Analytical and Computational Study of Wall Temperature Jumps in Supersonic Flow

Abstract

The local viscous ‐inviscid interaction e eld generated by a wall temperature jump on a e at plate in supersonic e ow is studied in detail by the use of both a Navier ‐Stokes numerical code and an analytical triple-deck model. Treatment oftherapid heat transferchangesboth upstream and downstream ofthejump isincluded. Closed-form relationships for the pressure and heating variations, including upstream ine uence, are derived from the tripledeck theory and are found to be in good agreement with the numerical solution of the compressible Navier ‐Stokes equations. Such relationships not only clarify the interactive physics involved, but also are useful in preliminary design of thermal protection systems and as an insertable module to improve computational e uid dynamics code efe ciency when applied to such small-scale interaction problems. Further examined is the connection between the triple-deck solution and the classical boundary-layer theory treatment of the wall temperature jump problem; the latter is shown to be similar to the far wake limit of the inner interactive behavior astride the jump.