Estimation methods for two-dimensional conduction effects of shock-shock heat fluxes

Highly localized heating rates occur in extreme thermal environments, such as shock-shock interaction at hypersonic speeds. Experimental estimation of heat Bur usually involves measurement of discrete unsteady surface tempera tures on low conductivity materials that are chosen to reduce conduction ef fects. Typically, temperature measurements are reduced to heat fluxes using one-dimensional conduction techniques. However, lateral conduction from lo calized high heat Bur regions into low heat Bur regions is significant and influences the one-dimensional solution. The one-dimensional solution also suffers mathematical instabilities. To evaluate the nonuniform, unsteady su rface flux from measured temperatures, an inverse technique was devised tha t damps instabilities in the temporal direction and resolves large and sudd en flux changes in the spatial direction. Based on previous work, a simple inverse method was used in time, and a function specification method was us ed in space. Furthermore, a technique was devised to expedite the solution by marching in space as well as in time. The new multidimensional inverse m ethod was found to resolve steep spatial gradients more accurately in Bur t han a one-dimensional method. Furthermore, the inverse procedure exhibits b etter stability than a multidimensional forward technique.