Compatibility of infrared band models with scattering

Techniques for the computation of radiative heating from aluminized solid propellant rocket exhaust plumes must account for infrared emission and absorption by hot H2O and CO2 in the presence of strong threedimensional aerosol scattering by micron-sized A12O3 droplets and particles. Radiative heating computations are usually performed over wide spectral intervals using infrared band models. However, no rigorous extension to infrared band models has been proposed for situations with scattering. Indeed, band models and scattering are widely held to be incompatible. Practical engineering calculations of plume radiative heating have therefore proceeded, using various approximations to the transport equation. Although the errors in these approximations are believed to be reasonably small, they have never been quantified because of the lack of rigorous results. In order to help remedy this deficiency, this article develops two different rigorous solutions. Although they are currently restricted to homogeneous media, they nevertheless provide a previously unavailable means of calibrating code performance and assessing the accuracy of various approximation schemes. Some sample applications are provided for the Space Shuttle Solid Rocket Booster.