Near-wall Taylor-series expansion solution for compressible Navier–Stokes–Fourier system

Tao Chen,Tianshu Liu

doi:10.1063/5.0081220

Abstract

This paper presents the Taylor-series expansion solution of near-wall velocity and temperature for a compressible Navier–Stokes–Fourier system with a no-slip curved boundary surface. When the shear viscosity is a single-valued function of local fluid temperature, the near-wall velocity and temperature are explicitly expressed using the surface quantities including skin friction, surface pressure, surface dilatation, surface heat flux, surface temperature, surface curvature, and their relevant derivatives at the wall. In addition, the wall-normal pressure gradient at the wall is found to be contributed by three physical mechanisms including the skin friction divergence and surface dilatation effect as well as the coupled skin friction and surface heat flux with varying shear viscosity. Furthermore, without losing generality, we derive the near-wall Taylor-series expansion solution for the Lamb vector under the assumption of constant viscosities. Different physical mechanisms that are responsible for initial formation of the Lamb vector in the viscous sublayer are elucidated. The significance of the skin friction divergence and surface dilatation to the near-wall Lamb vector is highlighted.

Highlights

The understanding of flow physics in the extremely near-wall region is very important but difficult in wall-bounded turbulent flows
High intermittency in the viscous sublayer has been proven as true physical feature of turbulence,[1,2,3] which poses a great challenge for both numerical simulations and experiments
Surface pressure, surface dilatation, surface heat flux, and surface curvature are explicitly elucidated at different orders as well as their coupling effects

Summary

INTRODUCTION

The understanding of flow physics in the extremely near-wall region is very important but difficult in wall-bounded turbulent flows. From the Navier–Stokes equations for incompressible viscous flow, Bewley and Protas[23] derived the near-wall Taylor-series expansion solution for a flat wall They found that the expansion coefficients could be uniquely expressed in terms of fundamental surface quantities including skin friction τ, surface pressure p∂B, and relevant temporal–spatial derivatives at the wall. Using the near-wall Taylor-series expansion, Chen et al.[5] studied the physical features of near-wall flow structures and related surface physical quantities near a strong wall-normal velocity event (SWNVE) in an incompressible turbulent channel flow at the friction Reynolds number Reτ = 180.

Navier–Stokes–Fourier system

Near-wall Taylor-series expansion solution with constant shear viscosity

Near-wall Lamb vector in compressible wall-bounded flows

CONCLUSIONS