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Research Papers: Multiphase Flows

Understanding Line Packing in Frictional Water Hammer

[+] Author and Article Information
Jim C. P. Liou

Mem. ASME
Department of Civil Engineering,
University of Idaho,
Moscow, ID 83844-1022
e-mail: liou@uidaho.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 10, 2015; final manuscript received March 21, 2016; published online June 8, 2016. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 138(8), 081303 (Jun 08, 2016) (6 pages) Paper No: FE-15-1815; doi: 10.1115/1.4033368 History: Received November 10, 2015; Revised March 21, 2016

For valve closure transients in pipelines, friction attenuates the amplitude of water hammer wave fronts and causes line packing. The latter is a sustained head increase behind the wave front. Line packing can lead to overpressure. Because of the nonlinearity of the friction term in the governing equations of water hammer, a satisfactory analytical explanation of line packing is not available. Although numerical methods can be used to compute line packing, an analytical explanation is desirable to better understand the phenomenon. This paper explains line packing analytically and presents a formula to compute the line packing that leads to the maximum pressure at the closed valve.

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Figures

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Fig. 1

Head and velocity profiles at two instants in a frictionless pipe

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Fig. 2

Head and velocity profiles at two instants in a pipe with friction

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Fig. 3

Dimensionless head at the valve showing different amounts of line packing

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Fig. 4

Dimensionless velocity along the C− characteristic. T = 0 corresponds to (L, 0) on the x–t plane, T = 1 corresponds to (0, L/a) on the x–t plane.

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Fig. 5

Dimensionless head along the C− characteristic. T = 0 corresponds to (L, 0) on the x–t plane, T = 1 corresponds to (0, L/a) on the x–t plane.

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Fig. 6

The x–t plane showing the propagation path of the C+ characteristic from b to d

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Fig. 7

Variation of velocity along the C+ characteristic issuing from (0, L/a) (i.e., T = 1) on the x–t plane

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Fig. 10

The maximum head at the valve computed from Eq.(25) and the simulated head traces at the valve for 60 and 180 s closure

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Fig. 9

The error of line packing estimation using Eq. (25) (top panel) and using the strain energy approximation (bottom panel)

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Fig. 8

Comparison between analytical (solid line) and numerical (dashed line) head at the valve after its sudden closure

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