Cavitation Modeling Using Lumped Parameter Approach Accounting for Bubble Dynamics and Mass Transport Through the Bubble Interface

Vaporous and gaseous cavitation cause several physical phenomena which are typically undesirable, such as reduction in compressibility and material damage. Therefore, the ability to capture these effects in simulation is highly valued. In the fluid power field, lumped parameter modeling technique has proven effective for analyzing components and systems, allowing for fast simulations. Past efforts in modeling cavitation using lumped parameter approach have assumed dependence of fluid properties such as bulk modulus, density, and viscosity directly to pressure and temperature. This cannot be considered as the fluid mixture is composed of different phases of matter. Some other formulations account for gaseous cavitation based on the equations that are derived from vaporous cavitation. This paper illustrates a better approach that combines the two cavitation effects by considering that both vapor and undissolved gas co-occupy a spherical bubble. The size of the spherical bubble is solved using the Rayleigh–Plesset equation, and the transfer of gas through the bubble interface is solved using Henry's law and diffusion of the dissolved gas in the liquid. These equations are coupled with a novel pressure derivative equation. To show the validity of the proposed approach, the instantaneous pressure of a closed fluid volume undergoing expansion/compression is compared with multiple experimental sources, showing an improvement in accuracy when compared to existing models. Integrating this modeling technique with current displacement chamber simulation can further improve the understanding of cavitation in hydraulic systems.