Flow Induced Vibrations - Classifications and Lessons from Practical Experiences

1.1 Design support system for FIV. 3

1.2 How will this half cylinder respond to wind flow? 5

1.3 Route to solution. 5

1.4 Mechanism of oscillation. 6

1.5 Classification of FIV and the corresponding sections. 7

1.6 Examples of models and mechanisms. 8

1.7 Vibration problems in design of feed water heater. 8

1.8 Vibration of tube array caused by cross-flow. 9

1.9 Decision based on importance. 10

1.10 Flowchart of simplified treatment. 10

1.11 Separate and distinct modeling of structure and flow. 11

1.12 Example of flow analysis and vibration model. 12

1.13 Dimensionless vortex shedding frequency dependence on Reynolds number. 15

1.14 Instability mechanism of elastic force coupled system. 18

1.15 Feedback forces. 20

2.1 Vortex-induced synchronization. 32

2.2 Tip-vortex shedding. 33

2.3 Cylinder motion and vortex shedding in oscillating flow. 33

2.4 Evaluation for vibration of a circular cylinder in cross-flow. 37

2.5 Range of avoidance and suppression of synchronization. 38

2.6 Suppression of in-line synchronization. 38

2.7 Lock-in in two-phase flow. 41

2.8 Suppression of synchronization by spiral strake. 42

2.9 In-line vibration of marine pile at Immingham. 43

2.10 Rain-induced vibration in Japan. 43

2.11 Example of coupling of a pipe and a thermo well. 44

2.12 Possible configurations of cylinder pairs in cross-flow: (a) two cylinders in tandem, (b) staggered arrangement of two cylinders, (c) two cylinders in parallel, (d) two staggered cylinders with different diameters, (e) two cylinders in criss-crossed configuration, and (f) intersecting cylinders. 45

2.13 Cylinder interaction regimes based on in-flow and transverse spacings. 48

2.14 Region within which control can be achieved for different diameter ratios D/d. 48

2.15 Pressure coefficient Cp variation and dependence on Z/D. 49

2.16 Experiments on upstream cylinder dynamics in the case where the downstream cylinder is fixed. 51

2.17 Cylinder configuration and coordinates. 53

2.18 Tube array patterns: (a) tube row, (b) tube column, (c) square tube array, and (d) triangular tube array. 55

2.19 Strouhal numbers for tube arrays related to pitch/diameter ratio: (a) in-line array, and (b) staggered array. 58

2.20 Example of stability boundary for fluidelastic instability. 60

2.21 Example of measured random force acting on array of circular tubes. 61

2.22 Example of measured damping ratio for tubes in two-phase flow. 64

2.23 Example of proposed random force liquid–gas two-phase flow. 65

2.24 Vibration modes for various types of structures: (a) parallel vibration, (b) rotational vibration, (c) in plane vibration, and (d) out of plane vibration. 68

2.25 Strouhal numbers for rectangular-cross-section bodies for various aspect ratios, attack angles, and rounded corners. 72

2.26 Effect of attack angle on Strouhal number for large aspect ratio (e/d = 10). 73

2.27 Effect of aspect ratio on possible vortex-induced vibration modes with zero attack angle: (a) ranges of possible FIV for lightly damped rectangular prisms in low-turbulence cross-flow (α = 0), cross-hatched and dotted regions represent prisms with transverse and streamwise degree-of-freedom, respectively, and (b) effects of aspect ratio on the mode of vortex formation. 74

2.28 Effects of attack angle on possible vortex-induced vibration modes for large aspect ratio (e/d = 10): (a) effects of attack angle on possible transverse vibration of rectangular cross-section body in cross-flow (lightly damped, low-turbulence flow, zero attack angle), and (b) effects of attack angle on the mode of vortex formation. 74

2.29 Galloping vibration amplitude of a square-cross-section body in the transverse degree-of-freedom. 79

2.30 Structures of guide vane and elbow splitter. 81

2.31 Overview of acoustic resonance in tube bundle. 82

2.32 Classification of acoustic resonance by mode shape: (a) transverse mode, and (b) longitudinal mode. 83

2.33 Resonance map for tube bundles, based on pitch-to-diameter ratio: (a) in-line, and (b) staggered array. 85

2.34 Examples of baffle placement for countermeasures against transverse acoustic modes: (a) irregular pitch, and (b) regular pitch. 85

2.35 Resonance suppression effect of cavity baffle: (a) baffle structure, and (b) sound pressure level. 86

2.36 View showing vortex–acoustic interaction: (a) stable, and (b) resonance. 86

2.37 Feed back mechanism between flow and acoustic field. 87

2.38 Experimental setup for stability evaluation by forced water-flow fluctuation. 87

2.39 Resonance occurrence in boiler scale model apparatus. 88

2.40 Mode shapes in boiler scale model apparatus: (a) transverse mode − 805 Hz, and (b) longitudinal mode − 990 Hz. 89

2.41 Typical experimental results of longitudinal mode suppression: (a) without bell-mouth, and (b) with bell-mouth. 90

2.42 Finned tubes: (a) serrated fin, and (b) solid fin. 91

2.43 Experimental validation of estimated Strouhal number using equivalent diameter and Fitz-Hugh Strouhal number. 91

2.44 Prediction of resonance based on Eisinger’s method: (a) parameter definition for staggered array, (b) setting of critical region, and (c) example of application. 94

2.45 Flow chart of Eisinger’s resonance suppression design. 94

2.46 Example of countermeasure by cavity baffle: (a) side view of boiler, (b) standing wave data, and (c) countermeasure (top view). 96

2.47 Example of countermeasure in shell and tube type heat exchanger: (a) structure of air cooler, and (b) relation between resonance frequency and flow. 96

2.48 Example of countermeasure with acoustic absorbers for coal fired boiler. 97

2.49 Region of occurrence of vortex shedding and maximum response of square cylinder as functions of Scruton number. (Solid line: boundary of occurrence; Broken line: maximum response.) 100

3.1 Schematic of: (a) BWR fuel bundle and (b) steam generator. 108

3.2 Circular cylinder subject to turbulent pressure fluctuations. 109

3.3 Turbulent wall pressure spectra. 110

3.4 Magnitude of cross-spectral density of turbulent wall pressure (longitudinal). 110

3.5 Magnitude of cross-spectral density of turbulent wall pressure (lateral). 111

3.6 Dependence of convection velocity on dimensionless frequency. 111

3.7 Mid-span rms displacement of fixed-fixed cylinders. 113

3.8 Parameters used for random vibration correlation: (a) parameter λ, and (b) parameter b. 116

3.9 Parameters for spatial correlation in air–water flow condition: (a) parameter ξ, and (b) parameter Vc. 116

3.10 Relationship between measured and predicted amplitudes of vibration according to Païdoussis’ empirical formula. 117

3.11 A two-dimensional airfoil. 121

3.12 Coupling between the bending and torsional motion. 121

3.13 Spring-supported rigid wing section in two-dimensional flow. 121

3.14 Dimensionless flutter speed versus frequency ratio. 122

3.15 Panel flutter. 123

3.16 Simply-supported plate of infinite width subjected to fluid flow over one side. 123

3.17 Dimensionless critical flow velocity versus mass ratio. 124

3.18 Jet engine after-burner. 125

3.19 Coupled sloshing and cylindrical weir shell vibration. 125

3.20 Sound spectrum for 90 degree elbow duct. 126

3.21 Examples of leakage-flow-induced vibration events: (a) PWR core barrel, and (b) feed-water sparger. 128

3.22 One-dimensional leakage passage under study and coordinate system: (a) tapered leakage-flow passage, and (b) arbitrary-shaped leakage-flow...