OJFD  Vol.3 No.4 , December 2013
Study on the Wake Shape behind a Wing in Ground Effect Using an Unsteady Discrete Vortex Panel Method
Abstract: The unsteady evolution of trailing vortex sheets behind a wing in ground effect is simulated using an unsteady discrete vortex panel method. The ground effect is included by image method. The present method is validated by comparing the simulated wake roll-up shapes to published numerical results. When a wing is flying in a very close proximity to the ground, the optimal wing loading is parabolic rather than elliptic. Thus, a theoretical model of wing load distributions is suggested, and unsteady vortex evolutions behind lifting lines with both elliptic and parabolic load distributions are simulated for several ground heights. For a lifting line with elliptic and parabolic loading, the ground has the effect of moving the wingtip vortices laterally outward and suppressing the development of the vortex. When the wing is in a very close proximity to the ground, the types of wing load distributions does not affect much on the overall wake shapes, but parabolic load distributions make the wingtip vortices move more laterally outward than the elliptic load distributions.
Cite this paper: C. Han and S. Kinnas, "Study on the Wake Shape behind a Wing in Ground Effect Using an Unsteady Discrete Vortex Panel Method," Open Journal of Fluid Dynamics, Vol. 3 No. 4, 2013, pp. 261-265. doi: 10.4236/ojfd.2013.34032.

[1]   K. V. Rozhdestvensky, “Wing-in-Ground Effect Vehicles,” Progress in Aerospace Sciences, Vol. 42, No. 3, 2006, pp. 183-211.

[2]   K. V. Rozhdestvensky, “Aerodynamics of a Lifting System in Extreme Ground Effect,” Springer, Heidelberg, 2000.

[3]   H. W. M. Hoeijmakers and W. Vaatstra, “A Higher Order Panel Method Applied to Vortex Sheet Roll-up,” AIAA Journal, Vol. 21, No. 4, 1983, pp. 516-523.

[4]   R. S. Ribeiro and I. Kroo, “Vortex-in-Cell Analysis of Wing Wake Roll-Up,” Journal of Aircraft, Vol. 32, No. 5, 1995, pp. 962-969.

[5]   K. Zhu and H. Takami, “Effect of Ground on Wake Roll-Up behind a Lifting Surface,” Proceedings of the 37th Japan National Congress for Applied Mechanics, Tokyo, 1987, pp. 115-123.

[6]   F. Lamarre and I. Paraschivoiu, “Efficient Panel Method for Vortex Sheet Roll-Up,” Journal of Aircraft, Vol. 29, No. 1, 1992, pp. 28-33.

[7]   T. Sarpkaya, “Computational Methods with Vortices— The 1988 Freeman Scholar Lecture,” Journal of Fluids Engineering, Vol. 111, No. 1, 1989, pp. 5-52.

[8]   D. I. Pullin, “The Large-scale Structure of Unsteady Self-Similar Rolled-Up Vortex Sheets,” Journal of Fluid Mechanics, Vol. 88, No. 3, 1978, pp. 401-430.

[9]   R. Krasny, “A Study of Singularity Formation in a Vortex Sheet by the Point-Vortex Approximation,” Journal of Fluid Mechanics, Vol. 167, 1986, pp. 65-93.

[10]   R. Krasny, “Computation of Vortex Sheet Roll-Up in the Trefftz Plane,” Journal of Fluid Mechanics, Vol. 184, 1987, pp. 123-155.

[11]   M. Morky, “Numerical Simulation of Aircraft Trailing Vortices Interacting with Ambient Shear or Ground,” Journal of Aircraft, Vol. 38, No. 4, 2001, pp. 636-643.

[12]   C. Han and J. Cho, “Unsteady Trailing Vortex Evolution Behind a Wing in Ground Effect,” Journal of Aircraft, Vol. 42, No. 2, 2005, pp. 429-434.

[13]   S. E. Windall, and T. M. Barrows, “An Analytic Solution for Two-and Three-Dimensional Wings in Ground Effect,” Journal of Fluid Mechanics, Vol. 41, No. 4, 1970, pp. 769-792.

[14]   A. Plotkin and C. H. Tan, “Lifting-Line Solution for a Symmetrical Thin Wing in Ground Effect,” AIAA Journal, Vol. 24, No. 7, 1986, pp. 1193-1194.

[15]   J. Anderson, “Fundamentals of Aerodynamics,” 5th Edition, McGraw Hill, New York, 2010.

[16]   J. Katz and A. Plotkin, “Low Speed Aerodynamics,” 2nd Edition, Cambridge University Press, Cambridge, 2001.

[17]   I. G. Sheldon, “Wing Tip Vortices,” In: I. G. Sheldon, Ed., Fluid Vortices, Kluwer Academic Publishers, Berlin, 1995, Chapter X.

[18]   M. Shigemi, T. Fujita, A. Iwasaki, T. Ohnuki, K. Rinoie, H. Nakayasu and M. Sagisaka, “Experimental Investigation of Static and Dynamic Ground Effect on HOPE ALFLEX Vehicle,” Technical Report of National Aerospace Laboratory TR-1236, National Aerospace Laboratory, Tokyo, 1994.

[19]   A. Ogawa, “Vortex Flow-CRC Series on Fine Particle Science and Technology,” CRC Press, Boca Raton, 1940.

[20]   G. C. Ling, P. W. Bearman and J. M. R. Graham, “A Further Simulation of Starting Flow around a Flat Plate by a Discrete Vortex Model,” Internal Seminar on Engineering Applications of the Surface and Cloud Vorticity Methods, Vol. 51, No. 14, 1986, pp. 118-138.

[21]   J. G. Leishman, “Principles of Helicopter Aerodynamics,” 2nd Edition, Cambridge University Press, Cambridge, 2000.