Wang, Y.-C. and Brennen, C. E. (1995) The Noise Generated by the Collapse of a Cloud of Cavitation Bubbles. In: Cavitation and Gas-Liquid Flow in Fluid Machinery and Devices, 1995: Presented at the 1995 ASME/JSME Fluids Engineering and Laser Anemometry Conference and Exhibition, August 13-18, 1995, Hilton Head, South Carolina. Fluids Engineering Division. Vol.FED-226. No.226. American Society of Mechanical Engineers , New York, NY, USA, pp. 17-29. ISBN 0791814815 http://resolver.caltech.edu/CaltechAUTHORS:WNGcglffmd95
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The focus of this paper is the numerical simulation of the dynamics and acoustics of a cloud of cavitating bubbles. The prototypical problem solved considers a finite cloud of nuclei that is exposed to a decrease in the ambient pressure which causes the cloud to cavitate. A subsequent pressure recovery then causes the cloud to collapse. This is typical of the perturbation experienced by a bubble cloud as it passes a headform or the blade of a ship propeller. The simulations employ the fully non-linear, non-barotropic, homogeneous flow equations coupled with the Rayleigh-Plesset dynamics for individual bubbles. This set of equations is solved numerically by an integral method. The computational results confirm the early speculation of Morch and his co-workers (Morch 1980 & 1981, Hanson et al. 1981) that an inwardly propagating shock wave may be formed in the collapse of a cavitating cloud. The structure of the shock is found to be similar to that of the steady planar shocks analyzed by Noordij and van Wijngaarden (1974). The shock wave grows rapidly not only because of the geometric effect of an inwardly propagating spherical shock but also because of the coupling of the single bubble dynamics with the global dynamics of the flow through the pressure and velocity fields (see also Wang and Brennen 1994). The specific circumstances which lead to the formation of such a shock are explored. Moreover, the calculations demonstrate that the acoustic impulse produced by the cloud is significantly enhanced by this shock-focusing process. Major parameters which affect the dynamics and acoustics of the cloud are found to be the cavitation number, [sigma], the initial void fraction, [alpha-zero], the minimum pressure coefficient of the flow, [C Pmin], the natural frequencies of the cloud, and the ratio of the length scale of low pressure perturbation to the initial radius of the cloud, [D/A-zero], where D can be, for example, the radius of the headform or chord length of the propeller blade. We examine how some of these parameters affect the far field acoustic noise produced by the volumetric acceleration of the cloud. The non-dimensional far-field acoustic impulse produced by the cloud collapse is shown to depend, primarily, on the maximum total volume of the bubbles in the cloud normalized by the length scale of the low pressure perturbation. Also, this maximum total volume decreases quasi-linearly with the increase of the cavitation number. However, the slope of the dependence, in turn, changes with the initial void fraction and other parameters. Non-dimensional power density spectra for the far-field noise are presented and exhibit the [equation] behavior, where n is between 0.5 and 2. After several collapse cycles, the cloud begins to oscillate at its natural frequency and contributes harmonic peaks in its spectrum.
|Item Type:||Book Section|
|Additional Information:||The authors are very grateful for the support for this research provided by the Office of Naval Research under Contract N00014-91-J-1295.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Christopher Brennen|
|Deposited On:||09 Nov 2004|
|Last Modified:||26 Dec 2012 08:39|
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