Direct Simulation of Turbulence Phenomena in Compressible Boundary Layers

Abstract

Turbulence in compressible subsonic boundary layers is simulated using the temporal simulation model. We have investigated various numerical discretization schemes in the wall normal direction with respect to stability, accuracy and numerical effort. The scheme chosen is based on compact finite differences in combination with a piecewise almost linear mapping function. The Navier-Stokes equations are formulated using the inverse of the density in order to reduce aliasing errors as much as possible. Excellent agreement of our method with primary and secondary instability theory is found. The classical transition mechanisms with overlapping nonlinear flow structures are simulated in qualitative good agreement with incompressible boundary layer transition simulations. Turbulent flow simulations are presented for (i) a zero pressure gradient flat plate boundary layer with small initial disturbances and (ii) a subsonic boundary layer on the heat shield of a reentry Capsula with localized initial disturbances. As in incompressible flows we observe characteristic features of fully turbulent flows as well as spot-like turbulence. It is shown, that the area of the iso-surface of the enstrophy can be used as a criterion for turbulence.