Radiative Transfer Effects on Reflected Shock Waves I. Transparent Gas

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Abstract
Analytical and numerical calculations are carried out for the effects of radiative cooling on the flow field and heat transfer behind a reflected shock wave. The analytical solutions are developed by an expansion procedure about the Newtonian limit; i.e., the flow variables are expanded in the small parameter ε representing the initial density ratio across the shock front. Solutions carried out through the zeroth- and first-orders in ε show an accuracy to the order of ε2; viz., for the specific conditions considered the analytically calculated enthalpy changes agree to within 2% with the numerically computed changes. The numerical procedure consists of a finite difference calculation with pressure gradients neglected. The analytical calculations show that pressure gradient effects may be neglected, except at very long times when the shocked gas has cooled by a large amount. Our calculations show much greater shock-wave attenuation than does a previous numerical computation. This difference is attributed to a better representation of the thermodynamic properties in the present calculations.