Ocean Systems Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Free surface effects on 2-D airfoils and 3-D wings moving over water

  • Bal, Sakir (Istanbul Technical University, Department of Naval Architecture and Marine Engineering)
  • Received : 2016.03.15
  • Accepted : 2016.08.25
  • Published : 2016.09.25
⟨ Previous Next ⟩

Abstract

The iterative boundary element method (IBEM) developed originally before for cavitating two-dimensional (2-D) and three-dimensional (3-D) hydrofoils moving under free surface is modified and applied to the case of 2-D (two-dimensional) airfoils and 3-D (three-dimensional) wings over water. The calculation of the steady-state flow characteristics of an inviscid, incompressible fluid past 2-D airfoils and 3-D wings above free water surface is of practical importance for air-assisted marine vehicles such as some racing boats including catamarans with hydrofoils and WIG (Wing-In-Ground) effect crafts. In the present paper, the effects of free surface both on 2-D airfoils and 3-D wings moving steadily over free water surface are investigated in detail. The iterative numerical method (IBEM) based on the Green's theorem allows separating the airfoil or wing problems and the free surface problem. Both the 2-D airfoil surface (or 3-D wing surface) and the free surface are modeled with constant strength dipole and constant strength source panels. While the kinematic boundary condition is applied on the airfoil surface or on the wing surface, the linearized kinematic-dynamic combined condition is applied on the free surface. The source strengths on the free surface are expressed in terms of perturbation potential by applying the linearized free surface conditions. No radiation condition is enforced for downstream boundary in 2-D airfoil and 3-D wing cases and transverse boundaries in only 3-D wing case. The method is first applied to 2-D NACA0004 airfoil with angle of attack of four degrees to validate the method. The effects of height of 2-D airfoil from free surface and Froude number on lift and drag coefficients are investigated. The method is also applied to NACA0015 airfoil for another validation with experiments in case of ground effect. The lift coefficient with different clearance values are compared with those of experiments. The numerical method is then applied to NACA0012 airfoil with the angle of attack of five degrees and the effects of Froude number and clearance on the lift and drag coefficients are discussed. The method is lastly applied to a rectangular 3-D wing and the effects of Froude number on wing performance have been investigated. The numerical results for wing moving under free surface have also been compared with those of the same wing moving above free surface. It has been found that the free surface can affect the wing performance significantly.

Keywords

References

  1. Amiri, M.M., Dakhrabadi, M.T. and Seif, M.S. (2016), "Formulation of a nonlinear mathematical model to simulate accelerations of an AAMV in take-off and landing phases", Ships Offshore Struct., 11(2), 198-212. https://doi.org/10.1080/17445302.2014.975171
  2. Bal, S. (2008), "Performance prediction of surface piercing bodies in numerical towing tank", Int. J. Offshore Polar Eng., 18(2), 106-111.
  3. Bal, S. (2007), "High-speed submerged and surface piercing cavitating hydrofoils, including tandem case", Ocean Eng., 34(14-15), 1935-1946. https://doi.org/10.1016/j.oceaneng.2007.03.007
  4. Bal, S. (2011), "The effect of finite depth on 2-D and 3-D cavitating hydrofoils", J. Marine Sci. Technol., 16(2), 129-142. https://doi.org/10.1007/s00773-011-0117-2
  5. Bal, S. and Kinnas, S.A. (2002), "A Bem for the prediction of free surface effect on cavitating hydrofoils", Comput. Mech., 28(3), 260-274. https://doi.org/10.1007/s00466-001-0286-7
  6. Bal, S., Kinnas, S.A. and Lee, H. (2001), "Numerical analysis of 2-D and 3-D cavitating hydrofoils under a free surface", J. Ship Res., 45(1), 34-49.
  7. Barber, J.T. (2007), "A study of water surface deformation due to tip vortices of a wing-in-ground effect", J. Ship Res., 51(2), 182-186.
  8. Cheng, A.H.D. and Cheng, D.T. (2005), "Heritage and early history of the boundary element method", Eng. Anal. Bound. Elem., 29(3), 268-302. https://doi.org/10.1016/j.enganabound.2004.12.001
  9. Dawson, D.W. (1977), "A practical computer method for solving ship-wave problems", Proceedings of the 2nd International Conference on Numerical Ship Hydrodynamics, USA.
  10. Fine, N.E. and Kinnas, S.A. (1993), "A boundary element method for the analysis of the flow around 3-D cavitating hydrofoils", J. Ship Res., 37(3), 213-224.
  11. Grundy, I. (1986), "Airfoils moving in air close to a dynamic water surface", J. Australian Math Soc. Series B, 27(3), 327-345. https://doi.org/10.1017/S0334270000004963
  12. Guanghua, H.E. (2013), "An iterative Rankine BEM for wave-making analyses of submerged and surface-piercing bodies in finite water depth", J. Hydrodynamics, 25(6), 839-847. https://doi.org/10.1016/S1001-6058(13)60431-X
  13. Jung, J.H., Kim, M.J., Yoon, H.S., Hung, P.A., Chun, H.H. and Park, D.W. (2012), "Endplate effect on aerodynamic characteristics of three-dimensional wings in close free surface proximity", Int. J. Naval Architect. Ocean Eng., 4(4), 477-487. https://doi.org/10.3744/JNAOE.2012.4.4.477
  14. Kinnas, S.A. and Fine, N.E. (1993), "A numerical nonlinear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils", J. Fluid Mech., 254, 151-181. https://doi.org/10.1017/S0022112093002071
  15. Kinnas, S.A. and Hsin, C.Y. (1992), "A boundary element method for the analysis of the unsteady flow around extreme propeller geometries", AIAA J., 30(3), 688-696. https://doi.org/10.2514/3.10973
  16. Lee, C.S., Lew, C.W. and Kim, Y.G. (1992), "Analysis of a two-dimensional partially or supercavitating hydrofoil advancing under a free surface with a finite Froude number", Proceedings of the 19th Symposium on Naval Hydrodynamics, Korea.
  17. Liang, H. and Zong, Z. (2011), "A subsonic lifting surface theory for wing-in-ground effect", Acta Mech., 219(3), 203-217. https://doi.org/10.1007/s00707-011-0444-8
  18. Liang, H., Zhou, L., Zong, Z. and Sun, L. (2013), "An analytical investigation of two-dimensional and three-dimensional biplanes operating in the vicinity of a free surface", J. Marine Sci. Technol., 18(1), 12-31. https://doi.org/10.1007/s00773-012-0187-9
  19. Matveev, K.I. (2013), "Modeling of finite-span ram wings moving above water of finite Froude numbers", J. Ship Res., 58(3), 146-156. https://doi.org/10.5957/JOSR.58.3.130046
  20. Rozhdestvensky, K.V. (2006), "Wing-in-ground effect vehicles", Progress in Aerospace Sciences, 42(3), 211-283.
  21. Zong, Z., Liang, H. and Zhou, L. (2012), "Lifting line theory for wing-in ground effect in proximity to a free surface", J. Eng. Mathematics, 74(1), 143-158. https://doi.org/10.1007/s10665-011-9497-x

Cited by

  1. Prediction of the turning and zig-zag maneuvering performance of a surface combatant with URANS vol.7, pp.4, 2017, https://doi.org/10.12989/ose.2017.7.4.435
  2. AI based control theory for interaction of ocean system vol.10, pp.2, 2020, https://doi.org/10.12989/ose.2020.10.2.227
  3. Airfoil Aerodynamics in Proximity to Wavy Ground for a Wide Range of Angles of Attack vol.10, pp.19, 2016, https://doi.org/10.3390/app10196773
  4. Airfoil Aerodynamics in Proximity to Wavy Water Surface vol.34, pp.2, 2021, https://doi.org/10.1061/(asce)as.1943-5525.0001238
  5. Numerical Study on Airfoil Aerodynamics in Proximity to Wavy Water Surface for Various Amplitudes vol.11, pp.9, 2021, https://doi.org/10.3390/app11094215