Laminar Heat Transfer Over Blunt-Nosed Bodies at Hypersonic Flight Speeds

Abstract

This paper deals wi th two l imit ing cases of laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds, or high s tagnat ion temperatures: (a) thermodynamic equil ibrium, in which the chemical reaction rates are regarded as fas compared to the rates of diffusion across streamlines; (b) diffusion as rate-governing, in which the volume recombination rates within the boundary layer are s low compared to diffusion across streamlines. In either case the gas density near the surface of a blunt-nosed body is m u c h higher than the density jus t outside the boundary layer, and the velocity and stagnation enthalpy profiles are m u c h less sensitive to pressure gradient than in the more familiar case of moderate temperature differences. In fact, in case (a), the nondimensionalized enthalpy gradient at the surface is represented very accurately by the classical zero pressure gradient value, and the surface heat-transfer rate distribution is obtained directly in terms of the surface pressure distribution. In order to i l lustrate the method , this solution is applied to the special cases of an unyawed hemisphere and an unyawed, b lunt cone capped by a spherical segment . In the opposite l imit ing case where diffusion is ratecontrolling the diffusion equation for each species is reduced to the same form as the low-speed energy equation, except that the Prandtl number is replaced by the Schmidt number . The simplifications introduced in case (a) are also applicable here, and the expression for surface heat transfer rate is similar; the maximum value of the ratio between the rate of heat transfer by diffusion alone and by heat conduction alone in the case of thermodynamic equil ibrium is given by: (Prandtl n o . / S c h m i d t no.)'. When the diffusion coefficient is es t imated by taking a reasonable value of a tom-molecule collision cross section this ratio is 1.30. Additional theoretical and (especially) experimental studies are clearly required before these s imple results are accepted.