The Influence of Fin Rigidity and Gusts on the Force Production in Fishes and Insects : a Computational Study

The three-dimensional unsteady computations of fish swimming with oscillating and deforming fins of varying rigidity were carried out. The objective of these variable rigidity computations was to investigate the importance of fin deformation on the fluid dynamics of force production. An unstructured grid-based unsteady Navier-Stokes solver with automatic adaptive remeshing was used to compute the flow about the wrasse through several complete cycles of pectoral fin oscillation for each of the fins studied. The computations show that when the fin is made rigid by specifying the motion with just the leading edge of the fin tip, the thrust produced during the upstroke is less than half of the peak thrust produced by the flexible cases. During the downstroke, the rigid fin and the fin with the motion prescribed with only the leading and trailing edges produced no positive thrust, while all the flexible cases considered reproduced the thrust production of the fully deformable fin. In the case of the rigid fin, there is a substantial penalty in lift during the upstroke. We have also computed the unsteady flow computations over the Drosophila wing with the flight conditions ranging from hovering to a downward gust velocity nearly equal to the mean wing tip velocity. We showed that the wake capture mechanism which is responsible for a peak in thrust production just after stroke reversal diminished with increasing downward velocity and is entirely absent when this velocity reaches the mean wing tip velocity. * Senior Member, Aerospace Engineer, Code 6410, Laboratory for Computational Physics and Fluid Dynamics. † Deputy Director, Code 6401, Laboratory for Computational Physics and Fluid Dynamics. + Professor, SCS/ Laboratory for Computational Fluid Dynamics. INTRODUCTION Flapping foil propulsion has received considerable attention in the past few years as an alternative to the propeller. This mode of propulsion which involves no body undulation, has many applications, such as submersibles propulsion, maneuvering and flow control which are of interest to the hydrodynamic community and unconventional aerodynamics of Micro Aerial Vehicles (MAV) and the study of aircraft flutter for the aerodynamic community. In order to develop practical MAVs, we have been investigating both fixed wings with propeller driven thrust and flapping wings as a possible propulsive mode. For vehicles with very small inertia, as in the case of MAVs, changes in wing loading can immediately affect the flight path. The need for suppressing the effects of wind gusts becomes important, more so when the airspeed of the vehicle decreases, wind gusts become a large percentage of the mean airspeed of the vehicle. This is further complicated by the fact that the gusts are not always head-on. Since control of these vehicles is one of the most important problems, it is important to suppress unwanted and sudden changes in direction, elevation and orientation. Flapping foil propulsion is also important in the area of bio-fluid dynamics, for the study of propulsion in insects, birds and certain aquatic animals. Flying animals generate the lift and thrust as a consequence of the interaction of the flapping motions of the wings with the surrounding air. These animals also perform rapid maneuvers involving rapid plunging and pitching motions. Conventional steady state theories are not sufficient to generate enough forces required for flight as shown by Ellington et al. (1996). Therefore, we need to understand the aerodynamics of flapping wings undergoing highly three-dimensional and unsteady motions with varying geometries. The wing strokes of the insects can be divided into two translational and two rotational phases. During the translational phases, upstroke and downstroke, the wing moves through the air with high angle of attack and during the rotational phases, pronation and supination, the wings rotate rapidly and reverse direction. Dickinson et al. (1999) has studied the effects of the wing rotation in the fruitfly, Drosophila, and Walker and Westneat (1997) have studied the kinematics of the fin motion in a class of fishes, namely the bird wrasse, experimentally. Liu and Kawachi (1998) have studied