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

Published online by Cambridge University Press:  03 June 2015

J. G. Zheng ,
B. C. Khoo  and
Z. M. Hu
J. G. Zheng*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Singapore 119260
B. C. Khoo*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Singapore 119260 Singapore-MIT Alliance, National University of Singapore, Singapore 117576 Temasek Laboratories, National University of Singapore, Singapore 117411
Z. M. Hu*
Affiliation:
Temasek Laboratories, National University of Singapore, Singapore 117411
*
Corresponding author.Email:mpekbc@nus.edu.
Email:mpezhen@nus.edu.sg
Email:huzm@imech.ac.en
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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.

Keywords

35L4065M0865M2276T10Cavitating flowisentropic cavitation modelshock-flow-cavitation interaction

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 2 , August 2013 , pp. 328 - 354
Copyright
Copyright © Global Science Press Limited 2013

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References

[1]Schmidt, D. P., Rutland, C. J. and Corradini, M. L., A fully compressible two-dimensional model of small high speed cavitating nozzles, Atomization Sprays, 9 (1999), 255–276.Google Scholar
[2]Liu, T. G., Khoo, B. C. and Xie, W. F., Isentropic one-fluid modeling of unsteady cavitating flow, J. Comput. Phys., 201 (2004), 80–108.Google Scholar
[3]Neaves, M. D. and Edwards, J. R., All-speed time-accurate underwater projectile calculations using a preconditioning algorithm, J. Fluids Eng., 128 (2006), 284–296.Google Scholar
[4]Hrubes, J. D., High-speed imaging of supercavitating underwater projectiles, Exp. Fluids, 30 (2001), 57–64.Google Scholar
[5]Goncalves, E. and Patella, R. F., Numerical simulation of cavitating flows with homogenous models, Comput. Fluids, 38 (2009), 1682–1696.CrossRefGoogle Scholar
[6]Goncalves, E. and Patella, R. F., Numerical study of cavitating flows with thermodynamic effect, Comput. Fluids, (39) 2010, 99–113.CrossRefGoogle Scholar
[7]Hu, Z. M., Dou, H. S. and Khoo, B. C., On the modified dispersion-controlled dissipative (DCD) scheme for computation of flow supercavitation, Comput. Fluids, 40 (2011), 315–323.CrossRefGoogle Scholar
[8]Toro, E. F., Riemann solvers and numerical methods for fluid Dynamics: a practical introduction, Springer-Verlag, Berlin Heidelberg, 1999.Google Scholar
[9]Blazek, J., Computational fluid dynamics: principles and applications, ELSEVIER, 2001.Google Scholar
[10]Leer, B. van, Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov’s method, J. Comput. Phys., 32 (1979), 101–136.Google Scholar
[11]Barth, T. J. and Jespersen, D. C., The design and application of upwind schemes on unstructured meshes, AIAA Report, (1989), 89–0366.Google Scholar
[12]Mavriplis, D. J., Revisiting the least-squares procedures for gradient reconstruction on unstructured meshs, in: Proceedings of the 16th AIAA Computational Fluid Dynamics Conference, Orlando, FL, AIAA Paper, (2003), 2003–3986.Google Scholar
[13]Balakrishnan, N. and Fernandez, G., Wall boundary conditions for inviscid compressible flows on unstructured meshes, Int. J. Numer. Methods Fluids, 28 (1998), 1481–1501.3.0.CO;2-B>CrossRefGoogle Scholar
[14]Park, J. S., Yoon, S. H. and Kim, C., Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids, J. Comput. Phys., 229 (2010), 788–812.Google Scholar
[15]Nikolos, I. K. and Delis, A. I., An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography, Comput. Meth. Appl. Mech. Eng., 198 (2009), 3723–3750.Google Scholar
[16]Delis, A. I., Nikolos, I. K. and Kazolea, M., Performance and comparison of cell-centered and node-centered unstructured finite volume discretizations for shallow water free surface flows, Arch. Comput. Meth. Eng., 18(1) (2011), 1–62.Google Scholar
[17]Shu, C. W. and Osher, S., Efficient implementation of essentially non-oscillatory shock capturing schemes, J. Comput. Phys., 77 (1988), 439–471.CrossRefGoogle Scholar
[18]Tang, H. S. and Huang, D., A second-order accurate capturing scheme for 1D inviscid flows of gas and water with vacuum zones, J. Comput. Phys., 128 (1996), 301–318.Google Scholar
[19]Hu, Z. M., Khoo, B. C. and Zheng, J. G., The simulation of unsteady cavitating flows with external perturbations, submitted for publication in 2011.Google Scholar
[20]Grady, R. J., Hydroballistics design handbook, Vol I, Naval Sea Systems Command, Technical Report No, SEAHAC/79-1, (1979), 38–45.Google Scholar
[21]Xie, W. F., Liu, T. G. and Khoo, B. C., Application of a one-fluid model for large scale homogeneous unsteady cavitation: The modified Schmidt model, Comput. Fluids, 35 (2006), 1177–1192.CrossRefGoogle Scholar
[22]Zhu, J., Liu, T. G., Qiu, J. X. and Khoo, B. C., RKDG methods with WENO limiters for unsteady cavitating flow, Comput. Fluids. 57 (2012), 52–65.CrossRefGoogle Scholar
[23]Delgosha, O. C., Patella, R. F., Reboud, J. L., Hakimi, N. and Hirsch, C., Numerical simulation of cavitating flow in 2D and 3D inducer geometries, Int. J. Numer. Methods Fluids, 48 (2005),135–167.Google Scholar
[24]Wallis, G. B., One-dimensional two-phase flow, New York: McGill-Hill, 1969.Google Scholar
[25]Leer, B. van, Upwind and High-Resolution Methods for Compressible Flow: From Donor Cell to Residual-Distribution Schemes, Commun. Comput. Phys., 1(2) (2006), 192–206.Google Scholar
[26]Saurel, R., Petitpas, F. and Berry, R. A., Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, J. Comput. Phys., (228) 2009, 1678–1712.Google Scholar
[27]Kunz, R. F., Boger, D. A. and Stinebring, D. R., A preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction, Comput. Fluids, 29 (2000), 849–875.Google Scholar