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Unsteady aerodynamics of two interacting yacht sails in two-dimensional potential flow

Published online by Cambridge University Press:  16 December 2010

F. C. GERHARDT ,
R. G. J. FLAY  and
P. RICHARDS
F. C. GERHARDT
Affiliation:
Yacht Research Unit, Department of Mechanical Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand
R. G. J. FLAY*
Affiliation:
Yacht Research Unit, Department of Mechanical Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand
P. RICHARDS
Affiliation:
Yacht Research Unit, Department of Mechanical Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, unsteady thin aerofoil theory is extended to the case of two interacting aerofoils that oscillate harmonically perpendicular to the direction of the incident flow. The two aerofoils represent the headsail and mainsail of a yacht that sails upwind in waves. The developed theory is validated against theoretical data from the literature and results from wind tunnel tests with rigid, high-aspect ratio sail models oscillating at reduced frequencies from k = 0 to k = 0.68. Good agreement is found between the predicted and measured chordwise pressure distributions. An application of the theory to the case of an International America's Cup Class yacht reveals that the time-varying components of the aerodynamic forces are small and that the thrust gain is minimal, i.e. only very little energy can be extracted from the unsteady flow about the sails. No attempt is made to investigate the influence of the flexibility of the sails, three-dimensional effects or phenomena related to dynamic stall.

JFM classification

Mathematical Foundations: Computational methods Vortex Flows: Vortex shedding Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 668 , 10 February 2011 , pp. 551 - 581
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions, 3rd edn. National Bureau of Standards.Google Scholar
Amiet, R. K. 1995 Airfoil leading-edge suction and energy conservation for compressible flow. J. Fluid Mech. 289, 227–242.CrossRefGoogle Scholar
Anderson, J. D. J. 1991 Fundamentals of Aerodynamics, 2nd edn. McGraw-Hill.Google Scholar
Bailey, K. I. 1999 The aerodynamic analysis of two-dimensional yacht mast and sail configurations. PhD dissertation, The University of Auckland.Google Scholar
Battistin, D. & Ledri, M. 2007 A tool for time-dependent performance prediction and optimization of sailing yachts. In Proceedings of the 18th Chesapeake Sailing Yacht Symposium, Annapolis, MD, pp. 90–101.Google Scholar
Birnbaum, W. 1924 Das ebene Problem des schlagenden Flügels. Z. Angew. Math. Mech. 4, 277–292.CrossRefGoogle Scholar
Birnbaum, W. & Ackermann, W. 1923 Die tragende Wirbelfläche als Hilfsmittel zur Behandlung des ebenen Problems der Tragflügeltheorie. Z. Angew. Math. Mech. 3, 290–297.CrossRefGoogle Scholar
Bosch, H. 1972 Instationäre Luftkräfte eines Tragflügelpaares in Tandemanordnung in ebener inkompressibler Strömung. Diploma thesis, TU München.Google Scholar
Charvet, T., Hauville, F. & Huberson, S. 1996 Numerical simulation of the flow over sails in real sailing conditions. J. Wind Engng Ind. Aero. 63, 111–129.Google Scholar
Claughton, A. 1999 Developments in the IMS VPP formulations. In Proceedings of the 14th Chesapeake Sailing Yacht Symposium, Annapolis, MD, pp. 1–20.Google Scholar
Day, S., Letizia, L. & Stuart, A. 2002 Challenges in the time-domain prediction of sailing yacht performance. In Proceedings of the First High Performance Yacht Design Conf. Auckland, New Zealand, pp. 255–266.Google Scholar
Fitt, A. D. & Lattimer, T. R. B. 2000 On the unsteady motion of two-dimensional sails. J. Appl. Maths 65, 147–171.Google Scholar
Flay, R. G. J. 1996 A twisted flow wind tunnel for testing yacht sails. J. Wind Engng Ind. Aero. 63, 171–182.Google Scholar
Fossati, F. & Muggiasca, S. 2009 Sails aerodynamic behavior in dynamic conditions. In Proceedings of the 19th Chesapeake Sailing Yacht Symposium, Annapolis, MD, pp. 109–124.Google Scholar
Garrick, I. E. 1936 Propulsion of a flapping and oscillating airfoil. NACA Tech. Rep. 567.Google Scholar
Gaunaa, M. 2010 Unsteady two-dimensional potential-flow model for thin variable geometry airfoils. J. Wind Energy 13, 167–192.Google Scholar
Gerhardt, F. C., Flay, R. G. J. & Richards, P. 2008 Unsteady aerodynamic phenomena associated with sailing upwind in waves. In Proceedings of the Third High Performance Yacht Design Conf. Auckland, New Zealand, pp. 148–157.Google Scholar
Glauert, H. 1948 The Elements of Aerofoil and Airscrew Theory, 2nd edn. Cambridge University Press.Google Scholar
Greenberg, M. D. 1964 An improved Glauert series for certain airfoil problems. AIAA J. 2, 1666–1667.Google Scholar
Halfman, R. 1952 Experimental aerodynamic derivatives of a sinusoidally oscillating airfoil in two-dimensional flow. NACA Tech. Rep. 1108.Google Scholar
Harris, D. H. 2002 Simulation of upwind manuevering of a sailing yacht. PhD dissertation, University of Maryland, College Park.Google Scholar
Hazen, G. 1980 A model of sail aerodynamics for diverse rig types. In Proceedings of the New England Sailing Yacht Symposium New London, CT, pp. 90–101.Google Scholar
Jacquin, E., Roux, Y., Guillerm, P. E. & Alessandrini, B. 2005 Toward numerical VPP with the full coupling of hydrodynamic and aerodynamic solvers for ACC yacht. In Proceedings of the 17th Chesapeake Sailing Yacht Symposium, Annapolis, MD, pp. 1–12.Google Scholar
Johnson, W. 1980 Helicopter Theory. Princeton University Press.Google Scholar
Jones, R. T. 1939 The unsteady lift of a finite wing. NACA Tech. Rep. 682.Google Scholar
von Kármán, T. & Burgers, J. M. 1976 General Aerodynamic Theory – Perfect Fluids (ed. Durand, W. F.), Vol. 2, §9. Peter Smith.Google Scholar
Katzmayr, R. 1922 Über das Verhalten der Flügelflächen bei periodischen Änderungen der Geschwindigkeitsrichtung. Z. Flugtech. Motorluftschiff. 6–7, 80–82 and 95–101.Google Scholar
Leishman, J. G. 2006 Principles of Helicopter Aerodynamics, 2nd edn. Cambridge University Press.Google Scholar
Lorillu, O., Weber, R. & Hureau, J. 2002 Numerical and experimental analysis of two-dimensional separated flows over a flexible sail. J. Fluid Mech. 466, 319–341.CrossRefGoogle Scholar
Masuyama, Y. & Fukasawa, T. 2008 Tacking simulations of sailing yachts with new model of aerodynamic force variation. In Proceedings of the Third High Performance Yacht Design Conf. Auckland, New Zealand, pp. 138–147.Google Scholar
Masuyama, Y., Fukasawa, T. & Sasagawa, H. 1995 Tacking simulations of sailing yachts, numerical integration of equation of motion and application of neural network technique. In Proceedings of the 12th Chesapeake Sailing Yacht Symposium, Annapolis, MD, pp. 117–131.Google Scholar
Masuyama, Y., Nakamura, I., Hisayoshi, T. & Ken, T. 1993 Dynamic performance of sailing cruiser by full-scale sea trials. In Proceedings of the 11th Chesapeake Sailing Yacht Symposium, Annapolis, MD, pp. 161–179.Google Scholar
Mendelson, A. & Carroll, R. W. 1954 Lift and moment equations for oscillating airfoils in an infinite unstaggered cascade. NACA Tech. Rep. 3263.Google Scholar
Milgram, J. H. 1968 The analytical design of yacht sails. Trans. SNAME 76, 118–152.Google Scholar
Molyneux, W. G. 1956 Measurement of the aerodynamic forces on oscillating airfoils. AGARD Tech. Rep. 35.Google Scholar
Munk, M. 1922 General theory of thin wing sections. NACA Tech. Rep. 142.Google Scholar
Myall, J. O. & Berger, S. A. 1969 Interaction between a pair of two-dimensional sails for the case of smoothly attached flow. Proc. R. Soc. Lond. A 310, 373–391.Google Scholar
Oliver, J. C., Letcher, J. S. & Salvesen, N. 1987 Performance predictions for Stars and Stripes. Trans. SNAME 95, 239–261.Google Scholar
Ottoson, P., Brown, M. & Larrson, L. 2002 The effect of pitch radius of gyration on sailing yacht performance. In Proceedings of the First High Performance Yacht Design Conf. Auckland, New Zealand, pp. 245–254.Google Scholar
Peters, D. A., Hsieh, M. A. & Torrero, A. 2007 A state-space airloads theory for flexible airfoils. J. Am. Helicopter Soc. 51, 329–342.Google Scholar
Postel, E. E. & Leppert, E. L. 1948 The theoretical pressure distributions for a thin airfoil oscillating in incompressible flow. J. Aeronaut. Sci. 15, 486–492.CrossRefGoogle Scholar
Richardt, T., Harries, S. & Hochkirch, K. 2005 Maneuvering simulations for ships and sailing yachts using FRIENDSHIP-Equilibrium as an open modular workbench. In Proceedings of the International EuroConf. on Computer Applications and Information Technology in the Maritime Industries, Hamburg, Germany, pp. 101–115.Google Scholar
de Ridder, E. J., Vermeulen, K. J. & Keuning, J. A. 2004 A mathematical model for the tacking manoeuvre of a sailing yacht. In Proceedings of the 18th International HISWA Symposium on Yacht Design and Construction, Amsterdam, Netherlands, pp. 1–34.Google Scholar
Roux, Y., Huberson, S., Hauville, F., Boin, J. F., Guilbaud, M. & Malick, B. 2002 Yacht performance prediction: towards a numerical VPP. In Proceedings of the First High Performance Yacht Design Conf. Auckland, New Zealand, pp. 213–220.Google Scholar
Schlichting, H. & Truckenbrodt, E. 2001 Aeorodynamik des Flugzeuges, 3rd edn. Springer.Google Scholar
Schoop, H. & Bessert, N. 2001 Instationary aeroelastic computation of yacht sails. Intl J. Numer. Meth. Engng 52, 787–803.CrossRefGoogle Scholar
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. NACA Advanced Restricted Report. Also published as NACA Tech. Rep. 496, 1949.Google Scholar
Viola, I. M. & Flay, R. G. J. 2010 Full-scale pressure measurements on a S&S 24 sailing yacht. J. Wind Engng Ind. Aero. (in press).Google Scholar
Voelz, K. 1950 Profil und Auftrieb eines Segels. Z. Angew. Math. Mech. 30, 301–317.CrossRefGoogle Scholar
van der Wall, B. & Leishman, J. G. 1994 The influence of variable flow velocity on unsteady airfoil behaviour. J. Am. Helicopter Soc. 39, 288–297.Google Scholar