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A Kriging-based elliptic extended anisotropic model for the turbulent boundary layer wall pressure spectrum

Published online by Cambridge University Press:  06 February 2018

Myriam Slama Open the ORCID record for Myriam Slama [Opens in a new window] ,
Cédric Leblond  and
Pierre Sagaut
Myriam Slama*
Affiliation:
M2P2, Aix Marseille Univ, CNRS, Centrale Marseille, 13451 Marseille, France Naval Group, Centre d’Expertise des Structures et Matériaux Navals, Technocampus Ocean, 44340 Bouguenais, France
Cédric Leblond
Affiliation:
Naval Group, Centre d’Expertise des Structures et Matériaux Navals, Technocampus Ocean, 44340 Bouguenais, France
Pierre Sagaut
Affiliation:
M2P2, Aix Marseille Univ, CNRS, Centrale Marseille, 13451 Marseille, France
*
†Email address for correspondence: slama.myriam@yahoo.com
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Abstract

The present study addresses the computation of the wall pressure spectrum for a turbulent boundary layer flow without pressure gradient, at high Reynolds numbers, using a new model, the Kriging-based elliptic extended anisotropic model (KEEAM). A space–time solution to the Poisson equation for the wall pressure fluctuations is used. Both the turbulence–turbulence and turbulence–mean shear interactions are taken into account. It involves the mean velocity field and space–time velocity correlations which are modelled using Reynolds stresses and velocity correlation coefficients. We propose a new model, referred to as the extended anisotropic model, to evaluate the latter in all regions of the boundary layer. This model is an extension of the simplified anisotropic model of Gavin (PhD thesis, 2002, The Pennsylvania State University, University Park, PA) which was developed for the outer part of the boundary layer. It relies on a new expression for the spatial velocity correlation function and new parameters calibrated using the direct numerical simulation results of Sillero et al. (Phys. Fluids, vol. 26, 2014, 105109). Spatial correlation coefficients are related to space–time coefficients with the elliptic model of He & Zhang (Phys. Rev. E, vol. 73, 2006, 055303). The turbulent quantities necessary for the pressure computation are obtained by Reynolds-averaged Navier–Stokes solutions with a Reynolds stress turbulence model. Then, the pressure correlations are evaluated with a self-adaptive sampling strategy based on Kriging in order to reduce the computation time. The frequency and wavenumber–frequency wall pressure spectra obtained with the KEEAM agree well with empirical models developed for turbulent boundary layer flows without pressure gradient.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , pp. 25 - 55
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Copyright
© 2018 Cambridge University Press 

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