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Simulation of turbulent boundary layer wall pressure fluctuations via Poisson equation and synthetic turbulence

Published online by Cambridge University Press:  04 August 2017

Nan Hu Open the ORCID record for Nan Hu [Opens in a new window] ,
Nils Reiche  and
Roland Ewert
Nan Hu*
Affiliation:
Institute of Aerodynamics and Flow Technology, Department of Technical Acoustics, German Aerospace Center (DLR), Lilienthalplatz 7, 38108 Braunschweig, Germany
Nils Reiche
Affiliation:
Institute of Aerodynamics and Flow Technology, Department of Technical Acoustics, German Aerospace Center (DLR), Lilienthalplatz 7, 38108 Braunschweig, Germany
Roland Ewert
Affiliation:
Institute of Aerodynamics and Flow Technology, Department of Technical Acoustics, German Aerospace Center (DLR), Lilienthalplatz 7, 38108 Braunschweig, Germany
*
†Email address for correspondence: [email protected]
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Abstract

Flat plate turbulent boundary layers under zero pressure gradient are simulated using synthetic turbulence generated by the fast random particle–mesh method. The stochastic realisation is based on time-averaged turbulence statistics derived from Reynolds-averaged Navier–Stokes simulation of flat plate turbulent boundary layers at Reynolds numbers $\mathit{Re}_{\unicode[STIX]{x1D70F}}=2513$ and $\mathit{Re}_{\unicode[STIX]{x1D70F}}=4357$. To determine fluctuating pressure, a Poisson equation is solved with an unsteady right-hand side source term derived from the synthetic turbulence realisation. The Poisson equation is solved via fast Fourier transform using Hockney’s method. Due to its efficiency, the applied procedure enables us to study, for high Reynolds number flow, the effect of variations of the modelled turbulence characteristics on the resulting wall pressure spectrum. The contributions to wall pressure fluctuations from the mean-shear turbulence interaction term and the turbulence–turbulence interaction term are studied separately. The results show that both contributions have the same order of magnitude. Simulated one-point spectra and two-point cross-correlations of wall pressure fluctuations are analysed in detail. Convective features of the fluctuating pressure field are well determined. Good agreement for the characteristics of the wall pressure fluctuations is found between the present results and databases from other investigators.

JFM classification

Acoustics: Aeroacoustics Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , pp. 421 - 454
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Copyright
© 2017 Cambridge University Press 

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