Time-dependent finite-difference techniques are used to obtain numerical solutions for the problem of the inviscid flow of radiating equilibrium air past sphere traveling at hyperbolic speeds. The effects of absorption are included, and results are presented for both gray and nongray absorption coefficient models for spheres with different radii. It is shown that the nondimensional heat-flux distributions for the gray and nongray models are similar and that these distributions are weak functions of the radius of the sphere and the altitude and strong functions of the flight velocity.

Results are presented for several numerical experiments using an analysis of the viscous radiating stagnation region shock layer and stagnation point heat transfer. A simple step model absorption coefficient, rationally constructed from existing quantum mechanical calculations, is shown to accurately predict shock layer nongray continuum radiative heat transfer in comparison to results obtained with detailed spectral absorption coefficients. Sensitivity of the heat transfer to uncertainties in gas radiative and transport properties is also examined, as well as the effect of artificially increased absorption in the boundary layer. (Author).

A singular perturbation solution to the blunt-body stagnation-region flow of an inviscid, radiating gas has been obtained by means of the Poincař-Lighthill-Kuo, or perturbation-of-coordinates, method. A number of results for a gray gas have been presented in order to provide some physical insight into the effects of various parameters on the shock-layer enthalpy profiles and the radiant heat-transfer rates. A nongray absorption-coefficient model was developed which includes, in an approximate way, the important vacuum-ultraviolet contributions of bound-free and line transitions. This model was used to obtain solutions pertinent to the case of reentry into the earth's atmosphere. While the results are restricted to small values of the radiation cooling parameter, which characterizes the relative importance of radiation and convection as energy-transport mechanisms, they cover broad ranges of vehicle velocity, altitude, and nose radius, which are of practical interest. The characteristic enthalpy variation of the model absorption coefficient was found to be nearly independent of altitude and nose radius for fixed vehicle velocity except for velocities lower than 10.67 km/sec. Thus it was possible to correlate certain quantities by plotting these quantities as functions of the nondimensional adiabatic radiant heat-transfer rate for various altitudes and nose radii at fixed vehicle velocity. Among the quantities correlated was the cooling factor (the ratio of the stagnation-point radiant heat-transfer rate to the adiabatic radiant heat-transfer rate). The cooling-factor correlation is particularly useful because it eliminates the need to perform nonadiabatic calculations whenever radiant heat-transfer rates are desired. Also correlated was the factor by which the convective heat-transfer rate is reduced because of radiation losses in the shock layer. Finally, upper-bound estimates were made of the effects of absorption of precursor radiation by the free-stream air on the radiant and convective heat-transfer rates.

A closed-form equation is derived for stagnation point reentry radiative heat transfer accounting for the combined effects of radiative cooling and nongray self-absorption within the shock layer. The equation can be applied for both continuum and atomic line radiation. In addition, the equation is shown to agree favorably with existing numerical data for stagnation point, continuum radiative heat transfer for a wide variety of conditions. Also, the equation is shown to apply to the end-wall radiative heat transfer behind a strong reflected shock wave in a shock tube. Finally, the equation provides a rapid means of obtaining, by hand, reasonably accurate engineering estimates for reentry radiative heat transfer including shock layer radiative cooling and nongray self-absorption.

A second-order time-asymptotic solution to radiation-coupled stagnation-region flows is presented. The solution is applied to the hypervelocity flow over blunt vehicles of inviscid, nonconducting, equilibrium air, emitting and absorbing nongray radiation. Velocities, nose radii, and altitudes covered by the analysis are sufficient to bracket reentry trajectories of current interest. Radiative heat-transfer rates for the range of interest and typical profiles of pressure, density, enthalpy, temperature, and velocity are shown. The nature of time-asymptotic solution is discussed and it is shown o be a feasible means of achieving second-order accurate solutions to radiation-coupled shock-layer flows. Step-function models of the absorption coefficient are used in order to evaluate the divergence of the radiation flux vector. An analysis is carried out to determine what effect variations in the spectral complexity of the step model absorption coefficients used in the analysis will have on the thermodynamic and flow profiles of interest and on the nongray radiative heat-transfer rates. In this connection use is made of consistent model absorption coefficients having one to nine spectral steps with free-free, free-bound (including atomic line transitions), and molecular transitions taken into account. Relatively simple models of the absorption coefficient can be used with no significant loss of accuracy. An existing correlation for the cooling factor, the ratio of the radiation heat-transfer rate to the adiabatic radiation heat-transfer rate, is extended to larger velocities than heretofore considered.