Critical Velocity of a Nonlinearly Supported Multispan Tube Bundle

[+] Author and Article Information
M. K. Au-Yang

3531 Round Hill Road, Lynchburg, VA 24503mkauyang@aol.com

J. A. Burgess

 AREVA Framatome-ANP, Lynchburg, VA 24502john.burgess@areva.com

J. Pressure Vessel Technol 129(3), 535-540 (Mar 23, 2007) (6 pages) doi:10.1115/1.2748836 History: Received August 17, 2006; Revised March 23, 2007

The phenomenon of fluid-elastic instability and the velocity at which a heat exchanger tube bundle becomes unstable, known as the critical velocity, was discovered and empirically determined based upon single-span, linearly supported tube bundles. In this idealized configuration, the normal modes are well separated in frequency with negligible cross-modal contribution to the critical velocity. As a result, a critical velocity can be defined and determined for each mode. In an industrial heat exchanger or steam generator, not only do the tube bundles have multiple spans, they are also supported in oversized holes. The normal modes of a multispan tube bundle are closely spaced in frequency and the nonlinear effect of the tube-support plate interaction further promotes cross-modal contribution to the tube responses. The net effect of cross-modal participation in the tube vibration is to delay the instability threshold. Tube bundles in industrial exchangers often have critical velocities far above what were determined in the laboratory based upon single-span, linearly supported tube bundles. In this paper, the authors attempt to solve this nonlinear problem in the time domain, using a time history modal superposition method. Time history forcing functions are first obtained by inverse Fourier transform of the power spectral density function used in classical turbulence-induced vibration analyses. The fluid-structure coupling force, which is dependent on the cross-flow velocity, is linearly superimposed onto the turbulence forcing function. The tube responses are then computed by direct integration in the time domain. By gradually increasing the cross-flow velocity, a threshold value is obtained at which the tube response just starts to diverge. The value of the cross-flow velocity at which the tube response starts to diverge is defined as the critical velocity of this nonlinearly supported, multispan tube bundle.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 2

Tube motion near the critical velocity. (a) V∕Vc=0.38 normal operation condition (Cfsi=−0.01165 at top span, x). (b) V∕Vc=0.913 (Cfsi=−0.05 at top span, x). (c) V∕Vc=0.9999 (Cfsi=−0.05999 at top span, x). (d) V∕Vc=1.0 (Cfsi=−0.06 at top span, x). Note in (d), change in scale in the x-axis and motion changes from random to orbital.

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Figure 3

Animation of tube motion at instability. Total time to instability=12sec. (Frames are not equally spaced in time.)

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Figure 4

Turbulence-induced responses with and without fluid-structure coupling

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Figure 1

Finite element model of steam generator tube




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