Finite Mass Transfer Effects in Cavitation Modelling
Author Schenke, S. and Terwisga, T.J.C. van
Title Finite Mass Transfer Effects in Cavitation Modelling
Conference/Journal 19th Numerical Towing Tank Symposium (NuTTS), St. Pierre d'Oléron, France
Month October
Year 2016

Abstract
The prediction of cavitation is of large interest for the design of ship propellers. Cavitation influences the propeller efficiency and causes undesired phenomena such as noise, vibrations and erosion. While potential flow solvers are routinely used for propeller design, viscous CFD calculations are used when a higher fidelity is needed. Within a finite volume framework, the flow domain is subdivided into grid cells and the governing equations are solved numerically in every cell. Essentially two approaches are possible to discretise the domain, with structured or unstructured meshes. In the former case, it is always possible to construct a mapping function between the physical grid and a uniform cartesian grid. In the unstructured mesh there is not such a correspondence. A structured mesh is easier to handle for a numerical solver, but for complex geometries it becomes difficult to generate. The size and quality of the mesh affect the quality of the flow solution. The objective of this work is to evaluate the effect of two different grid types when they are used to simulate cavitating flow using an unsteady Reynolds averaged Navier-Stokes (RANS) solver. The test case chosen is a 2D NACA0015 profile at 6 degrees angle of attack, confined in a water tunnel. Many numerical studies on the same test case are found in literature, e.g. Hoekstra (2011), Yakubov et al. (2015), and experimental tests, Arndt et al. (2000). After some preliminary wetted flow computations, which aim to investigate the numerical uncertainty, the maiOne of the key aspects classifying the various approaches in numerical simulation of cavitating flows is the equilibrium flow assumption. It states that internal processes in the flow always occur instantaneously compared to the time scale of the flow (s. Sezal (2009)). As a consequence, the density-pressure trajectory in a barotropic flow may follow a unique curve. Contrary to the equilibrium flow assumption, one may assume that the time to achieve a new state is governed by the magnitude of a finite mass transfer source term in a volume fraction transport equation (s. Asnaghi et al. (2015)). In this case, the set of possible density-pressure states is not predefined, but strongly depends on the rate at which pressure changes. Although it has been pointed out by Koukouvinis and Gavaises (2015) that the equilibrium assumption for a barotropic flow would theoretically be mimicked by the mass transfer model if the finite transfer rate tended to infinity, the model parameters triggering the finite transfer rate are generally considered as empirical (s. Frikha et al. (2008)).
In this paper, effects of the finite mass transfer rate with special focus on condensation will be studied in detail. First, a cavity collapse will be considered to demonstrate how the finite transfer source term must be modified to satisfy the equilibrium flow assumption. Second, a single bubble collapse is studied numerically and effects of the finite mass transfer rate will be discussed.n part of this work is a comparison of cavitating flow dynamics predicted with a structured and an unstructured mesh.

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