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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Damage, sources of heat exchangers Damkohler number: Damping:
capacity, anelasticity, and, of flow-induced vibration,
Tube Bundle Vibration Characteristics
Davis and Anderson criterion, for onset of nucleate boiling, Decal, heat transfer medium, Decane: 1-Decanol: 1-Decene: Degradation temperature, of polymers, Demisters, wire mesh, for multistage flash evaporators, Dengler and Addoms correlation, for forced convective heat transfer in two-phase flow, Density: Deposition of droplets in annular flow Deposition in fouling, Desalination plants: Desuperheaters for use in association with evaporators, Developing flow in ducts: Dew-poin corrosion, Diathermanous fluid, 1,1-Dibromoethane: Dibromomethane: 1,2-Dibromotetrafluoroethane (Refrigerant 114B2): Dibutylamine: Dibutyl ether: Dichloroacetic acid: o-Dichlorobenzene: Dichlorodifluoromethane (see Refrigerant 12) 1,1-Dichloroethane (Refrigerant 150a): 1,2-Dichloroethane (Refrigerant 150): 1,1-Dichloroethylene: cis-1,2-Dichloroethylene: trans-1,2-Dichloroethylene: Dichlorofluoromethane (see Refrigerant 21) Dichloromethane (Refrigerant 30): 1,2-Dichlorotetrafluoroethane (Refrigerant 114) 1,2,3-Dichlorotrifluoroethane (Refrigerant 123) Dielectric constant, of water, Diethylamine: n,n-Diethylaniline: Diethylene glycol: Diethyl ether: Diethyl ketone: Diethylsulfide: Differential condensation: Differential formulations for nonisothermal gas radiation, Differential resistance term in heat exchanger design, Differential vector operators in heat conduction, Diffraction models for radiative heat transfer from surfaces, Diffuse surfaces, radiative heat transfer between, Diffuse wall passages, radiative heat transfer in, Diffusers, single-phase flow and pressure drop in, Diffusion, in multi-component condensation, n,n-Diffusion coefficients: 1,1-Difluoroethane (Refrigerant 152a): Difluoromethane (Refrigerant 32): Diiodomethane: Diisobutylamine: Diisopropylamine: Diisopropylether: Dimensional analysis: Dimensionless groups: Dimethylacetylene: Dimethylamine: Dimethylaniline: 2,2-Dimethylbutane: 2,3-Dimethylbutane: 1,1-Dimethylcyclopentane: Dimethylether: Dimethylketone: 2,2-Dimethylpropane (neopentane): Dimethylsulfide: Dimpled surfaces, heat exchangers with, 1,4-Dioxane: Diphenyl: Diphenylamine: Diphenylether: Diphenylmethane: Dipropyl ether: Diisopropyl ether: Dipropyl ketone: Direct contact heat exchangers Direct contact heat transfer, Direct numerical simulation, of turbulence, Dirichlet boundary condition, finite difference method, Dished heads: Discretization in numerical analysis: Disk-and-doughnut baffled heat exchangers, Disks, free convective heat transfer from inclined, Dispersants, for fouling control, Dispersed flow (liquid-liquid), Dissipation of turbulent energy, Distillation: Distribution: Dittus-Boelter equation, for single-phase forced convective heat transfer, Dividing flow, loss coefficients in, Dodecane: 1-Dodecene: Donohue method, for shell-side heat transfer in shell-and-tube heat exchangers, Double-pipe heat exchangers: Double segmental baffled heat exchangers, Downward facing surfaces, free convective heat transfer from, Downward flow in vertical tubes, flow patterns in gas/liquid, Dowtherm A: Dowtherm J: Dowtherms, as heat transfer media, Drag coefficient: Drag force: Drag reduction, Drainage, of condensate, Dreitser, G, Drift flux model for two-phase flows, Drogemuller, P, Droplets: Dropwise condensation Dry wall desuperheating (in condensation), Dryers: Drying loft, Drying rates, prediction of, Dryout: Ducts, single-phase fluid flow and pressure drop in, Duplex stainless steels, Durand correlation for heterogeneous conveyance in solid/liquid flow, Dynamically stable foam, Dyphyl, heat transfer media, Dzyubenko, B,

Index

HEDH
A B C D
Damage, sources of heat exchangers Damkohler number: Damping:
capacity, anelasticity, and, of flow-induced vibration,
Tube Bundle Vibration Characteristics
Davis and Anderson criterion, for onset of nucleate boiling, Decal, heat transfer medium, Decane: 1-Decanol: 1-Decene: Degradation temperature, of polymers, Demisters, wire mesh, for multistage flash evaporators, Dengler and Addoms correlation, for forced convective heat transfer in two-phase flow, Density: Deposition of droplets in annular flow Deposition in fouling, Desalination plants: Desuperheaters for use in association with evaporators, Developing flow in ducts: Dew-poin corrosion, Diathermanous fluid, 1,1-Dibromoethane: Dibromomethane: 1,2-Dibromotetrafluoroethane (Refrigerant 114B2): Dibutylamine: Dibutyl ether: Dichloroacetic acid: o-Dichlorobenzene: Dichlorodifluoromethane (see Refrigerant 12) 1,1-Dichloroethane (Refrigerant 150a): 1,2-Dichloroethane (Refrigerant 150): 1,1-Dichloroethylene: cis-1,2-Dichloroethylene: trans-1,2-Dichloroethylene: Dichlorofluoromethane (see Refrigerant 21) Dichloromethane (Refrigerant 30): 1,2-Dichlorotetrafluoroethane (Refrigerant 114) 1,2,3-Dichlorotrifluoroethane (Refrigerant 123) Dielectric constant, of water, Diethylamine: n,n-Diethylaniline: Diethylene glycol: Diethyl ether: Diethyl ketone: Diethylsulfide: Differential condensation: Differential formulations for nonisothermal gas radiation, Differential resistance term in heat exchanger design, Differential vector operators in heat conduction, Diffraction models for radiative heat transfer from surfaces, Diffuse surfaces, radiative heat transfer between, Diffuse wall passages, radiative heat transfer in, Diffusers, single-phase flow and pressure drop in, Diffusion, in multi-component condensation, n,n-Diffusion coefficients: 1,1-Difluoroethane (Refrigerant 152a): Difluoromethane (Refrigerant 32): Diiodomethane: Diisobutylamine: Diisopropylamine: Diisopropylether: Dimensional analysis: Dimensionless groups: Dimethylacetylene: Dimethylamine: Dimethylaniline: 2,2-Dimethylbutane: 2,3-Dimethylbutane: 1,1-Dimethylcyclopentane: Dimethylether: Dimethylketone: 2,2-Dimethylpropane (neopentane): Dimethylsulfide: Dimpled surfaces, heat exchangers with, 1,4-Dioxane: Diphenyl: Diphenylamine: Diphenylether: Diphenylmethane: Dipropyl ether: Diisopropyl ether: Dipropyl ketone: Direct contact heat exchangers Direct contact heat transfer, Direct numerical simulation, of turbulence, Dirichlet boundary condition, finite difference method, Dished heads: Discretization in numerical analysis: Disk-and-doughnut baffled heat exchangers, Disks, free convective heat transfer from inclined, Dispersants, for fouling control, Dispersed flow (liquid-liquid), Dissipation of turbulent energy, Distillation: Distribution: Dittus-Boelter equation, for single-phase forced convective heat transfer, Dividing flow, loss coefficients in, Dodecane: 1-Dodecene: Donohue method, for shell-side heat transfer in shell-and-tube heat exchangers, Double-pipe heat exchangers: Double segmental baffled heat exchangers, Downward facing surfaces, free convective heat transfer from, Downward flow in vertical tubes, flow patterns in gas/liquid, Dowtherm A: Dowtherm J: Dowtherms, as heat transfer media, Drag coefficient: Drag force: Drag reduction, Drainage, of condensate, Dreitser, G, Drift flux model for two-phase flows, Drogemuller, P, Droplets: Dropwise condensation Dry wall desuperheating (in condensation), Dryers: Drying loft, Drying rates, prediction of, Dryout: Ducts, single-phase fluid flow and pressure drop in, Duplex stainless steels, Durand correlation for heterogeneous conveyance in solid/liquid flow, Dynamically stable foam, Dyphyl, heat transfer media, Dzyubenko, B,
E F G H I J K L M N O P Q R S T U V W X Y Z
D Damping: of flow-induced vibration,
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Tube Bundle Vibration Characteristics

DOI 10.1615/hedhme.a.000441

4.6.2 Tube bundle vibration characteristics

James M. Chenoweth

Every component of a shell-and-tube heat exchanger vibrates at its own unique natural frequencies. Tubes are generally the most flexible parts and thus the most easily excited. Tubes can and do vibrate at different frequencies. The lowest natural frequency for any tube is called the fundamental or first mode. Higher natural frequencies are referred as the second mode, third mode, and so on. For conservative design purposes, only the fundamental natural frequency will be considered and will be called simply the natural frequency.

The natural frequency of a tube, like that of a simple beam, depends on the length of spans, how the ends are supported (clamped or simply), the type of intermediate supports (simply supported, pinned, or clamped), the cross-sectional geometry, the number of spans, and the materials of construction. Although the natural frequency of tubes can be measured experimentally, predictive methods to estimate approximate values are suitable for most engineering purposes.

Tubes in shell-and-tube heat exchangers are generally considered to be (1) rigidly fastened in the tube-sheets and (2) simply supported at intermediate points of contact with baffles and/or support plates. Some tubes in the center of the bundle may be supported by every baffle, whereas tubes that pass through the baffle windows may be supported only by every second or third baffle. Furthermore, the end spacings are often wider than central baffle spacings to accommodate nozzles and shell flanges. Thus, tubes in various parts of a bundle have different patterns of support and this results in tubes with different natural frequencies in the same heat exchanger.

A. Natural frequencies of straight tubes

For the vibration analysis of most shell-and-tube heat exchangers, determination of the lowest natural tube frequency is adequate. This can be done using a rigorous approach (Gorman, 1975), a graphical approach (Moretti, 1973), or a finite-clement computer program such as NASTRAN (1973). These provide higher-mode natural frequencies in addition to the lowest and the mode shapes for each. Figure 1 shows natural frequencies and mode shapes for the first five modes of vibration for a typical six-cross-pass heat exchanger. Notice the similarity in the natural frequencies for first modes of vibration and the differences in mode shape. Such information is useful in interpreting the behavior of tube vibration.

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