Direct numerical simulation of turbulent supersonic boundary-layer flows

In this paper we review recent progress on the DNS of turbulent supersonic boundary layers. Specifically we address turbulent boundary layers at Mach numbers ranging from 3 to 6. For the zero-pressure-gradient cases,simulat ions are performed with an extended temporal DNS method,which is briefly described. Of particular interest is the significance of compressibility effects in a Mach number range around M_∞ ≃ 5 up to which limit Morkovin's hypothesis is believed to be valid. The results show that pressure dilatation and dilatational dissipation correlations are small throughout the considered Mach number range. On the other hand,c orrelations derived from Morkovin's hypothesis are not necessarily valid,as is shown for the Strong Reynolds Analogy. Shocks can appear in a supersonic flow and can interact with the flow turbulence. As an example we consider the turbulent boundary layer along a compression ramp at a free-stream Mach number of M = 3. We observe that a small area of mean-separated flow develops. No large-scale shock motion is detected,t he shock rather oscillates slightly around its mean location with a frequency of similar magnitude as the bursting frequency of the incoming boundary layer. Turbulent fluctuations are significantly enhanced due to the shock-boundary-layer interaction. Reynolds-stress maxima are amplified by a factor of about 4. Turbulent normal and shear stresses are amplified differently,r esulting in a change of the structure parameter. Compressibility affects the turbulence structure in the interaction area around the corner and during the relaxation after reattachment downstream of the corner. The strong Reynolds analogy is found to be invalid in the interaction area.