A numerical study of flexible flapping wings in highly compressible flows

Recent studies have identified the potential for using bio-inspired mechanisms in aircraft designs for low-density environments, which require high operational speeds associated with significant compressibility effects. This work numerically studies the effects of flexibility on the aerodynamic performance of flapping wings in highly compressible flows by using an immersed boundary method. Simulations were carried out by varying the frequency ratio of the wing from 0.3 to 0.7 and the Mach number (based on the mean velocity of the wing's leading edge) from 0.4 to 1.4. In addition, the Reynolds number and angle of attack of the wing varied in the range of 200–2000 and 30°–60°, respectively. It was observed that increasing the Mach number results in a weakly parabolic (near-linear) decay in the dimensionless lift generation for all cases considered. This decay was observed to be primarily due to the decrease in the lift coefficient peak in the mid-stroke. The decline in the peak lift coefficient was attributed to the increase in pressure and the spanwise flow mitigation of the leading-edge vortex induced by the shock wave generated at the wingtip at sufficiently high Mach numbers. Additional variations in cyclic lift behavior were attributed to a combination of the aerodynamic (pressure) forces, passive wing deformation, and elastic recovery of the wing. These observations were quantified by a local mass ratio effect, which was implemented into an updated scaling law for flexible wings, showing good convergence.