Study On The Wake Vortex Influence In Insect Flapping Hovering Flight

In insect flapping flight, controversial perspectives have been proposed on thecontribution of the wake to the lift force. This problem has been widely studied byresearchers from various fields. In this thesis, we study the evolution of wake vorticityand the aerodynamic force related to mutual interaction of the vortex rings in insecthovering flight using a flapping flight vortex model. We obtain the effect of wake vortexon lift force and the time variation of stroke-averaged lift force during the course ofwake establishment. The lift force trends predicted by our theoretical model agree quitewell with the experimental results provided by Birch&Dickinson[1].We establish a vortex model for insect flapping flight, which is decomposed intothe wing plane (wing-linked) vortex ring, a loop closed by the bound vortex and(arc-shaped) trailing vortex, and the wake (the vortex rings shed previously). The vortexmodel developed by Rayner[2]and Ellington[3]is applied to model the wake. Using thediscrete vortex mothod (Rayner[2]), we obtain the manners in which the wake vortexrings develop. During the initial stage of flapping, the vortex rings move in a disorderway after they are shed into the wake. A stable wake will gradually develop after severalstrokes.The vorticity moment theory (Wu[4]) is used to study the lift force related to thevortex system. We derive the formula for the aerodynamic force related to anarbitrarily-shaped vortex ring in a three-dimensional space. The aerodynamic force on aparticular direction related to a vortex ring is proportional to the time variation ofproduct of the projection area along this direction and the circulation of the vortex ring.We are able to identify the roles of vortex rings in lift production or reduction andexpress the lift as a function of areal contraction or expansion of vortex rings. The wakevortex rings induce areal contraction of the trailing vortex, which should decrease thelift. But this decrease is exactly compensated by the inducing effect of the trailing arc onthe wake. So, the mutual interactions of the vortex rings do not have a direct effect onthe aerodynamic force. The wake reduces the lift through inducing a downwash velocityon the wing plane, which reduces the effective angle of attack in the stroke plane.We derive the relation between the lift force related to the bound vortex and thevelocity in the wing plane induced by the wake vortex rings. The time variation of the lift force ever since the wake starts to develop has been obtained, which is shown todrop to a minimum at the2nd half stroke, and then increase to an asymptotic valueslightly below the lift at the first half stroke. This result follows very well with theexperimental observation of Birch&Dickinson[1]. We are able to explain the reason fornegative peak of lift. It is due to the first shed vortex ring which, just at the2nd halfstroke, lies in the close vicinity to the wing plane, leading to a peak of the wing planedownwash velocity. Although the number of vortex rings is increasing in the followinghalf strokes, the rings move downward quickly due to the induced velocity field, andtherefore induce a smaller velocity in the wing plane compared to the second halfstroke.We use image method to consider the walls in the flapping flow field and obtainthe form of vorticity moment theory when the image vortex rings exist. The effects ofbody and wing plane on the vortex ring evolution and lift force are studied. The resultshows that the lift force reduces when the insect body and wing plane is taken intoconsideration. The larger the body occupies, the greater it reduces the lift force.