Heat Transfer 1970/3. [antikvár]

HEAT TRANSFER IN SUPERSONIC COMBUSTION PROCESSESF. S. Billig and S. E. Grenleski The Johns Hopkins University, Applied Physics Laboratory Silver Spring, Maryland, United StatesAbstractThe momentum-integral method of solution for turbulent boundary layers has been extended to obtain heat transfer in supersonic flows with chemical reactions. An integral solution of the boundary layer equations is obtained simultaneously with a pseudo-one dimensional solution for heat addition in supersonic flow to obtain local heat transfer coefficients. Results from the analysis are compared with experimental measurements obtained in an arc-heated supersonic flow with gaseous hydrogen combustion. Reasonable agreement between theory and experiment is shown. Data are presented for both cross-stream, discrete-hole injection and partially downstream Injection from a narrow circumferential slot.NomenclatureA cross sectional area, m^ Cf skin friction coefficientCp specific heat at constantpressure, j/kg^K ER fuel/air equivalence ratio ERgff effective value of ER;ERgff = Ti^, ER hspecific enthalpy, j/kgHlocal heat transfer coef-ficient, W/n^OK kthermal conductivity, W/m°KMMach numberNexponent in velocity profile(see Eq. (7)) ppressure, N/m^Pr Prandtl number = \i Cp/k qconvective heat transfer rate,rradial coordinate, mReesStTuXyY 6*Tic eM-pTwmomentum thickness Reynolds number peUg 9/^ig coordinate along surface, m Stanton number H/c pgUg temperature, °K velocity, m/s axial coordinate, m normal coordinate, m ratio of specific heats boundary layer displacement thickness, m arbitrary constant (see Eq. (D)combustion efficiencyboundary layer momentumthickness, mdynamic viscosity, Ns/m^density, kg/mwall shearing stress, N/m^Subscriptsaconditions preceding combustorRreference conditions (seeshock (see Fig/. 1)Eq. (14))adadiabiatic wall conditionssconditions following shockbconditions at combustor exit(see Fig. 1)(see Fig. 1)ttotalb'conditions at first locationwconditions at wallhaving uniform flow (see Fig. 1)elocal conditions at edge ofboundary layerFC 6.1- 2 -INTRODUCTIONAir-breathing propulsion systems based on the use of supersonic rather than conventional subsonic combustion ramjets first received serious consideration about ten years ago (see e.g., Ref. 1). Since that time several investigators (Refs. 2-6) have demonstrated supersonic heat release in free-jet and direct-connect test apparatus. Evaluations of these test results together with complementary design studies of flight vehicles using supersonic combustion ramjets (scramjets) have shown that high heat transfer rates will be present in the combustion chamber. Typically these rates are 1-20 MW/m^ or higher, which means that in a regeneratively-cooled design sufficient cooling capacity may not be available for some desired flight conditions, even if a fuel with excellent heat capacity characteristics such as liquid hydrogen is used. To determine the limitations and specifications for the design of this type of engine cooling system, it is apparent that methods must be available for the prediction of heat transfer rates in a supersonic flow complicated by both shock waves and exothermic chemical reactions. This paper represents an effort to extend the momentum-integral method of solution for turbulent boundary layers (Ref. 7) to this problem. In this development it is assumed that the momentum thickness of the boundary layer entering the supersonic combustor is defined either by measurements or from a suitable analytical procedure.