A numerical strategy for gas cavity-body interactions from acoustic to incompressible liquid phases

The gas-cavity problem with initially high pressure, evolving in a surrounding liquid, and interacting with a near body, is a very interesting research topic because it involves several physical phenomena and is of practical interest in different contexts. For instance, underwater explosions represent an important issue for ships and offshore structures. Therefore it is necessary to predict structural effects and try to improve vessel design. To this purpose, physical tests were performed along the years and theories were developed (Cole 1948). Another important application is in medical field. Implosion of micro-bubbles with ultrasound in biological flows is used within a noninvasive technique to remove calculi in human bodies (Lingeman et al. 2009). Here we first focus on the first application. When an underwater explosion occurs, a chemical reaction and a detonation process cause the formation of a hot gas with high pressure and the release of a shock wave traveling in the surrounding fluid. Then a superheated, spherical, bubble is formed which will first expand while the high pressure reduces in time and propagates in the surrounding liquid. Eventually the bubble starts to oscillate and affect the local pressure. In the first stage (shock wave) both the gas and the surrounding liquid behave as compressible, in the later stages (gas bubble) the acoustic wave will disappear and the water can be considered incompressible. The interaction of this two-phase fluid with a body will then depend on the vicinity of the body from the explosion zone and by the presence or not of other boundaries, e.g. the sea floor, the free surface.