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Journal of Pressure Vessel Technology | Volume 131 | Issue 3 | Research Paper
Research Papers: Fluid-Structure Interaction

Two-Phase Flow-Induced Vibration of Parallel Triangular Tube Arrays With Asymmetric Support Stiffness

[+] Author and Article Information
Paul Feenstra, David S. Weaver

Department of Mechanical Engineering, McMaster University, Hamilton, ON, L8S 4L7, Canada

Tomomichi Nakamura

Department of Mechanical Engineering, Osaka Sangyo University, 3-1-1 Nakagaito, Daito, Osaka 574-8530, Japan

J. Pressure Vessel Technol 131(3), 031301 (Feb 04, 2009) (9 pages) doi:10.1115/1.3062964 History: Received August 11, 2006; Revised October 24, 2008; Published February 04, 2009
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Laboratory experiments were conducted to determine the flow-induced vibration response and fluidelastic instability threshold of model heat exchanger tube bundles subjected to a cross-flow of refrigerant 11. Tube bundles were specially built with tubes cantilever-mounted on rectangular brass support bars so that the stiffness in the streamwise direction was about double that in the transverse direction. This was designed to simulate the tube dynamics in the U-bend region of a recirculating-type nuclear steam generator. Three model tube bundles were studied, one with a pitch ratio of 1.49 and two with a smaller pitch ratio of 1.33. The primary intent of the research was to improve our understanding of the flow-induced vibrations of heat exchanger tube arrays subjected to two-phase cross-flow. Of particular concern was to compare the effect of the asymmetric stiffness on the fluidelastic stability threshold with that of axisymmetric stiffness arrays tested most prominently in literature. The experimental results are analyzed and compared with existing data from literature using various definitions of two-phase fluid parameters. The fluidelastic stability thresholds of the present study agree well with results from previous studies for single-phase flow. In two-phase flow, the comparison of the stability data depends on the definition of two-phase flow velocity.
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Copyright © 2009 by American Society of Mechanical Engineers
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+(a) Flow loop schematic. (1) Gear pump, (2) heater section, (3) test-section, (4) shell and tube condenser, (5) flow meters, and (6) control valves, T1, T2, thermocouples, P1, and pressure gage. (b) Tube bundle layout, x=monitored tube.
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(a) Flow loop schematic. (1) Gear pump, (2) heater section, (3) test-section, (4) shell and tube condenser, (5) flow meters, and (6) control valves, T1, T2, thermocouples, P1, and pressure gage. (b) Tube bundle layout, x=monitored tube.
Figure 1

(a) Flow loop schematic. (1) Gear pump, (2) heater section, (3) test-section, (4) shell and tube condenser, (5) flow meters, and (6) control valves, T1, T2, thermocouples, P1, and pressure gage. (b) Tube bundle layout, x=monitored tube.

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+Amplitude response of monitored tube for single-phase liquid R-11 cross-flow. (a) P/D=1.49 and (b) P/D=1.33. (◻) Fully flexible tube array; (×) fully flexible array with addition of a small amount of vapor bubbles (not shown in (a)); and (○) single flexible tube array.
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Amplitude response of monitored tube for single-phase liquid R-11 cross-flow. (a) P/D=1.49 and (b) P/D=1.33. (◻) Fully flexible tube array; (×) fully flexible array with addition of a small amount of vapor bubbles (not shown in (a)); and (○) single flexible tube array.
Figure 2

Amplitude response of monitored tube for single-phase liquid R-11 cross-flow. (a) P/D=1.49 and (b) P/D=1.33. (◻) Fully flexible tube array; (×) fully flexible array with addition of a small amount of vapor bubbles (not shown in (a)); and (○) single flexible tube array.

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+Sample frequency spectra of the fully flexible tube bundle A, P/D=1.33, in single-phase liquid cross-flow
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Sample frequency spectra of the fully flexible tube bundle A, P/D=1.33, in single-phase liquid cross-flow
Figure 3

Sample frequency spectra of the fully flexible tube bundle A, P/D=1.33, in single-phase liquid cross-flow

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+Critical flow velocities for fluidelastic instability of parallel triangular tube arrays in single-phase cross-flow. Present study: (◻) P/D=1.49; (△) P/D=1.33 (bundle A); (▽) P/D=1.33 (bundle B); and (○) Feenstra (12). Other data points, +, drawn from Weaver and Fitzpatrick (20).
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Critical flow velocities for fluidelastic instability of parallel triangular tube arrays in single-phase cross-flow. Present study: (◻) P/D=1.49; (△) P/D=1.33 (bundle A); (▽) P/D=1.33 (bundle B); and (○) Feenstra (12). Other data points, +, drawn from Weaver and Fitzpatrick (20).
Figure 4

Critical flow velocities for fluidelastic instability of parallel triangular tube arrays in single-phase cross-flow. Present study: (◻) P/D=1.49; (△) P/D=1.33 (bundle A); (▽) P/D=1.33 (bundle B); and (○) Feenstra (12). Other data points, +, drawn from Weaver and Fitzpatrick (20).

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+Sample amplitude responses for the fully flexible tube bundle subjected to two-phase R-11 cross-flow (lift direction only). (a) P/D=1.49 and Gp=403 kg/m2 s; (b) P/D=1.33 and Gp=426 kg/m2 s
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Sample amplitude responses for the fully flexible tube bundle subjected to two-phase R-11 cross-flow (lift direction only). (a) P/D=1.49 and Gp=403 kg/m2 s; (b) P/D=1.33 and Gp=426 kg/m2 s
Figure 5

Sample amplitude responses for the fully flexible tube bundle subjected to two-phase R-11 cross-flow (lift direction only). (a) P/D=1.49 and Gp=403 kg/m2 s; (b) P/D=1.33 and Gp=426 kg/m2 s

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+Sample frequency spectra for the fully flexible bundle, P/D=1.49, in two-phase cross-flow
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Sample frequency spectra for the fully flexible bundle, P/D=1.49, in two-phase cross-flow
Figure 6

Sample frequency spectra for the fully flexible bundle, P/D=1.49, in two-phase cross-flow

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+Critical flow velocities for fluidelastic instability of parallel triangular tube arrays in two-phase cross-flows. Data analysis using (a) HEM model, (b) interfacial velocity correlation for parallel triangular arrays (i.e., Ci=0.77) and slip ratio model, and (c) gas phase velocity and slip ratio model. (△,▽, and ◻) Present study in R11 for bundles A and B, respectively. Present study in R-11 (P/D=1.49); (○) Feenstra (12) in R-11; (+) Pettigrew (25) in air-water; (∗) Pettigrew (8) in R22; (◇) Pettigrew (9) in R134a; (×) Axisa (23) in steam-water; (———) Connors’ theory; and (——-) prediction of Li and Weaver (22).
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Critical flow velocities for fluidelastic instability of parallel triangular tube arrays in two-phase cross-flows. Data analysis using (a) HEM model, (b) interfacial velocity correlation for parallel triangular arrays (i.e., Ci=0.77) and slip ratio model, and (c) gas phase velocity and slip ratio model. (△,▽, and ◻) Present study in R11 for bundles A and B, respectively. Present study in R-11 (P/D=1.49); (○) Feenstra (12) in R-11; (+) Pettigrew (25) in air-water; (∗) Pettigrew (8) in R22; (◇) Pettigrew (9) in R134a; (×) Axisa (23) in steam-water; (———) Connors’ theory; and (——-) prediction of Li and Weaver (22).
Figure 7

Critical flow velocities for fluidelastic instability of parallel triangular tube arrays in two-phase cross-flows. Data analysis using (a) HEM model, (b) interfacial velocity correlation for parallel triangular arrays (i.e., Ci=0.77) and slip ratio model, and (c) gas phase velocity and slip ratio model. (△,▽, and ◻) Present study in R11 for bundles A and B, respectively. Present study in R-11 (P/D=1.49); (○) Feenstra (12) in R-11; (+) Pettigrew (25) in air-water; (∗) Pettigrew (8) in R22; (◇) Pettigrew (9) in R134a; (×) Axisa (23) in steam-water; (———) Connors’ theory; and (——-) prediction of Li and Weaver (22).

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+Flow regime analysis for the FEI threshold data of the present study. Flow regime boundaries determined by Ulbrich and Mewes (26).
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Flow regime analysis for the FEI threshold data of the present study. Flow regime boundaries determined by Ulbrich and Mewes (26).
Figure 8

Flow regime analysis for the FEI threshold data of the present study. Flow regime boundaries determined by Ulbrich and Mewes (26).

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+Normalized damping measurements for the single flexible tube bundle, P/D=1.33 (bundle A) in two-phase R-11 cross-flow as a function of the homogeneous void fraction. (●) Feenstra (21) in R-11; (▲) Pettigrew (24) in air-water; (▼) Pettigrew (7) in R22; and (◆) Pettigrew (9) in R134a.
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Normalized damping measurements for the single flexible tube bundle, P/D=1.33 (bundle A) in two-phase R-11 cross-flow as a function of the homogeneous void fraction. (●) Feenstra (21) in R-11; (▲) Pettigrew (24) in air-water; (▼) Pettigrew (7) in R22; and (◆) Pettigrew (9) in R134a.
Figure 9

Normalized damping measurements for the single flexible tube bundle, P/D=1.33 (bundle A) in two-phase R-11 cross-flow as a function of the homogeneous void fraction. (●) Feenstra (21) in R-11; (▲) Pettigrew (24) in air-water; (▼) Pettigrew (7) in R22; and (◆) Pettigrew (9) in R134a.

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