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The present study investigates the mechanisms of wake-induced flow dynamics in tandem National Advisory Committee for Aeronautics 0015 flapping foils at low Reynolds number of Re = 1100. A moving mesh arbitrary Lagrangian–Eulerian framework is utilized to realize the prescribed flapping motion of the foils while solving the flow via incompressible Navier–Stokes equations. The effect of the gap between the two foils on the thrust generation is studied for gaps of 1–10 times the chord of the downstream foil. The mean thrust as well as the propulsive efficiency vary periodically with the gap indicating alternate regions of higher and lower thrust generation, emphasizing the profound effect of upstream foil's wake interaction with the downstream foil. Five crucial wake–foil interactions leading to either favorable or unfavorable conditions for thrust generation are identified and different modes depending on the interactions are proposed for the tandem flapping foils. It is observed that the effect of the wake of the upstream foil on the downstream foil decreases with increasing gap. The study also focuses on the effect of the chord sizes of the upstream and the downstream foils on the propulsive forces, where the chord of the upstream foil is selected as 0.25–1 times the downstream foil's chord length. The effect of the chord size on the thrust is noticed to diminish as the chord size of the upstream foil decreases. Furthermore, the effect of the phase difference between the kinematics of the upstream and the downstream foils on flow dynamics is also explored along with its relationship with the chord sizes. For a fixed chord size, the effect of the phase difference on the propulsive performance is observed to be similar to that by varying the gap between the foils due to similar type of vortex interactions. The mechanisms of vortex interactions are linked to provide a comprehensive and generic understanding of the flow dynamics of tandem foils.

We performed numerical experiments on a one-dimensional elastic solid oscillating in a two-dimensional viscous incompressible fluid with the intent of discerning the interplay of vorticity and elastodynamics in flapping wing propulsion. Perhaps for the first time, we have established the role of foil deflection topology and its influence on vorticity generation, through spatially and temporally evolving foil slope and curvature. Though the frequency of oscillation of the foil has a definite role, it is the phase relation between foil slope and pressure that determines thrust or drag. Similarly, the phase difference between flapping velocity, and pressure and inertial forces, determine the power input to the foil, and in turn drives propulsive efficiency. At low frequencies of oscillation, the sympathetic slope and curvature of deformation of the foil allow generation of leading-edge vortices that do not separate; they cause substantial rise in pressure between the leading edge and mid-chord. The circulatory component of pressure is determined primarily by the leading-edge vortex and therefore thrust too is predominantly circulatory in origin at low frequencies.In the intermediate and high-frequency range, thrust and drag on the foil spatially alternate and non-circulatory forces dominate over circulatory and viscous forces. For the mass ratios we simulated, thrust due to flapping varies quadratically as a function of Strouhal number or trailing-edge flapping velocity; further, the trailing edge flapping velocities peak at the same set of frequencies where the thrust is also a maximum. Propulsive efficiency, on the other hand, is roughly a mirror image of the thrust variation with respect to Strouhal number. Given that most instances of flapping propulsion in nature are primarily through distributed muscular actuation that enables precise control of deformation shape, leading to high thrust and efficiency, the results presented here are pointers towards understanding some of the mechanisms that drive thrust and propulsive efficiency.

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This work reports a set of numerical experiments to understand flow-induced vibrations of the square columns kept in a tandem arrangement. Results on the coupled force and response dynamics are presented for an isolated column and for a pair of square columns in the tandem configuration where downstream column is elastically mounted and free to oscillate in in-line and transverse directions. We assess the combined wake-induced and sharp-corner based galloping effects on the downstream column by comparing with the isolated square column counterpart. It is known that the circular cylinders undergo vortex-induced motion alone whereas motion of a square column is vortex-induced at low Re and galloping at high Re. The simulations are performed by means of a Petrov-Galerkin based finite-element solver using Arbitrary Lagrangian-Eulerian technique to account for the fluid mesh motion. The predicted results of the isolated column agree well with the available numerical results in the literature. The dimensions of the square columns and the domain are set in order to a have total blockage area of 5 %. The effects of reduced velocity on the fluid forces, wake contours, and the phase angles are analyzed. This work is also an attempt to enhance our understanding on the origin of wake-induced vibrations in a tandem arrangement of bluff bodies. In the case of tandem arrangement, upstream vortex shifts the stagnation point on the downstream column to the lower suction region. Thus a larger lift force is observed for the downstream column as compared to a vibrating isolated column. Phase difference between the transverse load and velocity of the downstream column determines the extent of upstream wake interaction with downstream column. When the column velocity is in-phase with the transverse pressure load component, interaction of wake vortex with the downstream column is minimum. For higher reduced velocities (Ur > 15), the wake downstream is very wide and irregular and the phase angle is consistently close to 180°.