Compatability of infrared band models with particulate scattering

The prediction of the radiative heat emission from a gaseous medium which contains emitting and scattering particles has been a subject of much investigation. An example of one such problem is the calculation of the heat transfer from the exhaust of a solid propellant rocket motor to the vehicle base. Engineering approximations for the case of a purely absorbing medium have been in existence for a number of years and have withstood the test of time. One such approximation which has received much attention is called a "band model". A band model replaces the intricate emission spectra produced by a gaseous medium with essentially a bar chart representation of the spectrum; the width of each bar represents the spectral resolution of the band model, and the height of the bar represents the average value of the emission over the spectral width of the bar. Band models have many advantages in that they are based on solid physics, they provide a good representation of the real emission spectra, and computing a band model emission spectrum is relatively fast, compared to computing the true line-by-line spectrum. It is desired to exploit the band model formulation for problems with radiation scattering, such as the base heating problem mentioned previously. Upon the introduction of scattering particles to a gaseous medium, however, the band model formulation no longer applies. What was once a one-dimensional problem becomes a three-dimensional problem. Many useful mathematical approximations have been proposed to force the scattering problem into a band model type solution. These approximations retain the efficiency of the gaseous band model, however their mathematical and physical accuracy for a particular application is often unknown. The purpose of this thesis is to formulate a method by which a mathematically correct, albeit computationally slow, solution to the band model scattering problem can be generated. These mathematically correct solutions can then be used to evaluate the accuracy of various mathematical approximations applied to the scattering problem. Three approximate treatments for which an exact band model treatment is compared are the "hybrid" band model, the two-flux scattering model, and the emission averaging treatment for the case of unequal gas and particle temperatures. For the test case examined herein, the hybrid band model approximation led to an overprediction of the emission by as much as 50% in strong gaseous absorption bands, such as the 2.7-μm water band, and displays a non-physical curve of growth. The two flux approximation performs well in strong gaseous absorption bands but overpredicts the emission in the weak gaseous emission spectral regions. Emission averaging led to an underprediction of the emission of the test case by no more than 7%.