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Chapter 7
Fluid-Elastic Instability of Tube Bundles

## Excerpt

When a tube bundle is subject to cross-flow with increasing velocity, it will come to a point at which the responses of the tubes suddenly rapidly increase without bound, until tube-to-tube impacting or other non-linear effects limit the tube motions. This phenomenon is known as fluid-elastic instability. The velocity at which the vibration amplitudes of the tubes suddenly increase is called the critical velocity. Unlike vortex shedding, the vibration amplitudes of a fluid-elastically unstable tube bundle will continue to increase even when the critical velocity is exceeded. The motions of the tubes in the bundle become correlated and bear definite phase relationship to one another. Based on dimensional analysis, Connors, who first discovered the phenomenon of fluid-elastic instability in 1970, derived the following simple equation to predict the critical velocity of a tube bundle:

$Vc=βfn(2πζnmtρ)1∕2$

The constant β is subsequently known as the Connors' constant, or constant of fluid-elastic instability. Later theoretical formulation of tube bundle dynamics by Chen (1983) showed that β is not a true constant, especially for tube bundles vibrating in heavy fluids. However, when the fluid density is small, such as air or super-heated steam, β is approximately constant. There are several other theoretical formulations of the theory of fluid-elastic instability. However, all of them lead to equations very similar to the original Connors' Equation (7.4), and none of them offer distinct advantages over the Connors' equation in practical industrial applications.

• Summary
• Acronyms
• Nomenclature
• 7.1 Introduction
• 7.2 Geometry of Heat Exchanger Tube Arrays
• 7.3 Connors' Equation
• Fluid-Elastic Stability Margin
• Non-Uniform Cross-Flow Velocity
• Other Forms of Connors' Equation
• Example 7.1
• Example 7.2
• Example 7.3
• 7.4 Theoretical Approaches to Fluid-Elastic Instability
• Displacement Controlled Instability Theory
• Velocity Controlled Instability Theory
• Chen's Theory
• Constancy of β
• Fluid-Structure Coupling
• 7.5 ASME Guide
• Values for Connors' Constant and Damping Ratios
• 7.6 Time Domain Formulation of Fluid-Elastic Instability
• Equation of Fluid-Elastic Stability in the Time Domain
• The Crossing Frequency of a Vibrating Structure
• Critical Velocity for a Tube Bundle with Non-Linear Supports
• Example 7.4
• Case Study 7.1: Sudden Tube Crack in Nuclear Steam Generators
• References
Topics: Fluids
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