0
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,
117576Singapore
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,
117576Singapore

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Datta, S. and Gottenberg, W., 1975, “Instability of an Elastic Strip Hanging in an Airstream,” ASME J. Appl. Mech., 42, pp. 195–198. [CrossRef]
Kornecki, A., Dowell, E. H., and Orien, J., 1976, “On the Aeroelastic Instability of Two-Dimensional Panels in Uniform Incompressible Flow,” J. Sound Vib., 47(2), pp. 163–178. [CrossRef]
Blevins, R. D., 1990Flow-Induced Vibration, Van Nostrand Reinhold, New York.
Paidoussis, M. P., 2004, Fluid-Structure Interactions. Slender Structures and Axial Flow, Vol. 2, Academic, New York.
Brummelen, E. H., 2009, “Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction,” ASME J. Appl. Mech., 76, pp. 173–189. [CrossRef]
Brummelen, E. H., 2011, “Partitioned Iterative Solution Methods for Fluid–Structure Interaction,” Int. J. Numer. Methods Fluids, 65, pp. 3–27. [CrossRef]
Jaiman, R., Shakib, F., Oakley, O., and Constantinides, Y., 2009, “Fully Coupled Fluid-Structure Interaction for Offshore Applications,” Proceedings of the ASME Offshore Mechanics and Arctic Engineering Conference, Honolulu, HI, May 31–June 5, ASME Paper No. OMAE09-79804. [CrossRef]
Jaiman, R., 2012, “Advances in ALE Based Fluid-Structure Interaction Modeling for Offshore Engineering Applications,” 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna, Austria, September 10–14.
Forster, C., Wall, W. A., and Ramm, E., 2007, “Artificial Added Mass Instabilities in Sequential Staggered Coupling of Nonlinear Structures and Incompressible Viscous Flows,” Comput. Methods Appl. Mech. Eng., 196, pp. 1278–1293. [CrossRef]
Causin, P., Gerbeau, J. F., and Nobile, F., 2005, “Added-Mass Effect in the Design of Partitioned Algorithms for Fluid-Structure Problems,” Comput. Methods Appl. Mech. Eng., 194, pp. 4506–4527. [CrossRef]
Jones, R., 1946, “Properties of Low-Aspect Ratio Pointed Wings at Speeds Below and Above the Speed of Sound,” NASA Technical Report No. 835.
Dugundji, J., Dowell, E., and Perkin, B., 1963, “Subsonic Flutter of Panels on Continuous Elastic Foundations,” AIAA J., 1, pp. 1146–1154. [CrossRef]
Lucey, A. D., 1998, “The Excitation of Waves on a Flexible Panel in a Uniform Flow,” Philos. Trans. R. Soc. London, Ser. A, 356, pp. 2999–3039. [CrossRef]
Guo, C. and Paidoussis, M., 2000, “Stability of Rectangular Plates With Free Side-Edges in Two-Dimensional Inviscid Channel Flow,” ASME J. Appl. Mech., 67, pp. 171–176. [CrossRef]
Huang, L., 1995, “Flutter of Cantilevered Plates in Axial Flow,” J. Fluids Struct., 9(2), pp. 127–147. [CrossRef]
Yadykin, Y., Tenetov, V., and Levin, D., 2003, “The Added Mass of a Flexible Plate Oscillating in a Fluid,” J. Fluids Struct., 17, pp. 115–123. [CrossRef]
Shelley, M. J. and Zhang, J., 2011, “Flapping and Bending Bodies Interacting With Fluid Flows,” Annu. Rev. Fluid Mech., 43(1), pp. 449–465. [CrossRef]
Minami, H., 1998, “Added Mass of a Membrane Vibrating at Finite Amplitude,” J. Fluids Struct., 12, pp. 919–932. [CrossRef]
Mei, R., Lawrence, C. J., and Adrian, R. J., 1991, “Unsteady Drag on a Sphere at Finite Reynolds Number With Small Fluctuations in the Free-Stream Velocity,” J. Fluid Mech., 233, pp. 613–631. [CrossRef]
Chang, E. J. and Maxey, M. R., 1995, “Unsteady Flow About a Sphere at Low to Moderate Reynolds Number. Part 2. Accelerated Motion,” J. Fluid Mech., 303, pp. 133–153. [CrossRef]
Miles, J. W., 1951, “On Virtual Mass and Transient Motion in Subsonic Compressible Flow,” Q. J. Mech. Appl. Math., 4(4), pp. 388–400. [CrossRef]
Parmar, M., Haselbacher, A., and Balachandar, S., 2011, “Generalized Basset-Boussinesq-Oseen Equation for Unsteady Forces on a Sphere in a Compressible Flow,” Phys. Rev. Lett., 106(8), p. 084501. [CrossRef] [PubMed]
Parmar, M., Balachandar, S., and Haselbacher, A., 2012, “Equation of Motion for a Sphere in Non-Uniform Compressible Flows,” J. Fluid Mech., 699, pp. 352–375. [CrossRef]
Parmar, M., Haselbacher, A., and Balachandar, S., 2008, “On the Unsteady Inviscid Force on Cylinders and Spheres in Subcritical Compressible Flow,” Philos. Trans. R. Soc. London, Ser. A, 366(1873), pp. 2161–2175. [CrossRef]
Parmar, M., Balachandar, S., and Haselbacher, A., 2012, “Equation of Motion for a Drop or Bubble in Viscous Compressible Flows,” Phys. Fluids, 24, p. 056103. [CrossRef]
Batchelor, G., 1967, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, UK.
Moretti, P., 2003, “Tension in Fluttering Flags,” 10th International Congress on Sound and Vibration, Stockholm, Sweden, July 7–10, pp. 7–10.
Crighton, D. G. and Oswell, J. E., 1991, “Fluid Loading With Mean Flow. I. Response of an Elastic Plate to Localized Excitation,” Philos. Trans. R. Soc. London, Ser. A, 335, pp. 557–592. [CrossRef]
Briggs, R. J., 1964, Electron-Stream Interaction With Plasmas, MIT, Cambridge, MA.
Peake, N., 2001, “Nonlinear Stability of a Fluid-Loaded Elastic Plate With Mean Flow,” J. Fluid Mech., 434, pp. 101–118. [CrossRef]
Landahl, M. T., 1962, “On the Stability of a Laminar Incompressible Boundary Layer Over a Flexible Surface,” J. Fluid Mech., 13(4), pp. 609–632. [CrossRef]
Benjamin, T. B., 1963, “The Threefold Classification of Unstable Disturbances in Flexible Surfaces Bounding Inviscid Flows,” J. Fluid Mech., 16(3), pp. 436–450. [CrossRef]
Zhang, J., Childress, S., Libchaber, A., and Shelley, M., 2000, “Flexible Filaments in a Flowing Soap Film as a Model for One-Dimensional Flags in a Two-Dimensional Wind,” Nature (London), 408(6814), pp. 835–839. [CrossRef]
Shelley, M., Vandenberghe, N., and Zhang, J., 2005, “Heavy Flags Undergo Spontaneous Oscillations in Flowing Water,” Phys. Rev. Lett., 94, p. 094302. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
Fig. 8

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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In