| In order to study the aerodynamics of insect flight for Reynolds numbers in the range of 8--128, the Immersed Boundary Method was used to solve the two-dimensional incompressible Navier-Stokes equations with a flexible moving boundary. Although a number of experimental, numerical, and analytical studies have considered lift forces produced during flight in larger insects, only a few have considered Reynolds numbers below 100. To begin, the immersed boundary method was used to model two-dimensional stiff and flexible wings through one stroke cycle. Lift coefficients fell into two distinct patterns. For Reynolds numbers of 64 and higher, vortices were alternately shed from the wing forming the von Karman vortex street. For Reynolds numbers of 32 and below, leading and trailing edge vortices formed and remained 'attached' to the wing. The vortical symmetry produced at lower Reynolds numbers results in smaller lift forces and suggests that this transition is significant to flight in the smallest insects.; In order to study wing-wing interactions, the immersed boundary method was used to model two rigid or flexible wings performing an idealized 'clap and fling' stroke. The results for stiff wings show that the lift generated during constant translation following 'fling' is substantially higher than the lift generated during steady translation. This effect becomes more significant with decreasing Reynolds number, and could explain why all tiny insects use the 'clap and fling'. The results for flexible wings show that lift is also enhanced during translation following fling. In addition, the drag forces produced are significantly lower than those produced by a stiff wing using the same motion. |
