Quasi-periodic vortical signature of an elastically mounted flapping airfoil

The present study investigates the flow physics over an elastically mounted symmetric NACA 0012 airfoil with bending and torsion exibility in the low Reynolds number regime. The dynamical signature of the wake of the airfoil, with pitch and plunge dof, is investigated in a regime where structural and fluid-added mass are comparable (solid to uid added mass ratio, μ = 5) fitting the requirement of very light weight apping wing Micro Aerial Vehicles. The FSI solver is built by weakly coupling an incompressible Navier-Stokes solver with a 2-dof nonlinear structural model having cubic nonlinearity in the pitch stifiness. The present model is essentially a coupled nonlinear fluid-structure interaction (FSI) system which shows a rich bifurcation behaviour as the non-dimensional free stream velocity (U*) is increased as the control parameter. Due to the structural as well as fluid nonlinearity present in the system, successive Hopf bifurcations take place and the self-excited flapping response becomes quasi-periodic which in turn makes the flow-field quasi-periodic. The quasi-periodic flow dynamics has been explored in terms of the vortical signature of the wake followed by the phase averaged vorticity contours and correlation coefficient of the vorticity field. The nonlinear time series analysis of the aerodynamic loads has also been carried out to systematically establish the quasi-periodic flow dynamics.