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CLC number: TK83

On-line Access: 2012-01-18

Received: 2010-12-11

Revision Accepted: 2011-08-30

Crosschecked: 2011-12-14

Cited: 1

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Journal of Zhejiang University SCIENCE A 2012 Vol.13 No.2 P.105-120


Kinematic optimization of 2D plunging airfoil motion using the response surface methodology

Author(s):  Mahmoud Mekadem, Taha Chettibi, Samir Hanchi, Laurent Keirsbulck, Larbilabraga

Affiliation(s):  Fluids Mechanics Laboratory, Polytechnic Military School, Bordj el Bahri, Algiers 16045, Algeria; more

Corresponding email(s):   mahmoud.mekadem@univ-valenciennes.fr, mahmoud.mekadem@gmail.com

Key Words:  Plunging airfoil, Propulsive efficiency, Optimization, Response surface methodology (RSM)

Mahmoud Mekadem, Taha Chettibi, Samir Hanchi, Laurent Keirsbulck, Larbilabraga . Kinematic optimization of 2D plunging airfoil motion using the response surface methodology[J]. Journal of Zhejiang University Science A, 2012, 13(2): 105-120.

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author="Mahmoud Mekadem, Taha Chettibi, Samir Hanchi, Laurent Keirsbulck, Larbilabraga ",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Kinematic optimization of 2D plunging airfoil motion using the response surface methodology
%A Mahmoud Mekadem
%A Taha Chettibi
%A Samir Hanchi
%A Laurent Keirsbulck
%A Larbilabraga
%J Journal of Zhejiang University SCIENCE A
%V 13
%N 2
%P 105-120
%@ 1673-565X
%D 2012
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1000502

T1 - Kinematic optimization of 2D plunging airfoil motion using the response surface methodology
A1 - Mahmoud Mekadem
A1 - Taha Chettibi
A1 - Samir Hanchi
A1 - Laurent Keirsbulck
A1 - Larbilabraga
J0 - Journal of Zhejiang University Science A
VL - 13
IS - 2
SP - 105
EP - 120
%@ 1673-565X
Y1 - 2012
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1000502

The propulsive efficiency of a plunging NACA0012 airfoil is maximized by means of a simple numerical optimization method based on the response surface methodology (RSM). The control parameters are the amplitude and the reduced frequency of the harmonic sinusoidal motion. The 2D unsteady laminar flow around the plunging airfoil is computed by solving the Navier-Stokes equations for three Reynolds number values (Re=3.3×103, 1.1×104, and 2.2×104). The Nelder-Mead algorithm is used to find the best control parameters leading to the optimal propulsive efficiency over the constructed response surfaces. It is found that, for a given efficiency level and regardless of the considered Re value, it is possible either to obtain high thrust by selecting a high oscillation frequency or to reduce the input power by adopting a low plunging amplitude.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Anderson, J.M., Streitlien, K., Barrett, D.S., Triantafyllou, M.S., 1998. Oscillating foils of high propulsive efficiency. Journal of Fluid Mechanics, 360:41-72.

[2]Bansmer, S., Radespiel, R., Unger, R., Haupt, M., Horst, P., 2010. Experimental and numerical fluid-structure analysis of rigid and flexible flapping airfoils. AIAA Journal, 48(9):1959-1974.

[3]Betz, A., 1912. Ein beitrag zur erklarung des segelfluges. Zeitschrift fur Flugtechnik und Motorluftschiffahrt, 3:269-272 (in German).

[4]Box, G.E.P., Draper, N.R., 2007. Response Surfaces, Mixtures, and Ridge Analyses (2nd Ed.). John Wiley & Sons, Inc., USA.

[5]Dickinson, M.H., Gotz, K.G., 1993. Unsteady aerodynamic performance of model wings at low Reynolds numbers. Journal of Experimental Biology, 174:45-64.

[6]Dickinson, M.H., Lehmann, F.O., Sane, S.P., 1999. Wing rotation and the aerodynamic basis of insect flight. Science, 284(5422):1954-1960.

[7]Ellington, C.P., 1984. The aerodynamics of hovering in-sect flight. I. The quasi-steady analysis. Philosophical Transactions of the Royal Society B: Biological Sciences, 305(1122):1-15.

[8]Ellington, C.P., van den Berg, C., Willmott, A., Thomas, A.L.R., 1996. Leading edge vortices in insect flight. Nature, 384:626-630.

[9]Garrick, I.E., 1936. Propulsion of a Flapping and Oscillating Airfoil. NACA Technical Report No. 567.

[10]Haftka, R., Scott, E.P., Cruz, J.R., 1998. Optimization and experiments: a survey. Applied Mechanics Review, 51(7):435-448.

[11]Heathcote, S., Wang, Z., Gursul, I., 2008. Effect of spanwise flexibility on flapping wing propulsion. Journal of Fluids and Structures, 24(2):183-199.

[12]Isogai, K., Shinmoto, Y., Watanabe, Y., 1999. Effects of dynamic stall on propulsive efficiency and thrust of flapping airfoil. AIAA Journal, 37(10):1145-1151.

[13]Jones, K.D., Platzer, M.F., 1997. Numerical Computation of Flapping Wing Propulsion and Power Extraction. 35th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA, No. 97-0826.

[14]Jones, K.D., Platzer, M.F., 2001. On the Use of Vortex Flows for the Propulsion of Micro-Air and Sea Vehicles. Applied Vehicle Technology Panel (AVT), Norway, p.40-1-40-13.

[15]Jones, K.D., Dohring, C.M., Platzer, M.F., 1998. An experimental and computational investigation of the Knoller-Betz effect. AIAA Journal, 36(7):1240-1246.

[16]Katzmayr, R., 1922. Effect of Periodic Changes of Angle of Attack on Behaviour of Airfoils. NACA Technical Report No. TM 147.

[17]Kaya, M., Tuncer, I.H., 2006. Path Optimization of Flapping Airfoils Based on NURBS. Proceedings of International Conference on Parallel Computational Fluid Dynamics, Busan, Korea.

[18]Kaya, M., Tuncer, I.H., 2008a. Path Optimization of Dual Airfoils Flapping in a Biplane Configuration Using Response Surface Methodology in a Parallel Computing Environment. Proceedings of International Conference on Parallel Computational Fluid Dynamics, Lyon, France.

[19]Kaya, M., Tuncer, I.H., 2008b. Path Optimization of Thrust Producing Flapping Airfoils Using Response Surface Methodology. 5th European Congress on Computational Methods in Applied Sciences and Engendering, Venice, Italy.

[20]Knoller, R., 1909. Die gesetze des luftwiderstands. Flug-und Motortechnik, 3:1-7 (in German).

[21]Lai, J.C.S., Platzer, M.F., 1999. Jet characteristics of a plunging airfoil. AIAA Journal, 37(12):1529-1537.

[22]Lian, Y., Shyy, W., 2007. Aerodynamics of Low Reynolds Number Plunging Airfoil Under Gusty Environment. 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA, AIAA-2007-71.

[23]Miao, J.M., Ho, M.H, 2006. Effect of flexure on aero-dynamic propulsive efficiency of flapping flexible air-foil. Journal of Fluids and Structures, 22(3):401-419.

[24]Munch, C., Ausoni, P., Braun, O., Farhat, M., Avellan, F., 2010. Fluid-structure coupling for an oscillating hydrofoil. Journal of Fluids and Structures, 26(7):1018-1033.

[25]Platzer, M.F., Jones, K.D., Young, J., Lai, J.C.S., 2008. Flapping-wing aerodynamics: progress and challenges. AIAA Journal, 46(9):2136-2149.

[26]Ramamurti, R., Sandberg, W., 2001. Simulation of flow about flapping airfoils using finite element incompressible flow solver. AIAA Journal, 39(2):253-260.

[27]Raymer, D.P., 2002. Enhancing Aircraft Conceptual Design Using Multidisciplinary Optimization. PhD Thesis, Royal Institute of Technology, Stockholm, Sweden.

[28]Rodriguez, D.L., 2003. Response Surface Based Optimization with a Cartesian CFD Method. 41st AIAA Aerospace Sciences Meeting, Reno, Nevada, USA, AIAA-2003 -0465.

[29]Sane, S.P., 2003. The aerodynamics of insect flight. Journal of Experimental Biology, 206:4191-4208.

[30]Schouveiler, L., Hover, F.S., Triantafyllou, M.S., 2005. Performance of flapping foil propulsion. Journal of Fluids and Structures, 20(7):949-959.

[31]Shyy, W., Berg, M., Ljungqvist, D., 1999. Flapping and flexible wings for biological and micro air vehicles. Progress in Aerospace Sciences, 35(5):455-505.

[32]Soueid, H., Guglielmini, L., Airiau, C., Bottaro, A., 2009. Optimization of the motion of a flapping airfoil using sensitivity functions. Computers & Fluids, 38(4):861-874.

[33]Theodorsen, T., 1935. General Theory of Aerodynamic Instability and the Mechanism of Flutter. NASA Technical Report No. 496.

[34]Tuncer, I.H., Platzer, M.F., 2000. Computational study of flapping airfoil aerodynamics. AIAA Journal of Aircraft, 37(3):514-520.

[35]Tuncer, I.H., Kaya, M., 2005. Optimization of flapping airfoils for maximum thrust and propulsive efficiency. AIAA Journal, 43(11):2329-2336.

[36]Wang, G.G., Dong, Z., 2000. Design optimization of a complex mechanical system using adaptive response surface method. Transactions of the CSME, 24(1B):295-306.

[37]Yang, W.Y., Cao, W., Chung, T.S., Morris, J., 2005. Applied Numerical Methods Using Matlab. John Wiley & Sons Inc., USA.

[38]Yang, S., Luo, S., Liu, F., Tsai, H.M., 2006. Optimization of Unstalled Pitching and Plunging Motion of an Airfoil. 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, USA, No. 06-1055.

[39]Young, J., Lai, J.C.S., 2004. Oscillation frequency and amplitude effects on the wake of a plunging airfoil. AIAA Journal, 42(10):2042-2052.

[40]Young, J., Lai, J.C.S., 2007. Mechanisms influencing the efficiency of oscillating airfoil propulsion. AIAA Journal, 45(7):1695-1702.

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