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Research Papers: Fluid-Structure Interaction

# Fluid Excitation Forces on a Tightly Packed Tube Bundle Subjected in Cross-Flow

[+] Author and Article Information
Liyan Liu

School of Chemical Engineering
and Technology,
Tianjin University,
Haihe Educational Park,
Tianjin 300354, China
e-mail: liuliyan@tju.edu.cn

Jiaxiang Feng

School of Chemical Engineering
and Technology,
Tianjin University,
Haihe Educational Park,
Tianjin 300354, China
e-mail: fjx_tju@163.com

Hao Wu

School of Chemical Engineering
and Technology,
Tianjin University,
Haihe Educational Park,
Tianjin 300354, China
e-mail: wwwhha@126.com

Wei Xu

School of Chemical Engineering
and Technology,
Tianjin University,
Haihe Educational Park,
Tianjin 300354, China
e-mail: xw1224@tju.edu.cn

Wei Tan

School of Chemical Engineering
and Technology,
Tianjin University,
Haihe Educational Park,
Tianjin 300354, China
e-mail: wtan@tju.edu.cn

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received August 26, 2016; final manuscript received November 1, 2016; published online January 11, 2017. Assoc. Editor: Tomomichi Nakamura.

J. Pressure Vessel Technol 139(3), 031307 (Jan 11, 2017) (8 pages) Paper No: PVT-16-1154; doi: 10.1115/1.4035318 History: Received August 26, 2016; Revised November 01, 2016

## Abstract

Fluid excitation forces acting on stationary cylinders with cross-flow are the coupling of vortex shedding and turbulence buffeting. Those forces are significant in the analytical framework of fluid-induced vibration in heat exchangers. A bench-scale experimental setup with an instrumented test bundle is constructed to measure fluid excitation forces acting on cylinders in the normal triangular tube arrays (P/D = 1.28) with water cross-flow. The lift and drag forces on stationary cylinders are measured directly as a function of Reynolds number with a developed piezoelectric transducer. The results show that the properties of fluid excitation forces, to a great extent, largely depend upon the locations of cylinders within bundle by comparison to the inflow variation. A quasi-periodic mathematical model of fluid excitation forces acting on a circular cylinder is presented for a tightly packed tube bundle subjected to cross-flow, and the bounded noise theory is applied between $fR$ = 0.01 and $fR$ = 1. The developed model is illustrated with lots of identification results based on the dominant frequency, the intensity of random frequency, and the amplitude of fluid excitation forces. A second model has been developed for fluid excitation forces between $fR$ = 1 and $fR$ = 6 with the spectrum index introduced. Although still preliminary, each model can predict the corresponding forces relatively well.

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## Figures

Fig. 1

Schematic of the experimental set

Fig. 2

Schematic of the test-section

Fig. 3

Schematic of DAS

Fig. 4

Tube arrangement

Fig. 5

Fluctuating lift and drag forces

Fig. 6

Phase difference of fluid forces

Fig. 7

Characteristic parameters of the fluctuating lift force

Fig. 8

Characteristic parameters of the fluctuating drag force

Fig. 9

Median filtering to lift force PSD

Fig. 10

Processed normalized PSD with median filtering

Fig. 11

Normalized lift force PSD for low-frequency area

Fig. 12

Equivalent normalized excitation force coefficient for tube positions

Fig. 13

Equivalent power of fluid forces for low-frequency area

Fig. 14

Normalized lift force PSD for high-frequency area

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