Commun. Comput. Phys.,
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Volume 4.


A Preliminary Calculation of Three-Dimensional Unsteady Underwater Cavitating Flows Near Incompressible Limit

Yang-Yao Niu 1*, Wei-Yuan Hsu 1

1 Department of Mechanical Engineering, Chung-Hua University, Hsin-Chu, Taiwan, 30067, ROC.

Received 9 October 2007; Accepted (in revised version) 10 December 2007
Available online 29 May 2008

Abstract

Recently, cavitated flows over underwater submerged bodies have attracted researchers to simulate large scale cavitation. Comparatively Computational Fluid Dynamics (CFD) approaches have been used widely and successfully to model developed cavitation. However, it is still a great challenge to accurately predict cavitated flow phenomena associated with interface capturing, viscous effects, unsteadiness and three-dimensionality. In this study, we consider the preconditioned three-dimensional multiphase Navier-Stokes equations comprised of the mixture density, mixture momentum and constituent volume fraction equations. A dual-time implicit formulation with LU Decomposition is employed to accommodate the inherently unsteady physics. Also, we adopt the Roe flux splitting method to deal with flux discretization in space. Moreover, time-derivative preconditioning is used to ensure well-conditioned eigenvalues of the high density ratio two-phase flow system to achieve computational efficiency. Validation cases include an unsteady 3-D cylindrical headform cavitated flow and an 2-D convergent-divergent nozzle channel cavity-problem.

AMS subject classifications: 76B10, 76D05, 65M10

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Key words: Cavitation, incompressible, Roe Riemann solver, dual-time stepping.

*Corresponding author.
Email: yniu@chu.edu.tw (Y.-Y. Niu), m09408021@chu.edu.tw (W.-Y. Hsu)
 

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