Abstract
The unsteady cavitation evolution around the Clark-Y hydrofoil is investigated in this paper, by using an improved filter-base model (FBM) with the density correction method (DCM). To improve the prediction accuracy, the filter scale is adjusted based on the grid size. The numerical results show that a small filter scale is crucial for the unsteady simulations of the cavity shedding flow. The hybrid method that combines the FBM and the DCM could help to limit the overprediction of the turbulent viscosity in the cavitation region on the wall of the hydrofoil and in the wake. The large value of the maximum density ratio, ρl/ρv, clip promotes the mass transfer rate between the liquid phase and the vapor phase, which results in a large sheet cavity length and the vapor fraction rise inside the cavity. The cavity patterns predicted by the improved method are verified by the experimental visualizations. The time-average lift, the drag coefficient and the primary oscillating frequency St for the cavitation number σ = 0.8, the angle of attack, α=8α, at a Reynolds number Re = 7×10 are 0.735, 0.115 and 0.183, respectively, and the predicted errors are 3.29%, 3.36% and 8.93%. The typical three stages in one revolution are well-captured, including the initiation of the sheet/attached cavity, the growth toward the trailing edge (TE) with the development of the re-entrant jet flow, and the large scale cloud cavity shedding. It is observed that the cloud cavity shedding flow induces the vortex pairs of the TE vortices in the wake and the shedding vortices. The positive vorticity vortex of the re-entrant jet and the TE vortices interacts and merges with the negative vorticity vortex of the leading edge (LE) cavity to produce the shedding flow.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
BRENNEN C. E. Cavitation and bubble dynamics[M]. New York, USA: Cambridge University Press, 2013.
BRENNEN C. E. Hydrodynamics of pumps[M]. New York, USA: Cambridge University Press, 2011.
WANG G., SENOCAK I. and SHYY W. et al. Dynamics of attached turbulent cavitating flows[J]. Progress in Aerospace Sciences, 2001, 37(6): 551–581.
MATSUNARI H. Experimental/numerical study on cavitating flow around clark Y 11.7% hydrofoil[C]. Proceedings of the 8th International Sympositm on Cavitation, (CAV 2012). Singapore, 2012.
LEROUX J.-B., ASTOLFI J. A. and BILLARD J. Y. An experimental study of unsteady partial cavitation[J]. Journal of Fluids Engineering, 2004, 126(1): 94–101.
LEROUX J.-B., COUTIER-DELGOSHA O. and ASTOLFI J. A. A joint experimental and numerical study of mechanisms associated to instability of partial cavitation on two-dimensional hydrofoil[J]. Physics of Fluids, 2005, 17(5): 052101.
CALLENAERE M., FRANC J.-P. and MICHEL J. et al. The cavitation instability induced by the development of a re-entrant jet[J]. Journal of Fluid Mechanics, 2001, 444: 223–256.
COUTIER-DELGOSHA O., STUTZ B. and VABRE A. et al. Analysis of cavitating flow structure by experimental and numerical investigations[J]. Journal of Fluid Mechanics, 2007, 578: 171–222.
COUTIER-DELGOSHA O., REBOUD J. and DELANNOY Y. Numerical simulation of the unsteady behaviour of cavitating flows[J]. International Journal for Numerical Methods in Fluids, 2003, 42(5): 527–548.
GIRIMAJI S. S. Partially-averaged navier-stokes model for turbulence: A reynolds-averaged navier-stokes to direct numerical simulation bridging method[J]. Journal of Applied Mechanics, 2006, 73(3): 413–421.
GIRIMAJI S. S., ABDOL-HAMID K. S. Partially–averaged Navier-Stokes model for turbulence: Implementation and validation[R]. AIAA paper 502(2005), 2005.
JI B., LUO X. and WU Y. et al. Numerical analysis of unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoil[J]. International Journal of Multiphase Flow, 2013, 51: 33–43.
JOHANSEN S. T., WU J. and SHYY W. Filter-based unsteady rans computations[J]. International Journal of Heat and fluid flow, 2004, 25(1): 10–21.
SCHUMANN U. Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli[J]. Journal of Computational Physics, 1975, 18(4): 376–404.
ZWART P. J., GERBER A. G. and BELAMRI T. A two-phase flow model for predicting cavitation dynamics[C]. Fifth International Conference on Multiphase Flow. Yokohama, Japan, 2004.
REBOUD J., COUTIER-DELGOSHA O. and POUFFARY B. et al. Numerical simulation of unsteady cavitating flows: Some applications and open problems[C]. Fifth International Symposium on Cavitation. Osaka, Japan, 2003.
DULAR M., BACHERT R. and STOFFEL B. et al. Experimental evaluation of numerical simulation of cavitating flow around hydrofoil[J]. European Journal of Mechanics-B/Fluids, 2005, 24(4): 522–538.
HUANG Biao, WANG Guo-yu. Evaluation of a filter-based model for computations of cavitating flows[J]. Chinese Physics Letters, 2011, 28(2): 026401.
LUO X., JI B. and PENG X. et al. Numerical simulation of cavity shedding from a three-dimensional twisted hydrofoil and induced pressure fluctuation by large-eddy simulation[J]. Journal of Fluids Engineering, 2012, 134(4): 041202.
MORGUT M., NOBILE E. Numerical predictions of cavitating flow around model scale propellers by CFD and advanced model calibration[J]. International Journal of Rotating Machinery, 2012, (2012): 1–11.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Grant Nos. 51479083, 51579118) the Key Research and Development Project of Jiangsu Province (Grant No. BE2015001-3).
Biography: ZHANG De-sheng (1982-), Male, Ph. D., Associate Professor
Rights and permissions
About this article
Cite this article
Zhang, Ds., Wang, Hy., Shi, Wd. et al. Numerical analysis of the unsteady behavior of cloud cavitation around a hydrofoil based on an improved filter-based model. J Hydrodyn 27, 795–808 (2015). https://doi.org/10.1016/S1001-6058(15)60541-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S1001-6058(15)60541-8