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Research Papers: Piper and Riser Technology

Damping Effect on the Wave Propagation in Carbon Steel Pipelines Under Fluid Hammer Conditions

[+] Author and Article Information
Dimitrios G. Pavlou

Department of Mechanical and Structural
Engineering and Materials Science,
University of Stavanger,
Stavanger 4036, Norway
e-mail: dimitrios.g.pavlou@uis.no

Muk Chen Ong

Department of Mechanical and Structural
Engineering and Materials Science,
University of Stavanger,
Stavanger 4036, Norway
e-mail: muk.c.ong@uis.no

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received March 17, 2016; final manuscript received March 15, 2017; published online May 16, 2017. Assoc. Editor: Celso P. Pesce.

J. Offshore Mech. Arct. Eng 139(4), 041702 (May 16, 2017) (7 pages) Paper No: OMAE-16-1028; doi: 10.1115/1.4036374 History: Received March 17, 2016; Revised March 15, 2017

A sudden reduction of the fluid flow yields a pressure shock, which travels along the pipeline with a high-speed. Due to this transient loading, dynamic hoop stresses are developed that may cause catastrophic damages in pipeline integrity. The vibration of the pipe wall is affected by the flow parameters as well as by the elastic and damping characteristics of the material. Most of the studies on dynamic response of pipelines: (a) neglect the effect of the material damping and (b) are usually limited to harmonic pressure oscillations. The present work is an attempt to fill the above research gap. To achieve this target, an analytic solution of the governing motion equation of pipelines under moving pressure shock is derived. The proposed methodology takes into account both elastic and damping characteristics of the steel. With the aid of Laplace and Fourier integral transforms and generalized function properties, the solution is based on the transformation of the dynamic partial differential equation into an algebraic form. Analytical inversion of the transformed dynamic radial deflection variable is achieved, yielding the final solution. The proposed methodology is implemented in an engineering example; and the results are shown and discussed.

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Figures

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Fig. 1

(a) Mechanical model of an infinite-length pipe subjected to a pressure shock which travels with a velocity α and (b) cross section of the pipe

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Fig. 2

Normalized radial deformations along pipeline for: (a) t = T/4, (b) t = T/2, and (c) t = 3T/4

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Fig. 3

Effect of the composition of harmonic components in the series of Eq. (58). Deformed shape of the pipeline at t = 3T/4. Composition of: (a) j = 5 harmonic components, (b) j = 10 harmonic components, (c) j = 20 harmonic components, (d) j = 30 harmonic components, (e) j = 40 harmonic components, and (f) j = 50 harmonic components.

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Fig. 4

Damping effect on the radial vibration on x = L/2

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Fig. 5

Length effect on the radial vibration on x = L/2

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