# An iterative boundary element method for a wing-in-ground effect

• Kinaci, Omer Kemal (Yildiz Technical University, Faculty of Naval Architecture and Maritime)
• Published : 2014.06.30

#### Abstract

In this paper, an iterative boundary element method (IBEM) was proposed to solve for a wing-in-ground (WIG) effect. IBEM is a fast and accurate method used in many different fields of engineering and in this work; it is applied to a fluid flow problem assessing a wing in ground proximity. The theory and the developed code are validated first with other methods and the obtained results with the proposed method are found to be encouraging. Then, time consumptions of the direct and iterative methods were contrasted to evaluate the efficiency of IBEM. It is found out that IBEM dominates direct BEM in terms of time consumption in all trials. The iterative method seems very useful for quick assessment of a wing in ground proximity condition. After all, a NACA6409 wing section in ground vicinity is solved with IBEM to evaluate the WIG effect.

#### References

1. Abramowski, T., 2007. Numerical investigation of airfoil in ground proximity. Journal of Theoretical and Applied Mechanics, 45(2), pp.425-436.
2. Ahmed, M.R. and Sharma, S.D., 2005. An investigation on the aerodynamics of a symmetrical airfoil in ground effect. Experimental Thermal and Fluid Science, 29(6), pp.633-647. https://doi.org/10.1016/j.expthermflusci.2004.09.001
3. Bal, S., 2003. A numerical wave tank model for cavitating hydrofoils. Computational Mechanics, 32(4-6), pp.259-268. https://doi.org/10.1007/s00466-003-0483-7
4. 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 Science, 221(12), pp.1623-1633.
5. Bal, S., 2008. Prediction of wave pattern and wave resistance of surface piercing bodies by a boundary element method. International Journal for Numerical Methods in Fluids, 56(3), pp.305-329. https://doi.org/10.1002/fld.1527
6. Bal, S., 2011. The effect of finite depth on 2D and 3D cavitating hydrofoils. Journal of Marine Science and Technology, 16(2), pp.129-142. https://doi.org/10.1007/s00773-011-0117-2
7. Barber, T.J., 2007. A study of water surface deformation due to tip vortices of a wing-in-ground effect. Journal of Ship Research, 51(2), pp.182-186.
8. Daichin, K.W., 2007. PIV measurements of the near-wake flow of an airfoil above a free surface. Journal of Hydrodynamics, 19(4), pp.482-487. https://doi.org/10.1016/S1001-6058(07)60143-7
9. Djavareshkian, M.H., Esmaeli, A. and Parsani, A., 2010. Aerodynamics of smart flap under ground effect. Aerospace Science and Technology, 15(8), pp.642-652.
10. Firooz, A. and Gadami, M., 2006. Turbulence flow for NACA 4412 in unbounded flow and ground effect with different turbulence models and two ground conditions; fixed and moving ground conditions. BAIL 2006, Germany, 23-28 July 2006, pp.81-84.
11. Halloran, M. and O'Meara, S., 1999. Wing in ground effect craft review. [pdf] Melbourne: DSTO Aeronautical and Maritime Research Laboratory. Available at: < http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA361836 > [Accessed 29 July 2013].
12. Jamei, S., Maimun, A., Mansor, S., Azwadi, N. and Priyanto, A., 2012. Numerical investigation on aerodynamic characteristics of a compound wing-in-ground effect. Journal of Aircraft, 49(5), pp.1297-1305. https://doi.org/10.2514/1.C031627
13. Jung, K.H., Chun, H.H. and Kim, H.J., 2008. Experimental investigation of wing-in-ground effect with a NACA6409 section. Journal of Marine Science and Technology, 13(4), pp.317-327. https://doi.org/10.1007/s00773-008-0015-4
14. Katz, J. and Plotkin, A., 1991. Low speed aerodynamics-from wing theory to panel methods. 1st ed. Singapore: Mc-Graw Hill Inc.
15. Kim, H.J., Chun, H.H. and Kwang, H.J., 2009. Aeronumeric optimal design of a wing-in-ground-effect craft. Journal of Marine Science and Technology, 14(1), pp.39-50. https://doi.org/10.1007/s00773-008-0020-7
16. Kinaci, O.K., Kukner, A. and Bal, S., 2011. Interactive effects of 2-D bodies in non-lifting flows. INT-NAM 2011, Turkey, 24-25 October 2011, pp.817-826.
17. Kinaci, O.K., Kukner, A. and Bal, S., 2012. A parametric study on tandem hydrofoil interaction. HYDMAN 2012, Poland, 19-20 September 2012, pp.145-155.
18. Lee, J., Han, C.S. and Bae, C.H., 2010. Influence of wing configurations on aerodynamic characteristics of wings in ground effect. Journal of Aircraft, 47(3), pp.1030-1040. https://doi.org/10.2514/1.46703
19. Lesnic, D., Elliott, L. and Ingham, D.B., 1997. An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation. Engineering Analysis with Boundary Elements, 20(2), pp.123-133. https://doi.org/10.1016/S0955-7997(97)00056-8
20. Liang, H. and Zong, Z., 2011. A subsonic lifting surface theory for wing-in-ground effect. Acta Mechanica, 219(3-4), pp.203-217. https://doi.org/10.1007/s00707-011-0444-8
21. 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. Journal of Marine Science and Technology, 18(1), pp.12-31. https://doi.org/10.1007/s00773-012-0187-9
22. Luo, S.C. and Chen, Y.S., 2012. Ground effect on flow past a wing with a NACA0015 cross-section. Experimental Thermal and Fluid Science, 40, pp.18-28. https://doi.org/10.1016/j.expthermflusci.2012.01.014
23. Ockfen, A.E. and Matveev, K.I., 2009. Aerodynamic characteristics of NACA4412 airfoil section with flap in extreme ground effect. International Journal of Naval Architecture and Ocean Engineering, 1(1), pp.1-12. https://doi.org/10.3744/JNAOE.2009.1.1.001
24. Phillips, W.F. and Hunsaker, D.F., 2013. Liftring-line predictions for induced drag and lift in ground effect. Journal of Aircraft, 50(4), pp.1226-1233. https://doi.org/10.2514/1.C032152
25. Reeves, J.M.L., 1993. The case for surface effect research, platform applications and development opportunities. In: NATOA- GARD fluid mechanics panel (FMP) symposium in long range and long range endurance operation of aircraft, 24- 27 May 1993.
26. Rozhdestvensky, K.V., 2006. Wing-in-ground effect vehicles. Progress in Aerospace Sciences, 42, pp.211-283. https://doi.org/10.1016/j.paerosci.2006.10.001
27. Zhigang, T. and Wei, Y., 2010. Complex flow for wing-in-ground effect craft with power augmented ram engine in cruise. Chinese Journal of Aeronautics, 23, pp.1-8. https://doi.org/10.1016/S1000-9361(09)60180-1
28. Zong, Z., Liang, H. and Zhou, L., 2012. Lifting line theory for wing-in-ground effect in proximity to a free surface. Journal of Engineering Mathematics, 74, pp.143-158. https://doi.org/10.1007/s10665-011-9497-x