Application of the Wray-Agarwal turbulence model in the numerical simulation of unsteady cavitation around a three-dimensional hydrofoil

Abstract

This research investigates the performance of the Wray-Agarwal (WA) one-equation turbulence model for simulating multiphase flows, particularly focusing on cloud cavitation around a three-dimensional Clark-Y hydrofoil. Using unsteady Reynolds-Averaged Navier-Stokes (RANS) equations, numerical simulations with three different turbulence models—WA, k-ω, and Shear Stress Transport (SST) k-ω—are compared to experimental results. The comparison highlights key aspects such as hydrodynamic behavior, cavitation periodicity, and the interactions between cavitation and vortex structures. The WA model consistently demonstrates improved alignment with experimental data, showing smaller error margins than both k-ω and SST k-ω models, and effectively predicting the cyclical nature of cavitation. Analysis of vortex behavior through the Q-criterion and vorticity transport equation reveals that changes in vorticity are strongly influenced by the shape and dynamics of the cavity, with vortex stretching and volumetric expansion/contraction playing significant roles in the observed fluctuations. The interaction between the re-entrant jet and main flow is identified as the critical factor initiating sheet cavitation shedding, leading to the formation of cloud cavitation. These findings underscore the WA model’s effectiveness in accurately modeling cavitating flows and deepen the understanding of cavitation mechanisms.