Compressible Velocity Transformations for Various Noncanonical Wall-Bounded Turbulent Flows

Abstract

Although several velocity transformations for compressible zero-pressure-gradient boundary layers have been proposed in the past decades, their performance for noncanonical compressible wall-bounded turbulent flows has not been systematically investigated. This work assesses several popular transformations for the velocity profile through their application to several types of noncanonical compressible wall-bounded turbulent flows. Specifically, this work explores direct numerical simulation databases of high-enthalpy boundary layers with dissociation and vibrational excitation, supercritical channel and boundary-layer flows, and adiabatic boundary layers with pressure gradients. The transformations considered include the van Driest (“Turbulent Boundary Layer in Compressible Fluids,” Journal of the Aeronautical Sciences, Vol. 18, No. 3, 1951, pp. 145–216), Zhang et al. (“Mach-Number-Invariant Mean-Velocity Profile of Compressible Turbulent Boundary Layers,” Physical Review Letters, Vol. 109, No. 5, 2012, Paper 054502), Trettel and Larsson (“Mean Velocity Scaling for Compressible Wall Turbulence with Heat Transfer,” Physics of Fluids, Vol. 28, No. 2, 2016, Paper 026102), data-driven (Volpiani et al., “Data-Driven Compressibility Transformation for Turbulent Wall Layers,” Physical Review Fluids, Vol. 5, No. 5, 2020, Paper 052602), and total-stress-based (Griffin et al., “Velocity Transformation for Compressible Wall-Bounded Turbulent Flows with and Without Heat Transfer,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 118, No. 34, 2021, Paper e2111144118) transformations. The Trettel–Larsson transformation collapses velocity profiles of high-enthalpy temporal boundary layers but not the spatial boundary layers considered. For supercritical channel flows, the Trettel–Larsson transformation also performs well over the entire inner layer. None of the aforementioned transformations work for supercritical boundary layers. For all the considered methods, the transformed velocity profiles of boundary layers with weak pressure gradients coincide well with the universal incompressible law of the wall. In summary, all these popular methods fail to deliver uniform performance for noncanonical compressible wall-bounded flows in the logarithmic region, and a more sophisticated version, which accounts for these different physics, is needed. The data-driven and total-stress-based transformations perform well in the viscous sublayer for all the considered flows. Nevertheless, the present assessment provides a useful guideline on the deployment of these transformations on various noncanonical flows.