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A wall model for large-eddy simulation of highly compressible flows based on a new scaling of the law of the wall

Published online by Cambridge University Press:  29 January 2024

Romain Debroeyer Open the ORCID record for Romain Debroeyer [Opens in a new window] ,
Michel Rasquin Open the ORCID record for Michel Rasquin [Opens in a new window] ,
Thomas Toulorge Open the ORCID record for Thomas Toulorge [Opens in a new window] ,
Yann Bartosiewicz Open the ORCID record for Yann Bartosiewicz [Opens in a new window]  and
Grégoire Winckelmans Open the ORCID record for Grégoire Winckelmans [Opens in a new window]
Romain Debroeyer*
Affiliation:
Institute of Mechanics, Materials, and Civil Engineering (iMMC), Université catholique de Louvain (UCLouvain), 1348 Louvain-la-Neuve, Belgium
Michel Rasquin
Affiliation:
Cenaero, 6041 Gosselies, Belgium
Thomas Toulorge
Affiliation:
Cenaero, 6041 Gosselies, Belgium
Yann Bartosiewicz
Affiliation:
Institute of Mechanics, Materials, and Civil Engineering (iMMC), Université catholique de Louvain (UCLouvain), 1348 Louvain-la-Neuve, Belgium
Grégoire Winckelmans
Affiliation:
Institute of Mechanics, Materials, and Civil Engineering (iMMC), Université catholique de Louvain (UCLouvain), 1348 Louvain-la-Neuve, Belgium
*
†Email address for correspondence: romain.debroeyer@uclouvain.be
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Abstract

Wall modelling in large-eddy simulation (LES) is of high importance to allow scale resolving simulations of industrial applications. Numerous models were developed and validated for incompressible flows, including a simple quasi-analytical model based on Reichardt's formula that approximates the law of the wall. In this paper, a scaling is proposed to generalize this wall model to highly compressible flows. First, the results of wall-resolved LES (wrLES) of adiabatic compressible turbulent channel flows at $Re_\tau = 1000$ and at centreline Mach numbers of $M_c= 0.76$ and $1.5$ are presented. Then, three potential scalings of the incompressible wall model are proposed, and their a priori performance is evaluated : (i) the Howarth–Stewartson scaling, (ii) an improved Van Driest scaling and (iii) a new scaling obtained from a blending of those two. The results of wall-modelled LES (wmLES) of compressible channel flows using these three models are compared with the reference wrLES data, showing the superior accuracy of the hybrid scaling. The consistency of the new wall model at low Mach numbers is also verified by comparing the results of a wmLES at $M_c= 0.25$ with those of reference incompressible DNS data at $Re_\tau = 1000$ and $5200$. Finally, the proposed wall model is also applied to a turbulent channel flow at $M_c=1.5$ and $Re_\tau =5200$.

JFM classification

Turbulent Flows: Turbulence modelling Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 980 , 10 February 2024 , A9
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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