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Technical Brief

Alternative Approach to Convolution Term of Viscoelasticity in Equations of Unsteady Pipe Flow

[+] Author and Article Information
Katarzyna Weinerowska-Bords

Faculty of Civil and Environmental Engineering,
Gdansk University of Technology,
Narutowicza 11/12,
Gdansk 80-233, Poland
e-mail: kwein@pg.gda.pl

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 22, 2014; final manuscript received January 9, 2015; published online February 16, 2015. Assoc. Editor: Alfredo Soldati.

J. Fluids Eng 137(5), 054501 (May 01, 2015) (9 pages) Paper No: FE-14-1393; doi: 10.1115/1.4029573 History: Received July 22, 2014; Revised January 09, 2015; Online February 16, 2015

In the paper, the selected aspects concerning description of viscoelastic behavior of pipe walls during unsteady flow are analyzed. The alternative convolution expression of the viscoelastic term is presented and compared with the corresponding term referring to unsteady friction. Both approaches indicate similarities in the forms of impulse response functions and the parameter properties. The flow memory was introduced into convolution and its impact on the solution was analyzed. To reduce the influence of the numerical errors, implicit Preissmann scheme was applied. The calculation results were verified based on laboratory tests. The study indicated that the flow memory is related to pipe material properties and significantly influences the calculation results. It also showed the role of retardation time in calculations and its relation to flow memory. The proposed approach enabled more detailed analysis of viscoelasticity impact on the pressure characteristics.

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Figures

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Fig. 1

Modified Kelvin–Voigt model of viscoelastic behavior of the structure

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Fig. 3

Illustration of the flow memory

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Fig. 4

Observed and calculated pressure heads at the end of a pipeline (test 1)

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Fig. 5

Observed and calculated pressure heads at the end of a pipeline. Influence of the system memory m.

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Fig. 6

Observed and calculated pressure heads (test 3)

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