Compressible Boundary Layer Velocity Transformation Based on a Generalized Form of the Total Stress

Abstract

A new mean velocity transformation for compressible boundary layer flow is derived. We identify the effects of density fluctuations and integrate these effects into the derivation of the transformation. Indepth analysis of compressibility effects from density fluctuations is enabled by direct numerical simulation data existing in the literature and from the CRoCCo laboratory. The compressible and incompressible flow data include wall-cooling, semi-local Reynolds numbers ranging from 800 to 34000 and Mach numbers ranging from subsonic to 12. The role, significance and physical mechanisms connecting density fluctuations to the momentum balance and to the viscous, turbulent and total stresses are presented. Density-fluctuation corrected formulations are derived from these insights. We identify the significant properties that thus-far are neglected in the derivation of velocity transformations: (1) the Mach-invariance of the nearwall momentum balance of the density-fluctuation-corrected total stress, and (2) the Mach-invariance of the relative contributions by the density-fluctuation-corrected viscous and Reynolds stresses to the total stress. The proposed velocity transformation integrates both properties into a single transformation equation and successfully demonstrates a collapsing of all currently considered compressible cases onto to the incompressible law of the wall. Analyses of the log-layer intercept and the slope demonstrate that the transformation parameters are well within the bounds reported for incompressible data. Based on the physics embedded in the two scaling properties, the success of the newly proposed transformation is attributed to considering the effect of the viscous stress, Reynolds stress, mean density and, lastly, density fluctuations, in a single transformation form.

Thermochemical non-equilibrium effects in turbulent hypersonic boundary layers

“…This results in a better collapse of u GFM onto the universal logarithmic profile with respect to u TL , for which the slope of the logarithmic region is largely overestimated. Yet, the u GFM transformation still predicts a higher slope and intercept in the logarithmic region compared with the classical incompressible values, in accordance with the recent study of Lee, Martin & Williams (2021). Finally, we verified that the transformation based on the constant-stress-layer assumption (i.e.…”

Compressibility effects in supersonic and hypersonic turbulent boundary layers subject to wall disturbances

“…Directly neglecting this term could lead to the over-estimation of the Reynolds shear stress by 30 % in cases at M ∞ = 6 with wall disturbances according to Morkovin's hypothesis that assumes ρu i u j ≈ ρu i u j and hence a possibly incorrect mean velocity in the wake region. A recent study by Lee, Williams & Martin (2023) evaluated the significance of the terms related to the density fluctuations in the mean momentum equation. It is concluded that these terms exceed 20 % of the wall shear stress under hypersonic conditions.…”