以板格法求解二維具彈性平板在勢流場中擺動所產生之推力

Abstract

本論文旨在以二維具彈性的平板來模擬魚在水中尾鰭的擺動情形。流場計算上考慮非黏性及非旋性的勢流場來化簡問題，數值方法上採用渦流板格法(vortex panel method)來建構流場，並考慮平板尾端渦流剝離(vortex shedding)的情形，作用在平板上的力則以非穩態伯努力方程式(unsteady Bernoulli equation)來求得。平板形變方面則引用振動學中Euler-Bernoulli 樑方程式來模擬平板的彈性變形與運動，並與流體方程式配合以求得流固耦合(fluid-structure interaction)下之推力，計算之結果則與剛體平板擺動所產生之推力做比較。本文的研究顯示，在平板小幅度擺動下，大多數的彈性變形對於推力並沒有幫助，魚尾若只是單純的藉由被動式的形變擺動是無法有效產生前行的推力。

The present study aims at using a two-dimensional flexible flat plate to simulate the swimming motion of a fish. The flow field is assumed to be an inviscid and irrotational potential flow, along with the unsteady Kutta condition to simulate the vortex shedding phenomenon at the end of the flat plate. The vortex panel method is adopted to solve the flow field, and the force acting on the plate is calculated from the unsteady Bernoulli equation. The Euler-Bernoulli beam equation is used to obtain the deformation and transverse motion of the flat plate, which are then coupled with the pressure field of the flow to establish the fluid-structure interaction status. Calculated thrust is compared with that produced by a swinging rigid flat plate. Present results show that, under the assumption of small swinging amplitudes of the plate, the elastic nature of the plate offers no help to increase the thrust in most of the cases. It suggests that the undulating motion of the fish body is not caused by the fluid-structure interaction, a fish can not generate thrust effectively to assist it move forward in the fluid by this passive-type of body motion.