Reynolds number dependency in supersonic spatially-developing turbulent boundary layers
Guillermo Araya, Christian Lagares, Kenneth E. Jansen
Abstract
Direct Numerical Simulation (DNS) of compressible spatially-developing turbulent boundary layers (SDTBL) is performed at a Mach number of 2.5 and low/high Reynolds numbers over isothermal Zero-Pressure Gradient (ZPG) flat plates. Turbulent inflow information is generated via a dynamic rescaling-recycling approach (J. Fluid Mech., 670, pp. 581-605, 2011), which avoids the use of empirical correlations in the computation of inlet turbulent scales. The range of the low Reynolds number case is approximately 400-800, based on the momentum thickness, freestream velocity and wall viscosity. DNS at higher Reynolds numbers (~3,000, about four-fold larger) is also carried out with the purpose of analyzing the effect of Reynolds number on the transport phenomena in the supersonic regime. Additionally, low/high order flow statistics are compared with DNS of an incompressible isothermal ZPG boundary layer at similar low Reynolds numbers and the temperature regarded as a passive scalar. Peaks of turbulence intensities move closer to the wall as the Reynolds number increases in the supersonic flat plate. Furthermore, Reynolds shear stresses depict a much larger "plateau" (constant shear layer) at the highest Reynolds number considered in present study.