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TECHNICAL PAPERS

# Modeling of Wall Pressure Fluctuations Based on Time Mean Flow Field

[+] Author and Article Information
Yu-Tai Lee

Naval Surface Warfare Center, Carderock Division, 9500 MacArthur Blvd., West Bethesda, MD 20817LeeYT@nswccd.navy.mil

William K. Blake, Theodore M. Farabee

Naval Surface Warfare Center, Carderock Division, 9500 MacArthur Blvd., West Bethesda, MD 20817

J. Fluids Eng 127(2), 233-240 (Sep 20, 2004) (8 pages) doi:10.1115/1.1881698 History: Received May 24, 2004; Revised September 20, 2004

## Abstract

Time-mean flow fields and turbulent flow characteristics obtained from solving the Reynolds averaged Navier-Stokes equations with a $k‐ε$ turbulence model are used to predict the frequency spectrum of wall pressure fluctuations. The vertical turbulent velocity is represented by the turbulent kinetic energy contained in the local flow. An anisotropic distribution of the turbulent kinetic energy is implemented based on an equilibrium turbulent shear flow, which assumes flow with a zero streamwise pressure gradient. The spectral correlation model for predicting the wall pressure fluctuation is obtained through a Green’s function formulation and modeling of the streamwise and spanwise wave number spectra. Predictions for equilibrium flow agree well with measurements and demonstrate that when outer-flow and inner-flow activity contribute significantly, an overlap region exists in which the pressure spectrum scales as the inverse of frequency. Predictions of the surface pressure spectrum for flow over a backward-facing step are used to validate the current approach for a nonequilibrium flow.

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## Figures

Figure 1

The function for the anisotropic factor

Figure 2

Comparison of spectra for equilibrium flows using (a) outer; (b) mixed; and (c) inner variables

Figure 3

Regional contributions of equilibrium flows

Figure 4

Flow field over the BFS

Figure 5

Computational grid for BFS

Figure 6

Inflow conditions for the BFS calculations

Figure 7

Velocity comparisons for the BFS calculations

Figure 8

Comparisons in turbulent kinetic energy for the BFS

Figure 9

Comparisons in velocity and turbulent kinetic energy for BFS at x∕h=10

Figure 10

Comparison in the anisotropic factor for BFS

Figure 11

Predicted and measured spectra for BFS at x∕h=10 and 72

Figure 12

Predicted spectra at three streamwise locations for BFS

Figure 13

Regional contributions for BFS at inlet and x∕h=72

Figure 14

Regional contributions for BFS at x∕h=10 and 72

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