Oscillatory motions of a prestrained compliant membrane caused by fluid–membrane interaction

Flow over a compliant membrane is a complex problem where the interaction between fluid and membrane determines the nature of the aerodynamic characteristics of the membrane wing. This investigation is concerned with the deformation and oscillatory motion of a membrane under aerodynamic loading. The approach is computational, but the analytical solution is also presented for a constant pressure loading. The computational results are compared with the experimental data available in the literature as well as with the present analytical solution. In this study, the values of Reynolds number are 38 416 and 141 500, and the angle of attack and prestrain range from 10° to 40° and from 0 to 0.074, respectively. This range of parameters makes the outcome of the investigation more relevant to applications involving the flight of micro air vehicles and the membrane wings of flying mammals such as bats. The computations indicate a mostly asymmetric deflection with the point of maximum camber located nearly at 40% of the chord length from the leading edge. The deflection is decreased with prestrain, and it is increased with Reynolds number. Moreover, the lift coefficient generally increases with the angle of attack. However, for Re=141 500, it increases first to a peak at 20–30° angle of attack, and then decreases. The drag coefficient is much higher than that of conventional airfoils. The membrane oscillates in the streamwise and vertical directions. The largest amplitude of oscillations is observed at 40° for Re=38 416. The oscillations are caused by the oscillatory nature of the flow due to fluid–membrane interaction and the formation of the leading edge and trailing edge vortices. Compared with a rigid membrane of the same camber, the compliant membrane has a smaller recirculation region which may lead to a delayed stall.