Estimating thrust from shedding vortex surfaces in the wake of a flapping plate

We elucidate the vortex dynamics of flows past a flapping plate using the vortex-surface field (VSF) and develop models for estimating thrust from shedding vortex surfaces in wakes. The VSF evolution is calculated from numerical simulation using the immersed boundary method. The VSF visualization reveals that a spoon-like vortex surface dominated by tip vortex lines is formed and periodically shed into the wake owing to the alternating upstroke and downstroke of the flapping plate. We simplify the finite-domain impulse theory based on a particular vortex surface. The simplified theory demonstrates that the force on the plate is only dependent on the vortical impulse and Lamb-vector integral of the vortex surface enclosing the plate. Then, we propose a time-averaged thrust model from near-wake discrete vortex surfaces, where the incorporation of the Lamb-vector integral significantly improves the model estimation from the impulse model. Furthermore, we estimate the mean thrust based on two arbitrary vortex surfaces in the far wake from the linear impulse decay of periodically shedding vortex surfaces, which provides a possible approach to infer the state of the moving body in experimental investigation and practical applications.

Automated summary

The study elucidates vortex dynamics of flows past a flapping plate using vortex-surface field and develops models for estimating thrust from shedding vortex surfaces in wakes. Numerical simulations reveal a spoon-like vortex surface shed into the wake from the flapping plate. Simplified theories and time-averaged thrust models offer possible approaches for thrust estimation.