Supersonic turbulent boundary layer on a plate. I. Closure relations

Abstract

The turbulent boundary layer on a flat plate in a supersonic flow is considered. The study consists of several parts. In this first one, we prove that the turbulent shear stress and turbulent enthalpy flux can be represented as functions of dimensionless parameters that are expressed in terms of the distance from the wall and mean velocity and enthalpy gradients. The existence of such functional relationships is a consequence of the fact that the flow on the plate is completely determined by a finite set of constant quantities: the free-stream parameters, the wall enthalpy, and the parameters specifying the dependence of viscosity on temperature and the equation of state for a perfect gas. The asymptotic structure of the relationships between the mean quantities is derived from the properties possessed by the solutions of the Navier–Stokes and energy equations. The established functional relations are closure relations of a general form, which together with the boundary-layer and energy equations give a well-posed problem for the velocity and enthalpy fields. For various characteristic flow regions in the boundary layer, this problem will be solved in subsequent parts of the study. This will make it possible to develop a theory of compressible boundary layers based on first principles, without involving particular hypotheses and approximate turbulence models.