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CFD-based prediction of wall-pressure spectra under a turbulent boundary layer with adverse pressure gradient

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Abstract

A model of the spectrum of wall-pressure fluctuations under a turbulent boundary layer based on an analytical solution of the Poisson equation is presented. This model is suited for aeroacoustic prediction based on CFD-extracted flow information but requires statistical properties of the boundary-layer turbulence that are not resolved in steady-state simulations and need to be modelled. For this reason, this paper uses Lattice-Boltzmann (DNS-LBM) and Navier-Stokes Direct Numerical Simulations (DNS-NS) of an airfoil in a wind-tunnel jet to investigate the link between turbulence and wall-pressure statistics and validate the assumptions made in the application of the analytical model. The use of input from two numerical simulation methods allows generalizing the results of the analytical model.

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Abbreviations

c :

Airfoil chord-length

\(\delta\) :

Boundary layer thickness

\({\varvec{k}}=(k_{1},k_{3})\) :

Planar wavenumber vector

\(k=\sqrt{k_{1}^{2} +k_{3}^{2}}\) :

Planar wavenumber amplitude

\({\tilde{k}}=kl\) :

Dimensionless wavenumber

\(\mathrm{K}_{z}\) :

Modified Bessel function of the second kind

l :

Turbulence characteristic length scale

M :

Mach number

p :

Fluctuating pressure variable

\(T_c\) :

Through-flow time over the airfoil

\(Re_c\) :

Reynolds number based on the airfoil chord

\(u_{i}\) :

Fluctuating velocity component

\(U_{0}\) :

Wind-tunnel exit velocity

\(U_{c}\) :

Convective speed of wall-pressure fluctuations

\(U_{e}\) :

External velocity above the boundary layer

\(\alpha\) :

Ratio of longitudinal to transverse integral length scale

\(\varLambda\) :

Longitudinal integral length scale of turbulence

\(\varphi _{pp}\) :

Power spectral density of wall-pressure fluctuations

\(\varphi _{22}\) :

Cross-spectral density of vertical velocity fluctuations

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Authors and Affiliations

  1. Univ. Lyon, École 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, 69134, Écully, France

    Gabriele Grasso, Susanna Orestano & Michel Roger

  2. École de Technologie Supérieure, Montréal, QC, H3C 1K3, Canada

    Marlène Sanjosé

  3. Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada

    Hao Wu & Stéphane Moreau

Authors
  1. Gabriele Grasso
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  2. Hao Wu
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  3. Susanna Orestano
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  4. Marlène Sanjosé
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  5. Stéphane Moreau
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  6. Michel Roger
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Correspondence to Gabriele Grasso.

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The authors gratefully acknowledge the support of the European Union's Horizon 2020 research and innovation program under grant agreement no. 755543 (SCONE) and the Canadian NSERC Discovery grant (no RGPIN-2014-04111). This research was enabled in part by support provided by Calcul Québec (www.calculquebec.ca) and Compute Canada (www.computecanada.ca). This work was performed within the framework of the LABEX CeLyA (ANR-10-LABX- 0060) of Université de Lyon, within the programme “Investissements d'Avenir” (ANR-16- IDEX-0005) operated by the French National Research Agency (ANR)

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Grasso, G., Wu, H., Orestano, S. et al. CFD-based prediction of wall-pressure spectra under a turbulent boundary layer with adverse pressure gradient. CEAS Aeronaut J 12, 125–133 (2021). https://doi.org/10.1007/s13272-020-00484-5

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