Mach-Number-Invariant Mean-Velocity Profile of Compressible Turbulent Boundary Layers

Abstract

A series of Mach-number-(M) invariant scalings is derived for compressible turbulent boundary layers (CTBLs), leading to a viscosity weighted transformation for the mean-velocity profile that is superior to van Driest transformation. The theory is validated by direct numerical simulation of spatially developing CTBLs with M up to 6. A boundary layer edge is introduced to compare different M flows and is shown to better present the M-invariant multilayer structure of CTBLs. The new scalings derived from the kinetic energy balance substantiate Morkovin's hypothesis and promise accurate prediction of the mean profiles of CTBLs.

The influence of near-wall density and viscosity gradients on turbulence in channel flows

“…The van Driest velocity u vD is plotted as a function of y + in figure 6(b). A satisfying collapse for the compressible and incompressible boundary layer is obtained, except in the wake region, which has been studied in more detail by Zhang et al (2012). The transformed velocity u * as a function of y * is shown in figure 6(c).…”

Quantifying wall turbulence via a symmetry approach. Part 2. Reynolds stresses

“…Finally, owing to the universal nature of wall dilation symmetry, the analysis is applicable to many other wall flows with different flow conditions, such as incompressible (Wu et al 2013;Chen & She 2016) and compressible TBL (She et al 2010;Zhang et al 2012;Wu et al 2017), roughness effects , with and without mild pressure gradients, and turbulent Rayleigh-Bénard convection (to be communicated soon). The results have also been extended to improve turbulent engineering models (Chen et al 2015(Chen et al , 2016a.…”

Eulerian–Lagrangian direct numerical simulation of preferential accumulation of inertial particles in a compressible turbulent boundary layer

“…2011): For small particles in case A, the particle relaxation time scale is smaller than the Kolmogorov time scale , such that the second-order correction can be neglected, and the evolution of particle velocity can be given as Taking the divergence of this equation, we can obtain an equation representing the dilatation of particles (Zhang et al . 2016; Dai et al . 2017): where the subscript p represents the fluid properties calculated at particle positions.…”

“…These density-based scaling laws could collapse well the mean streamwise velocity, Reynolds stresses and skin friction coefficients onto the results of incompressible TBLs. Although some new scaling laws have been proposed recently (Zhang et al 2012;Patel, Boersma & Pecnik 2016;Trettel & Larsson 2016;Wu et al 2017), these classic scaling laws can serve as a basis for validating experimental measurements and numerical simulation results. For recent studies on scaling of CTBLs, see the works of Wenzel et al (2018) and Williams et al (2018).…”