Assessment of Reynolds number effects in supersonic turbulent boundary layers

Abstract

Wall-resolved large-eddy simulations (LES) are performed to investigate Reynolds number effects in supersonic turbulent boundary layers (TBLs) at Mach 2.0. The resulting database covers more than a decade of friction Reynolds number Reτ, from 242 to 5554, which considerably extends the parameter range of current high-fidelity numerical studies. Reynolds number trends are identified on a variety of statistics for skin-friction, velocity and thermodynamic variables. The efficacy of recent scaling laws as well as compressibility effects are also assessed. In particular, we observe the breakdown of Morkovin’s hypothesis for third-order velocity statistics, in agreement with previous observations for variable-property flows at low Mach number. Special attention is also placed on the size and topology of the turbulent structures populating the TBL, with an emphasis on the outer-layer motions at high Reynolds number. The corresponding streamwise spectra of streamwise velocity fluctuations show a clear separation between inner and outer scales, where energetic peaks are found at streamwise wavelengths of λx+≈700 and λx/δ0≈6. The spanwise spacing of the outer-layer structures, in turn, is found to be insensitive to the Reynolds number and equal to ∼0.7δ0. It is also found that the integral length-scales in spanwise direction for the temperature, streamwise and spanwise velocity fields appear to progressively collapse with increasing Reynolds number. The modulating influence that the outer-layer structures exert on the near-wall turbulence is also clearly visible in many of the metrics discussed. In addition, the present LES data is further exploited to assess the Reτ-sensitivity of uniform momentum regions in the flow. We find that the resulting probability density function of the number of zones as well as its evolution with Reτ agrees well with incompressible data. This suggests that uniform zones, which have been associated with outer-layer dynamics, are not strongly influenced by compressibility at the considered Mach number.