Laminar Heat Transfer Around Blunt Bodies in Dissociated Air

Abstract

S = Eq. (8) T = absolute temoerature u = x-component of velocity v = y component of velocity x = distance along meridian profile of body y = distance normal to body surface V = Eq. (6) 0 = Eq. (8) \x = absolute viscosity * = Eq. (5) p = mass density a = Prandtl Number c p fx/kA method of predicting laminar heat-transfer rates to blunt, highly cooled bodies with constant wall temperature in dissociated air flow is developed. Attention is restricted to the case of axisymmetric bodies at zero incidence, although two-dimensional bodies could be treated the same way. The method is based on the use of the "local similarity" concept and an extension of the ideas used by Fay and Riddell. 1 A simple formula is given for predicting the ratio of local heat-transfer rate to stagnation-point rate. It depends on wall conditions and pressure distribution, but not on the thermodynamic or transport properties of the hot external flow, except at the stagnation point.Experimental heat-transfer rates obtained with correct stagnation-point simulation and high wall cooling in shock tubes are also presented and compared with the theoretical predictions. On the whole, the agreement is good, although in regions of rapidly varying pressure there is evidence that the local similarity assumption breaks down, and the theory underestimates the actual heat-transfer rate by up to 25 per cent. SYMBOLS Ci Cp D DT f g h h hi 0 h D H k I Li U T L M 8 P Pi = = = = = = = = = = = = = = = = = = = mass fraction of ith component Vd(dhi/dT) diffusion coefficient thermal diffusion coefficient Eq.(7) Eq.(8) enthalpy per unit mass of ith component enthalpy per unit mass of the mixture, including dissociation energy, Xci(hi -hi 0 ) heat evolved in the formation of component i at 0°K., per unit mass average atomic dissociation energy times atom mass fraction in external flow h + (l/2)u 2 thermal conductivity PM/' PwP<w Lewis Number Dipc p /k = Dipa/fi thermal Lewis Number Di T p c p /k = Di T por/ii Lewis Number for atom molecule mixture Mach Number of moving shock in shock tube, referred to speed of sound in quiescent gas in front of it pressure initial pressure in shock tube (measured in cm. of merq = heat-transfer rate qi = vector diffusion velocity, Eq. (1) r = cylindrical radius of body, recover}^ factor R = body-nose radius in meridian plane The numerical calculations were performed efficient^ by Robert Laubner, and many helpful discussions were held with F. R. Riddell and J. A. Fay. * Principal Research Scientist. Subscripts i = ith. component e = external flow conditions w = wall conditions, rj = 0 or y = 0 ^ = stagnation-point conditions £» y, x > y = differentiation with respect to indicated variable oo = free-stream conditions o = local similarity solution E = equilibrium (1) INTRODUCTION T HE THEORY of heat transfer at a stagnation point in a dissociating gas has been discussed by Fay and Riddell. 1 They considered the mechanism of heat transfer, with the pertinent physical and chemical effects which arise because of gas dissociation. It was shown ...

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