Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature

TLDR

This study conducts DNS of Mach 5 turbulent boundary layers with wall‑to‑edge temperature ratios from 1.0 to 5.4 to evaluate how wall cooling affects scaling laws, turbulence statistics, and near‑wall coherent structures. The authors use direct numerical simulation of Mach 5 turbulent boundary layers with varying wall temperatures to analyze scaling, turbulence budgets, and near‑wall structures, and to elucidate the mechanism by which cooling increases turbulence coherence. The results show that standard compressible scaling relations remain valid for non‑adiabatic walls, compressibility effects are amplified yet still minor, dissipation stays solenoidal, and wall cooling increases the coherence of near‑wall turbulent structures without contradicting the weakly compressible hypothesis.

Abstract

In this paper, we perform direct numerical simulation (DNS) of turbulent boundary layers at Mach 5 with the ratio of wall-to-edge temperature T w / T δ from 1.0 to 5.4 (Cases M5T1 to M5T5). The influence of wall cooling on Morkovin's scaling, Walz's equation, the standard and modified strong Reynolds analogies, turbulent kinetic energy budgets, compressibility effects and near-wall coherent structures is assessed. We find that many of the scaling relations used to express adiabatic compressible boundary-layer statistics in terms of incompressible boundary layers also hold for non-adiabatic cases. Compressibility effects are enhanced by wall cooling but remain insignificant, and the turbulence dissipation remains primarily solenoidal. Moreover, the variation of near-wall streaks, iso-surface of the swirl strength and hairpin packets with wall temperature demonstrates that cooling the wall increases the coherency of turbulent structures. We present the mechanism by which wall cooling enhances the coherence of turbulence structures, and we provide an explanation of why this mechanism does not represent an exception to the weakly compressible hypothesis.