Surface Pressure Fluctuations Produced By Boundary Layer Turbulence

Surface pressure fluctuations produced by boundary layer turbulence developed above a rigid plane surface are investigated theoretically. For an incompressible flow which obeys the Navier-Stokes equations, the boundary pressure is determined by a volume integration over quadrupole sources. Three different classes of source terms may be identified. These involve second, third, and fourth order velocity correlations. The contribution of the fourth order or turbulence-turbulence terms to the boundary pressure cross spectral density at high frequencies is obtained. The results show that the turbulence-turbulence boundary pressure sources are located at an effective height, and travel with an effective convection speed, both of which depend upon frequency and the shape of the mean velocity profile. At high frequencies, the pressure spectrum is found to be roughly proportional to the sixth power of the free stream velocity, and to the inverse cube of the frequency. Finally, the effect of the finite size of the transducer upon the measured boundary pressure spectrum is discussed. (Author).

Surface pressure fluctuations below turbulent boundary layers were studied, in part, because they can be regarded as 'footprints' of passing turbulent eddies. The pressure fluctuations are formally described by a Poisson equation, implying that the pressure fluctuation at a given point is mathematically represented by the integral of a 'source' term over the whole flow field, with a weighting inversely proportional to the distance of the source from the given point. In turbulent boundary layers, fluctuations were made in a low-speed constant pressure the high-frequency part of the wall pressure fluctuations is generated mainly within the inner layer - say, the first 20% of the boundary layer thickness - and the low-frequency part is generated mainly in the outer layer. Measurements of velocity and surface-pressure turbulent boundary layer well downstream of an extensive region of wall roughness. The turbulence near the wall was representative of a smooth-wall flow, while that in the outer layer was typical of the upper stream rough-wall flow. Comparison with previous measurements on an entirely smooth wall illustrates the relative contributions of the inner and outer layers to the surface pressure fluctuations. Further work has been done to compare the VITA (Variable ge) conditional-sampling algorithm withuctuations were more advanced algorithms. Keywords: Turbulent boundary layer, Noise measurement, Statistical analysis, Surface roughness, and VITA algorithm.

Surface pressure fluctuations on a circular disk placed normal to a turbulent air stream were investigated. Turbulence intensities of approximately 10% were produced by a coarse grid installed at the test-section entrance. The turbulent field in the neighborhood of the disk was homogeneous and nearly isotropic. Experimental results indicate that existing linear theories which do not consider distortion of the flow fail to predict the nature of surface pressure fluctuations on a bluff body. Only for wavelengths which are large compared to the body do these theories yield satisfactory results. A strong attenuation of the high frequency components occurs as the flow stagnates. This is accompanied by a transfer of energy from short to long wavelengths. The opposite effect is observed as the flow attains a radial direction and approaches the edge of the disk. A neutral wavelength which undergoes little change in energy was observed. Integral scales of surface pressure fluctuations are much larger than the lateral integral scale of the free-stream turbulence. (Author).

Measurements were obtained of the pressure fluctuations on a solid surface immersed in a supersonic stream for Mach numbers up to 5.0. The pressures resulting from both the attached and separated turbulent boundary layers were investigated. The results for the attached layer show that the root mean square value of the pressure fluctuation is proportional to the mean shear stress at the wall with a proportionality constant that is only weakly dependent on Mach number. The convection velocity characterizing the space-time correlations of pressure on the wall decreases with increasing Mach number, as does the ratio of the scale of the pressure fluctuations to the geometrical boundary layer thickness. The pressures associated with the separated flow produced by a forward facing step were significantly larger than the pressures produced by an attached boundary layer. The data can be interpreted as showing that the pressure fluctuations originate from two distinct causes, fluctuations due to changes in geometry of the separated region and fluctuations due to the disturbed motion within the separation bubble. (Author).