Integral theory for supersonic turbulent base flows.

Abstract

The integral near- wake analysis of Reeves and Lees developed for supersonic laminar base flows with viscous-inviscid interaction is extended to the case of fully turbulent separated adiabatic flow behind a rearward-facin g step at supersonic speeds. A turbulent eddy viscosity model is formulated for the shear stress scaling of the dissipation integral in the mechanical energy equation. It is shown that the eddy viscosity can be described simply by one incompressible constant (valid for both shear layers and wakes) and one reference density pr. Using a compressibility transformation, theoretical solutions for the spreading rates of free shear layers are found to agree with experiment when the reference density is chosen to be the centerline density for the wake flow. The wake flow solution, uniquely determined by the wake critical point, is joined to the body through a turbulent free shear layer mixing solution. A simple conservation model is presented to relate the viscous sublayer after expansion to the initial boundary layer ahead of the step. For freestream Mach numbers MI < 2.3, where lip shock effects may be neglected, the integral theory is found to give good estimates for the length scales and centerline pressure variations measured experimentally for both wake flows and step flows (where reattachment is to a solid surface). b C f f'M h