Mathematical Basis and Validation of the Full Cavitation Model

TLDR

Cavitating flows involve phase change that produces large density variations in low‑pressure regions and are highly sensitive to bubble dynamics, turbulence, and noncondensable gas content. The authors present a full cavitation model that incorporates these first‑order effects and outline extensions to nonisothermal flows, gas ingestion, noise, and surface‑damage predictions. The model derives phase‑change rates from a reduced Rayleigh‑Plesset equation, depends on local pressure, velocity, turbulence, and fluid properties, uses two empirically calibrated constants, and is implemented in CFD‑ACE+. Validation demonstrates the model accurately predicts cavitation around hydrofoils, submerged cylinders, and sharp‑edged orifices.

Abstract

Cavitating flows entail phase change and hence very large and steep density variations in the low pressure regions. These are also very sensitive to: (a) the formation and transport of vapor bubbles, (b) the turbulent fluctuations of pressure and velocity, and (c) the magnitude of noncondensible gases, which are dissolved or ingested in the operating liquid. The presented cavitation model accounts for all these first-order effects, and thus is named as the “full cavitation model.” The phase-change rate expressions are derived from a reduced form of Rayleigh-Plesset equation for bubble dynamics. These rates depend upon local flow conditions (pressure, velocities, turbulence) as well as fluid properties (saturation pressure, densities, and surface tension). The rate expressions employ two empirical constants, which have been calibrated with experimental data covering a very wide range of flow conditions, and do not require adjustments for different problems. The model has been implemented in an advanced, commercial, general-purpose CFD code, CFD-ACE+. Final validation results are presented for flows over hydrofoils, submerged cylindrical bodies, and sharp-edged orifices. Suggestions for possible extensions of the model implementation, e.g., to nonisothermal flows, for ingestion and mixing of noncondensible gases, and for predictions of noise and surface damage are outlined.