Stabilized formulation for phase-transforming flows with special emphasis on cavitation inception

Abstract

Despite significant advancement in the field of cavitation, the inception of vapor bubbles from pure liquid is still not well understood. In this paper, we propose a numerical algorithm to solve the Navier–Stokes–Korteweg equations, which are phase-field equations that govern the dynamics of multiphase compressible flows. These equations can predict cavitation inception without phenomenological assumptions about mass transfer. We present a modification to the bulk free energy of the fluid that can help us simulate cavitation at much larger length scales than previously possible. We propose a numerical scheme based on a Taylor–Galerkin discretization, a residual-based discontinuity capturing operator and a spatial filtering scheme. Our numerical method can be used for high speed flows with large pressure gradients, which are distinctive features of flows where we observe cavitation inception. We present numerical examples that show the accuracy, stability and robustness of our scheme. Finally, we use the proposed numerical scheme to study benchmark problems in the field of cavitation inception such as flow past a wedge and flow past a bluff body. The proposed numerical scheme opens opportunities to understand different aspects of cavitation in general and inception in particular, in much more detail.