William K. Blake

Wavenumber‐Frequency Spectra of Turbulent Boundary Layer Pressure Measured by Microphone Arrays

Measurements of frequency spectra of smooth‐wall pressures have been made by single microphones and by a longitudinal array of four flush 0.8‐in. circular microphones connected with alternating and with common phase. The microphones were selected to suppress high wavenumbers. The measured levels set upper limits on low‐wavenumber boundary‐layer pressure. The array was designed to suppress, by its wavenumber filtering, the background acoustic duct noise at frequencies near 3 kHz. Analysis indicates that a very high phase‐speed low wavenumber pressure field dominates near this frequency. At low frequencies, single‐microphone and array spectra are dominated by the convective wavenumber component of boundary‐layer pressure and satisfactory agreement is found with theoretical predictions. [This work was supported by the Acoustics Branch of the Office of Naval Research.]

The Aeroacoustics of Trailing Edges

Trailing edge sound is an aeroacoustic phenomenon which contributes to the noise from lifting surface flaps, rotating machines and certain turbulent nozzle flows. Part I of this paper is a survey which describes the physics of aerodynamic sound generation by trailing edge flows; it is particularly relevant to lifting surfaces. The survey will describe the importance of the geometry of the surface, its upstream boundary layer, and its trailing edge wake in determining the nature of the aeroacoustic sources. Techniques for measurement will be discussed and recent results will be brought forth which will further elucidate the relevant features of flow structure. Part 2 of the paper will deal with the trailing edge flow sources in more depth. A distinction is to be made between continuous-spectrum surface pressures that are locally generated by the immediate separated flow and narrower band pressures which are developed by superimposed orderly structures developing in the wake. The paper will also examine this distinction as well as the relevance of existing analytical models of trailing edge sound to each mechanism, and it will compare those theories to measurements of the sound generated by the separated trailing edge flow. General agreement is found between measurement and theory for both tonal and random aerodynamic sound depending on the frequency and the geometry of the trailing edge.

On the flow−excited vibrations of cantilever struts in water. I. Flow−induced damping and vibration

The general problem of the response of a cantilever beam to flow over its surface is considered experimentally and theoretically. The model response of a beam in flowing water is shown normalized on the dynamic head of the inflow, the total mass of the beam, and the modal loss factors. Results are presented for a series of beams of varying length and chord. The magnitude of hydrodynamically induced damping is also characterized experimentally. It is shown that results agree favorably with an approximate expression based on finite aspect−ratio, unsteady airfoil theory. Loss factors, based on entrained mass, are found to be inversely proportional to a reduced frequency based on the width of the strut and inflow speed.Subject Classification: 40.35, 40.22; 30.50.

On the flow‐excited vibrations of cantilever struts in water. II. Surface‐pressure fluctuations and analytical predictions

Analytical predictions of the flow‐excited vibration of resonant bending modes of cantilever struts are made. These predictions are compared to selected samples of measured responses of struts in a water tunnel. The measurements have been described in Part I. As a basis for the estimates, a wind tunnel study of the statistical properties of the boundary layer formed by flow on a rigid strut is described. The air measurements were made on a Reynolds‐number‐scaled model of one of the cantilever struts which were excited by water. For the crude geometry used, the wind results disclose that flow separation at the leading edge (which is sensitive to angle of attack) generates a low‐frequency pressure field which is markedly higher than that normally encountered in boundary layers. At high frequencies the pressure field is influenced by the local flow parameters normally used in boundary‐layer scaling. Predictions of the response of the struts to inflow turbulence are based on existing theory and measured water...

Chamber for reverberant acoustic power measurements in air and in water

A reverberant chamber for use with both air and water media is described. The chamber is used to investigate the acoustic coupling of simple vibrating structures under conditions of light or of heavy fluid loading. Calibration was effected by measuring 60−dB reverberation times in 1/3−octave bands; decay times on the order of 2 sec in air and the order of 0.2 sec in water were observed. These results were cross checked in water by measuring the spectrum of acoustic pressure in the chamber generated by a calibrated hydrophone source. Sound−pressure levels measured in narrow (50−Hz) bands varied ±3 dB spatially in the air−filled chamber and ±5 dB spatially in the water−filled chamber.Subject Classification: 55.65; 50.25; 45.10.

Short‐wavelength diffracted surface pressures on a prolate spheroid

This paper will describe measurements of sound pressures on the surface of a prolate spheroid whose length to diameter ratio is 6.9. The sound source was positioned a distance from the illuminated pole equal to the length of the body; irradiation was axisymmetric. Data at surface locations along the axis of the body was collected for acoustic wavelengths λ ranging from 1/150 to 1/38 of the interfocal distance d. A condenser microphone equipped with a long probe tube was used to avoid extraneous scattering from the sensor. Sound pressure levels, expressed relative to those measured on the illuminated pole, showed the existence of expected creeping‐wave interference patterns near the antipode and an illuminated spot on the pole. The measured levels on that pole are shown to decrease roughly as the reciprocal of frequency; they are 13 dB less than those at the illuminated pole for d/λ = 38. In the shadow zone the measurements are shown to be well approximated by Kellers deo‐metric theory of diffraction. Dev...

A near‐wake model for the aerodynamic pressures exerted on singing trailing edges

Periodic vortex streets are formed in the wakes of blunted trailing edges on airfoils and struts. The pressures generated on the shedding struts by the vortices in these wakes are periodic in time with a frequency that is set by the shedding rate for the vortices. A simple analytical formulation is derived to relate wake‐induced pressures to the characteristics of the wake near the edge. The chordwise distribution and magnitude of the pressure is shown as a function of the circulation of shed vortices, as well as the formation distance and the spacing of the vortices in the street. Predictions from the theory are compared to some recent measurements which were obtained in the wakes downstream of different trailing edges. These measurements were made at Reynolds numbers, based on trailing edge thickness, on the order of 104 to 105.Subject Classification: [43]28.65; [43]50.55.

Turbulent‐Boundary‐Layer Pressure Fluctuations over Rough Walls

The effect of distributed wall roughness on surface pressure fluctuations has been measured with very small (relative to a boundary‐layer displacement thickness) “pinhole” microphones. Measurements were also made on smooth walls for comparison. The rough‐wall rms pressure levels increase over the smooth‐wall value in approximate proportion to the increase in wall shear by the roughness. In addition, intermediate‐ and high‐frequency pressure levels are predominantly determined by roughness size, whereas low‐frequency levels are influenced by roughness separation and by boundary‐layer displacement thickness. Cross‐spectral density measurements made with 5‐Hz bandwidth filters disclose lower rough wall phase speeds. The pressure‐field coherence loss is higher; pressure eddies of any frequency lose their coherence over rough walls in one‐third to one‐half the streamwise distance over smooth walls. Very low phase speeds at low frequencies were measured over both smooth and rough walls. The broad‐band space‐tim...

Turbulent boundary layer wall pressure spatial filtering with sensors constructed of polyvinylidene fluoride (PVDF)

Piezoelectric pressure transducers constructed of electrically polarized polyvinylidene fluoride (PVDF) were assessed as spatial filters for a spatially homogeneous turbulent boundary layer induced wall pressure field. Rectangular‐shaped transducers were constructed of lengths ranging from 0.25 to 7.3 times the displacement thickness of the boundary layer in the streamwise direction and widths of 0.25 the displacement thickness. Measurements of the power spectral levels of the wall pressure fluctuations are compared for each transducer with the predicted levels determined by the integration over the spatial extent of each transducer of the Corcos model of the wall pressure cross spectrum. [Work supported by ONR.]

Prospects for computational techniques in basic engineering flow noise evaluations

Advances in computational fluid dynamics techniques for predicting viscous turbulent flows suggest the plausibility for making appropriate extensions to aero‐ and hydroacoustics. Furthermore, the developments in our understanding of mechanisms of flow‐induced sound and vibration over the past 30 years have provided useful insights on how to make these extensions. Using some example problems, this paper will explore how large‐scale computation might play useful roles in the modeling of flow sources. Emphasis will be on subsonic sources of flow and vibration. Examples of some numerical modeling requirements for computational solutions for these model cases will be derived from the fundamental theories for these sources and their applications. Suggestions will be made for certain measurement techniques which could provide both code validation and necessary coefficients that may be necessary for empirically based code elements.