Mach Number and Thermal Effects in Wall-Bounded Compressible Turbulent Flows Using High-Resolution Direct Numerical Simulations

Abstract

The understanding of wall-bounded flows is of paramount importance in high-speed vehicle design. Estimating aircraft thermal and viscous loads require robust turbulence models that can accurately predict turbulent statistics close to the wall. Unfortunately, the existing turbulent models are mostly extended versions of models constructed for incompressible flows in thermal equilibrium and fail to accurately predict the heat flux in high-speed regimes. It is, therefore, critical to understand the physics underlying high-speed turbulent boundary layers in order to improve our modeling capabilities for a wide range of flow regimes. Knowledge of correct near-wall asymptotic behavior of turbulence statistics is critical in formulating accurate turbulent models. While turbulence scaling laws are well known in incompressible flows, the transition from incompressible to compressible scaling and the limiting behavior of the latter are largely unknown. Part one of this work focuses on understanding Mach number effects on near-wall turbulence asymptotic behavior. For this, we perform direct numerical simulations of channels with isothermal walls for a wide range of Mach numbers. These high-fidelity simulations comprising near-wall resolutions that are an order of magnitude higher than commonly used resolutions in the literature, unveil the near-wall asymptotic power laws for turbulent stresses and turbulent heat fluxes in high-speed regimes. We show that widely used strategies to collapse compressible statistics fail to collapse near-wall turbulent fluxes with wall-normal velocity component. A critical question is the transition nature of the scaling laws from solenoidal to non-solenoidal regime. We answer this by systematically varying the Mach number from a virtually incompressible regime to supersonic speeds. We extend this study to understand thermal boundary condition effects and our aim is to compare the near-wall asymptotic scaling laws for various wall thermal boundary conditions. The similarities and differences between isothermal, adiabatic and pseudo-adiabatic walls are studied in great detail. In these two studies, we compared our results with well-established theory and provided scaling parameters to attain universality for the near-wall turbulence behavior. A key finding is the significance of near-wall dilatation motions, which is often ignored. This undermines Morkovin’s hypothesis and its ability to collapse all near-wall turbulent statistics. In our third part, we extend our investigation to study the effect of thermal non-equilibrium (TNE) on turbulence mixing. In particular, we focus on the turbulent Prandtl number for vibrational energy, which is essential in understanding mixing and developing turbulence modeling strategies. We find that TNE can enhance mixing as well as oppose it depending on the relative gradients of translational-rotation and vibrational modes. We explore the physical mechanisms behind this behavior and find a novel parameter to collapse DNS data. This work presents, for the first time, a systematic study of asymptotic behavior needed to anchor theories and models at high speeds and turbulence mixing of vibrational energy in flows with thermal non-equilibrium.