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Research Papers

# Vibrations of a Simply Supported Cross Flow Heat Exchanger Tube With Axial Load and Loose Supports

[+] Author and Article Information
Anwar Sadath, V. Vinu

Department of Mechanical and
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi 502285, Telangana, India

C. P. Vyasarayani

Department of Mechanical and
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi 502285, Telangana, India
e-mail: vcprakash@iith.ac.in

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 7, 2015; final manuscript received January 24, 2017; published online March 9, 2017. Assoc. Editor: Mohammad Younis.

J. Comput. Nonlinear Dynam 12(5), 051001 (Mar 09, 2017) (7 pages) Paper No: CND-15-1283; doi: 10.1115/1.4035880 History: Received September 07, 2015; Revised January 24, 2017

## Abstract

In this work, a mathematical model is developed for simulating the vibrations of a single flexible cylinder under crossflow. The flexible tube is subjected to an axial load and has loose supports. The equation governing the dynamics of the tube under the influence of fluid forces (modeled using quasi-steady approach) is a partial delay differential equation (PDDE). Using the Galerkin approximation, the PDDE is converted into a finite number of delay differential equations (DDE). The obtained DDEs are used to explore the nonlinear dynamics and stability characteristics of the system. Both analytical and numerical techniques were used for analyzing the problem. The results indicate that, with high axial loads and for flow velocities beyond certain critical values, the system can undergo flutter or buckling instability. Post-flutter instability, the amplitude of vibration grows until it impacts with the loose support. With a further increase in the flow velocity, through a series of period doubling bifurcations the tube motion becomes chaotic. The critical flow velocity is same with and without the loose support. However, the loose support introduces chaos. It was found that when the axial load is large, the linearized analysis overestimates the critical flow velocity. For certain high flow velocities, limit cycles exist for axial loads beyond the critical buckling load.

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## References

Mitra, D. R. , 2005, “ Fluid-Elastic Instability in Tube Arrays Subjected to Air-Water and Steam-Water Cross-Flow,” Ph.D. thesis, University of California, Los Angeles, CA.
Roberto, B. , 1962, “ Low Frequency, Self-Excited Vibration in a Row of Circular Cylinders Mounted in an Airstream,” Ph.D. thesis, University of Cambridge, Cambridge, UK.
Connors, H. J., Jr. , 1970, “ Fluidelastic Vibration of Tube Arrays Excited by Cross Flow,” Flow-Induced Vibration in Heat Exchangers, D. D. Reiff , ed., ASME, New York, pp. 42–56.
Blevins, R. , 1974, “ Fluid Elastic Whirling of a Tube Row,” ASME J. Pressure Vessel Technol., 96(4), pp. 263–267.
Dalton, C. , and Helfinstine, R. A. , 1971, “ Potential Flow Past a Group of Circular Cylinders,” ASME J. Basic Eng., 93(4), pp. 636–642.
Price, S. , and Paidoussis, M. , 1986, “ A Single-Flexible-Cylinder Analysis for the Fluidelastic Instability of an Array of Flexible Cylinders in Cross-Flow,” ASME J. Fluids Eng., 108(2), pp. 193–199.
Tanaka, H. , and Takahara, S. , 1981, “ Fluid Elastic Vibration of Tube Array in Cross Flow,” J. Sound Vib., 77(1), pp. 19–37.
Hassan, Y. , Bagwell, T. , and Steininger, D. , 1990, “ Large Eddy Simulation of the Fluctuating Forces on a Square Pitched Tube Array and Comparison With Experiment,” Flow-Induced Vib., 189, pp. 45–50.
Lever, J. , and Weaver, D. , 1986, “ On the Stability of Heat Exchanger Tube Bundles, Part I: Modified Theoretical Model,” J. Sound Vib., 107(3), pp. 375–392.
Price, S. , and Paidoussis, M. , 1984, “ An Improved Mathematical Model for the Stability of Cylinder Rows Subject to Cross-Flow,” J. Sound Vib., 97(4), pp. 615–640.
Paidoussis, M. , and Li, G. , 1992, “ Cross-Flow-Induced Chaotic Vibrations of Heat-Exchanger Tubes Impacting on Loose Supports,” J. Sound Vib., 152(2), pp. 305–326.
Halle, H. , Chenoweth, J. , and Wambsganss, M. , 1981, “ Flow-Induced Tube Vibration Tests of Typical Industrial Heat Exchanger Configurations,” ASME Paper No. 81-DET-37.
Halle, H. , Chenoweth, J. , and Wambsganss, M. , 1984, “ Flow-Induced Tube Vibration Thresholds in Heat Exchangers From Shellside Water Tests,” ASME Paper No. G00269.
Chen, S. , 1983, “ Instability Mechanisms and Stability Criteria of a Group of Circular Cylinders Subjected to Cross-Flow. Part I: Theory,” ASME J. Vib. Acoust., 105(1), pp. 51–58.
Chen, S. , 1983, “ Instability Mechanisms and Stability Criteria of a Group of Circular Cylinders Subjected to Cross-Flow—Part 2: Numerical Results and Discussions,” ASME J. Vib. Acoust., 105(2), pp. 253–260.
Yetisir, M. , and Weaver, D. , 1993, “ An Unsteady Theory for Fluidelastic Instability in an Array of Flexible Tubes in Cross-Flow. Part I: Theory,” J. Fluids Struct., 7(7), pp. 751–766.
Yetisir, M. , and Weaver, D. , 1993, “ An Unsteady Theory for Fluidelastic Instability in an Array of Flexible Tubes in Cross-Flow. Part II: Results and Comparison With Experiments,” J. Fluids Struct., 7(7), pp. 767–782.
Rzentkowski, G. , and Lever, J. , 1998, “ An Effect of Turbulence on Fluidelastic Instability in Tube Bundles: A Nonlinear Analysis,” J. Fluids Struct., 12(5), pp. 561–590.
Ibrahim, R. A. , 2010, “ Overview of Mechanics of Pipes Conveying Fluids—Part I: Fundamental Studies,” ASME J. Pressure Vessel Technol., 132(3), p. 034001.
Ibrahim, R. A. , 2011, “ Mechanics of Pipes Conveying Fluids—Part II: Applications and Fluidelastic Problems,” ASME J. Pressure Vessel Technol., 133(2), p. 024001.
Rogers, R. , and Pick, R. , 1976, “ On the Dynamic Spatial Response of a Heat Exchanger Tube With Intermittent Baffle Contacts,” Nucl. Eng. Des., 36(1), pp. 81–90.
Rogers, R. , and Pick , 1977, “ Factors Associated With Support Plate Forces Due to Heat-Exchanger Tube Vibratory Contact,” Nucl. Eng. Des., 44(2), pp. 247–253.
Jacquart, G. , and Gay, N. , 1993, “ Computation of Impact-Friction Interaction Between a Vibrating Tube and Its Loose Supports,” Electricite de France (EDF), 92-Clamart (France), Report No. 94NB00040.
Wang, L. , Dai, H. , and Han, Y. , 2012, “ Cross-Flow-Induced Instability and Nonlinear Dynamics of Cylinder Arrays With Consideration of Initial Axial Load,” Nonlinear Dyn., 67(2), pp. 1043–1051.
Wang, L. , and Ni, Q. , 2010, “ Hopf Bifurcation and Chaotic Motions of a Tubular Cantilever Subject to Cross Flow and Loose Support,” Nonlinear Dyn., 59(1), pp. 329–338.
Xia, W. , and Wang, L. , 2010, “ The Effect of Axial Extension on the Fluidelastic Vibration of an Array of Cylinders in Cross-Flow,” Nucl. Eng. Design, 240(7), pp. 1707–1713.

## Figures

Fig. 1

Schematic of the heat exchanger tube

Fig. 2

Stability regions of the linearized model (Eqs. (20) and (21)) of the tube under axial load

Fig. 3

Time responses of the flexible tube without loose supports at different values of axial load p0 and for U = 1.0: (a) p0 = −15, stable equilibrium, (b) p0 = 0, stable equilibrium, (c) p0 = 9, stable limit cycle (flutter), and (d) p0 = 15, buckled equilibrium

Fig. 4

Bifurcation diagrams of the flexible tube without loose support for different values of axial load p0: (a) p0 = −15, (b) p0 = 0, (c) p0 = 9, and (d) p0 = 15

Fig. 5

Bifurcation diagrams of flexible tube with loose supports modeled as cubic spring for different values of axial load p0: (a) p0 = −15, (b) p0 = 0, (c) p0 = 9, and (d) p0 = 15

Fig. 6

Time response, phase plot, and FFT spectrum of the flexible tube with loose supports for p0 = 0 and for different flow velocities U: (a)–(c) U = 4, (d)–(f) U = 6.5, and (g)–(i) U = 7.5

Fig. 7

Stability regions for the tube under axial loads and fluid forces. The red-dashed lines are for linearized model (Fig. 2). The blue-solid line, black-dash-doted line, and black dotted line are for the nonlinear model. The region (d) indicates the buckled equilibrium. The region (e) is the chaotic region for the flexible tube with loose support.

Fig. 8

Time responses of the flexible tube with loose supports at p0 = 13: (a) buckled equilibrium at U = 0.2 and (b) stable limit cycle at U = 1

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