Direct simulation of the turbulent boundary layer along a compression rampat M=3 and Re-theta=1685

The turbulent boundary layer along a compression ramp with a deflection ang le of 18 degrees at a free-stream Mach number of M = 3 and a Reynolds numbe r of Re-theta = 1685 with respect to free-stream quantities and mean moment um thickness at inflow is studied by direct numerical simulation. The conse rvation equations for mass, momentum, and energy are solved in generalized coordinates using a 5th-order hybrid compact-finite-difference-ENO scheme f or the spatial discretization of the convective fluxes and 6th-order centra l compact finite differences for the diffusive fluxes. For time advancement a 3rd-order Runge-Kutta scheme is used. The computational domain is discre tized with about 15 x 10(6) grid points. Turbulent inflow data are provided by a separate zero-pressure-gradient boundary-layer simulation. For statis tical analysis, the flow is sampled 600 times over about 385 characteristic timescales delta(0)/U-infinity defined by the mean boundary-layer thicknes s at inflow and the free-stream velocity. Diagnostics show that the numeric al representation of the how field is sufficiently well resolved. Near the corner, a small area of separated flow develops. The shock motion is limited to less than about 10% of the mean boundary-layer thickness. The shock oscillates slightly around its mean location with a frequency of sim ilar magnitude to the bursting frequency of the incoming boundary layer. Tu rbulent fluctuations are significantly amplified owing to the shock-boundar y-layer interaction. Reynolds-stress maxima are amplified by a factor of ab out 4. Turbulent normal and shear stresses are amplified differently, resul ting in a change of the structure parameter. Compressibility affects the tu rbulence structure in the interaction area around the corner and during the relaxation after reattachment downstream of the corner. Correlations invol ving pressure fluctuations are significantly enhanced in these regions. The strong Reynolds analogy which suggests a perfect correlation between veloc ity and temperature fluctuations is found to be invalid in the interaction area.