Simulation of Flight States for Flexible Falling Plates by the Immersed Boundary Method

Abstract

The falling of a plate is a simply posed problem that offers complex fluid-structure interactions. It also gives rise to different flow structures in relation to specific flight patterns of a plate such as autorotating tumble, side-to-side flutter, or constant abrupt turning in a chaotic manner depending on the Reynolds number and the non-dimensional moment of inertia In actual falling flights such as tree leaves and organisms, the bodies possess flexibility. Here, direct numerical simulation is used to portray the free fall of a flexible plate. The Navier-Stokes equations are solved via the upper-lower decomposition method. The effect of the flow on the solid plate is transferred through the immersed boundary method. A strictly spatially dependent stencil of the IB is adapted to provide a solution to the fourth-order beam equation via the pent-diagonal matrix algorithm. Comparing to the conventional method that couples with the temporal domain, this enables stability of solution through a range of bending rigidity k from k= 50 to k = 0.01. A plate with high stiffness resembles to a plate of non-flexible solution. The tumbling flight trajectory is found to change as a plate is more flexible, or as k is decreased. Further decrease in k result in changes flight states.

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