axial Position (in)

Results for a RP1-LO2 EngineThe specifications of this engine are:Chamber pressure2,000 psiO/F (mixture ratio) 1.8Contraction ratio 3.4Expansion ratio 7.20Throat diameter2.6 inchPropellantRP1-LO2CoolantLO2Total coolant flow rate32.893 lb/sCoolant inlet temperature 160°RCoolant inlet pressure3,000 psiNumber of cooling channels 100Throat region channel aspect ratio 2.5

Contour of the RP1-LOX engine108Liner radius ( in )6420-10 -8 -6 -4 -2 0 2 4Axial location (in)

Effects of radiation on the wallheat flux of the RP1-LOX engine5045QW, BTU/s in 24035302520No radiationWith Radiation HITEMP151050-10 -5 0 5Axial location (in)

Effects of radiation on the walltemperature of the RP1-LOXengine140012001000TW (R)800600No RaditionWith Radition HITEMP400200-10 -5 0 5Axial location (in)

Effects of radiation on the coolanttemperature of the RP1-LOXengine450400Coolant temperature, R350300250No RadiationWith Rdiation HITEMP200150-10 -5 0 5Axial location, in

Effects of radiation on the coolantstagnation pressure of the RP1-LOX3000engine2900Coolant stagnation pressure, psi28002700260025002400No radiationWith radiation2300-10 -5 0 5Axial location, in

Effects of radiation on the coolant Mach0.35number of the RP1-LOX engine0.3Coolant Mach number0.250.20.150.1No radiationWith Radiation, HITEMP0.050-10 -5 0 5Axial location, in

Concluding Remarks• The effects of gas and surface radiation onthe wall temperature, coolant pressure,temperature and Mach number werestudied• The results presented demonstrate thatalthough the increase in heat flux due toradiation is small, it can have a significanteffect on the wall temperature and coolantflow characteristics

Concluding Remarks• For a LH2/LO2 engine it is shown that theradiation has a small effect on the walltemperature of the diverging section of thenozzle• the radiation results in a substantial increase inthe wall temperature of the thrust chamber andconverging section of the nozzle, such that thelocal peak temperature is the same order ofmagnitude as the throat temperature

Concluding Remarks• For the RP1/LO2 engine, radiative heattransfer resulted in a 30% increase in walltemperature. Additionally, it significantlyincreased the coolant pressure drop andMach number• neglecting radiation during the designphase may result in a faulty coolingsystem

Availability of the Radiation CodeRAD2005• The model presented is incorporated in aprogram (RAD2005) which can be linkedto TDK and RTE• TDK from Software EngineeringAssociates, Inc. (seainc.com)• RTE from Tara Technologies, LLC(tara-technologies.com)