## An Experimental Investigation of Pressure Fluctuations in Three-Dimensional Turbulent Boundary Layers

##### Abstract

An Experimental Investigation of Pressure Fluctuations in Three-Dimensional
Turbulent Boundary Layers

by Michael C. Goody

Roger L. Simpson, Chairman

Aerospace and Ocean Engineering

(ABSTRACT)

This dissertation presents experimental measurements and analysis of the surface pressure fluctuations beneath several turbulent boundary layers of practical interest. Pressure fluctuations in turbulent boundary layers are a source of noise and vibration that can accelerate structural fatigue. Pressure fluctuations and their correlation with velocity fluctuations is an important diffusive mechanism of turbulence transport. The approach was to study the statistics of both the surface pressure and the velocity field through new measurements of the fluctuating surface pressure and existing measurements of the velocity field and the covariance of the surface pressure and fluctuating velocity components.

Measurements were made in three types of flows. The first type of flow was a zero pressure gradient, two-dimensional, turbulent boundary layer (Re(theta) = 7300 and Re(theta) = 23400). The two-dimensional flows serve as a baseline for comparison to the other three-dimensional flows and validate the experimental techniques used in the present study through comparison with existing measurements. The second type of flow was a three-dimensional, pressure-driven, turbulent boundary layer that forms away from a wing-body junction. Two of this type of boundary layer were studied - Re(theta) = 5940 and Re(theta) = 23200. The third type of flow was the separating flow about the leeside of a 6:1 prolate spheroid at angle of attack. Measurements were made at two angles of attack, 10Â° and 20Â°, and two axial locations, x/L = 0.600 and x/L = 0.772, in this type of flow.

Spectral scaling is discussed and various scaling combinations of the spectral power density of surface pressure fluctuations beneath two-dimensional boundary layers that cover a wide range of Reynolds number (1400 < Re(theta) < 23400) are presented. The spectral power density of surface pressure fluctuations beneath the separating flow on the leeside of a 6:1 prolate spheroid at 10Â° angle of attack collapse when normalized using viscous scales. However, the spectral power density of surface pressure fluctuations beneath highly three-dimensional flow contain nearly constant spectral levels within a middle to high frequency range. The nearly constant spectral levels are due to a lack of overlapping frequency structure between the large-scale motions and the viscous-dominated motions since each of these types of motion may have different flow histories due to the three-dimensional flow structure. This effect amplifies the importance of the middle frequency range to p' as compared to two-dimensional flows. In terms of instrumentation, accurate p' measurements in a three-dimensional flow require accurate high frequency (f > 20 kHz) p measurements.

The lack of similarity in the shape of the spectral power density preclude
a direct extension of "universal" generalizations that are true
for surface pressure fluctuations beneath two-dimensional boundary layers.
The resulting RMS surface pressure fluctuation distributions reflect the
importance of the high frequency wall region contributions. Scaling parameters
for the p spectra beneath three-dimensional flows must incorporate local
flow structure in order to be successful. Analysis based on the Poisson
equation shows that variation of the high frequency spectral levels are
related to the variation in near-wall mean velocity gradients and v^{2}
structure. In the 6:1 prolate spheroid flow, near regions of crossflow
separation there is a local minimum in RMS surface pressure fluctuations,
whereas around reattachments and under the large shed vortices there is
a local maximum in RMS surface pressure fluctuations.

Measurements of the correlation coefficient between surface pressure and velocity fluctuations show that there can be sources of p away from the wall in three-dimensional flows. Sources of p away from the wall are significant in terms of fluid-structure interaction since they contribute low frequency fluctuations. Structures typically have low resonant frequencies. Sources of p away from the wall are also significant in terms of radiated sound since they are likely to interact with the free-stream and be radiated away as sound.

##### Collections

- Doctoral Dissertations [11228]