H. Haj-Hariri
Dept. of Mech., Aerospace and Nuclear Eng., Univ. of Virginia, Charlottesville, VA 22903
K. Herbert
P. Leehey
MIT, Cambridge, MA 02139
Wall-pressure measurements are performed using an array of pinhole microphones mounted into the test wall of a low noise, low turbulence flow facility. The frequency-wave-number spectra for both streamwise and spanwise directions are obtained through the spatial Fourier transformation of cross-spectral measurements in the said directions. The results of the wind-tunnel measurements reveal an interesting behavior of the low wave number portion of the wall-pressure spectrum. Namely, this portion of the spectrum does not exhibit any Mach-number dependence for nearly incompressible flows. The bulk of this talk addresses the analytical investigations undertaken in order to establish the validity of the experimental observations. The existing theories---which are inviscid---predict a low-wave-number wall pressure proportional to the Mach number. Initially, the complete problem is analyzed while allowing for the effect of a finite Reynolds number (viscosity). The low-Mach-number analytical model shows the wall-pressure spectrum to have a leading term independent of the Mach number. There is good frequency trend agreement between the theoretical and the experimental spectra. The physical mechanism for the Mach-number independence of the spectrum is attributed to a hydrodynamic contribution to the wall pressure resulting from a Stokes layer induced by the sound-generating turbulent eddies. Next, a simple model problem is presented which isolates the viscous mechanism responsible for the hydrodynamic contribution to the wall pressure and the subsequent contribution to the sound field brought about by this interaction. It is argued that the physical process involved is akin (albeit inversely) to that operative in the boundary-layer receptivity problem for nearly incompressible flows.