Commun. Comput. Phys., 14 (2013), pp. 328-354.


Simulation of Wave-Flow-Cavitation Interaction Using a Compressible Homogenous Flow Method

J. G. Zheng 1, B. C. Khoo 2*, Z. M. Hu 3

1 Department of Mechanical Engineering, National University of Singapore, Singapore 119260.
2 Department of Mechanical Engineering, National University of Singapore, Singapore 119260; Singapore-MIT Alliance, National University of Singapore, Singapore 117576; and Temasek Laboratories, National University of Singapore, Singapore 117411.
3 Temasek Laboratories, National University of Singapore, Singapore 117411.

Received 5 April 2012; Accepted (in revised version) 14 August 2012
Available online 27 November 2012
doi:10.4208/cicp.050412.140812a

Abstract

A numerical method based on a homogeneous single-phase flow model is presented to simulate the interaction between pressure wave and flow cavitation. To account for compressibility effects of liquid water, cavitating flow is assumed to be compressible and governed by time-dependent Euler equations with proper equation of state (EOS). The isentropic one-fluid formulation is employed to model the cavitation inception and evolution, while pure liquid phase is modeled by Tait equation of state. Because of large stiffness of Tait EOS and great variation of sound speed in flow field, some of conventional compressible gasdynamics solvers are unstable and even not applicable when extended to calculation of flow cavitation. To overcome the difficulties, a Godunov-type, cell-centered finite volume method is generalized to numerically integrate the governing equations on triangular mesh. The boundary is treated specially to ensure stability of the approach. The method proves to be stable, robust, accurate, time-efficient and oscillation-free. Novel numerical experiments are designed to investigate unsteady dynamics of the cavitating flow impacted by pressure wave, which is of great interest in engineering applications but has not been studied systematically so far. Numerical simulation indicates that cavity over cylinder can be induced to collapse if the object is accelerated suddenly and extremely high pressure pulse results almost instantaneously. This, however, may be avoided by changing the traveling speed smoothly. The accompanying huge pressure increase may damage underwater devices. However, cavity formed at relatively high upstream speed may be less distorted or affected by shock wave and can recover fully from the initial deformation. It is observed that the cavitating flow starting from a higher freestream velocity is more stable and more resilient with respect to perturbation than the flow with lower background speed. These findings may shed some light on how to control cavitation development to avoid possible damage to operating devices.

AMS subject classifications: 35L40, 65M08, 65M22, 76T10

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Key words: Cavitating flow, isentropic cavitation model, shock-flow-cavitation interaction.

*Corresponding author.
Email: mpezhen@nus.edu.sg (J. G. Zheng), mpekbc@nus.edu.sg (B. C. Khoo), huzm@imech.ac.cn (Z. M. Hu)
 

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