Keywords: sheet cavitation, unsteady cavitation model, boundary element method, panel method, potential theory, propeller flow.

In this paper a three-dimensional potential based boundary element method for the computation of unsteady sheet cavitation on marine propellers is presented. The governing equations are derived from Laplace's equation combined with appropriate boundary conditions on the body and cavity surface. The continuous equations are discretised and solved numerically by means of a three-dimensional panel method [1]. Panel methods are widely spread in propeller design as a result of their short computation time which enables parameter studies within a wider range compared for example to viscous flow solvers.

The present study focuses on the implementation of a reliable unsteady sheet cavitation model in the in-house simulation tool panMARE [2]. panMARE is a command-driven programme developed for the simulation of arbitrary potential flows. The development of an efficient numerical scheme for the calculation of sheet cavitation is motivated by the difficulties which can occur when a liquid is subjected to high propeller rotational speed near a free water surface. The high number of revolutions can cause rapid pressure reductions in the flow which can lead to formation of cavitation. Cavitation is a physical effect where the pressure falls below the vapour pressure such that a vapour region or vapour bubbles develop in the flow. Cavitation can lead to material damage or cause vibration on the ship hull. In the present study only the modelling of sheet cavitation is considered, other forms of cavitation such as bubble cavitation or tip vortex cavitation are not addressed.

The most relevant features of the unsteady sheet cavitation model are described in the first part of the paper. Hereby, the physical boundary conditions as well as the specifics in dealing with unsteady terms in the cavitation model are discussed and a solution algorithm for an accurate prediction of the cavity length and thickness is outlined.

In the second part of the paper the abilities of the numerical method developed are demonstrated for a three-dimensional wing and for a marine propeller flow under cavitating conditions. Additionally, the results obtained using panMARE are compared to results obtained by other authors, e.g. published in [3].

1

J. Katz, A. Plotkin, "Low-Speed Aerodynamics", Cambridge University Press, Cambridge, 2001.

2

M. Bauer, M. Abdel-Maksoud, "A 3-D Potential Based Boundary Element Method for the Modelling and Simulation of Marine Propeller Flows", 7th Vienna Conference on Mathematical Modelling, Vienna, Austria, 2012.

3

S. Phoemsapthawee, J.-B. Leroux, J.-M. Laurens, F. Deniset, "A Transpiration Velocities Based Sheet Cavitation Model", Ship Technology Reasearch, 56, 191-176, 2009.

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