Abstract
The objective of this paper is to improve the understanding of the influence of multiphase flow on the turbulent closure model, the interplay between vorticity fields and cavity dynamics around a pitching hydrofoil. The effects of pitching rate on the subcavitating and cavitating response of the pitching hydrofoil are also investigated. In particular, we focus on the interactions between cavity inception, growth, and shedding and the vortex flow structures, and their impacts on the hydrofoil performance. The calculations are 2-D and performed by solving the incompressible, multiphase Unsteady Reynolds Averaged Navier Stokes (URANS) equations via the commercial CFD code CFX. The k-ω SST (Shear Stress Transport) turbulence model is used along with the transport equation-based cavitation models. The density correction function is considered to reduce the eddy viscosity according to the computed local fluid mixture density. The calculation results are validated with experiments conducted by Ducoin et al. (see Computational and experimental investigation of flow over a transient pitching hydrofoil, Eur J Mech/B Fluids, 2009, 28: 728–743 and An experimental analysis of fluid structure interaction of a flexible hydrofoil in various flow regimes including cavitating flow, Eur J Mech B/fluids, 2012, 36: 63–74). Results are shown for a NACA66 hydrofoil subject to slow (quasi static, \(\dot \alpha = {{6^ \circ } \mathord{\left/ {\vphantom {{6^ \circ } s}} \right. \kern-\nulldelimiterspace} s}\), \(\dot \alpha ^ * = 0.18\)) and fast (dynamic, \(\dot \alpha = {{63^ \circ } \mathord{\left/ {\vphantom {{63^ \circ } s}} \right. \kern-\nulldelimiterspace} s}\), \(\dot \alpha ^ * = 1.89\)) pitching motions from α = 0° to α = 15°. Both subcavitaing (σ=8.0) and cavitating (σ=3.0) flows are considered. For subcavitating flow (σ=8.0), low frequency fluctuations have been observed when the leading edge vortex shedding occurs during stall, and delay of stall is observed with increasing pitching velocity. For cavitating flow (σ=3.0), small leading edge cavities are observed with the slow pitching case, which significantly modified the vortex dynamics at high angles of attack, leading to high frequency fluctuations of the hydrodynamic coefficients and different stall behaviors compared to the subcavitating flow at the same pitching rate. On the other hand, for the fast pitching case at σ=3.0, large-scale sheet/cloud cavitation is observed, the cavity behavior is unsteady and has a strong impact on the hydrodynamic response, which leads to high amplitude fluctuations of the hydrodynamic coefficients, as well as significant changes in the stall and post-stall behavior. The numerical results also show that the local density modification helps to reduce turbulent eddy viscosity in the cavitating region, which significantly modifies the cavity lengths and shedding frequencies, particularly for the fast pitching case. In general, compared with the experimental visualizations, the numerical results with local density correction have been found to agree well with experimental measurements and observations for both slow and fast transient pitching cases.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Arndt R E A. Cavitation in fluid machinery and hydraulic structure. Annu Rev Fluid Mech, 1981, 13: 273–326
Luo X W, Ji B, Peng X X, et al. Numerical simulation of cavity shedding from a three-dimensional twisted hydrofoil and induced pressure fluctuation by large-eddy simulation. J Fluids Eng, 2012, 134(4): 041202
Ji B, Luo X W, Peng X X, et al. Numerical analysis of cavitation evolution and excited pressure fluctuation around a propeller in non-uniform wake. Int J Multiphase Flow, 2012, 43: 13–21
Liu Z, Young Y L. Performance-based design and analysis of flexible composite propulsors. J Fluids Struct, 2011, 27: 1310–1325
McCroskey W J. Unsteady airfoils. Ann Rev Fluid Mech, 1982, 14: 285–311
Carr L W. Progress in analysis and prediction of dynamic stall. J Aircr, 1988, 25: 6–17
Carr L W, McCroskey W J. A review of recent advances in computation and experimental analysis of dynamic stall. International Union of Theoretical and Applied Mechanics on Fluid Dynamics at High Angle of Attack, Tokyo, 1992
Ohmi K, Coutanceau M, Loc T P, et al. Vortex formation around an oscillating and translating airfoil at large incidences. J Fluid Mech, 1990, 211: 37–60
Oshima Y, Natsume A. Flow field around an oscillating foil. 2nd Int Symp on Flow Visualization, Bochum, 1980
Freymuth P. Propulsive vortical signatures of plunging and pitching airfoils, AIAA J, 1988, 26: 881–883
Koochesfahani M M. Vortical patterns in the wake of an oscillating airfoil, AIAA J, 1989, 27: 1200–1205
Lorber P F, Carta F O. Airfoil dynamic stall at constant pitch rate and high Reynolds number. J Aircr, 1988, 25: 548–556
Lee T, Gerontakos P. Investigate of flow over an oscillating airfoil. J Fluid Mech, 2004, 512: 313–341
Triantafyllou G S, Triantafyllou M S, Grosenbaugh M A. Optimal thrust development in oscillating foils with application to fish propulsion. J Fluids Struct, 1993, 7: 205–224
Jumper E J, Schreck S J, Dimnick R L. Lift-curve characteristics for an airfoil pitching at constant rate. J Aircr, 1987, 24: 680–687
Ducoin A, Astolfi J A, Deniset F, et al. Computational and experimental investigation of flow over a transient pitching hydrofoil. Eur J Mech/B Fluids Elsevier, 2009, 28: 728–743
Joseph D D. Cavitation in a flowing liquid. Phys Rev E, 1995, 51: 1649–1650
Knapp R T, Daily J W, Hammitt F G. Cavitation, New York: McGraw Hill, 1970
Callenaere M, Franc J P, Michel J M, et al. The cavitation instability induced by the development of a re-entrant jet. J Fluid Mech, 2001, 444: 223–256
Wang G, Senocak I, Shyy W, et al. Dynamics of attached turbulent cavitating flows. Prog Aero Sci, 2001, 37: 551–581
Huang B, Wang G. Experimental and numerical investigation of unsteady cavitating flows through a 2D hydrofoil. Sci China Tech Sci, 2011, 54: 1801–1812
Stutz B, Legoupil S. X-ray measurements within unsteady cavitations. Exp Fluids, 2003, 35: 130–138
Foeth E J. The structure of three-dimensional sheet cavitation. Ph.D. Thesis. Delft: Delft University of Technology, 2008
Kunz R F, Boger D A, Stinebring D R, et al. A preconditioned Navier-stokes method for two phase flows with application to cavitation prediction. Comput Fluids, Elsevier, 2000, 29: 849–875
Singhal A K, Athavale M M, Li H, et al. Mathematical basis and validation of the full cavitation model. J Fluids Eng, 2002, 124: 617–624
Coutier-Delgosha O, Fortes-Patella R, Reboud J L. Evaluation of the turbulence model influence on the numerical simulations of unsteady cavitations. ASME J Fluids Eng, 2003, 125(1): 38–45
Senocak I, Shyy W. A pressure-based method for turbulent cavitating flow computations. J Comput Phys, 2002, 176: 363–383
Kim S, Brewton S. A multiphase approach to turbulent cavitating flows. Proceedings of 27th Symposium on Naval Hydrodynamics, Seoul, 2008
Seo J H, Lele S K. Numerical investigation of cloud cavitation and cavitation noise on a hydrofoil section. Proceedings of 7th Int Symp on Cavitation, Ann Arbor, MI, USA, 2009
Kubota A, Kato H, Yamaguchi H, et al. Unsteady structure measurement of cloud cavitation on a foil section using conditional sampling technique. J Fluids Eng, 1989, 111(2): 204–210
Huang B, Wang G Y, Zhao Y, et al. Physical and numerical investigation on transient cavitating flows. Sci China Tech Sci, 2013, 56(9): 2207–2218
Ji B, Luo X W, Peng X X, et al. Three-dimensional large eddy simulation and vorticity analysis of unsteady cavitating flow around a twisted hydrofoil. J Hydrodyn, 2013, 25(4): 510–519
Wu J, Wang G, Shyy W. Time-dependent turbulent cavitating flow computations with interfacial transport and filter based models. Int J Numer MethFluids, 2005, 49: 739–761
Wang G, Ostoja-Starzewski M. Large eddy simulation of a sheet/ cloud cavitation on a NACA0015 hydrofoil. Appl Math Model, 2007, 31(3): 417–447
Shen Y T, Peterson F B. Unsteady cavitation on an oscillating hydrofoil. Proceedings of 12th Symp on Naval Hydrodynamics, Washington D C, 1978
Shen Y T, Peterson F B. The influence of hydrofoil oscillation on boundary layer transition and cavitation noise. Proceedings of 13th Symp on Naval Hydrodynamics, Tokyo, 1980
Franc J P, Michel J M. Unsteady attached cavitation on an oscillating hydrofoil. J Fluid Mech, 1988, 193: 171–189
Hart D P, Brennen C E, Acosta A J. Observations of cavitation on a three-dimensional oscillating hydrofoil. Proc ASME Conf on Cavitation and Multiphase, New York, 1990
Kato K, Dan H, Matsudaira Y. Lock-in phenomenon of pitching hydrofoil with cavitation breakdown. Int J Ser B Fluids Therm Eng, 2006, 49: 797–805
Uchiyama T. Numerical study on bubbly flow around a hydrofoil in pitching and heaving motions. Proc Institute Mech Eng, 2003, 217: 811–816
Ducoin A, Astolfi J A, Sigrist J -F. An experimental analysis of fluid structure interaction of a flexible hydrofoil in various flow regimes including cavitating flow. Eur J Mech B/Fluids, 2012, 36: 63–74
Merkle C L, Feng J, Buelow P E O. Computational modeling of sheet cavitations. Proceedings of Third International Symposium on Cavitation, Grenoble, 1998
Huang B, Ducoin A, Young Y L. Evaluation of cavitation models for prediction of transient cavitating flows around a pitching hydrofoil. Proceedings of 8th International Symposium on Cavitation, Singapore, 2012
Menter F R. Improved two-equation k-ω turbulence models for aerodynamic flows. NASA Tech Memorandu, 1992, 34: 103975
Huang B, Young Y L, Wang G, et al. Combined experimental and computational investigation of unsteady structure of sheet/cloud cavitation. J Fluids Eng, 2013, 135: 071301
Ji B, Luo X W, Wu Y L, et al. Numerical analysis of unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoil. Int J Multiphase Flow, 2013, 51: 33–43
Huang B, Wang G Y. Evaluation of a filter-based model for computations of cavitating flows. Chin Phys Lett, 2011, 28(2): 026401
Ji B, Luo X W, Wu Y L. Partially-Averaged Navier-Stokes method with modified k-epsilon model for cavitating flow around a marine propeller in a non-uniform wake. Int J Heat Mass Tran, 2012, 55: 6582–6588
Huang B, Wang G Y. Partial averaged Navier-Stokes method for time-dependent turbulent cavitating flows. J Hydrodyn, 2011, 23(1): 26–33
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Huang, B., Wu, Q. & Wang, G. Numerical simulation of unsteady cavitating flows around a transient pitching hydrofoil. Sci. China Technol. Sci. 57, 101–116 (2014). https://doi.org/10.1007/s11431-013-5423-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-013-5423-y