Cavitation&nbsp;has been well known as&nbsp;an unsteady phenomenon appeared in fluid machinery such as pumps and screws, in which the liquid pressure becomes lower than the vapor pressure when liquid moves with high speed and it induces many cavities as a resultant of phase transition. In particular, it is considered that the collapse of a cloud of such cavities may induce a shock wave, which makes serious damage to fluid machinery,&nbsp;however it has not been precisely understood how the cloud collapses to induce a shock wave. There have been presented&nbsp;many experimental and numerical&nbsp;researches in order to study&nbsp;the cloud cavitation and the induced shock wave.&nbsp;Most of them&nbsp;principally assumed that there may exist an inward shock wave associated with the collapse of the cloud; see, for instance,&nbsp;Wang and Brennen (1999), and Shimada, Matsumoto and Kobayashi (1999). However, the notion of the cloud has some ambiguity in its mathematical modeling and it has not been well understood how the cavities can be formed as a cloud and also how the cloud may behave as&nbsp;an unsteady behavior&nbsp;to induce shock waves using the Navier-Stokes equations.In our previous work of Ushioku and Yoshimura (FEDSM2020), we made a numerical study on&nbsp;a cloud cavitation that may appear in a submerged water-jet injection into still water through a nozzle, in which we showed a mixture model for the multiphase flow of&nbsp;two-dimensional compressible two-phase Navier-Stokes equations&nbsp;using the Smoothed Particle Hydrodynamics (SPH) method. We specifically proposed an idea that a cloud can be regarded as a hole surrounded by fluid particles where the hole implies an area where a phase transition occurs from the liquid phase to the vapor phase. Then, we showed that a set of twin vortices appeared in the velocity fields induced by the injected jet and also that the unsteady behavior of the cloud, namely, the growth, shrink and collapse of the cloud, was clarified in conjunction with the motion of twin vortices.In this paper, we further make a numerical analysis on the unsteady phenomena of the cloud that occurs in a submerged water-jet injection into still water through a nozzle, specifically, in order to clarify how a shock wave may be induced by the collapse of the cloud of cavities and also to explain how the induced shock wave may propagate&nbsp;outward&nbsp;from the boundary of the cloud by using the SPH method.From our numerical investigations, we have gained the following knowledge of the shock wave emitted from the collapse of the cloud:(1)&nbsp;&nbsp;The set of twin vortices moves along boundaries of the cloud and it disappears at the bottom of the cloud. Then the velocity field surrounding the cloud changes its direction inward to shrink the cloud, which implies that the motion of twin vortices plays an essential role to trigger the collapse of the cloud.(2)&nbsp;&nbsp;At the time when the cloud collapses, an intensive shock wave is emitted around at the center of the cloud and it propagates outward. By the collapse, the main cloud totally disappeared but&nbsp;instead several small portions of cavities appear, each of which performs repeatedly a similar unsteady motion of rebounding and then is to be disappeared.&nbsp;(3)&nbsp;&nbsp;More precisely, before the main shock wave is emitted, several small shock waves are released from different points near the center of the cloud. Therefore it may be considered that the main shock wave can be formed by accumulating the small shock waves.In the paper, we will show the details on the numerical investigations of the unsteady motion of the cloud and we will clarify the mechanisms of the emission of the shock wave induced from the collapse of the cloud.

Numerical Investigation of Cloud Cavitation and Its Induced Shock Waves

Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2021/volume/85284

ASME 2021 Fluids Engineering Division Summer Meeting (FEDSM2021)

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