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Analytical models of the wall-pressure spectrum under a turbulent boundary layer with adverse pressure gradient

Published online by Cambridge University Press:  02 September 2019

G. Grasso Open the ORCID record for G. Grasso [Opens in a new window] ,
P. Jaiswal ,
H. Wu Open the ORCID record for H. Wu [Opens in a new window] ,
S. Moreau  and
M. Roger
G. Grasso*
Affiliation:
Univ Lyon, Ecole Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon I, CNRS, Laboratoire de Mécanique des Fluides et d’Acoustique, UMR 5509, 36 Avenue Guy de Collongue, F-69134, Écully, France Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada
P. Jaiswal
Affiliation:
Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada
H. Wu
Affiliation:
Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada
S. Moreau
Affiliation:
Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada
M. Roger
Affiliation:
Univ Lyon, Ecole Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon I, CNRS, Laboratoire de Mécanique des Fluides et d’Acoustique, UMR 5509, 36 Avenue Guy de Collongue, F-69134, Écully, France
*
†Email address for correspondence: gabriele.grasso@ec-lyon.fr
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Abstract

This paper presents a comprehensive analytical approach to the modelling of wall-pressure fluctuations under a turbulent boundary layer, unifying and expanding the analytical models that have been proposed over many decades. The Poisson equation governing pressure fluctuations is Fourier transformed in the wavenumber domain to obtain a modified Helmholtz equation, which is solved with a Green’s function technique. The source term of the differential equations is composed of turbulence–mean shear and turbulence–turbulence interaction terms, which are modelled separately within the hypothesis of a joint normal probability distribution of the turbulent field. The functional expression of the turbulence statistics is shown to be the most critical point for a correct representation of the wall-pressure spectrum. The effect of various assumptions on the shape of the longitudinal correlation function of turbulence is assessed in the first place with purely analytical considerations using an idealised flow model. Then, the effect of the hypothesis on the spectral distribution of boundary-layer turbulence on the resulting wall-pressure spectrum is compared with the results of direct numerical simulation computations and pressure measurements on a controlled-diffusion aerofoil. The boundary layer developing over the suction side of this aerofoil in test conditions is characterised by an adverse pressure gradient. The final part of the paper discusses the numerical aspect of wall-pressure spectrum computation. A Monte Carlo technique is used for a fast evaluation of the multi-dimensional integral formulation developed in the theoretical part.

JFM classification

Turbulent Flows: Turbulent boundary layers Acoustics: Aeroacoustics Boundary Layers: Boundary layer structure

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 877 , 25 October 2019 , pp. 1007 - 1062
Copyright
© 2019 Cambridge University Press 

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