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Research Papers: Flows in Complex Systems

Numerical Prediction of Fluid-Elastic Instability in Normal Triangular Tube Bundles With Multiple Flexible Circular Cylinders

[+] Author and Article Information
Hamed Houri Jafari

Faculty Member Department of National Energy Master Plan,
Institute for International Energy Studies (IIES),
Tehran, Iran
e-mail: hhjafari@gmail.com; h_jafari@iies.net

Behzad Ghadiri Dehkordi

Faculty Member Department of Mechanical Engineering,
School of Engineering,
Tarbiat Modares University,
Tehran, Iran

1Corresponding author.

Manuscript received April 19, 2011; final manuscript received October 27, 2012; published online February 22, 2013. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 135(3), 031102 (Feb 22, 2013) (14 pages) Paper No: FE-11-1174; doi: 10.1115/1.4023298 History: Received April 19, 2011; Revised October 27, 2012

Prediction of fluid-elastic instability onset is a great matter of importance in designing cross-flow heat exchangers from the perspective of vibration. In the present paper, the threshold of fluid-elastic instability has been numerically predicted by the simulation of incompressible, unsteady, and turbulent cross flow through a tube bundle in a normal triangular arrangement. In the tube bundle under study, there were single or multiple flexible cylinders surrounded by rigid tubes. A finite volume solver based on a Cartesian-staggered grid was implemented. In addition, the ghost-cell method in conjunction with the great-source-term technique was employed in order to directly enforce the no-slip condition on the cylinders' boundaries. Interactions between the fluid and the structures were considered in a fully coupled manner by means of intermittence solution of the flow field and structural equations of motion in each time step of the numerical modeling algorithm. The accuracy of the solver was validated by simulation of the flow over both a rigid and a flexible circular cylinder. The results were in good agreement with the experiments reported in the literatures. Eventually, the flow through seven different flexible tube bundles was simulated. The fluid-elastic instability was predicted and analyzed by presenting the structural responses, trajectory of flexible cylinders, and critical reduced velocities.

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Figures

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Fig. 1

Two-dimensional model of a flexible cylinder

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Fig. 2

Main grid cells that are cut by a cylinder boundary. Cut-cells are in gray and internal cells are hatched. Location of u-velocity in ghost cell of u-staggered grid. Location of v-velocity in ghost cell of v-staggered grid. • Location of pressure in main grid. Location of u in the flow field. Location of v in the flow field. ○ Location of pressure for a cell located in the flow field [18,19].

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Fig. 3

Algorithm of a fluid-structure interaction modeling

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Fig. 4

Effective viscosity distribution for flow around a fixed circular cylinder at Re = 104 and tU/D = 87; (a) standard k-ɛ, (b) extended k-ɛ, (c) RNG-k-ɛ

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Fig. 5

Mean drag coefficient versus time step size for the flow around a single circular cylinder in Re = 104

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Fig. 6

The nondimensional vibration amplitude in the y direction versus the reduced velocity for a single flexible circular cylinder

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Fig. 7

The displacement of the single flexible cylinder versus the nondimensional time for U/fD = 10 and Re = 10,000

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Fig. 8

The schematic of flow through the tube bundle in a normal triangular arrangement with tube pitch P, tube diameter D, and pitch to diameter ratio P/D

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Fig. 9

The different tube bundles regarding the flexibility of cylinders (the gray cylinders are flexible and the white cylinders are rigid)

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Fig. 10

Root mean square of the flexible cylinder displacement versus free-stream velocity for tube bundle in normal triangular arrangement (P/D = 1.32)

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Fig. 11

The vibration amplitude of cylinder 5 in the x and y directions for tube bundle I

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Fig. 12

The vibration amplitude of cylinder 5 in the x and y directions for tube bundle II

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Fig. 16

The vibration amplitude of cylinder 5 in the x and y directions for tube bundle VI

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Fig. 17

The vibration amplitude of cylinder 5 in the x and y directions for tube bundle VII

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Fig. 18

The nondimensional vibration amplitude of cylinder 5 in different tube bundles

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Fig. 13

The vibration amplitude of cylinder 5 in the x and y directions for tube bundle III

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Fig. 14

The vibration amplitude of cylinder 5 in the x and y directions for tube bundle IV

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Fig. 15

The vibration amplitude of cylinder 5 in the x and y directions for tube bundle V

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Fig. 19

The vibration orbit of cylinder 5 for U/fnD=2.3. (a) Tube bundle I, (b) tube bundle IV, (c) tube bundle VII.

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Fig. 20

The vibration orbit of flexible cylinders of tube bundle VII for U/fnD=2.3

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