Flow periodicity analysis past a flapping airfoil using proper orthogonal decomposition

The transition in the flow-periodicity behind a pitching-plunging airfoil is explored by proper orthogonal decomposition (POD) analysis. The high fidelity simulation of the vortical flow past a flapping airfoil is carried out in a low Reynolds number regime (Re = 1000) by a finite volume based incompressible Navier-Stokes solver. The flow topology transitions from a periodic to chaotic dynamics as the non-dimensional plunge amplitude (h) is increased at a constant pitch amplitude and flapping frequency. POD is opted to decompose the flow field into a set of orthogonal modes of varying energy content using the numerically obtained flow snapshots. It is observed that 99.35% of the total kinetic energy is captured by the first 10 high energy POD modes in the periodic regime (h = 0:5). However, the number of POD modes required to reconstruct the flow-field accurately in- creases as the periodicity of flow is lost. It is seen that the first 10 POD modes capture only 51.19% of the total energy in the chaotic state (h = 1:25). Interesting insights into the change of flow periodicity are obtained by comparing the formation and symmetry of the dominant POD modes of different disparate dynamics with the increase in h. Moreover, the time histories and phase portraits of the corresponding temporal coefficients reflect the dynamical transition as well.