Measurement of the Nonsteady Flow Field in the Opening of a Resonating Cavity Excited by Grazing Flow

Abstract

Flow Flow past past the the opening opening of of a a cavity cavity can can excite excite acoustic acoustic resonance. resonance. TheThe periodic periodic velocity velocity field field in in the the region region of of the the cavity cavity opening opening has has been been measured measured for for various various flow flow conditions conditions and and the the vorticity vorticity distribution distribution has has been been computed computed from from the the measured measured data data using using numerical numerical differentiation. differentiation. The The results results indicate indicate that that the the shear shear layer layer rolls rolls up up into into discrete discrete vortices, vortices, which which travel travel across across the the cavity cavity opening. opening. Two Two resonances resonances were were found. found. The The first first is is characterized characterized by by a a single single vortex vortex being being present present and and results results in in the the greatest greatest amplitude. amplitude. The The second second is is characterized characterized by by the the presence presence of of two two vortices vortices which which excite excite a a distinct distinct but but lesser lesser amplitude amplitude resonance. resonance. As As the the flow flow velocity velocity changes, changes, the the position position of of these these vortices vortices shifts shifts relative relative to to the the phase phase of of the the acoustic acoustic cycle. cycle. TheThe timing timing of of the the interaction interaction between between the the moving moving vortices vortices and and the the acoustic acoustic particle particle velocity velocity determines, determines, to to a a large large extent, extent, the the intensity intensity of of the the excitation, excitation, and and therefore therefore also also the the oscillation oscillation amplitude. amplitude. TheThe measurements measurements also also indicate indicate that that the the boundary boundary layer layer upstream upstream of of the the leading leading edge edge pulsates pulsates considerably. considerably.

Parallel Blade–vortex Interaction

“…Rockwell & Knisely (1979) and Graf & Durgin (1990) made use of the natural instabilities inherent in a free shear layer to investigate vortex impingement upon a corner. Ziada & Rockwell (1982) Kaykayoglu & Rockwell (1985) and Sohn & Rockwell (1987) have also employed mixing layers in the examination of vortex impingement with sharp and elliptical leading edges at zero angle of incidence.…”

Fluid mechanics of the flow-excited Helmholtz resonator

“…A thorough review was given by Rockwell & Naudascher (1978). More recent work involving shallow cavities includes that of Graf & Durgin (1993) and Chatellier et al (2004). Note, however, that the flow-excited Helmholtz resonator is considered to be unique and distinct from similar configurations involving shallow cavities and the like.…”

On sound transmission loss across a Helmholtz resonator in a low Mach number flow duct

“…One can also notice that the Strouhal number of the resonator resonance frequency f d ͑ϳ660 Hz͒ based on the aperture slot width ͑w =30 mm͒ and a mean flow velocity U of 20 m/s is 0.99 ͑=f d w / U͒, which is much higher than the expected fundamental frequency of the aerodynamic excitation, which has a Strouhal number of 0.25 as discussed in Nelson et al 9 A Strouhal number of 0.25 corresponds to a frequency of 167 Hz at U =20 m/ s for the present resonators. This further suggests that the shear layer rollup as seen in Graf and Durgin 17 was not likely to affect the results of the present study. Figure 5͑a͒ shows the pressure fluctuation spectra at P1 within the range of U tested.…”

“…One can therefore expect complicated aeroacoustical activities occur when the resonator interacts with flow turbulence. In the building services practice, the dimensions of the Helmholtz resonator may not enable the kind of shear layer/ vortex impingements studied in Dequand et al 12 and Graf and Durgin 17 to occur, especially when the mean flow is of very low Mach number and the resonator cavity is small. The theories adopted by Meissner 11 and Innes and Crighton 18 assumed a continuous sinusoidal excitation at the mouth of the resonator by shear layer rollup/vortex shedding while the initiation of the oscillating flow was not explicitly shown in their formulations.…”