Direct numerical simulations and spectral proper orthogonal decomposition analysis of shocklet-containing turbulent channel counter-flows

Abstract

Counter-flow configurations in a confined channel flow provide an efficient framework to study high intensity turbulent mixing processes. In a previous study (Physical Review Fluids, 6(9), p.094603), a wall-bounded counter-flow turbulent channel configuration was presented as an effective framework for addressing certain challenges related to the study of compressibility effects on turbulence as an alternative to free shear layer and Poiseuille/Couette type flows. Here, the previous direct numerical simulations are extended to a higher Mach number (M=0.7) to quantify direct and indirect effects of compressibility. It is found that the configuration is able to produce large numbers of embedded shocklets, leading to significant asymmetry in probability density functions of dilatation. Reducing the Prandtl number from 0.7 to 0.2 increases the compressibility effect further by reducing the bulk heating in the channel. A peak turbulent Mach number close to unity is obtained, for which the contribution of the dilatational dissipation to the total dissipation is nevertheless found to be limited to ∼6%. Indirect effects of compressibility are much larger, with changes of up to 40% in Favre normal stresses, despite the mean flow and shear stress being almost unaffected by compressibility in this configuration. Given the inflectional nature of the turbulent mean flow it is also interesting to identify large structures. Spectral Proper Orthogonal Decomposition (SPOD) reveals a full spectrum with a slow decay of energy with mode number. Mode shapes are three-dimensional with the low frequencies displaying elongated streaks in the velocity field at the channel centre plane.