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Research Papers

Dynamics of Slightly Curved Pipe Conveying Hot Pressurized Fluid Resting on Linear and Nonlinear Viscoelastic Foundations

[+] Author and Article Information
O. D. Owoseni

Department of Mechanical Engineering,
University of Lagos,
Lagos 100213, Nigeria
e-mail: owosenid@yahoo.com

K. O. Orolu

Department of Systems Engineering,
University of Lagos,
Lagos 100213, Nigeria
e-mail: korolu@unilag.edu.ng

A. A. Oyediran

Department of Mechanical Engineering,
University of Lagos,
Lagos 100213, Nigeria
e-mail: ayooyediran@hotmail.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 14, 2017; final manuscript received August 9, 2017; published online October 4, 2017. Assoc. Editor: Stefano Lenci.

J. Vib. Acoust 140(2), 021005 (Oct 04, 2017) (13 pages) Paper No: VIB-17-1156; doi: 10.1115/1.4037703 History: Received April 14, 2017; Revised August 09, 2017

One of the most important facilities in the oil and gas industry is the pipeline. These pipelines convey high pressure with high temperature (HPHT) fluids and transit several kilometers traveling through different seafloor soils. The topography of seabed which acts as viscoelastic foundation to the pipeline is rough and irregular, thereby making the pipelines to be slightly curved. This erratic behavior of these soils presents several problems to the constructor and threatens the lifespan of the pipeline. The nonlinear governing partial differential equations (PDEs) were derived and solved using energy and eigenfunction expansion methods, respectively. The resultant ordinary differential equations (ODEs) were truncated after the fourth mode and solved numerically using eighth-seventh order Runge–Kutta code in matlab. Two types of foundations were investigated: both with viscous damping but one was with linear spring, while the other was with nonlinear spring. Bifurcation and orbit diagrams with their corresponding phase portraits that show periodic and chaotic motions of the system trajectories are generated and presented. It was examined that foundation, initial curvature, and tension could stiffen the pipe, while pressure and temperature did the rule of softening. Nonlinear stiffness made the pipe to undergo chaotic oscillation which was absent in the linear case, meaning that linear foundations could enhance the life span of pipelines than the nonlinear ones.

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Figures

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Fig. 1

Slightly curved simply supported pipe conveying hot pressurized fluid and resting on viscoelastic foundations

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Fig. 2

Effect of Winkler foundation on the pipe conveying fluid

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Fig. 3

Effect of mass ratio on the critical velocity of flow at (a) β = 0.2, (b) β = 0.4, and (c) β = 0.8

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Fig. 4

Effects of foundation viscoelastic damping with fluid viscosity on the pipe conveying fluid at (a) μ0 = 0 and (b) μ0 = 1

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Fig. 5

Effect of initial curvature on the pipe conveying fluid at (a) various values of a, (b) a = 0, (c) a = 0.25, (d) a = 0.50, (e) a = 0.75, and (f) a = 1

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Fig. 6

Effect of pretension on the pipe conveying fluid

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Fig. 7

Effects of hot and pressurized fluid on the pipe: (a) temperature and (b) pressure

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Fig. 8

Effect of nonlinear elastic foundation

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Fig. 9

Phase plane plot of the effect of elastic foundation at (a) K = 0, (b) K = 50, (c) K = 100, (d) K = 150, and (e) K = 200

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Fig. 10

Effect of mass ratio at (a) β = 0.2, (b) β = 0.4, and (c) β = 0.8

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Fig. 11

Effect of fluid viscosity and viscous foundation on the pipe: (a) viscosity and (b) viscous foundation

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Fig. 12

Effect of initial curvature at (b) a = 0, (c) a = 0.25, (d) a = 0.50, (e) a = 0.75, and (f) a = 1

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Fig. 13

Effect of pretension

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Fig. 14

Evolution of phase portraits of pretension at (a) T = 0, (b) T = 5, (c) T = 10, and (d) T = 15

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Fig. 15

Effect of (a) temperature and (b) pressure

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Fig. 16

Route to chaos: (a) bifurcation diagram, (b) orbital diagram, and (c) phase plane plot of orbital diagram

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Fig. 17

Superimposed plots: (a) bifurcation diagram and (b) phase plane plot

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