Abstract
A doublet integral equation is formulated for the two-dimensional dissipative potential flow around a hydrofoil submerged below a free-water surface. The free-water surface is assumed to involve energy dissipation, and thus it is the source of damping. A doublet panel method is developed from incorporation of the dissipative Green function approach and the doublet distributions on the hydrofoil surface. Numerical computations are implemented, and the derived numerical results are in good agreement with analytic solutions and experimental measurements.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Batchelor, G. K. An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 131–170 (1967)
Lamb, H. Hydrodynamics, 6th ed., Cambridge University Press, Cambridge (1932)
Newman, J. N. Evaluation of the wave-resistance Green function: part 1—the double integrals. Journal of Ship Research, 31(2), 79–90 (1987)
Inglis, R. B. and Price, W. G. Calculation of the velocity potential of a translating pulsating source. Transactions of Royal Institution of Naval Architects, 123, 163–175 (1981)
Inglis, R. B. and Price, W. G. A three-dimensional ship motion theory: comparison between theoretical predictions and experimental data of the hydrodynamic coefficients with forward speed. Transactions of Royal Institution of Naval Architects, 124, 141–157 (1981)
Hess, J. L. and Smith, A. M. O. Calculation of potential flow about arbitrary bodies. Progress in Aeronautical Sciences, 8, 1–138 (1966)
Giesing, J. P. and Smith, A. M. O. Potential flow about two-dimensional hydrofoil. Journal of Fluid Mechanics, 28, 113–129 (1967)
Dawson, C. W. A practical computer method for solving ship wave problems. Proceedings of 2nd International Conference on Numerical Ship Hydrodynamics, University of California, Berkeley, 30–38 (1977)
Kouh, J. S., Lin, T. J., and Chau, S. W. Performance analysis of two-dimensional hydrofoil under free surface. Journal of Engineering at National Taiwan University, 86, 113–123 (2002)
Yeung, R. W. and Bouger, Y. C. Hybrid integral-equation method for the steady ship-problem. Proceedings of 2nd International Conference on Numerical Ship Hydrodynamics, University of California, Berkeley, 160–175 (1977)
Yeung, R. W. and Bouger, Y. C. A hybrid integral-equation method for steady two-dimensional ship waves. International Journal for Numerical Methods in Engineering, 14(3), 317–336 (1979)
Faltinsen, O. M. and Semenov, Y. A. The effect of gravity and cavitation on a hydrofoil near the free surface. Journal of Fluid Mechanics, 597, 371–394 (2008)
Wehausen, J. V. and Laitone, E. V. Surface Waves, Handbuch der Physik, Vol. 9, Springer, Berlin, 446–778 (1960)
Bessho, M. On the fundamental singularity in the theory of ship motions in a seaway. Memories of the Defense Academy Japan, 17(3), 95–105 (1977)
Iwashita, H. and Ohkusu, M. The green function method for ship motions at forward speed. Ship Technology Research, 39(2), 3–21 (1992)
Chen, Z. M. A vortex based panel method for potential flow simulation around a hydrofoil. Journal of Fluids and Structures, 28, 378–391 (2012)
Katz, J. and Plotkin, A. Low-Speed Aerodynamics, Cambridge University Press, Cambridge (2001)
Havelock, T. H. Wave resistance. Proceedings of the Royal Society of London, Series A, 118(779), 24–33 (1928)
Bondarenko, N. F., Gak, M. Z., and Dolzhanskiy, F. V. Laboratory and theoretical models of plane periodic flows. Izvestiya, Atmospheric and Oceanic Physics, 15(10), 711–716 (1979)
Chen, Z. M. and Price, W. G. Supercritical regimes of liquid-metal fluid motions in electromagnetic fields: wall-bounded flows. Proceedings of the Royal Society of London, Series A, 458(2027), 2735–2757 (2002)
Chen, Z. M. and Price, W. G. Secondary fluid flows driven electromagnetically in a twodimensional extended duct. Proceedings of the Royal Society of London, Series A, 461(2058), 1659–1683 (2005)
Ausman, J. S. Pressure Limitation on the Upper Surface of a Hydrofoil, Ph. D. dissertation, University of California, Berkeley (1954)
Chen, Z. M. A dissipative free-surface approach for an underwater body in a uniform stream. Journal of Marine Science and Technology DOI 10.1007/s00773-012-0199-5
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, Zm., Price, W.G. Dissipative free-surface solver for potential flow around hydrofoil distributed with doublets. Appl. Math. Mech.-Engl. Ed. 33, 1467–1480 (2012). https://doi.org/10.1007/s10483-012-1636-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-012-1636-9