LES wall modeling for heat transfer at high speeds

TL;DR

This paper develops a wall model for high-speed heat transfer that incorporates aerodynamic heating, explaining why semi-local scaling fails but the eddy conductivity derived from it remains effective.

Contribution

It introduces an improved semi-local scaling that accounts for aerodynamic heating, enhancing wall modeling accuracy in high-speed turbulent flows.

Findings

Semi-local scaling does not collapse high-speed DNS data.

Inclusion of aerodynamic heating in the scaling improves data collapse.

Eddy conductivity remains consistent regardless of aerodynamic heating inclusion.

Abstract

A practical application of universal wall scalings is near-wall turbulence modeling. In this paper, we exploit temperature's semi-local scaling [Patel, Boersma, and Pecnik, {Scalar statistics in variable property turbulent channel flows}, Phys. Rev. Fluids, 2017, 2(8), 084604] and derive an eddy conductivity closure for wall-modeled large-eddy simulation of high-speed flows. We show that while the semi-local scaling does not collapse high-speed direct numerical simulation (DNS) data, the resulting eddy conductivity and the wall model work fairly well. The paper attempts to answer the following outstanding question: why the semi-local scaling fails but the resulting eddy conductivity works well. We conduct DNSs of Couette flows at Mach numbers from $M=1.4$ to 6. We add a source term in the energy equation to get a cold, a close-to-adiabatic wall, and a hot wall. Detailed analysis of the flows' energy budgets shows that aerodynamic heating is the answer to our question: aerodynamic heating is not accounted for in Patel et al.'s semi-local scaling but is modeled in the equilibrium wall model. We incorporate aerodynamic heating in semi-local scaling and show that the new scaling successfully collapses the high-speed DNS data. We also show that incorporating aerodynamic heating or not, the semi-local scaling gives rise to the exact same eddy conductivity, thereby answering the outstanding question.