Estimation Methods for Two-Dimensional Conduction Effects of Shock-Shock Heat Fluxes

Abstract

Highly localized heating rates occur in extreme thermal environments, such as shock ‐shock interaction at hypersonic speeds. Experimental estimation of heat e ux usually involves measurement of discrete unsteady surface temperatures on low conductivity materials that are chosen to reduce conduction effects. Typically, temperature measurementsarereducedtoheate uxesusingone-dimensionalconductiontechniques.However,lateralconduction from localized high heat e ux regions into low heat e ux regions is signie cant and ine uences the one-dimensional solution. The one-dimensional solution also suffers mathematical instabilities. To evaluate the nonuniform, unsteady surface e ux from measured temperatures, an inverse technique was devised that damps instabilities in the temporal direction and resolves large and sudden e ux changes in the spatial direction. Based on previous work, a simple inverse method was used in time, and a function specie cation method was used in space. Furthermore, a technique was devised to expedite the solution by marching in space as well as in time. The new multidimensional inversemethodwasfound toresolvesteep spatialgradientsmoreaccuratelyine uxthana one-dimensionalmethod. Furthermore, the inverse procedure exhibits better stability than a multidimensional forward technique.