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Research Papers

Blocking in the Rotating Axial Flow in a Corotating Flexible Shell

[+] Author and Article Information
F. Gosselin

LadHyX, École Polytechnique, Palaiseau Cedex 91128, Francefrederick.gosselin@ladhyx.polytechnique.fr

M. P. Païdoussis1

Department of Mechanical Engineering, McGill University, Montréal, QC, H3A 2K6, Canadamary.fiorilli@mcgill.ca

1

Corresponding author.

J. Appl. Mech 76(1), 011001 (Oct 23, 2008) (6 pages) doi:10.1115/1.2998486 History: Received August 23, 2007; Revised August 26, 2008; Published October 23, 2008

By coupling the Donnell–Mushtari shell equations to an analytical inviscid fluid solution, the linear dynamics of a rotating cylindrical shell with a corotating axial fluid flow is studied. Previously discovered mathematical singularities in the flow solution are explained here by the physical phenomenon of blocking. From a reference frame moving with the traveling waves in the shell wall, the flow is identical to the flow in a rigid varicose tube. When the ratio of rotation rate to flow velocity approaches a critical value, the phenomenon of blocking creates a stagnation region between the humps of the wall. Since the linear model cannot account for this phenomenon, the solution blows up.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Streamlines and velocity profile showing the flow pattern of blocking encountered at the first critical Rossby number in a swirling axisymmetric flow in a convergent-divergent nozzle. Figure reproduced from Ref. 7.

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Figure 2

Schematic of the considered shell

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Figure 3

Evolution of the complex frequencies of the system with Ω¯=0 and k¯=7.2

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Figure 4

Stability curve of Lai and Chow (9) for the system with Ω¯=0.1 and k¯=10. Figure reproduced from Ref. 9.

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Figure 5

Evolution of the real frequency of the mode k¯=10 and n=0 of the system for Ω¯=0.1 over the contour plot of the absolute value of Λ

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Figure 6

For small rates of rotation, effect of increasing the rate of rotation on the relative axial velocity profile at the throat x¯=π/k¯ for k¯=3 and w¯=0.1

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Figure 7

For small rates of rotation, effect of increasing the rate of rotation on the relative axial velocity profile at θ=0 and x¯=0 for k¯=10, n=3, and w¯=0.01

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