Abstract
Unsteady cavitating turbulent flow around a twisted hydrofoil was analyzed to illustrate the physical mechanism of the cavitygenerated pressure fluctuations. The numerical simulations of cavitating flow were based on the Partially-Averaged Navier-Stokes (PANS) method and a mass transfer cavitation model. The validity of PANS model has been evaluated and confirmed in cavitation simulations by present authors using three different cases, 2D hydrofoil (Ji et al. 2012 [37]), 3D hydrofoil (Ji et al. 2013 [31]) and marine propeller (Ji et al. 2012 [38]), which shows that the PANS model with f k = 0.2 and f ε = 1 can obtain more accurate estimates of unsteady cavitating flows with large-scale fluctuations at a reasonable cost. In present paper we intended to shed light on the physical process responsible for the pressure fluctuations excited by cavitation. The cavity volume was analyzed to illustrate the relationship between the cavitation evolution and the pressure fluctuations. The results show that the cavity volumetric acceleration curve tracks remarkably well with the main features of the time-dependent pressure fluctuations except for the high frequency component. Thus, the cavity volumetric acceleration is the main source of the excited pressure fluctuations by cavitation. It is noted that the cavitation induced pressure fluctuations are transmitted along the suction surface of the hydrofoil and are synchronized with those on the pressure surface at the midplane of the twisted hydrofoil. Further, the pressure fluctuations on the pressure surface decrease towards the center from both the leading and trailing edges of the hydrofoil, with a minimum at 60% chord length from the leading edge.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. E. A. Arndt, Cavitation in vortical flows, Annual Review of Fluid Mechanics, 34 (2002) 143–175.
Y. L. Wu, S. C. Li, S. H. Liu, H. S. Dou and Z. D. Qian, Vibration of Hydraulic Machinery, Springer, Berlin (2013).
Y. Tsujimoto, S. Watanabe and H. Horiguchi, Cavitation Instabilities of Hydrofoils and Cascades, International Journal of Fluid Machinery and Systems, 1 (1) (2008) 38–46.
A. Kubota, H. Kato and H. Yamaguchi, A new modeling of cavitating flows-a numerical study of unsteady cavitation on a hydrofoil section, Journal of Fluid Mechanics, 240 (1992) 59–96.
S. Gopalan and J. Katz, Flow structure and modeling issues in the closure region of attached cavitation, Physics of Fluids, 12 (4) (2000) 895–911.
M. Callenaere, J. P. Franc, J. M. Michel and M. Riondet, The cavitation instability induced by the development of a reentrant jet, Journal of Fluid Mechanics, 444 (2001) 223–256.
X. B. Zhang, L. M. Qiu, H. Qi, X. J. Zhang and Z. H. Gan, Modeling liquid hydrogen cavitating flow with the full cavitation model, International Journal of Hydrogen Energy, 33 (23) (2008) 7197–7206.
B. Huang and G. Y. Wang, Evaluation of a filter-based model for computations of cavitating flows, Chinese Physics Letters, 28 (2) (2011) 026401.
H. Sun, Numerical study of hydrofoil geometry effect on cavitating flow, Journal of Mechanical Science and Technology, 26 (8) (2012) 2535–2545.
J. Decaix and E. Goncalves, Compressible effects modeling in turbulent cavitating flows, European Journal of Mechanics B-Fluids, 39 (2013) 11–31.
H. L. Liu, Y. Wang, D. X. Liu, S. Q. Yuan and J. Wang, Assessment of a turbulence model for numerical predictions of sheet-cavitating flows in centrifugal pumps, Journal of Mechanical Science and Technology, 27 (9) (2013) 2743–2750.
M. S. Jin, C. T. Ha and W. G. Park, Numerical study of ventilated cavitating flows with free surface effects, Journal of Mechanical Science and Technology, 27 (12) (2013) 3683–3691.
D. F. De Lange and G. J. De Bruin, Sheet cavitation and cloud cavitation, re-entrant jet and three-dimensionality, Applied Scientific Research, 58 (1–4) (1998) 91–114.
K. R. Laberteaux and S. L. Ceccio, Partial cavity flows. Part 2. cavities forming on test objects with spanwise variation, Journal of Fluid Mechanics, 431 (2001) 43–63.
M. Dular, R. Bachert, C. Schaad and B. Stoffel, Investigation of a re-entrant jet reflection at an inclined cavity closure line, European Journal of Mechanics B-Fluids, 26 (5) (2007) 688–705.
J. Dang and G. Kuiper, Re-entrant jet modeling of partial cavity flow on two-dimensional hydrofoils, Journal of Fluids Engineering, 121 (4) (1999) 773–780.
Y. Saito, R. Takami, I. Nakamori and T. Ikohagi, Numerical analysis of unsteady behavior of cloud cavitation around a NACA0015 foil, Computational Mechanics, 40 (1) (2007) 85–96.
Y. Kawanami, H. Kato, H. Yamaguchi, M. Maeda and S. Nakasumi, Inner structure of cloud cavity on a foil section, JSME International Journal Series B-Fluids and Thermal Engineering, 45 (3) (2002) 655–661.
G. H. Schnerr, I. H. Sezal and S. J. Schmidt, Numerical investigation of three-dimensional cloud cavitation with special emphasis on collapse induced shock dynamics, Physics of Fluids, 20 (4) (2008) 040703.
X. W. Luo, B. Ji, X. X. Peng, H. Y. Xu and M. Nishi, Numerical simulation of cavity shedding from a threedimensional twisted hydrofoil and induced pressure fluctuation by large-eddy simulation, Journal of Fluids Engineering, 134 (4) (2012) 041202.
S. Park and S. H. Rhee, Numerical analysis of the threedimensional cloud cavitating flow around a twisted hydrofoil, Fluid Dynamics Research, 45 (2013) 015502.
S. Park and S. H. Rhee, Computational analysis of turbulent super-cavitating flow around a two-dimensional wedgeshaped cavitator geometry, Computers & Fluids, 70 (2012) 73–85.
J. Decaix and E. Goncalvès, Investigation of threedimensional effects on a cavitating Venturi flow, International Journal of Heat and Fluid Flow, 44 (2013) 576–595.
E. J. Foeth, C. W.H. van Doorne, T. van Terwisga and B. Wieneke, Time resolved PIV and flow visualization of 3D sheet cavitation, Experiments in Fluids, 40 (4) (2006) 503–513.
E. J. Foeth, T. van Terwisga and C. van Doorne, On the collapse structure of an attached cavity on a threedimensional hydrofoil, Journal of Fluids Engineering, 130 (7) (2008) 071303.
E. J. Foeth, The structure of three-dimensional sheet cavitation, Ph. D. Thesis, Delft University of Technology, Wageningen, the Netherlands (2008).
D. Q. Li, M. Grekula and P. Lindell, Towards numerical prediction of unsteady sheet cavitation on hydrofoils, Journal of Hydrodynamics, 22 (5) (2010) 741–746.
R. E. Bensow, Simulation of the unsteady cavitation on the the delft twist11 foil using RANS, DES and LES, Proceedings of the 2nd International Symposium on Marine Propulsors, Hamburg, Germany (2011).
J. B. Leroux, J. A. Astolfi and J. Y. Billard, An experimental study of unsteady partial cavitation, Journal of Fluids Engineering, 126 (1) (2004) 94–101.
J. B. Leroux, O. Coutier-Delgosha and J. A. Astolfi, A joint experimental and numerical study of mechanisms associated to instability of partial cavitation on two-dimensional hydrofoil, Physics of Fluids, 17 (5) (2005) 052101.
B. Ji, X. W. Luo, Y. L. Wu, X. X. Peng and Y. L. Duan, Numerical analysis of unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoil, International Journal of Multiphase Flow, 51 (2013) 33–43.
S. S. Girimaji, Partially-averaged Navier-Stokes model for turbulence: A Reynolds-averaged Navier-Stokes to direct numerical simulation bridging method, Journal of Applied Mechanics, 73 (3) (2006) 413–421.
J. T. Liu, Y. L. Wu and L. Q. Wang, Instability analysis of a model pump-turbine with MGV Based on nonlinear partially averaged Navier-Stokes methods, Advances in Mechanical Engineering, 2013 (2013) 710769.
J. M. Ma, F. J. Wang, X. Yu and Z.Q. Liu, A partiallyaveraged Navier-Stokes model for hill and curved duct flow, Journal of Hydrodynamics, 23 (4) (2011) 466–475.
S. Lakshmipathy and S. S. Girimaji, Partially averaged Navier-Stokes (PANS) method for turbulence simulations: Flow past a circular cylinder, Journal of Fluids Engineering, 132 (12) (2010) 121202.
B. Huang and G. Y. Wang, Partially averaged Navier-Stokes method for time-dependent turbulent cavitating flows, Journal of Hydrodynamics, 23 (1) (2011) 26–33.
B. Ji, X. W. Luo, Y. L. Wu and H. Y. Xu, Unsteady cavitating flow around a hydrofoil simulated using the partiallyaveraged Navier-Stokes model, Chinese Physics Letters, 29 (7) (2012) 076401.
B. Ji, X. W. Luo, Y. L. Wu, X. X. Peng and H.Y. Xu, Partiallyaveraged Navier-Stokes method with modified kepsilon model for cavitating flow around a marine propeller in a non-uniform wake, International Journal of Heat and Mass Transfer, 55 (23–24) (2012) 6582–6588.
B. E. Launder and D. B. Spalding, The numerical computation of turbulent flows, Computer Methods in Applied Mechanics and Engineering, 3 (2) (1990) 269–289.
M. Morgut, E. Nobile and I. Bilus, Comparison of mass transfer models for the numerical prediction of sheet cavitation around a hydrofoil, International Journal of Multiphase Flow, 37 (6) (2011) 620–626.
X. W. Luo, W. Wei, B. Ji, Z. B. Pan, W. C. Zhou and H. Y. Xu, Comparison of cavitation prediction for a centrifugal pump with or without volute casing, Journal of Mechanical Science and Technology, 27 (6) (2013) 1643–1648.
Y. L. Wu, J. T. Liu, Y. K. Sun, S. H. Liu and Z.G. Zuo, Numerical analysis of flow in a Francis turbine on an equal critical cavitation coefficient line, Journal of Mechanical Science and Technology, 27 (6) (2013) 1635–1641.
P. J. Zwart, A. G. Gerber and T. Belamri, A two-phase flow model for predicting cavitation dynamics, Proceedings of International Conference on Multiphase Flow, Yokohama, Japan (2004).
B. Ji, X. W. Luo, X. X. Peng and Y. L. Wu, Threedimensional large eddy simulation and vorticity analysis of unsteady cavitating flow around a twisted hydrofoil, Journal of Hydrodynamics, 25 (4) (2013) 510–519.
E. Huse, Pressure Fluctuations on the Hull Induced by Cavitating Propellers, Norwegian Ship Model Experiment Tank Report (1972).
M. E. Duttweiler and C. E. Brennen, Surge instability on a cavitating propeller, Journal of Fluid Mechanics, 458 (2002) 133–152.
B. Ji, X. W. Luo, X. X. Peng, Y. L. Wu and H. Y. Xu, Numerical analysis of cavitation evolution and excited pressure fluctuation around a propeller in non-uniform wake, International Journal of Multiphase Flow, 43 (2012) 13–21.
C. E. Brennen, Cavitation and bubble dynamics, Oxford University Press, New York (1995).
B. Ji, X. W. Luo, R. E. A. Arndt and Y. L. Wu, Numerical simulation of three dimensional cavitation shedding dynamics with special emphasis on cavitation-vortex interaction, Ocean Engineering, 87 (2014) 64–77.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Recommended by Associate Editor Donghyun Yoo
Rights and permissions
About this article
Cite this article
Ji, B., Luo, X., Wu, Y. et al. Numerical investigation of three-dimensional cavitation evolution and excited pressure fluctuations around a twisted hydrofoil. J Mech Sci Technol 28, 2659–2668 (2014). https://doi.org/10.1007/s12206-014-0622-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-014-0622-4