Self-excited depth-mode resonance for a wall-mounted cavity in turbulent flow

Abstract

Experimental and theoretical results are presented for a wall-mounted cavity in turbulent flow, oscillating at Helmholtz or depth-mode resonance, where the mouth dimensions are small compared with acoustic wavelength. A new, computerized, hot-wire method was employed to investigate the oscillating flow field in the cavity mouth. Measured wavelength of the interface wave agrees well with predictions of Michalke, using an equivalent laminar flow model based on the oscillating mean velocity profile. By means of a forward transfer function derived from the theoretical interface wave model and a backward transfer function derived from organ-pipe theory, a root locus solution of the frequency lock-in problem has been obtained. Predicted frequencies and sound pressure amplitudes are in good agreement with experimental values at the lower modes. Both resonant and off-resonant oscillation was investigated. For resonant oscillation, the streamwise slot width is required to be M−1/4 times the disturbance wavelength, where M is an integer. For situations in which the equations are applicable, the method can be used to predict design parameters for nonoscillating wall cavities in moving vessels.

Generation of tones due to flow past a deep cavity: Effect of streamwise length

“…These configurations include jet excitation of a long (closed) organ pipe (Cremer and Ising, 1967;Fletcher, 1974Fletcher, , 1976Fletcher, , 1979, jet-sequential orifice plates (Howe, 1975(Howe, , 1980Flatau and Van Moorhem, 1990;Hourigan et al, 1990), wake from a plate in a test section (Parker, 1966;Cumpsty and Whitehead, 1971;Stoneman et al, 1988), shear layer-cavity resonator (DeMetz and Farabee, 1977;Elder, 1978;Nelson et al, 1981Nelson et al, , 1983, and cavity shear layer-long pipeline (Pfizenmaier, 1973;Schachenmann and Rockwell, 1980;Schachenmann, 1982a, 1982b;Karadogan, 1982, 1983;Davies, 1981Davies, , 1996aDavies, , 1996bRockwell et al, 2003;Geveci et al, 2003;Oshkai et al, 2004). The configuration of a cavity shear layer-side branch (deep cavity) is not addressed in the foregoing.…”

Imaging of the Self-Excited Oscillation of Flow Past a Cavity During Generation of a Flow Tone

“…They include a jet through a system of orifice plates (Hourigan et al, 1990;Stoubos et al 1999), a separated shear layer past a cavity resonator (DeMetz & Farabee, 1977;Elder, 1978;Elder, Farabee & DeMetz, 1982;andNelson et al 1981, 1983), and a separated layer past a resonant side branch in the form of a duct or pipe (Pollack, 1980;Bruggeman et al 1989Bruggeman et al , 1991Kreisels ef al. 1995;Ziada & Biihlmann, 1992;and Ziada & Shine, 1999).…”

“…Approaches include the use of hot wire and laser Doppler anemometry, which yielded phase-or time-averaged representations of flow quantities. Elder (1978) and Elder et d. (1982) employed hatwire measurements to determine the unsteady deflection of the wave-like interface along the mouth of a cavity undergoing resonant oscillations in the depthwise mode.…”

Imaging of acoustically coupled oscillations due to flow past a shallow cavity: effect of cavity length scale

“…Previous studies have provided considerable insight into the generation of flow tones. The variety of configurations addressed in these studies include a jet through a system of orifice plates (Hourigan et al 1990;Stoubos et al 1999), a separated shear layer past a cavity resonator (DeMetz & Farabee, 1977;Elder, 1978;Elder et al, 1982;and Nelson et al 198 1, 1983), and a separated layer past a resonant side branch in the form of a duct or pipe (Pollack, 1980;Bruggeman et al 1989Bruggeman et al , 1991 Kreisels et al 1995 ;Ziada & Buhlmann, 1992;and Ziada & Shine, 1999). Rockwell (1983) and Blake (1986) describe the common elements associated with purely hydrodynamic oscillations.…”

“…(Cremer & king, 1967;Bruggernan, 1987;Ziada, 1994;Kriesels el al. 1995;Hourigan et al 1990;Nelson et al 1981;and Huang & Weaver, 1991) and pointwise measurements of flow characteristics (Elder, 1978;Elder et al 1982;Schachenmann & Rockwell, 1980;Rockwell & Schachenmann, 1982a, 1982bNelson et al 1981;and Coccola, 2000).…”