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Title:: Numerical Simulation of the Flow around Two-dimensional Partially Cavitating Hydrofoils

Author(s):: Fahri Celik; Yasemin Arikan Ozden and Sakir Bal

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Keywords:: boundary element method (BEM); sheet cavitation; CFD; hydrofoil; cavity closure model; 2D hydrofoils

DOI:: 10.1007/s11804-014-1254-x

Abstract:: In the present study, a new approach is applied to the cavity prediction for two-dimensional (2D) hydrofoils by the potential based boundary element method (BEM). The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by the use of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code (FLUENT). Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others.

References:

Acosta AJ (1955). A note on partial cavitation of flat plate hydrofoils. Tech. Rep. E-19.9, California Institute of Technology, Hydrodynamics Lab. Pasadena, USA.
Ar?kan Y, Çelik F, Do?rul A, Bal ? (2012). Prediction of cavitation on two- and three-dimensional hydrofoils by an iterative BEM, Proceedings of the 8th International Symposium on Cavitation, CAV2012, Singapore, 696-702.
Bal S, Kinnas SA (2003). A numerical wave tank model for cavitating hydrofoils. Computational Mechanics, 32(4-6), 259-268.
Bal S (2007). A numerical method for the prediction of wave pattern of surface piercing cavitating hydrofoils. Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Sciences, 221(12), 1623-1633.
Bal S (2008). Performance prediction of surface piercing bodies in numerical towing tank. International Journal of Offshore and Polar Engineering, 18(2), 106-111.
Bal S (2011). The effect of finite depth on 2-D and 3-D cavitating hydrofoils. Journal of Marine Science and Technology, 16(2), 129-142.
Berntsen GS, Kjeldsen M, Arndt REA (2001). Numerical modeling of sheet and tip vortex cavitation with fluent 5. Proceedings of the 4th International Symposium on Cavitation, Paris, France, CAV2001: Session, B5.006.
Chow C (1979). An introduction to computational fluid mechanics. John WileyandSons, Inc, Colorado.
Dang J, Kuiper G (1998). Re-entrant jet modeling of partial cavity flow on three-dimensional hydrofoils. Proceedings of ASME FEDSM’98, Washington DC, USA.
Dang J (2001). Numerical simulation of partial cavity flows. PhD Thesis, Technical University Delft, Delft, Netherlands.
de Lange D, de Bruin G (1998). Sheet cavitation and cloud cavitation, re-entrant jet and three-dimensionality. Applied Scientific Research, 58, 91-114.
Deshpande MD, Feng J, Merkle CL (1993). Navier–stokes analysis of 2-d cavity flows. Proceedings of Cavitation and Multi-Phase Flow Forum, ASME FED, 153-158.
Deshpande MD, Feng J, Merkle CL (1994). Cavity flow predictions based on the euler equation. Transactions of the ASME 116, 36-44.
Dupont P, Avellan F (1991). Numerical computation of a leading edge cavity. Proceedings of Cavitation’91, ASME FED, Portland, Oregon, USA, 116, 47 - 54.
Fine NE, Kinnas SA (1993). A boundary element method for the analysis of the flow around 3-D cavitating hydrofoils. Journal of Ship Research, 37(3), 213-224.
Fluent 6.3 User’s Guide (2006).
Geurst JA, Timman R (1956). Linearized theory of two-dimensional cavitational flow around a wing section. IX Intl Cong. Applied Mech, Brussels 1, 486.
Hess J, Smith A (1966). Calculation of potential flow about arbitrary bodies. Progress in Aeronautical Sciences, 3,138.
Hess J (1973). Higher order numerical solution of the integral equation for the two-dimensional Neumann problem. Computer Methods in Applied Mechanics and Engineering, 2, 1-15.
Hess J (1975). The use of higher-order surface singularity distributions to obtain improved potential flow solutions for two-dimensional lifting airfoils. Computer Methods in Applied Mechanics and Engineering, 5, 11-35.
Hirschi R, Dupont P, Avellan F (1997). Centrifugal pump performance drop due to leading edge cavitation: Numerical predictions compared with model tests. FEDSM’97, Vancouver, Canada, 3342.
Hoekstra M, Vaz G (2009). The partial cavity on a 2-d foil revisited. Proceedings of the 7th International Symposium on Cavitation, CAV2009, Grenoble, France, No:43.
Huang S, He M, Wang C, Chang X (2010). Simulation of cavitating flow around a 2-D hydrofoil. Journal of Marine Science and Application, 9(1), 63-68.
Katz J, Plotkin A (2001). Low-speed aerodynamics, 2nd edition. Cambridge University Press, Cambridge, UK.
Kinnas S (1991). Leading-edge corrections to the linear theory of partially cavitating hydrofoils. Journal of Ship Research, 35(1), 15-27.
Kinnas SA, Fine NE (1991). Analysis of the flow around supercavitating hydrofoils with midchord and face cavity detachment. Journal of Ship Research, 35(3), 198-209.
Kinnas SA, Fine NE (1992). A nonlinear boundary element method for the analysis of unsteady propeller sheet cavitation. Proceedings of 19th ONR, Seoul, Korea.
Kinnas SA, Fine NE (1993). A numerical nonlinear analysis of the flow around two- and three- dimensional partial cavitating hydrofoils. Journal of Fluid Mechanics, 254, 151-181.
Kinnas SA, Fine NE (1993a). MIT-PCPAN and MIT-SCPAN (Partially cavitating and super cavitating 2-D panel methods) User’s Manual, Version 1.0.
Kinnas SA, Mishima S, Brewer WH (1996). Non-linear analysis of viscous flow around cavitating hydrofoils. Proceedings of 20th ONR, Santa Barbara, USA, 446-465.
Kinnas SA (1998). The prediction of unsteady sheet cavitation. Proceedings of the Third International Symposium on Cavitation, Grenoble, France, 16-36.
Kim YG, Lee CS, Suh JC (1994). Surface panel method for prediction of flow around a 3-D steady or unsteady cavitating hydrofoil. Proceedings of the 2nd International Symposium on Cavitation, Tokyo, Japan, 113-120.
Kim YG, Lee CS (1996). Prediction of unsteady performance of marine propellers with cavitation using surface-panel method. Proceedings of 21st Symposium on Naval Hydrodynamics, Trondheim, Norway, 913-929.
Krishnaswamy P (2000). Flow modeling for partially cavitating hydrofoils. PhD Thesis, Technical University of Denmark, Lyngby, Denmark.
Li Ziru, Pourquie M, Terwisga TJC (2010). A numerical study of steady and unseady cavitation on a 2D hydrofoil. 9th International Conference on Hydrodynamics, Shanghai, China, 728-735.
Longuet-Higgins MS, Cokelet ED (1976). The deformation of steep surface waves on water (I)—a numerical method of computation. Proceedings of Royal Society of London, Series A , 350, 1-26.
Singhal AK, Li HY, Athavale MM, Jiang Y (2001). Mathematical basis and validation of the full cavitation model. ASME FEDSM’01, New Orleans, Louisiana, USA.
Tulin MP (1953). Steady two-dimensional cavity flows about slender bodies. DTMB Technical Report N. 834.
Uhlman JJS (1987). The surface singularity method applied to partially cavitating hydrofoils. Journal of Ship Research, 31(2), 107-124.

Journal of Marine Science and Application[ISSN:1002-2848/CN:61-1400/f]

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