  Cavitation is an unsteady phenomenon typically appeared in a fluid moving with high speed, whose phase changes from liquid to gas, and it occurs when the local pressure of the liquid falls below the saturated vapor pressure. The generated portion of a cavity which is called a cloud performs a collective unsteady motion of repeating the process of growth and collapse. It is considered that a pressure shock wave propagates outward associated with the collapse of the cavitation cloud. In order to understand such unsteady behaviors of the cavitation cloud, much effort has been made to construct mathematical models such as the mixture model of liquids and gas bubbles, which was proposed by Wijngaarden (1968). Using the mixture model of liquids and gas bubbles, Wang and Brennen (1994) analyzed the collapse of a spherical cloud accompanied by the formation of an inward propagating bubbly shock wave, and Shimada, Matsumoto and Kobayashi (1999) investigated the internal phenomena of the cloud cavitation considering the compressibility of liquid. These numerical studies mainly focused on the inward shock wave propagation in conjunction with the collapse of the cloud of bubbles, while it has not been enough understood how the cavitation cloud itself is generated and how the unsteady collective motion, namely, the process of generation, growth and collapse of the cavitation cloud is performed from the viewpoint of the multiphase flow.

  In this study, in order to understand such unsteady collective behaviors of the caviation cloud, we make a two-dimensional numerical analysis of the multiphase flow of the submerged water-jet injection into water through a nozzle. As a numerical model of the bubbly water-jet, we employ the mixture model of liquid and gas, in which liquid phase and gas phase are considered as one mixture phase with a void fraction and we specifically employ the method of Smoothed Particle Hydrodynamics to numerically observe the dynamical behavior of the boundary of the cavitation cloud in the Lagrangian description. For the numerical test, we consider a rigid tank fulfilled with water liquid setting a nozzle located below the water surface, from which a water-jet is ejected. Assume that there exist many tiny bubbles initially set inside the nozzle and also that a water-jet is ejected from the nozzle by forcing high pressure. The governing equations are given by a two-dimensional compressible liquid-gas two-phase Navier-Stokes equations.

  From our numerical analysis, we have gained the following knowledge of the generation and the unsteady behaviors of the cavitation cloud:

\(1\) Injecting the water-jet into still water, a set of two vortices appears symmetrically on the downstream side, namely, a twin vortex is formed in such a way that it is surrounded by the injected water.

\(2\) Associated with the flows of the twin vortex, a part of the water in the tank is pushed away to generate two portions of cavities whose areas gradually grow up and finally the two portions of cavities are combined into one single large portion of cavity, which is considered as a birth of cloud.

\(3\) The cloud grows up until when the area of the cavity becomes largest, and then it rapidly shrinks by the pressure of the surrounded water and eventually collapses. The cloud is totally torn apart into several smaller portions, each of which repeats the rebounding behavior and is finally disappeared.

  Further, we examine the numerical tests with different cases of several void fractions. In this study, we explain the scenarios of how the cloud is generated from the multiphase flow and of how a series of collective motions of the generation, rebound and disappearance of the cloud is made.


Numerical Study of Unsteady Behavior of Cloud Cavitation by Smoothed Particle Hydrodynamics

Division / Sponsors: 
Heat Transfer Division (HTD), Fluids Engineering Division (FED)

Heat Transfer Summer Conference
Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2020/volume/83709

18th International Conference on Nanochannels, Microchannels, and Minichannels
Paper Proceedings: https://asmedigitalcollection.asme.org/ICNMM/ICNMM2020/volume/83693

Fluids Engineering Division Summer Meeting
Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2020/volume/83716

HT-ICNMM2020 - Virtual Conference, SHTC - Virtual Conference, FEDSM2020 - Virtual Conference

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