Modeling of combined effects of surface roughness and blowing for Reynolds-averaged Navier–Stokes turbulence models

Abstract

A new modeling strategy adapted to Reynolds-Averaged Navier-Stokes (RANS) turbulence models is proposed to predict combined effects of roughness and blowing boundary conditions. First, an analysis of experimental data is presented, leading to a specific description of the velocity profile in the logarithmic region of transpired turbulent boundary layers over rough walls. This analysis points out the deficiencies of existing roughness corrections to predict the effect of blowing in the presence of surface roughness. Indeed, these corrections tend to underestimate skin friction coefficients and Stanton numbers with addition of blowing. The failure of existing models derives from an inaccurate estimation of the velocity shift of the logarithmic law given by roughness corrections. Concretely, roughness corrections underestimate the apparent velocity shift of the logarithmic law with blowing. To recover the expected law of the wall, an additional contribution on the velocity shift, characterizing blowing/roughness interactions, is integrated to standard roughness corrections. To that end, a modification of the equivalent sand grain height, adapted to k − ω based turbulence models, is proposed to take blowing effects into account. Furthermore, an extension of Aupoix's thermal correction [B. Aupoix, International Journal of Heat and Fluid Flow 56, 160 (2015)] to blowing is presented to predict combined thermal effects of roughness and blowing. The assessment of the proposed corrections is performed using k − ω Shear Stress Transport (SST) model on a large set of experimental data and proves the relevance of the strategy for incompressible and compressible turbulent boundary layers.

Hypersonic Turbulent Flow Reynolds-Averaged Navier–Stokes Simulations with Roughness and Blowing Effects

“…The latter relies on the equivalent sand grain concept k s and is built on the basis of the k-ω SST turbulent model [18]. The Aupoix roughness model was extended to blowing effects by Marchenay et al [25], allowing the combined effects of blowing and roughness to be considered. In addition, compressible effects due to high Mach numbers must be accounted for to simulate hypersonic flows.…”

“…Because roughness and blowing corrections adapted to k-ω-based models impact the same wall boundary conditions, they cannot be employed simultaneously to reproduce the combined effects of roughness and blowing. Recently, Marchenay et al [25] proposed a modification of the equivalent sand grain height k s to take blowing effects over smooth or rough walls into account. The idea of this correction is to impose the correct velocity shift ΔU in the inertial region, which depends on the roughness parameter k s and the blowing parameter v w .…”

“…The idea of this correction is to impose the correct velocity shift ΔU in the inertial region, which depends on the roughness parameter k s and the blowing parameter v w . By relying on Healzer et al's [35], Pimenta et al's [36], and Voisinet's [2] experiments, Marchenay et al [25] decomposed the velocity shift in the following manner:…”

“…Equation ( 22) is included directly in the Aupoix roughness correction by modifying the equivalent sand grain height k s . The correction was detailed by Marchenay et al [25]. The combination of the Marchenay roughness/blowing correction and the Aupoix roughness model is retained in this study to reproduce blowing effects over smooth and rough walls for hypersonic turbulent boundary layers.…”

“…Regarding k-ω-based turbulence models, Wilcox [24] proposed to impose the wall specific dissipation ω w as a function of the blowing velocity. Recently, Marchenay et al [25] derived a new correction to take blowing effects into account in the equivalent sand grain approach. This correction relies on the characterization of the velocity profile in the log-law region of turbulent boundary layers over rough walls with blowing, and it was successfully applied for subsonic and supersonic flows.…”