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Flow Induced Vibration of Power and Process Plant Components: A Practical WorkbookAvailable to Purchase
By
M. K. Au-Yang, Ph.D., P.E.
M. K. Au-Yang, Ph.D., P.E.
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ISBN-10:
0791801667
No. of Pages:
494
Publisher:
ASME Press
Publication date:
2001
eBook Chapter
9 Turbulence-Induced Vibration in Cross-Flow Available to Purchase
By
M. K. Au-Yang, Ph.D., P.E.
M. K. Au-Yang, Ph.D., P.E.
Search for other works by this author on:
Page Count:
50
-
Published:2001
Citation
Au-Yang, MK. "Turbulence-Induced Vibration in Cross-Flow." Flow Induced Vibration of Power and Process Plant Components: A Practical Workbook. Ed. Au-Yang, MK. ASME Press, 2001.
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The response of one-dimensional structures such as beams and tubes to cross-flow turbulence has important applications to heat exchanger design, operation and maintenance. In cross-flows, because the front of the pressure wave reaches all points on the structure at the same time, the forces along the length of the structure are always in phase, contrary to the case of parallel flow-induced vibration. This greatly simplifies the acceptance integral method of turbulence-induced vibration analysis discussed in the previous chapter. By making the additional assumption that the random pressure is fully coherent across the width of the structure, the equation for the mean square response of the structure derived in the last chapter is simplified to:
Here GF =D2Gp is the random force PSD, expressed in (force/length)2/Hz and Jnn are the joint acceptance integrals in the axial (cross-stream) direction. Because of the absence of the phase angle in the coherence function, Jnn are much easier to compute in cross-flow over 1D structures compared with those for parallel flows discussed in the previous chapter. Using the finite-element technique, the joint and cross-acceptances for cross-flow over beams and tubes with arbitrary boundary conditions are computed as a function of λ/L and are given as design charts in Appendix 9B. In particular, it is shown that as long as the correlation length is small compared with the half flexural wavelength of the structure, the following relationship: is true irrespective of the boundary conditions of the beam.
Summary
Acronyms
Nomenclature
9.1 Introduction
9.2 Exact Solution for the Joint Acceptance Integrals
9.3 Finite Element Method of Evaluating the Acceptance Integrals
Case 1: Spring-Supported Rigid Beam with Uniform Mass Density
Case 2: Simply-Supported Beam with Uniform Mass Density
9.4 Correlation Length and Power Spectral Density for Single-Phase Cross-Flows
Correlation Length
The Random Pressure PSD for Single-Phase Cross-Flow
Vortex-Induced Response
Example 9.1
9.5 The Acceptance Integral for a Structure with Non-uniform Mass Density
9.6 Practical Heat Exchanger Tubes with Multiple Supports
Partial Span Loading
Example 9.2
Example 9.3
9.7 Cross-Modal Contributions to Responses
Example 9.4
9.8 Vibration due to Turbulent Two-Phase Cross-Flow
Two-Phase Flow Regimes
Two-Phase Parameters
Two-Phase Damping
Random Pressure PSD in Two-Phase Flows
Example 9.5
Appendix 9A: Derivation of Equation (9.11)
Appendix 9B: Charts of Acceptance Integrals
References
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