FED-Vol. 226, Cavitation and Gas-Liquid Flow in Fluid Machinery Devices

The focus of this paper is the numerical simulation of the dynam~cs and acoustics of a cloud of cavitating bubbles. The prob~t~ypical prohlet~~ solved considers a finite c lo~~ t l of 1111clei that is exposed to a decrease in the ambient, pressure which carlscs the cloud to cavitate. A so l ) sc~l~~ent pressure recovery then causes the c l o ~ ~ d to collapse. This is typical of the perturbation t~xperic~nctd by a t ~ ~ b b l e cloud as it passes a headform or the hlatle of a ship propeller. The simulations employ i.hc fully non-linear, non-barotropic, homogeneous flow equations coupled with the Rayleigh-Plesset dynamics for individ~~al bubbles. This set of equations is solved ~iumerically by an integral method. The computational results confirm the early speculation of M ~ r c h and his co-workers (Msrch 1980 Ri 1981, EIanson e l al. 1981) that an inwardly propagating shock wave may he 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 Wa11g 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, r r , the initial void fraction, tun , the minimum pressure coefficient, of the flow, CPM [ N , the natural frequencies of the cloud, and the ratio of the length scale o f low pressure p~rturbat~ion to the initial radius of the cloud, D/A(l , where D can be, for example, the radius of the headform or chord length of the propeller blade. We t~xamint~ how some of these parameters affect the far field aconstic noise prodncetl by thc volumetric acceleration of tlhe clontl. The non-dimensional far-field acoustic impulse produced by the cloud collapse is shown t,o depend, primarily, on the ~~~ax i r t i um total volume of the bnb1)lcs in the cloud nor~nalizetl by the length scale of the low pressure perturbation. Also, this maximum total voln~ue tlecreases quasi-linearly with the increase of t,he cavitation number. IIowevrr, the slope of the dcpendence, 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 f -" behavior, where n is between 0.5 and 2. After several collapse cycles, the cloud begins t o oscillate a t its natural frequency and contributes harmonic peaks in its spectrum.