Effects of flexibility on propulsive force acting on a heaving foil

The hybrid Cartesian/immersed boundary method is applied to simulate effects of flexibility on propulsive force acting on a heaving foil in a viscous flow. Immersed boundary nodes are distributed inside an instantaneous fluid domain. Velocity vector is reconstructed at the immersed boundary node based on an interpolation along a local normal line. Using the staggered/non-staggered grid method, the demand for pressure at boundary nodes is removed. Elastic deformation of the flexible foil is modelled based on the dynamic thin-plate mechanics. The developed code is validated through comparisons with other computations on flow fields around a flapping foil. The generation of the reverse Karman vortex street is investigated. Forces acting on heaving foils are compared for flexible and rigid cases and the increased thrust of the flexible foil is attributed to the deformed configuration near the tip. The flexibility of the heaving foil decreases vertical force and improves propulsion efficiency. The variations of force and deformation are investigated according to bending stiffness of the foil.