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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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References

1
Weaver, D. S., and Schneider, W. G., 1983, “The Effect of Flat Bar Supports on the Crossflow Induced Response of Heat Exchanger U-Tubes,” ASME J. Eng. Power, 105 , pp. 775–781.
2
Weaver, D. S., and Koroyannakis, D., 1983, “Flow-Induced Vibrations of Heat Exchanger U-Tubes: A Simulation to Study the Effects of Asymmetric Stiffness,” ASME J. Vib., Acoust., Stress, Reliab. Des., 105 , pp. 67–75.
3
Mureithi, N. W., Zhang, C., and Pettigrew, M. J., 2004, “Fluidelastic Instability Tests on an Array of Tubes Preferentially Flexible in the Flow Direction,” "Proceedings of the 8th International Conference on Flow-Induced Vibrations", Paris, France, E.de Langre and F.Axisa, eds.
4
Violette, R., Pettigrew, M. J., and Mureithi, N. W., 2006, “Fluidelastic Instability of an Array of Tubes Preferentially Flexible in the Flow Direction Subjected to Two-Phase Cross-Flow,” ASME J. Pressure Vessel Technol.  [CrossRef], 128 , pp. 148–159.
5
Janzen, V. P., Hagberg, E. G., Pettigrew, M. J., and Taylor, C. E., 2005, “Fluidelastic Instability and Work Rate Measurements of Steam Generator U-Tubes in Air-Water Cross-Flow,” ASME J. Pressure Vessel Technol., 127 , pp. 84–91.
6
Weaver, D. S., Ziada, S., Au-Yang, M. K., Chen, S. S., Paidoussis, M. P., and Pettigrew, M. J., 2000, “Flow-Induced Vibrations in Power and Process Plant Components-Progress and Prospects,” ASME J. Pressure Vessel Technol.  [CrossRef], 122 , pp. 339–348.
7
Pettigrew, M. J., and Taylor, C. E., 1994, “Two-Phase Flow-Induced Vibration: An Overview,” ASME J. Pressure Vessel Technol.  [CrossRef], 116 , pp. 233–253.
8
Pettigrew, M. J., Taylor, C. E., Jong, J. H., and Currie, I. G., 1995, “Vibration of a Tube Bundle in Two-Phase Freon Cross-Flow,” ASME J. Pressure Vessel Technol.  [CrossRef], 117 , pp. 321–329.
9
Pettigrew, M. J., Taylor, C. E., Janzen, V. P., and Whan, T., 2002, “Vibration Behaviour of Rotated Triangular Tube Bundles in Two-Phase Cross-Flows,” ASME J. Pressure Vessel Technol.  [CrossRef], 124 , pp. 144–153.
10
Pettigrew, M. J., and Taylor, C. E., 2004, “Vibration of a Normal Triangular Tube Bundle in Two-Phase Freon Cross-Flow,” "Flow-Induced Vibration 2004", Paris, France, E.de Langre and F.Axisa, eds., A.A. Balkema, The Netherlands.
11
Nakamura, T., Hirota, K., Tomomatsu, K., Kasahara, J., and Takamatsu, H., 1999, “On Positional Effect of Flexible Tubes in a Square Array Subjected to Freon Two-Phase Flow,” "Proceedings of the ASME PVP Symposium, Flow Induced Vibration 1999", Boston, MA, M.J.Pettigrew, ed., PVP-Vol. 389 , pp. 73–80.
12
Feenstra, P. A., Judd, R. L., and Weaver, D. S., 1995, “Fluidelastic Instability in a Tube Array Subjected to Two-Phase R-11 Cross-Flow,” J. Fluids Struct., 9 , pp. 747–771.
13
Feenstra, P. A., Weaver, D. S., and Judd, R. L., 2000, “Modelling Two-Phase Flow-Excited Fluidelastic Instability in Tube Arrays,” "Proceedings of Flow-Induced Vibration 2000", Lucerne, Switzerland, S.Ziada and T.Staubli, eds., A.A. Balkema, The Netherlands, pp. 545–554.
14
Feenstra, P. A., Weaver, D. S., and Judd, R. L., 2000, “An Improved Void Fraction Model for Two-Phase Cross-Flow Through Horizontal Tube Arrays,” Int. J. Multiphase Flow, 26 , pp. 1851–1873.
15
Consolini, L., Robinson, D., and Thome, R., 2006, “Void Fraction and Two-Phase Pressure Drops for Evaporating Flow over Horizontal Tube Bundles,” Heat Transfer Eng., 27 (3), pp. 5–21.
16
Feenstra, P. A., Weaver, D. S., and Nakamura, T., 2003, “Vortex Shedding and Fluidelastic Instability in a Normal Square Tube Array by Two-Phase Cross-Flow,” J. Fluids Struct., 17 , pp. 793–811.
17
Judd, R. L., Dam, R., and Weaver, D. S., 1992, “A Photo-Optical Technique for Measuring Flow-Induced Vibrations in Cantilevered Tube Bundles,” Exp. Therm. Fluid Sci.  [CrossRef], 5 , pp. 747–754.
18
Nakamura, T., Hirota, K., and Tomomatsu, K., 2000, “Some Problems on the Estimation of Flow-Induced Vibration of a Tube Array Subjected to Two-Phase Flow,” "Proceedings of Flow-Induced Vibration 2000", Lucerne, Switzerland, S.Ziada and T.Staubli, eds., A.A. Balkema, The Netherlands, pp. 537–544.
19
Ziada, S., and Oengoren, A., 2000, “Flow Periodicity and Acoustic Resonance in Parallel Triangular Arrays,” J. Fluids Struct., 14 , pp. 197–219.
20
Weaver, D. S., and Fitzpatrick, J. A., 1988, “A Review of Cross-Flow Induced Vibrations in Heat Exchanger Tube Arrays,” J. Fluids Struct., 2 , pp. 73–93.
21
Feenstra, P. A., Weaver, D. S., and Judd, R. L., 2002, “Modelling Two-Phase Flow-Excited Damping and Fluidelastic Instability in Tube Arrays,” J. Fluids Struct., 16 (6), pp. 811–840.
22
Li, M., and Weaver, D. S., 1997, “A Fluidelastic Instability Model With an Extension to Full Flexible Multi-Span Tube Arrays,” "Proceedings of the ASME PVP Conference, 4th International Symposium on Fluid Structure Interaction, Aeroelasticity, Flow-Induced Vibration and Noise", Vol. II , Dallas, TX, M.P.Païdoussiset al. , ed., ASME AD-Vol. 53-2, pp. 163–172.
23
Axisa, F., Boheas, M. A., and Villard, B., 1985, “Vibration of Tube Bundles Subjected to Steam-Water Cross-Flow: A Comparative Study of Square and Triangular Arrays,” Eighth International Conference on Structural Mechanics in Reactor Technology , Brussels, Belgium, Paper No. B1/2.
24
Pettigrew, M. J., Taylor, C. E., and Kim, B. S., 1989, “Vibration of Tube Bundles in Two-Phase Cross Flow: Part 1—Hydrodynamic Mass and Damping,” ASME J. Pressure Vessel Technol., 111 , pp. 466–477.
25
Pettigrew, M. J., Tromp, J. H., Taylor, C. E., and Kim, B. S., 1989, “Vibration of Tube Bundles in Two-Phase Cross-Flow: Part 2—Fluid-Elastic Instability,” ASME J. Pressure Vessel Technol., 111 , pp. 478–487.
26
Ulbrich, R., and Mewes, D., 1994, “Vertical, Upward Gas-Liquid Two-Phase Flow Across a Tube Bundle,” Int. J. Multiphase Flow  [CrossRef], 20 , pp. 249–272.

Figures

Grahic Jump Location
+(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.

Grahic Jump Location
+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.

Grahic Jump Location
+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

Grahic Jump Location
+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).

Grahic Jump Location
+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

Grahic Jump Location
+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

Grahic Jump Location
+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).

Grahic Jump Location
+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).

Grahic Jump Location
+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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