Effect of flexion on the propulsive performance of a flexible flapping wing

A numerical study was carried out to investigate the effect of chordwise flexion on the propulsive performance of a two-dimensional flexible flapping wing. The wing undergoes a prescribed sinusoidal heaving motion with a local deflection. A deformable overset grid dynamic mesh method was employed to implement the motion of the grid instantaneously. The effect of flexural pattern, flexural amplitude and flapping frequency in terms of Strouhal number are evaluated. Unsteady flow around the wing is computed using an in-house developed Unsteady Reynolds-Averaged Navier-Stokes (URANS) solver. The results show that the different flexural patterns will create different flow fields, and thus the thrust generation will be significantly varied. The thrust and propulsive efficiency do not increase monotonically with the flexure amplitude while a peak value is revealed. It is found that the wake vortices after the flapping motion assembly behave as a reverse von-Karman vortex street, which can principally create thrust. The thrust is found to increase with increasing Strouhal number. Propulsive efficiency is beneficial from the chordwise flexibility and peaks within the range of 0.2 < St < 0.4, which is evidenced by natural flyers.

[1]  I. E. Garrick Propulsion of a flapping and oscillating airfoil , 1936 .

[2]  Tianhang Xiao,et al.  A preconditioned dual time-stepping procedure coupled with matrix-free LU-SGS scheme for unsteady low speed viscous flows with moving objects , 2007 .

[3]  Sam Heathcote,et al.  Flexible flapping airfoil propulsion at low Reynolds numbers , 2005 .

[4]  T. Weis-Fogh Quick estimates of flight fitness in hovering animals , 1973 .

[5]  Ning Qin,et al.  Fast dynamic grid deformation based on Delaunay graph mapping , 2006 .

[6]  R. B. Srygley,et al.  Unconventional lift-generating mechanisms in free-flying butterflies , 2002, Nature.

[7]  Max F. Platzer,et al.  Numerical Computation of Flapping-Wing Propulsion and Power Extraction , 1997 .

[8]  R Katzmayr,et al.  Effect of Periodic Changes of Angle of Attack on Behavior of Airfoils , 1922 .

[9]  Adrian L. R. Thomas,et al.  Leading-edge vortices in insect flight , 1996, Nature.

[10]  Ismail H. Tuncer,et al.  Thrust Generation Caused by Flapping Airfoils in a Biplane Configuration , 2003 .

[11]  M. Koochesfahani Vortical patterns in the wake of an oscillating airfoil , 1987 .

[12]  Joseph Katz,et al.  Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility , 1978, Journal of Fluid Mechanics.

[13]  Anthony Colozza,et al.  Force Measurements on a Flapping and Pitching Wing At Low Reynolds Numbers , 2006 .

[14]  R. Ramamurti,et al.  Simulation of Flow About Flapping Airfoils Using Finite Element Incompressible Flow Solver , 2001 .

[15]  Wayne A. Smith,et al.  Preconditioning Applied to Variable and Constant Density Flows , 1995 .

[16]  P. Roe Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[17]  M. Dickinson,et al.  Wing rotation and the aerodynamic basis of insect flight. , 1999, Science.

[18]  T. Kármán General aerodynamic theory. Perfect fluids , 1963 .

[19]  Adrian L. R. Thomas,et al.  Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency , 2003, Nature.

[20]  Keiji Kawachi,et al.  Regular Article: A Numerical Study of Undulatory Swimming , 1999 .