Near-wall turbulence alteration with the Transpiration-Resistance Model

TL;DR

This paper investigates the Transpiration-Resistance Model (TRM) as a boundary condition to alter near-wall turbulence, capturing effects of surface textures and roughness on flow behavior, with empirical relations linking transpiration factors to roughness.

Contribution

It introduces the TRM boundary conditions for modeling near-wall turbulence, including transpiration effects, and establishes empirical relations between transpiration factors and surface roughness.

Findings

TRM can replicate effects of surface roughness up to k+≈18.

Transpiration factor correlates linearly with roughness function.

Transpiration effects are predominantly coupled to spanwise shear.

Abstract

A set of boundary conditions called the Transpiration-Resistance Model (TRM) are investigated in altering near-wall turbulence. The TRM has been previously proposed by \citet{Lacis2020} as a means of representing the net effect of surface micro-textures on their overlying bulk flows. It encompasses conventional Navier-slip boundary conditions relating the streamwise and spanwise velocities to their respective shears through the slip lengths $\ell_x$ and $\ell_z$. In addition, it features a transpiration condition accounting for the changes induced in the wall-normal velocity by expressing it in terms of variations of the wall-parallel velocity shears through the transpiration lengths $m_x$ and $m_z$. Greater levels of drag increase occur when more transpiration takes place at the boundary plane, with turbulent transpiration being predominately coupled to the spanwise shear component for canonical near-wall turbulence. The TRM can reproduce the effect of a homogeneous and structured roughness up to ${k^+}\,{\approx18}$. In this transitionally rough flow regime, the transpiration lengths of the TRM must be empirically determined. The \emph{transpiration factor} is defined as the product between the slip and transpiration lengths, i.e. $(m\ell)_{x,z}$. This factor contains the compound effect of the wall-parallel velocity occurring at the boundary plane and increased permeability, both of which lead to the transport of momentum in the wall-normal direction. A linear relation between the transpiration factor and the roughness function is observed for regularly textured surfaces in the transitionally rough regime of turbulence. The relations obtained between the transpiration factor and the roughness function show that such effective flow quantities can be suitable measures for characterizing rough surfaces in this flow regime.