Unsteady Aerodynamics of Multiple Airfoils in Configuration

A potential flow model is used to study the unsteady flow past two airfoils in configuration, each of which is suddenly set into motion. The airfoil bound vortices are modeled using lumped vortex elements and the wake behind the airfoil is modeled by discrete vortices. This consists of solving a steady state flow problem at each time-step where unsteadiness is incorporated through the “zero normal flow on a solid surface" boundary condition at every time instant. Additionally, along with the “zero normal flow on a solid surface" boundary condition Kelvin-s condition is used to compute the strength of the latest wake vortex shed from the trailing edge of the airfoil. Location of the wake vortices is updated at each time-step to get the wake shape at each time instant. Results are presented to show the effect of airfoil-airfoil interaction and airfoil-wake interaction on the aerodynamic characteristics of each airfoil.

Authors:

• Hossain Aziz
• Rinku Mukherjee

Keywords:

• Aerodynamics
• Airfoils
• Configuration
• Unsteady.

References:

[1] Seiler, P., Pant, A. and Hedrick, K. "Analysis of bird formations",
Proceedings of 41st IEEE Conference on Decision and Control, Las
Vegas, Nevada, USA, December 2002.
[2] Poore, S. O., Sanchez-Heiman, A. and Goslow, G. E. Jr., "Aircraft
upstroke and evolution of flapping flight", Nature, Vol 387, pp 799-802,
June 1997.
[3] Steven Hoa, Hany Nassefa, Nick Pornsinsirirakb, Yu-Chong Taib, Chih-
Ming Hoa, "Unsteady aerodynamics and flow control for flapping wing
flyers", Progress in Aerospace Sciences, 39, 635-681, 2003.
[4] Bangash, Z. A., Sanchez, R. P. and Ahmed, A., "Aerodynamics of
Formation Flight, Journal of Aircraft", Vol 43, No. 4, pp 907-912, July-
August 2006.
[5] Vachon M., Ray R., Walsh K., Ennix, K., "F/A-18 Aircraft Performance
Benefits Measured During the Autonomous Formation Flight Project",
AIAA 2002-4491, Aug 2002.
[6] Bowles R. G. A. and Smith F. T., "Lifting multi-blade flows with
interaction", J. Fluid Mech., vol. 415, pp. 203-226, 2000.
[7] D. Fanjoy, and D. J. Dorney, "A study of tandem-airfoil interaction in
different flight regimes," AIAA 97-0515, 1997.
[8] L. Zannetti, F. Gallizio, and G. M. Ottino, "Vortex motion in doubly
connected domains," J. Fluid Mech., vol. 612, pp. 143 - 152, 2008.
[9] Z. Husain, M. J. Abdullah, and T. C. Yap, "Two-dimensional analysis of
tandem/staggered airfoils using computational fluid dynamics,"
International Journal of Mechanical Engineering Education 33/3.
[10] Katz, J. and Plotkin, A., Low-speed Aerodynamics, Cambridge University
Press, 2001.
[11] A. J. Chorin, and P. S. Bernard, "Discretization of a vortex sheet, with an
example of roll-up," J. of Computational Physics., vol. 13, No. 3, 1973.
[12] A. Fage and F. C. Johansen, "On the flow of air behind an inclined flat
plate of infinite span" Proc. Roy. Soc. A 116, 170, 1927.
[13] T. Nakagawa, "On Unsteady Airfoil-Vortex Interaction", ACTA
MECHANICA 75, 1-13, 1988
[14] H. Wagner, "Uber die Entstehung des Dynamischen Autriebes von
Tragflugeln", Z.F.A.M.M., Vol. 5, No. 1, pp 17-35, 1925.