Numerical simulation of the unsteady aerodynamics of flapping airfoils

Abstract

There is currently a great deal of interest within the aviation community in the design of small, slow-flying but manoeuvrable uninhabited vehicles for reconnaissance, surveillance, and search and rescue operations in urban environments. Inspired by observation of birds, insects, fish and cetaceans, flapping wings are being actively studied in the hope that they may provide greater propulsive efficiencies than propellers and rotors at low Reynolds numbers for such Micro-Air Vehicles (MAVs). Researchers have posited the Strouhal number (combining flapping frequency, amplitude and forward speed) as the parameter controlling flapping wing aerodynamics in cruising flight, although there is conflicting evidence. This thesis explores the effect of flapping frequency and amplitude on forces and wake structures, as well as physical mechanisms leading to optimum propulsive efficiency. Two-dimensional rigid airfoils are considered at Reynolds number 2,000 – 40,000. A compressible Navier-Stokes simulation is combined with numerical and analytical potential flow techniques to isolate and evaluate the effect of viscosity, leading and trailing edge vortex separation, and wake vortex dynamics. The wake structures of a plunging airfoil are shown to be sensitive to the flapping frequency independent of the Strouhal number. For a given frequency, the wake of the airfoil exhibits ‘vortex lock-in’ as the amplitude of motion is increased, in a manner analogous to an oscillating circular cylinder. This is caused by interaction between the flapping frequency and the ‘bluff-body’ vortex shedding frequency apparent even for streamlined airfoils at low Reynolds number. The thrust and propulsive efficiency of a plunging airfoil are also shown to be sensitive to the flapping frequency independent of Strouhal number. This dependence is the result of vortex shedding from the leading edge, and an interaction between the flapping frequency and the time for vortex formation, separation and convection over the airfoil surface. The observed propulsive efficiency peak for a pitching and plunging airfoil is shown to be the result of leading edge vortex shedding at low flapping frequencies (low Strouhal numbers), and high power requirements at large flapping amplitudes (high Strouhal numbers). The efficiency peak is governed by flapping frequency and amplitude separately, rather than the Strouhal number directly.