Added Mass and Aeroelastic Stability of a Flexible Plate Interacting With Mean Flow in a Confined Channel

Abstract

This work presents a review and theoretical study of the added-mass and aeroelastic instability exhibited by a linear elastic plate immersed in a mean flow. We first present a combined added-mass result for the model problem with a mean incompressible and compressible flow interacting with an elastic plate. Using the Euler-Bemoulli model for the plate and a 2D viscous potential flow model, a generalized closed-form expression of added-mass force has been derived for a flexible plate oscillating in fluid. A new compressibility correction factor is introduced in the incompressible added-mass force to account for the compressibility effects. We present a formulation for predicting the critical velocity for the onset of flapping instability. Our proposed new formulation considers tension effects explicitly due to viscous shear stress along the fluid-structure interface. In general, the tension effects are stabilizing in nature and become critical in problems involving low mass ratios. We further study the effects of the mass ratio and channel height on the aeroelastic instability using the linear stability analysis. It is observed that the proximity of the wall parallel to the plate affects the growth rate of the instability, however, these effects are less significant in comparison to the mass ratio or the tension effects in defining the instability. Finally, we conclude this paper with the validation of the theoretical results with experimental data presented in the literature.

Flutter instability of a thin flexible plate in a channel

“…The plate in a highly confined channel resembles an oscillating flat plate near a wall, and since m is real at small H/L ratio, there is no dissipation of energy from the added-mass term (i.e. the first term on the right-hand side of (3.1)) (Jaiman, Parmar & Gurugubelli 2014). This suggests that unlike a plate in unbounded flow in which the energy lost from the added-mass term due to pressure radiation to the far field (physically in terms of acoustic waves), in a very confined channel, the flow acts as a virtual mass and exchanges energy with the plate in a non-dissipative manner.…”

Flag flutter in inviscid channel flow

“…Third, we develop an infinite-flag model for which the stability boundary can be computed analytically, extending similar work from the unconfined case 9,14 to the confined case. We also note the work of Jaiman et al 26 which briefly considered the effects of channel walls together with fluid compressibility and viscous skin friction on the flag stability boundary.…”

The boundary layer development and traveling wave mechanisms during flapping of a flexible foil

“…This coupled fluid-structure interactions solver is stable for very small mass ratios subjected to strong added mass effects, which is typically the case of flexible plate flapping. The major challenge in simulating flapping dynamics with strong added mass effects using traditional numerical techniques such as looselycoupled and strongly-coupled partitioned staggered schemes is that these schemes suffer from numerical instabilities and convergence related issues, respectively (Causin et al 2005;Jaiman et al 2013). The numerical stability of the CFEI scheme for any mass ratio and its ability to simulate single plate flapping have been demonstrated systematically in Lui et al (2014) and Gurugubelli et al (2014).…”

“…Various studies (Eloy et al, 2008;Argentina and Mahadevan, 2004;Shelley et al, 2005) performed stability analyses to predict the onset of the limitcycle and chaotic flapping regimes. Jaiman et al (2013) proposed a generalized added-mass expression and a new formulation to predict the critical velocity for the onset of flapping instability. However, these linear stability theories underestimate the critical velocity as compared to experimental data reported in Tang and Paidoussis (2007).…”