Computation of Radiation in the Apollo AS-501 Reentry Using Opacity Distribution Functions

Abstract

F ORcalculating radiation in reentry problems, the variation of the radiation with frequency must be addressed. Complex frequency dependence appears in both the source function and the opacity (or absorption coefficient, cm ) field of the radiative transfer equation (RTE). This complexity is due to a very large number of bound–bound and bound–free transitions happening in very hot, partially ionized, nonequilibrium air. Full resolution of the problem is possible but requires treatment of the radiation transport at 10 frequencies. Such computations are commonly done at NASA Ames Research Center using theNEQAIR96 code [1] to postprocess flowfield data. This fully resolved approach is infeasible in a timedependent computation due to extreme computational cost. There are many methods to reduce the cost of the solution, and we can divide these into two families [2]. One can divide the frequency spectrum into ng contiguous groups, average, and solve the transport for each group; these are the multigroup methods. Or one can reorganize the frequency spectra into nb opacity bins or pickets, according to the value of the opacity [2]. This creates disjointed sets of frequencies , the bins or pickets, with similar mean opacities. The second method is usually referenced as the opacity distribution function (ODF) method and as been in use formany years [2–6]. It is based on the key recognition that transport depends on the value of the opacity, not the value of the frequency, as stated in [7]. In its usual and sophisticated form, theODFmethod, also called themultibandmethod [8], merges both approaches by reorganizing the opacity into nb bins inside each of the ng groups. In our case, we compare the results of 1) the multiband technique in which ng n groups are defined but with a single bin nb 1 inside each group (this is simply the multigroup approach), versus 2) the multiband technique in which a single group is defined for the whole spectrum (ng 1) but which is divided into nb n bins. For simplicity and clarity, we designate this as the multibin method. The multibin method has notably been used by astrophysicists for solar computations [5,9]. The goal of this paper is to compare the multigroup andmultibinmethods for theApolloAS-501 reentry.We demonstrate that it allows solution of this reentry radiation problem with high accuracy for a very low number of bins (10 bins), an accuracy that is attained by the multigroup approach for only a very large number of groups.