A ROBUST NUMERICAL METHODOLOGY FOR STEADY-STATE CAVITATING FLOWS

Abstract

Modeling of cavitation is critical for the design of centrifugal pumps, marine propellers, and fuel injectors. Cavitating flows often exhibit transient characteristics due to the sudden growth and collapse of vapor cavities. A numerically robust steady-state approach can provide quick analysis with reasonable accuracy saving significant simulation time as compared to transient simulations. As we demonstrate in this paper, the effective steady-state modeling of cavitating flow is strongly governed by several key factors, such as mesh resolution, pressure velocity coupling, pseudo-transient method, and initialization techniques along with the linearization of mass transfer terms and the inclusion of turbulence diffusion treatment. The pseudo-transient method improves numerical robustness of steady-state simulations by improving diagonal dominance and providing a local under-relaxation based on a pseudo-time-step size. The coupled approach of solving continuity and momentum equations, the linearization of mass transfer source terms, and the modeling of turbulent diffusion play an important role in the solution stability and faster convergence. A hybrid initialization technique provides start-up stability by solving Laplace equations for pressure and velocity. The Zwart-Gerber-Belamri cavitation model, which originates from the simplification of Rayleigh-Plesset equation, is chosen for simulating cavitating flow within a homogeneous mixture multiphase framework. A highly resolved mesh has been used in the cavitating region to obtain accurate results. In addition, an overset mesh has also been used to demonstrate the ease of mesh generation and parametrization in complex geometries. The aforementioned methods are utilized in two different simulations: (i) flow in a cavitating orifice and (ii) flow in a fuel injector. A realistic evolution of the cavitation cloud in the first case and the inception of the classic "hydraulic flip" in the second clearly demonstrate the robust nature of the numerical method and its ability to accurately capture complex multiphase flow and mass transfer.