Research Papers

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

[+] Author and Article Information
Rajeev K. Jaiman

Assistant Professor
Department of Mechanical Engineering,
National University of Singapore,
e-mail: mperkj@nus.edu.sg

Manoj K. Parmar

Research Assistant
Scientist University of Florida,
Gainesville, FL 32611

Pardha S. Gurugubelli

Graduate Research Assistant
National University of Singapore,

1Corresponding author.

Manuscript received May 26, 2013; final manuscript received August 20, 2013; accepted manuscript posted August 28, 2013; published online September 23, 2013. Assoc. Editor: Kenji Takizawa.

J. Appl. Mech 81(4), 041006 (Sep 23, 2013) (9 pages) Paper No: JAM-13-1214; doi: 10.1115/1.4025304 History: Received May 26, 2013; Revised August 20, 2013; Accepted August 28, 2013

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–Bernoulli 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.

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Fig. 1

Depiction of the problem of the two-dimensional elastic plate interacting with the mean flow

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Fig. 2

Compressible correction factor to the added-mass, as given in Eq. (29) for kxH = {1, 2}

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Fig. 3

Integration of kernel K(t) given by Eq. (32), where the early time response (top) and the long time behavior (bottom) are shown

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Fig. 4

Comparison between the observed experimental values and the predicted values using Eq. (49). Dots represent Huang's experimental values and the solid and dashed lines coincide in the figure.

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Fig. 5

Comparison between the observed experimental values and the predicted values using Eq. (45)

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Fig. 6

Effects of the mass ratio μ on the instability growth rate, where H = ∞ and U0 = 0.05. For μ = 1.6, the stability boundaries are shown.

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Fig. 7

(a) Effects of the mass ratio μ on the convective growth rate of the instability, where H = ∞ and U0 = 0.05. The solutions kx(ω) of D(kx,ω) = 0 are plotted for real positive ω. (b) The spatial dispersion diagram for μ = 0.8 and U0 = 0.05. The dashed line denotes the complex modes and the solid line denotes the neutral modes.

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Fig. 8

The stability limit for the flow velocity and critical velocity Ucr versus μ for various heights of the channel




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