In naval hydrodynamics the problem of the bubbles evolution has been mostly linked to the noise generated by the bubbles oscillations and fragmentation. The most common causes of generation, and consequent oscillation and collapse, of bubbles are the breaking of the free surface induced by marine vehicles and the generation of cavitational bubbles by propellers. Besides a significant environmental impact, the noise generated in these cases has a military interest because it can make a vessel visible to sonar devices. More recently, the importance of dispersed bubbles compressibility has been highlighted also in the case of waves impacting against breakwaters, Peregrine and Thaus (1996). The calculations of a free-surface wave impacting against a vertical wall can underestimate the actual measured loads on long breakwaters. Experimental investigations, aiming to analyze the air fraction in water, have shown that the loads recorded are linked to the amount of air in water. These practical problems ask for numerical solvers able to capture the evolution of violent motions and fragmentation of multi-phase interfaces, and require the modeling of compressibility for the air entrapped in sufficiently small cavities. Differently, most of the solvers dealing with air and water assume that both fluids are incompressible. The easiest way to account for the compressibility is to allow the density of the air to vary in time. This solution has been adopted for example by Caiden et al. (2001). It gives reliable results but faces some computational challenges connected with the coupling of the two different fluids. Most of all, the numerical time step of the simulations is fixed by the speed of sound in the lighter fluid. This represents a significant limitation. The technique shown here aims to avoid the computational effort due to the description of the compressibility waves in the air medium. The pressure oscillations inside the bubble are assumed related only to the change in volume of the bubble and the pressure is taken uniform in the gas, and therefore calculated through the polytropic equation.
Simplified model for compressible air bubbles in water
Colicchio;Greco;
2006
Abstract
In naval hydrodynamics the problem of the bubbles evolution has been mostly linked to the noise generated by the bubbles oscillations and fragmentation. The most common causes of generation, and consequent oscillation and collapse, of bubbles are the breaking of the free surface induced by marine vehicles and the generation of cavitational bubbles by propellers. Besides a significant environmental impact, the noise generated in these cases has a military interest because it can make a vessel visible to sonar devices. More recently, the importance of dispersed bubbles compressibility has been highlighted also in the case of waves impacting against breakwaters, Peregrine and Thaus (1996). The calculations of a free-surface wave impacting against a vertical wall can underestimate the actual measured loads on long breakwaters. Experimental investigations, aiming to analyze the air fraction in water, have shown that the loads recorded are linked to the amount of air in water. These practical problems ask for numerical solvers able to capture the evolution of violent motions and fragmentation of multi-phase interfaces, and require the modeling of compressibility for the air entrapped in sufficiently small cavities. Differently, most of the solvers dealing with air and water assume that both fluids are incompressible. The easiest way to account for the compressibility is to allow the density of the air to vary in time. This solution has been adopted for example by Caiden et al. (2001). It gives reliable results but faces some computational challenges connected with the coupling of the two different fluids. Most of all, the numerical time step of the simulations is fixed by the speed of sound in the lighter fluid. This represents a significant limitation. The technique shown here aims to avoid the computational effort due to the description of the compressibility waves in the air medium. The pressure oscillations inside the bubble are assumed related only to the change in volume of the bubble and the pressure is taken uniform in the gas, and therefore calculated through the polytropic equation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
