Rayleigh–Plesset-based Eulerian mixture model for cavitating flows

Abstract

The homogeneous mixture model (HMM) is widely in use for simulation of cavitating flows. The mass transfer is typically ruled by simplified models whose efficiency is strictly dependent on the empirical choice of vaporization/condensation constants. In the present paper, we formulate a physically based mass-transfer model relying on the solution of the complete Rayleigh–Plesset (RP) equation. The latter can model the elasticity of the bubbles and non-linear interaction with the external pressure field. The model is tested in different configurations, also considering comparisons with the Schnerr–Sauer model (SSm) and the linearized version of the RP equation. The preliminary simplified tests show that the SS model responds statically to pressure variations and thus in not able to reproduce the actual dynamics of cavitation, under certain circumstances. On the other hand, the linearized RP model (RPl), although dynamically responsive to pressure variations, produces unrealistic small-amplitude bubble fluctuations, whereas the complete RP model (RPc) gives more realistic results. Tests on the performance of the SSm and RP models were carried out considering the turbulent flow in a convergent–divergent Venturi channel, already tested in numerical and experimental reference research. Here, we use the incompressible HMM. The study highlights various crucial aspects of the RPc model, emphasizing its own ability in replicating the shedding cycle as a three-dimensional, and non-stationary phenomenon. On the other hand, the SSm model results as a valid approximation for initial growth stages but fails to capture complex dynamics during the collapse phase. The results are consistent with recent literature findings, and refinements in grid resolution enhance accuracy in capturing the non-stationary sheet-to-cloud vapor dynamics. Neglecting compressibility may account for disparities between numerical and experimental outcomes, especially concerning shock waves generation and propagation. The RPc model emerges as a good candidate in reproducing bubble cloud dynamics and, in the next future, can be implemented in compressible HMM.