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About the role of the Hanratty correction in the linear response of a turbulent flow bounded by a wavy wall

Published online by Cambridge University Press:  27 July 2023

François Chedevergne Open the ORCID record for François Chedevergne [Opens in a new window] ,
Maxime Stuck Open the ORCID record for Maxime Stuck [Opens in a new window] ,
Marina Olazabal-Loumé  and
Jacques Couzi
François Chedevergne*
Affiliation:
DMPE, ONERA, Université de Toulouse, Toulouse, France
Maxime Stuck
Affiliation:
CEA-CESTA, 15 Avenue des Sablières, CS60001, 33116 Le Barp CEDEX, France
Marina Olazabal-Loumé
Affiliation:
CEA-CESTA, 15 Avenue des Sablières, CS60001, 33116 Le Barp CEDEX, France
Jacques Couzi
Affiliation:
CEA-CESTA, 15 Avenue des Sablières, CS60001, 33116 Le Barp CEDEX, France
*
†Email address for correspondence: francois.chedevergne@onera.fr
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Abstract

Scallop patterns forming on erodible surfaces were studied historically using a linear analysis of the inner region of a turbulent boundary layer growing on a corrugated wall. Experimental observations show a phase shift between the shear stress at the wall and the wall oscillation that depends on the wavenumber. An ad hoc correction applied to the turbulent closure and due to Hanratty et al. (Thorsness et al., Chem. Engng Sci., vol. 33, issue 5, 1978, pp. 579–592; Abrams & Hanratty, J. Fluid Mech., vol. 151, issue 1, 1985, p. 443; Frederick & Hanratty, Exp. Fluids, vol. 6, issue 7, 1988, pp. 477–486) was systematically used to recover the reference experimental results. In this study, Reynolds-averaged Navier–Stokes (RANS) and direct numerical simulations (DNS) were performed and revealed the role of the Boussinesq assumption in the results obtained. We show that the Hanratty correction acts as a palliative to the misrepresentation of Reynolds stresses due to the use of the Boussinesq hypothesis. The RANS calculations based on a turbulence model using a second-order moment closure recovered the expected results obtained in the reference DNS calculations, in particular with respect to wall heat transfer. The analysis of these results highlights the critical importance of the anisotropy of the diagonal Reynolds stresses on the prediction of wall transfer under these conditions and their implication in the occurrence of scalloping.

JFM classification

Boundary Layers: Boundary layer stability Turbulent Flows: Turbulence modelling Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 967 , 25 July 2023 , A39
Copyright
© The Author(s), 2023. Published by Cambridge University Press.

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