Date: 05/21/09

Speaker: S. Banerjee 

Title: Flapping Dynamics of a three dimensional flag

Abstract:
We present investigations of the flapping instability and response of
a three dimensional flag of high extensional rigidity and low bending
rigidity in a uniform and incompressible flow. The soft cloth of the
flag is represented by very low bending rigidity and the subsequent
dominance of flow-induced tension as the main structural restoring
force. The flutter modes are calculated in three dimensions for
different values of aspect ratio taking into account the inertial
fluid loading. In this limit, the flutter instability arises from a
competition between the destabilising fluid pressure and the
stabilizing drag induced tension of the flag. We compute the linear
stability domain which agrees with previous approximate models in
scaling but differs by large multiplicative factors. The critical flow
velocity is calculated as a function of the mass ratio and the aspect
ratio of the plate. To study the nonlinear stability and response, we
use a 3D fluid-structure direct simulation (FSDS) capability, coupling
a direct numerical simulation of the Navier-Stokes equations to a
solver for thin-membrane dynamics of arbitrarily large motion. With
the flow grid fitted to the structural boundary using span-wise
periodicity, external forcing to the structure is calculated from the
boundary fluid dynamics. We solve the fully-nonlinear dynamics
numerically and find a transition from a power spectrum dominated by
discrete frequencies to an apparently continuous spectrum of
frequencies.