Fluid-Elastic Instability In Tube Arrays

209 Pages·2005·3.14 MB·English

by  Vijay Dhir

UNIVERSITY OF CALIFORNIA
Los Angeles

Fluid-Elastic Instability In Tube Arrays Subjected To
Air-Water And Steam-Water Cross-Flow

A dissertation submitted in partial satisfaction of the
requirements for the degree Doctor of Philosophy
in Mechanical Engineering

By

Deepanjan Ranjit Mitra

2005
© Copyright by
Deepanjan Ranjit Mitra
2005

CONTENTS
List of Figures vi
List of Tables xiv
Nomenclature xvii
Acknowledgments xx
Vita xxi
Abstract xxiii
1. Introduction 1
1.1. Nature of fluid-elastic instability 3
1.2. Single-phase flow 7
1.3. Two-phase flow 10
1.4. Theoretical studies in fluid-elastic instability 21
1.5. Objective of present study 23
2. Experimental Setup 25
2.1. Flow loop 25
2.2. Test section 29
2.3. Tube array 33
2.4. Strain gauge vibration measurement system 36
2.5. Construction of Heated tube 38
2.6. Measurement Methodology 39
2.6.1. Flow velocity 39
2.6.2. Frequency 41
iii
2.6.3. Damping ratio 41
2.6.4. Void fraction 44
2.6.5. Amplitude 45
3. Results: Frequency, Damping and Single phase flow 48
3.1. Test tube characteristics 48
3.2. Damping ratio in still fluid 51
3.3. Damping ratio in two-phase flow 53
3.4. Single phase fluid-elastic instability experiments 58
3.4.1. Single flexible tube in a rigid array 58
3.4.2. Fully flexible array 64
4. Results: Air-water two-phase flow 73
4.1. Void fraction measurement 74
4.2. Single flexible tube in a rigid array 76
4.3. Fully flexible array 81
5. Results: Steam-water two-phase flow 87
5.1. Mass quality calculation 88
5.2. Single flexible tube in a rigid array 91
5.3. Fully flexible array 95
5.4. Experiments with boiling on tube surface 100
6. Discussion 108
6.1. Single phase flow 109
6.2. Air-water two-phase flow 114
iv
6.3. Steam-water two-phase flow 124
6.4. Effect of boiling on the onset of instability 128
6.5. Comparison between air-water and steam-water flow 130
6.6. Comparison with existing data 137
7. Conclusions 143
APPENDIX A 146
APPENDIX B 170
APPENDIX C 172
References 175

v
LIST OF FIGURES

1.1: Mechanism of fluid-elastic instability in a tube array 3
1.2: Typical shell and tube heat exchanger (Walker, 1982) 4
1.3: Single-phase fluid-elastic instability map (Reproduced from Pettigrew 9
and Taylor, 1991)
1.4: Fluid-elastic Instability in continuous two-phase flows 19
(Reproduced from Pettigrew et al., 1998)
1.5: Schematic of heat exchanger tube represented as a spring-mass-damper 21
system
2.1: Flow loop schematic for fluid-elastic instability experiments 26
2.2: Photographs of flow loop and test section (a) Flow loop, (b) Test section 27
assembly, (c) Test section (Half cylinders can be seen), (d) Test section
(End view)
2.3: Schematic of test section assembly (Dimension in meters) 30
2.4: Cut-section schematic view of test tube section 32
2.5: Normal square tube-array pattern 33
2.6: Details of tube-wire tensioning system 35
2.7: Bonding of strain gauges to shims 36
2.8: Schematic of tube-wire system 37
2.9: Schematic of test-tube installed with cartridge heaters (Cut view shown 39
to display embedded cartridge heater and end cap)
vi
2.10: Time decay of tube vibration 42
2.11: Damping ratio measurement from amplitude spectrum of strain gauge 43
signal
3.1: Natural frequency of tube-wire system in still water 50
3.2: Damping ratio of single flexible aluminum tube in (a) air and (b) water 52
3.3: Comparison of the amplitude spectra of strain gauge signal for a single 54
flexible aluminum tube and flexible aluminum array; Q = 40 gpm; α =
l
15%
3.4: Curve fit of equation 2.9 to data of figure 3.4 for a single flexible 55
aluminum tube in air-water flow; Q = 40 gpm; α = 15%
l
Fitted ζ = 3.32%
3.5: Damping ratio correlation of aluminum tube at Q= 40 gpm (air-water 56
l
flow)
3.6: Tube vibration amplitude as a function of flow pitch velocity in single 60
phase flow (a) aluminum tube, (b) stainless steel tube with aluminum
ends, (c) stainless steel tube with stainless steel ends, (d) solid brass rod
3.7: Time sequence of strain gauge signal for the case of fluid-elastic 62
instability in aluminum tube
3.8: Amplitude spectrum of strain gage signal for aluminum tube 63
3.9: Tube numbering of monitored tubes in a fully flexible tube array 64
vii
3.10: Tube vibration amplitude for a fully flexible aluminum tube array in 66
single-phase flow
3.11: Tube vibration amplitude for a fully flexible stainless steel tube array 67
in single-phase flow
3.12: Tube vibration amplitude for a fully flexible brass tube array in 68
single-phase flow
3.13: Comparison of the tube vibration amplitude of central tube 11 for a 69
single flexible tube and a fully flexible array for (a) aluminum tubes,
(b) stainless steel tube
3.14: Tube vibration amplitude using (a) visual observations and (b) strain gauge 71
signal
4.1: Comparison of measured void fraction with correlations at water flow 76
rates of (a) 20 gpm, (b) 40 gpm, (c) 60 gpm, (d) 80 gpm
4.2: Vibration amplitude of aluminum tube as a function of void fraction in 79
air-water flow (single flexible tube)
4.3: Vibration amplitude of stainless steel tube as a function of void fraction 80
in air-water flow (single flexible tube)
4.4: Vibration amplitude of brass rod as a function of void fraction in air- 81
viii
water flow (Single flexible tube)
4.5: Amplitude response of central aluminum tube no. 11 as a function of 83
void fraction Fully flexible array)
4.6: Amplitude response as a function of void fraction for stainless steel 84
tubes (a) Ql = 50 gpm (tube 11), (b) Ql = 40 gpm (tube 14)
4.7: Amplitude vibration of brass rod as a function of void fraction for 84
central tube 11 (fully flexible array)
4.8: Comparison of the vibration amplitude of central tube 11 for a single 85
flexible brass rod and a fully flexible brass array; Q = 60 gpm
l
5.1: Temperature and pressure measurement in the test section for 88
determination of mixture quality
5.2: Vibration amplitude of aluminum tube as a function of void fraction in 92
steam-water flow (Single flexible tube)
5.3: Vibration amplitude of stainless steel tube as a function of void fraction 93
in steam-water flow (Single flexible tube)
5.4: Vibration amplitude of brass rod as a function of void fraction in 94
steam-water flow (Single flexible tube)
5.5: Tube vibration amplitude as a function of void fraction for aluminum 97
ix