Comparisons of numerical and exact solutions for oblique detonationswith structure

Abstract

Numerical predictions of the two-dimensional, inviscid, supersonic, reactive flow of a calorically perfect ideal gas over a straight wedge are compared with the predictions of a linear asymptotic model valid in the hypersonic limit. Solution features predicted by the asymptotic model include a curved shock attached to the wedge tip, a reaction layer parallel to the shock, and a vorticity layer parallel to the wedge surface. For sufficiently high Mach number and heat release, the numerical model predicts similar behavior, and the differences in the predictions of the two methods are of the same order of magnitude as the inherent error of the asymptotic method. As heat release is lowered and Mach number held constant, apparent numerical artifacts obscure features predicted by the asymptotic method. The results suggest that the asymptotic solution has utility as a benchmark to verify the predictions of many high-speed, multidimensional, reacting flow codes.

Comparison of numerical oblique detonation solutions with an asymptotic benchmark

“…Similar agreement and disagreement are found when reaction progress and vorticity contours are compared. 3 In this and all cases, the domain is sufficiently large such that the flow has nearly completely relaxed to the equilibrium, irrotational state.…”

“…As shown in detail in Ref. 3, as Mach number is held fixed and q is lowered, numerical errors overwhelm the effects of heat release so that the differences are primarily attributable to truncation errors in the numerical method.…”

“…ox dy p ay P (3) average magnitude of the difference of the predictions of the two methods over the domain. Here the pressure differences are chosen, although any flow variable would do as well.…”