American Institute of Aeronautics and Astronautics 1 Measuring Surface Pressure with Far Field Acoustics William Devenport 1 and Elisabeth A. Wahl 2 Virginia Tech, Blacksburg VA 24061 Stewart A. L. Glegg 3 Florida Atlantic University, Boca Raton FL 33431 W. Nathan Alexander 2 and Dustin L. Grissom 4 Virginia Tech, Blacksburg VA 24061 Abstract This paper introduces a new method for measuring the spectral character of wall pressure fluctuations under turbulent boundary layers by measuring the sound that they radiate in the presence of hydrodynamically smooth sinusoidal ridges in the surface. The theoretical basis for the method and experimental tests demonstrating its viability are described. The sound spectrum radiated by the sinusoidal surface reveals a cut through the full three-dimensional wavenumber frequency spectrum of the wall pressure at the wavenumber of the surface. Since sinusoidal ridges can be made with very small wavelengths, this technique can be used to probe the structure of the wall pressure spectrum on scales far smaller than those that can be reached using conventional wall-mounted transducers. Furthermore, the method reveals the wavenumber frequency spectrum directly, without the need for multi-point measurements. The wall pressure wavenumber frequency spectra measured using this technique bear a close qualitative and quantitative similarity to Chase’s (1980, 1987) model forms, with the exception that they show a high frequency decay that occurs at different rates than assumed in the models. I. Introduction This paper introduces a new method for measuring the spectral character of wall pressure fluctuations under turbulent boundary layers by measuring the sound that they radiate in the presence of hydrodynamically smooth sinusoidal ridges in the surface. Following the analysis of Glegg and Devenport (2009), consider a textured surface in the y 1 ,y 3 plane with a surface elevation y 2 =[(y 1 ,y 3 ), subjected to a homogeneous fluctuating hydrodynamic pressure field, p s . As can be established directly from Lighthill’s equation, with an appropriate selection of the Green’s function, the pressure fluctuations will scatter off the surface generating sound. The pressure field associated with the sound p heard at position x and frequency Z is ｳ S | N Z Z 3 1 3 1 3 1 | | | | ) , ( ) , , ( | | 2 ) , ( dk dk k k k k p e ik p s ik o o x x.ȗ x x x (1) Here k 1 and k 3 are the wavenumbers corresponding to y 1 and y 3, and k o is the acoustic wavenumber. The surface pressure appears in terms of its Fourier transform with respect to y 1 ,y 3 and time p s . The function ] is the vector wavenumber spectrum of the surface gradient, i.e. 3 , 1 ) 2 ( 1 ) , ( ) ( 2 3 1 ) ( 3 3 1 1  6 S   6 ｳ j d e y k k y ik y k i j j w w[ ] (2) where 6 is the area of the surface projected on to the y 1 ,y 3 plane. We have simplified this result assuming the variations in surface height are small compared to the acoustic wavelength. The above result forms the basis of the theory of roughness noise. It shows that the sound spectrum is essentially the result of wavenumber filtering of the wall pressure. The filter is the wavenumber transform of the surface slope taken in the direction of the observer. 1 Professor, Department of Aerospace and Ocean Engineering, AIAA Associate Fellow. 2 Graduate Research Assistant, Department of Aerospace and Ocean Engineering, AIAA Student Member. 3 Professor, Department of Ocean Engineering, AIAA Associate Fellow. 4 Graduate Research Assistant, Department of Aerospace and Ocean Engineering, AIAA Member. Currently at Ratheon Missile Systems, Tuscon AZ. 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference) 11 - 13 May 2009, Miami, Florida AIAA 2009-3281 Copyright © 2009 by W Devenport, E Wahl, S Glegg, N Alexander and D Grissom. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.