A viscous-layer compressibility correction for two-equation Reynolds-averaged Navier-Stokes models

The baseline two-equation Reynolds-averaged Navier-Stokes (RANS) models include fluid density but lack calibration for compressible flows, making them inadequate for high Mach numbers. Various compressibility corrections have been proposed to integrate the van Driest transformation or the semi-local transformation, i.e., a given compressible law of the wall, into the RANS formulation. Prior work has focused mainly on the logarithmic layer, but upon evaluating these log-layer compressibility corrections, we find that they do not significantly improve skin friction estimates.To overcome this challenge, we develop viscous-layer compressibility corrections. We do that by altering the dissipation terms. These corrections conform the RANS model to the semi-local scaling, resulting in more accurate predictions of mean velocity and temperature in a posteriori tests. Although not the primary focus of this study, we also find that the baseline one-equation Spalart-Allmaras model, which was proposed before the concept of semi-local scaling, produces results consistent with the semi-local scaling in a posteriori tests without requiring any compressibility correction.