Mach number and wall thermal boundary condition effects on near-wall compressible turbulence

TL;DR

This study examines how Mach number and wall thermal boundary conditions influence near-wall turbulence behavior, revealing that these factors significantly affect asymptotic power-law exponents and correlations, with dilatation serving as a universal scaling parameter.

Contribution

It provides new insights into the combined effects of Mach number and wall thermal conditions on near-wall turbulence, introducing a universal scaling law based on dilatation.

Findings

Power-law exponents vary with Mach number and thermal boundary conditions.

Dilatation at the wall is a key universal scaling parameter.

Correlation coefficients between velocity and temperature are affected by these factors.

Abstract

We investigate the effects of thermal boundary conditions and Mach number on turbulence close to walls. In particular, we study the near-wall asymptotic behavior for adiabatic and pseudo-adiabatic walls, and compare to the asymptotic behavior recently found near isothermal cold walls (Baranwal et al. (2022)). This is done by analyzing a new large database of highly-resolved direct numerical simulations of turbulent channels with different wall thermal conditions and centerline Mach numbers. We observe that the asymptotic power-law behavior of Reynolds stresses as well as heat fluxes does change with both centerline Mach number and thermal-condition at the wall. Power-law exponents transition from their analytical expansion for solenoidal fields to those for non-solenoidal field as the Mach number is increased, though this transition is found to be dependent on the thermal boundary conditions. The correlation coefficients between velocity and temperature are also found to be affected by these factors. Consistent with recent proposals on universal behavior of compressible turbulence, we find that dilatation at the wall is the key scaling parameter for this power-law exponents providing a universal functional law which can provide a basis for general models of near-wall behavior.