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Research Papers: Fluid-Structure Interaction

A Simulation Study on the Dynamic Stability of a Fluid-Conveying Pipe With a Constant Velocity Leakage

[+] Author and Article Information
Shuai Meng, Xuefeng Wang

State Key Laboratory of Ocean Engineering,
Collaborative Innovation Center for
Advanced Ship and Deep-Sea Exploration,
Shanghai Jiao Tong University,
Shanghai 200240, China

Ye Li

State Key Laboratory of Ocean Engineering,
Collaborative Innovation Center for
Advanced Ship and Deep-Sea Exploration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: ye.li@sjtu.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 November 22, 2016; final manuscript received April 14, 2017; published online May 26, 2017. Assoc. Editor: Tomomichi Nakamura.

J. Pressure Vessel Technol 139(4), 041303 (May 26, 2017) (11 pages) Paper No: PVT-16-1222; doi: 10.1115/1.4036657 History: Received November 22, 2016; Revised April 14, 2017

Motivated by the fact that a leaking pipe can lose or gain energy from the leaking flow, this study attempts to explore the nonconservative leaking flow effect on the dynamic stability of a simply supported pipe with a constant velocity leakage. It employs a two-dimensional nonlinear longitudinal and lateral coupling model, and the leakage effect is accounted for by virtual work due to virtual momentum transport at the leaking point. The equations of motion are solved by Galerkin-based multimode approach and the Houbolt's finite difference time integration. It demonstrates that when there is a leaking flow, a stable pipe can be refined or destabilized via a static pitchfork bifurcation, and a buckling pipe can be stabilized or deteriorated into a worse divergence condition. The critical leaking flow velocities and the excited buckling modes depend on the leaking fluid mass and the leak's position. This study may provide some insights to assist the leak detection system (LDS) of a pipe transporting high-pressure oil or gas in modern engineering.

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Figures

Grahic Jump Location
Fig. 1

A sketch of a pinned–pinned pipe with a constant velocity leakage

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Fig. 2

The envelopes of the time traces of P1* in the lateral direction when u1=3.0, β1=0.47, Λ  = 1000, and γ1=Π=Γ=0

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Fig. 3

The time traces of P1* in the lateral direction when u1=3.3, β1=0.47, Λ  = 1000, and γ1=Π=Γ=0

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Fig. 4

The buckling shapes of the pipe when u1=3.3, β1=0.47, Λ  = 1000, and γ1=Π=Γ=0: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 5

The predicted |p1| versus u1 when β1=0.47, Λ=1000, 4000, and 10,000, and γ1=Π=Γ=0. —: the present simulation; ○: the study by Sadeghi and Païdoussis [8].

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Fig. 6

The time traces of the adopted modal coordinates when u1=3.3, β1=0.47, Λ  = 1000, and γ1=Π=Γ=0: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 7

The predicted |p1| versus u1 when β1=0.47, γ1=−10, 0, 20, and 40, Λ=1000, and Π=Γ=0. —: the present simulation; ○: the study by Sadeghi and Païdoussis [8].

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Fig. 8

The time traces of the adopted modal coordinates when u1=5.0, β1=0.47, Λ = 1000, γ1=20, and Π=Γ=0: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 9

The buckling shapes of the pipe when u1=5.0, β1=0.47, Λ = 1000, γ1=20, and Π=Γ=0: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 10

The predicted |p1| versus u1 when β1=0.47, Γ=−9.9, 0, 9.9, and 20, and γ1=Π=Γ=0. —: the present simulation; ○: the study by Sadeghi and Païdoussis [8].

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Fig. 11

The time traces of the adopted modal coordinates at u1=5.0 when β1=0.47, Λ = 1000, Γ=9.9, and γ1=Π=0: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 12

The pipe is subject to a refined damping oscillation, an aperiodic damping vibration, and a static pitchfork bifurcation with the increase of uleak at u1=2.0 when leakage occurs in P1* and c=0.1: (a) the envelopes of the damping oscillations of P1*when uleak = 0.0, 2.0, 10, and 20 and (b) the time traces of P1* when uleak = 60, 70, 80, 90, and 96

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Fig. 13

The time traces of the first four dominant modal coordinates at u1=2.0 when leakage occurs in P1* and uleak=96, c=0.1: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 14

The buckling shapes of the pipe at u1=2.0 when leakage occurs in P1* and uleak=96, c=0.1: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 15

The first two dominant modal coordinates at u1=2.0 when leakage occurs in P1* and c=0.1: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 16

The time traces of P1* at u1=3.3 in the lateral direction when leakage occurs in P1* and uleak=2.0, c=0.1

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Fig. 17

The first two dominant modal coordinates at u1=3.3 when leakage occurs in P1* and c=0.1: (a) in the longitudinal direction and (b) in the lateral direction—○ denotes |p1| for the intact pipe

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Fig. 18

The first two dominant modal coordinates at u1=4.0 when leakage occurs in P1* and c=0.1: (a) in the longitudinal direction—○ denotes |q2| for the intact pipe and (b) in the lateral direction—○ denotes |p1| for the intact pipe

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Fig. 19

The first two dominant modal coordinates at u1=2.0 when leakage occurs in P1* and c=0.2: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 20

The first two dominant modal coordinates at u1=3.3 when leakage occurs in P1* and c=0.2: (a) in the longitudinal direction and (b) in the lateral direction—○ denotes |p1| for the intact pipe

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Fig. 21

The first two dominant modal coordinates at u1=4.0 when leakage occurs in P1* and c=0.2: (a) in the longitudinal direction and (b) in the lateral direction—○ denotes |p1| for the intact pipe

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Fig. 22

The envelopes of the damping oscillations of P1* at uleak=0.0, 2.0, 10, and 20 when leakage occurs in P1* and c=0.1 and 0.2

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Fig. 23

The first three dominant modal coordinates at u1=2.0 when leakage occurs in P2* and c=0.1: (a) in the longitudinal direction and (b) in the lateral direction

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Fig. 24

The first three dominant modal coordinates at u1=3.3 when leakage occurs in P2* and c=0.1: (a) in the longitudinal direction and (b) in the lateral direction—○ denotes |p1| for the intact pipe

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Fig. 25

The buckling shapes of the pipe at u1=2.0 when leakage occurs in P2* and c=0.1, uleak=50: (a) in the longitudinal direction and (b) in the lateral direction

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