Lagrangian Coherent Structures in Tandem Flapping Wing Hovering

Lagrangian Coherent Structures (LCS) of tandem wings hovering in an inclined stroke plane is studied using ImmersedBoundary Method (IBM) by solving two dimensional (2D) incompressible Navier-Stokes equations.Coherent structures responsible for the force variation are visualized by calculating Finite Time Lyapunov Exponents (FTLE),and vorticity contours.LCS is effective in determining the vortex boundaries,flow separation,and the wing-vortex interactions accurately.The effects of inter-wing distance and phase difference on the force generation are studied.Results show that in-phase stroking generates maximum vertical force and counter-stroking generates the least vertical force.In-phase stroking generates a wake with swirl,and counter stroking generates a wake with predominant vertical velocity.Counter stroking aids the stability of the body in hovering.As the hindwing operates in the wake of the forewing,due to the reduction in the effective Angle of Attack (AoA),the hindwing generates lesser force than that of a single flapping wing.