Compatibility of infrared band models with scattering

Abstract

Techniques for the computation of radiative heating from aluminized solid propellant rocket exhaust plumes must account for infrared emission and absorption by hot H 2 O and CO 2 in the presence of strong threedimensional aerosol scattering by micron-sized A1 2 O 3 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.

Application of Statistical Narrowband Model to Three-Dimensional Absorbing-Emitting-Scattered Media

“…(14), was conducted rst without iteration. Once the nonscattered part was obtained, the scattered part was calculated with terms containing N I nm acting as known source terms.…”

“…The transfer equation for nonscattered radiation, Eq. (14), was solved using the ray-tracingmethod described by Liu. 7 Ray tracing was performed at the center of each computational grid along all the directions de ned by the T 4 quadrature set (128 directions).…”

“…(5)]. This dif culty of applying a narrowband model to scattering problems was termed band model-scattering incompatibility by Reed et al 14 The incompatibility is inherent for scattering problems when using the band model methodology and cannot be eliminated.…”

“…Therefore, the computationallyintensive ray-tracing procedure described by Liu 7 can be used to solve Eq. (14). Second, the nonscattered part I nm , which is in general greater in magnitude than the scattered part, is calculated accurately.…”

“…Secondly, it encounters the so-called band model-scatteringincompatibilitywhen applied to scatteringmedia. 13,14 The incompatibility constitutes the major obstacle to the application of the SNB model to multidimensional scattering problems.…”