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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

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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Figures

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Fig. 1

Schematic of the heat exchanger tube

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Fig. 2

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

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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

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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

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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

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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

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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.

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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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