Efficient Tools for the Simulation of Flapping Wing Flows

The development of novel strategies for lift and propulsion using flapping wings requires the use of computational tools that are at once e!cien t and capable of handling complex deforming boundary motion. In this work we present the use of a viscous vortex particle method for the simulation of the flow produced by a two-dimensional rigid wing in pitching and plunging motion of moderate Reynolds number. By its Lagrangian nature, this method is able to automatically adapt to important flow structures. E! ciency is ensured by using vorticity-bearing computational elements that are distributed only to the extent that vorticity itself is spread through its convection and di"u sion; no e" ort is needed for irrotational regions of flow. Moreover, the correct behavior of the velocity at infinity is automatically satisfied, obviating the need for an artificial boundary treatment. Results of the dynamically shed vorticity and the forces exerted are presented for a single stroke of a flapping elliptical wing.

[1]  G. Winckelmans,et al.  Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry , 2000 .

[2]  Petros Koumoutsakos,et al.  Vortex Methods: Theory and Practice , 2000 .

[3]  J. Monaghan.  Particle methods for hydrodynamics , 1985 .

[4]  K. Gersten.  Introduction to Boundary-Layer Theory , 1998 .

[5]  A. Chorin.  Numerical study of slightly viscous flow , 1973, Journal of Fluid Mechanics.

[6]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[7]  K. Kawachi,et al.  A Numerical Study of Insect Flight , 1998 .

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

[9]  P. Degond,et al.  The weighted particle method for convection-diffusion equations , 1989 .

[10]  Michael S. Warren,et al.  Vortex Methods for Direct Numerical Simulation of Three-Dimensional Bluff Body Flows , 2002 .

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

[12]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[13]  R. Ramamurti,et al.  A three-dimensional computational study of the aerodynamic mechanisms of insect flight. , 2002, The Journal of experimental biology.

[14]  Tim Colonius,et al.  A general deterministic treatment of derivatives in particle methods , 2002 .

[15]  Z. J. Wang.  Vortex shedding and frequency selection in flapping flight , 2000, Journal of Fluid Mechanics.

[16]  Z. J. Wang,et al.  A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow , 2003 .

[17]  P. Koumoutsakos,et al.  Boundary Conditions for Viscous Vortex Methods , 1994 .