Simulating Cavitation Bubble Dynamics: Acoustic Interactions and Characterization of the Onset of Cavitation

This project deals with two topics associated with low-order cavitation modeling. First, a new model accounting for time-delayed acoustic interactions in bubble clusters is proposed, based upon the quasi-acoustic assumption. This assumption takes into account the compressibility of the liquid and its finite speed of sound and is accurate up to the first order of the Mach number. A consistent set of equations representing the radial dynamics, acoustic emissions and interactions of cavitation bubbles is derived. To validate its relevancy, a selection of representative test cases involving systems of few interacting bubbles or dense mono-or polydisperse bubble clusters subjected to pressure changes is proposed. On the one hand, results are in excellent agreement with previously reported characteristic dynamics of interacting bubble systems, like for instance the strong influence of larger bubbles on smaller neighbors. On the other hand, noticeable differences with the commonly used instantaneous interaction models are found in the cases of large and dense bubble clusters. These differences are a consequence of a competition between the characteristic period of the excitation and the characteristic time of propagation of the radiated pressure waves through the whole bubble system, leading to richer and more intricate global dynamics. The second topic consists of the proposal of a standardized methodology designed to characterize the pressure conditions that allow cavitation onset. Cavitation onset is here defined as an unstable state in which the bubble radius expands quickly without bound when the liquid is sufficiently put into tension, i.e., its pressure is negative. The methodology relies on a dynamical threshold called the unstable equilibrium radius to determine if cavitation onset occurs. The unstable equilibrium radius varies in time and is dependent of the intrinsic properties of the gas-liquid system. Considering two representative transient pressure fields, a sudden pressure drop resulting in a constant tension and a single tension pulse, a dimensionless framework is constructed. The framework is based upon timescales representing the physical properties involved in the bubble radius evolution, i.e., inertia, viscosity and surface tension, the characteristic time duration of the transient pressure fields and the Blake threshold, a quasi-static cavitation onset pressure threshold. For a single isolated bubble, the Blake threshold is an upper bound limit of the critical tension for the sudden pressure drop while it is a lower bound limit for the single tension pulse. In both scenarios, the critical tension converges towards the Blake threshold as the duration of the pressure change increases. When accounting for the radiated pressure waves emitted by a larger neighbor bubble, the critical tension for cavitation onset increases compared to the single-bubble case. This increases is stronger as the neighbor is close to the bubble of interest and becomes larger.