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RESEARCH PAPERS

The Wavenumber-Phase Velocity Representation for the Turbulent Wall-Pressure Spectrum

[+] Author and Article Information
Ronald L. Panton

Mechanical Engineering Department, University of Texas, Austin, TX 78712

Gilles Robert

Laboratorie de Mecanique des Fluids et d’Acoustique, Ecole Centrale de Lyon, 69131 Ecully Cedex, France

J. Fluids Eng 116(3), 477-483 (Sep 01, 1994) (7 pages) doi:10.1115/1.2910301 History: Received January 25, 1993; Revised September 29, 1993; Online May 23, 2008

Abstract

Wall-pressure fluctuations can be represented by a spectrum level that is a function of flow-direction wavenumber and frequnecy, Φ (k1 , ω). In the theory developed herein the frequency is replaced by a phase speed; ω = ck1 . At low wavenumbers the spectrum is a universal function if nondimensionalized by the friction velocity u* and the boundary layer thickness δ, while at high wavenumbers another universal function holds if nondimensionalized by u* and viscosity ν. The theory predicts that at moderate wavenumbers the spectrum must be of the form Φ+ (k+ 1 , ω+ = c+ k+ 1 ) = k+ 1 − 2 P+ (Δc+ ) where P+ (Δc+ ) is a universal function. Here Δc+ is the difference between the phase speed and the speed for which the maximum of Φ+ occurs. Similar laws exist in outer variables. New measurements of the wall-pressure are given for a large Reynolds number range; 45,000 < Re = Uo δ/ν < 113,000. The scaling laws described above were tested with the experimental results and found to be valid. An experimentally determined curve for P+ (Δc+ ) is given.

Copyright © 1994 by The American Society of Mechanical Engineers
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