Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

Transpiration Cooling of Rocket Thrust Chamber with Liquid OxygenLiu Weicpang+ Chen Qizhi * *

Department of Space Technology, National University of Defense Technology, Changsha410073

WuBaoyuan^The llthResearch Inst, Xi'an, 710100

AbstractThe study on thermal management of platelet

transpiration cooling with liquid oxygen is made forthe thrust chamber of liquid rocket engine. Theanalysis of heat transfer is performed using the Barfleand Leadon correlation to determine the heat fluxblockage for transpiration cooled wall A heattransfer model for platelet and liquid oxygen in thewall is used to obtain the thermal penetration depthand the temperature profiles of the platelet and thecoolant Both steady and unsteady processes beingconsidered, the analytical solution and numericalsolution are obtained for them separately. Theeffects of the blowing ratio on the temperature of thechamber wall are discussed in detail

1. Introduction

High chamber pressure rocket engines usingliquid oxygen/hydrocarbon as propellants have beenconsidered for future launch vehicle propulsion.Recent advances in liquid rocket engine developmenthave intensified the problem of effective cooling forthe thrust chamber under the condition of high heattransfer flux. Generally, in cooled engines, the fuel isused as coolant to cool the combustion chamber.However, hydrocarbons such as RP-1 are limited^in their cooling capability at high temperature and

Associate Professor, •Engineer

Copyright © 1998 by Liu WeiqiangPublished by AIAA Inc. with permission

Professor, Member AIAA

high pressure and thus limited in transpiration coolingfor oxygen rich combustion chamber and prebumer.Therefore., LOX is considered as an alternativecoolant for hydrocarbon rocket engines. AmericaAerojet Propulsion Division has extensive experiencein transpiration cooling and successfullydemonstrated a structure of transpiration cooledchamber and nozzle fabricated using platelets*2' ̂ \Nevertheless transpiration cooling of formed plateletnozzle operating under the conditions of high heatflux and oxygen rich combustion belongs to a frontproblem now. This paper shows a transpirationcooling model and the solution of the transpirationgoverning equations about this problem.

2. Analytical Model and Methodology

Platelet transpiration cooling technology involvesphoto-etching channels into very thin layers ofmaterial and bonding these layers together to form acomposite structure. The general transpirationcooling chamber wafl can be simplified™ andillustrated in Fig 1 and Fig 2. In the coolant diffusionregion, the two- or three-dimensional effects of thecoolant flow appear to be less and the analyticalmodel treats the oxygen transpiration coolant asone-dimensional problem.

2.1 The governing equations for theunsteady state

If the temperatures of the platelet and the coolantare described by TS and TC at any x position, theenergy equations for platelet temperature TS and

Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

oxygen temperature TC are given as follows:

a.

where

—i —hC

»P(*~PC

hC72 " AcPcCpc

Bovmdary condition :x=0 Tc=Tc,o

d x

s _dx

= 0

dx

- f PSCpsAs -jr<k-\ PcCpAc

Cpcm

Initial condition:7X0,*) =TS, oTc(0,x)=Tc, a

1.2 Numerical solution for the unsteady state

Using finite difference method with the givenboundary condition and mfrM condition, thenumerical solution of equations (1) can be obtained.The FTCS and Mac Cormack schemes are used inthe computation process. It is important that thecomputation region L must be chosen wider man thethermal penetration depth Dj.

2.3 Analytical solution for the steady state

equations (1) equal to zero for the steady stateanalysis. The single-phase and two-phase coolingmust be investigated according to the subcritical orsupercritical liquid oxygen flow. When local pressurein the cooled wafl is tower man 50.80 xlO5 Pa andthe inlet temperature of oxygen is lower than 154.8K,for sub-critical flow state, the coolant may evaporatein the diffusion platelets, and the governing equationof me coolant must be written for different regions.When the LOX flow is supercritical, only theequation for a single-phase region is needed.Single-phase region:

a x (2a)

x

If the temperature of the two-phase flow is thesaturation temperature TC,S, the governing equationsof this region are:

(2b)dc2

§•*dxThe analytical solution can be obtained for the

governing equations of the steady state.Liquid phase region:

Two-phase region:

Gas phase cooling:3

n=l

The terms on the right hand side of the governing The boundary conditions are needed to evaluate

Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

the eleven constants of integration ( E^, J5,, /-", ) for thegoverning equations. For determining the locations ofthe two-phase region (xt and x2) and flie thermalpenetration depth Dj , three more boundaryconditions are necessary. They are:

Region I '•/tT

=0

dx= 0

d T, ~ *

Region I :

x=x2

Region 1x=x2

x=x>=DjTc=Tc,s Ts,TS- TV

dx

2.4 Hot gas side heat transfer

If the transpiration cooling is used throughout thechamber watt, there is a decrease in heat flux fromthe hot gas to the wall. Barfle and Leadonscorrelation is used to generate the blockage dataWith the unblocked heat flux for the waH fabricatednsi"g platelet, the Bartzs equation'4' is used for theheat transfer coefficient in the smoothing chamberwithout transpiration cooling flow and it must beaugmented for the rough surface. The augmentationis correlated by a Powars' factor. The two

correlations are described by reference [4] in detail.

3. Results and discussion

The governing equations (1) have been solvednumerically to predict the temperature and thethermal penetration depth of the chamber wall. As anumerical example, let the chamber wall befabricated using stainless steel platelets andLOX/RP-1 is used as propellants operating at achamber pressure about 1000 Psi (6.895 MPa). Thefinite difference numerical calculation of unsteadystate equations (1) for the chamber operating forlong time has shown that the smaBer the differencestep Ax is, the closer the difference solutionapproaches the analytical steady state solutionobtained from equation (2a). It is found that theprocess from the unsteady state to the stabletemperature distribution of transpiration cooled wallcosts much shorter time than that of film cooled andregeneration cooled wall Fig. 3 shows the historyof the temperature Ts at the chamber waH surfaceand tiie middle of the diffusion region in thefabricated platelet It can be seen that the processcosts only about two seconds from the initialtemperature to the stable temperature. Thetemperature distributions of the platelets and thecoolant in the diffusion region are illustrated in Fig 4.It is obvious mat transpiration cooling results in amuch steeper temperature gradient than mat ofnormal regeneration cooled or film cooled wall. Withsmall blowing ratio B (B=pwvw / pgug), thesurface temperature of the transpiration cooled waOcan achieve a lower value than that of regenerationcooling or film cooling. Fig 5 shows the effect of theblowing ratio on the distribution of the platelettemperature Ts. The result shows that the thermalpenetration depth Dj is only about 4.15 mm when .8is 0.019 and 3.40 mm when B is 0.026.

When the local pressure of the hot gas is lowerman 50.80 xlO5 Pa and the temperature of the

Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

coolant is lower than 154.8 K., the vaporization ofLOX may take place -within the wall structure, andboth the heat capacity and latent heat of the coolantmay contribute to the cooling effect on the watt.Using the governing equation (2a) and (2b) thedifferent analytical steady state solution for the threeregions can be obtained . Fig 6 shows thetemperature distribution of the three regions in thewan platelets for the chamber pressure 3.0 MPa andthe coolant blowing ratio 0.017.

The numerical method and the analyticalmethod are employed to predict the effect oftranspiration cooling with liquid oxygen on rocketthrust chamber fabricated with platelets. Thecomputational results obtained are consistent to acertain extent with the experiment results using other

initial low *flMfmd region Ai sub-igjel of fee coolant"̂̂ "" " — """

\

Fig. 1 The general structure of the cooled wall

coolant obtained in former study by America AerojetPropulsion Division'4, but the blowing ratio B ofLOX is greater man that of hydrogen for the samesurface temperature since the heating capacity ofoxygen is lower. Bom the analytical solution and thenumerical solution can give the importantinformation for the modern design of the tranpirationcooled engine wim LOX. The results of calculationinclude the thermal penetration depth or theminimum allowable distance between the hot waUsurface and metering channels, the chamber walltemperature distribution, the blowing ratio for a givensurface temperature and the outlet temperature ofthe transpiration coolant.

W7/77/77////

4£or steady state)

3o(forunsteady state)

Fig. 2 The A-A sectional drawing from Fig. 1

T25O

1OOO-

75O-

5OO-

250 :

x=LPc = 6.S95MPa

( 1000 Psi)5=0.019

x=0.5L

O.OO

120O

300

400

Sec2.00 4.00 6.00

Fig 3. The hiitory of die temperature Ts Athe surface and the middle of the platelet

Fig 4. The steady state temperature profileTs and Tc obtaied from the numerical solution

Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

t200

BOO( 1000 Psi)JB=0.019

X

2 3 *

Fig 5. The effect of blowing ratio on the distributionof platelet temperature T$

Fig 6. Ts and Tc distribution of the steady statesupercritical analytical solution

NOMENCLATUREA Cross-sectional areaB Blowing ratioC Wetted perimeterCp Specific heatDj Thermal penetration depthH Enthalpyh Coolant heat transfer coefficienthg Hot gas heat transfer coefficientL Diffusion platelet depth/ Length of the flow rate control channelM Coefficient of the thermal conductivitym Coolant flow rateh Heat transfer rate per unit area

T Temperature

u, v Hot gas and coolant flow rateA, Coefficient of thermal conductivity8 Platelet thicknessVj Root of the characteristic equationt Timep Mass densityT Latent heat

SubscriptsSC

nw

PlateletCoolantHot gas

1,2 or 3Chamber wall surface

Reference1. Rudi Beichel's Unique Dual Fuel/Dual Expander Reusable Rocket Engine. AIAA-96-3127

S. Elizabeth et al. Cooling of Rocket Thrust Chamber with Liquid Oxygen AIAA-90-21203 Mueggenburg, H.H. et aL Platelet Actively Cooled Thermal Management Devices, AIAA 92-31274. H. W. Vafler. Performance of a Transpiration-Regenerative Cooled Rocket Thrust Chamber, NASA CR159742 ,N80-141895. Dieter K. Huzel et al. Modern Engineering of Design of Liquid Propellant Rocket Engines. 1992, pp86