Nonadiabatic and three-dimensional effects in compressible turbulentboundary layers

Abstract

A defect stream function formulation for nonadiabatic flow with small crossflow is developed. The first-integral property of this formulation provides for two removal of the streamline curvature term in the governing equation so that the form of the reduced equation for small crossflow is the same as that for two dimensional flow. The combined law of the wall and wake is used in place of the no-slip boundary condition. The tangential velocity equation for law-of-the-wall flow is shown to be the same for three-dimensions as for two when the Boussinesq approximation applies, and a closed form solution for the crossflow angle in the inner region is obtained. Analytic solutions for nonadiabatic, compressible, equilibrium flow with a Clauser outer-region eddy-viscosity model are obtained, and excellent agreement with experimental skin friction and velocity profile data for nonadiabatic, compressible flat-plate flow is achieved. An analytic solution for a linear inner-region eddy-viscosity model is also obtained; the wake function part of this solution is found to be inconsistent with the empirically established law of the wake.