An algebraic model for dissipation in supersonic boundary layers

Abstract

With increasing mainstream Mach number, viscous dissipation becomes a progressively important influence in high-speed compressible turbulent boundary layers. An asymptotic analysis is carried out for high Reynolds numbers and Mach numbers of order 1, and it is shown that viscous dissipation gives rise to important terms in the solution of the total enthalpy equation. For simplicity, the case of supersonic flow over an adiabatic wall is considered. An expression for the adiabatic wall temperature is derived. It is shown that the asymptotic analysis constrains the types of turbulence models that can be used to represent the effects of viscous dissipation. A simple algebraic turbulence model is proposed and comparisons with measured total enthalpy profile data show good agreement.