A dual-time implicit preconditioned Navier-Stokes method for solving 2D steady/unsteady laminar cavitating/noncavitating flows using a Barotropic model

A two-dimensional, time-accurate, homogeneous multiphase, preconditioned Navier-Stokes method is applied to solve steady and unsteady cavitating laminar flows over 2D hydrofoils. A cell-centered finite-volume scheme employing the suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the multiphase Navier-Stokes equations. This numerical resolution is coupled to a single-fluid model of cavitation that the evolution of the density is governed by a barotropic sate law. A preconditioning strategy is used to prevent the system of equations to be stiff. A dual-time implicit procedure is applied for time accurate computation of unsteady cavitating flows. A sensitivity study is conducted to evaluate the effects of various parameters such as numerical dissipation coefficients and preconditioning on the accuracy and performance of the solution. The computations are presented for steady and unsteady laminar cavitating flows around the NACA0012 hydrofoil for different conditions. The solution procedure presented is shown to be accurate and efficient for predicting steady/unsteady laminar cavitating/noncavitating flows over 2D hydrofoils. INTRODUCTION Cavitation can occur in a wide range of flows and this physical process is of particular interest for studying marine propellers, water crafts, turbine blades and low speed centrifugal pumps. This phenomenon strongly affects the flow field, the neighbouring structures and it plays an important role in the design of hydrodynamic machines. Several physical and numerical models have been developed to investigate steady cavitating flows. The reason for the absence of a more detailed explanation of the physics of cavitation is, of course, the need for a discussion of the unsteady viscous cavitating flow phenomena. The shape and collapse of the vapor structures usually fluctuate in time and this unstable behavior causes to be important for understanding of unsteady two-phase flow structure of cavitation. Most studies for unsteady cavitating flows known in the literatures are performed for turbulent flows, and a little work can be found for laminar flows. The lift disintegration is a major flow feature in cavitating flows and is due to the increased bubble size on the hydrofoil. Since the lift and especially drag calculations depend on viscous effects, thus the choice of turbulence model has a strong impact on the results. There is no widely acceptable turbulence model that can handle the uncertainties of unsteady cavitating two-phase flows. Inspection of the studies on laminar cavitating flows making it possible to model cavitation behavior in a physically more realistic manner. A numerical analysis of cavitating flow of viscous fluid is a challenging computational problem. In fact, one has to deal with localized large variations of density which are present within a predominantly incompressible liquid medium, interactions between phases, turbulence, irregularly shaped interfaces, compressibility effects and the stiffness in the numerical model. A number of different approaches have been developed to investigate cavitation numerically. Kueny et al. [1] described the vapor/liquid interface as a stream sheet at constant static pressure equal to the vapor pressure and simulated the steady sheet cavitation. Kubota et al. [2] described the behavior of small gas bubbles in the fluid by the Rayleigh-Plesset equation with the changing pressure field. Delannoy and Kueny [3] assumed that the liquid and gas phases are represented by a single continuous equation of state that strongly links the mixture density to the static pressure. This barotropic flow model has been applied by Song et al. [5] and