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Research Papers: Fundamental Issues and Canonical Flows

Water Hammer Peak Pressures and Decay Rates of Transients in Smooth Lines With Turbulent Flow

[+] Author and Article Information
David A. Hullender

Department of Mechanical and
Aerospace Engineering,
The University of Texas at Arlington,
Arlington, TX 76019
e-mail: hullender@uta.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 16, 2016; final manuscript received January 3, 2018; published online February 23, 2018. Assoc. Editor: Elias Balaras.

J. Fluids Eng 140(6), 061204 (Feb 23, 2018) (10 pages) Paper No: FE-16-1833; doi: 10.1115/1.4039120 History: Received December 16, 2016; Revised January 03, 2018

Transient pressure peak values and decay rates associated with water hammer surges in fluid lines are investigated using an analytical method that has been formulated, in a previous publication, to simulate pressure transients in turbulent flow. The method agrees quite well with method of characteristics (MOC) simulations of unsteady friction models and has been verified with experimental data available for Reynolds numbers out to 15,800. The method is based on the formulation of ordinary differential equations from the frequency response of a pressure transfer function using an inverse frequency algorithm. The model is formulated by dividing the line into n-sections to distribute the turbulence resistance along the line at higher Reynolds numbers. In this paper, it will be demonstrated that convergence of the analytical solution is achieved with as few as 5–10 line sections for Reynolds numbers up to 200,000. The method not only provides for the use of conventional time domain solution algorithms for ordinary differential equations but also provides empirical equations for estimating peak surge pressures and transient decay rates as defined by eigenvalues. For typical sets of line and fluid properties, the trend of the damping ratio of the first or dominate mode of the pressure transients transfer function is found to be an approximate linear function of a dimensionless parameter that is a function of the Reynolds number. In addition, a reasonably accurate dimensionless trend formula for estimates of the normalized peak pressures is formulated and presented.

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Figures

Grahic Jump Location
Fig. 2

Line length L with a lumped resistance RT/n at the end of each line segment of length L/n

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Fig. 1

Schematic of a fluid line with the input and output variables

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Fig. 14

First mode damping ratios as a function of the dimensionless parameter P [106]

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Fig. 15

Peak values of normalized pressures as a function of the dimensionless parameter H

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Fig. 13

Relationship between the first mode damping ratio and the dimensionless parameter H

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Fig. 3

Inverse frequency curve fit to water hammer transfer function for Rn = 15,800

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Fig. 4

Inverse frequency curve fit to water hammer transfer function for Rn = 15,800

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Fig. 5

Convergence of water hammer normalized pressure transients, valve close time 0.03 s

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Fig. 6

Convergence of water hammer normalized pressure transients, valve close time 0.008 s

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Fig. 7

Convergence of water hammer normalized pressure transients, valve close time 0.05 s

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Fig. 8

Convergence of water hammer normalized pressure transients, valve close time 1 s

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Fig. 9

Convergence of water hammer normalized pressure transients, valve close time 1 s

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Fig. 10

Convergence of water hammer normalized pressure transients, valve close time 1 s

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Fig. 11

Convergence of water hammer normalized pressure transients, valve close time 1 s

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Fig. 12

First mode damping ratio convergence versus number of line sections and for Reynolds numbers from 25,000 to 200,000 when keeping the line and fluid parameters the same

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