0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Liou, C. P. , and Wylie, E. B. , 2016, “ Water Hammer,” Handbook of Fluid Dynamics, 2nd ed., R. W. Johnson , ed., CRC Press—Taylor & Francis Group, Boca Raton, FL, Chap. 25.
Roberson, J. A. , Crowe, C. T. , and Elger, D. F. , 2001, Engineering Fluid Mechanics, 7th ed., Wiley, New York.
Houghtalen, R. J. , Akan, A. O. , and Hwang, N. H. C. , 2010, Fundamentals of Hydraulic Engineering Systems, 4th ed., Pearson Higher Education, Inc., Upper Saddle River, NJ.
Prasuhn, Al. L. , 1987, Fundamentals of Hydraulic Engineering, Holt, Rinehart and Winston, New York.
Wylie, E. B. , and Streeter, V. L. , 1993, Fluid Transients in Systems, Prentice Hall, Englewood Cliffs, NJ.
Chaudhry, M. H. , 1979, Applied Hydraulic Transients, Van Nostrand Reinhold Company, New York.
Ziekle, W. , 1968, “ Frequency-Dependent Friction in Transient Pipe Flow,” ASME J. Basic Eng., 90(1), pp. 109–115. [CrossRef]
Szymkiewicz, R. , and Mitosek, M. , 2014, “ Alternative Convolution Approach to Friction in Unsteady Pipe Flow,” ASME J. Fluids Eng., 136(1), p. 011202. [CrossRef]
Vardy, A. E. , Brown, J. M. B. , He, S. , Ariyaratne, C. , and Gorji, S. , 2015, “ Applicability of Frozen-Viscosity Models of Unsteady Wall Shear Stress,” ASCE J. Hydraulic Eng., 141(1), p. 04014064. [CrossRef]
Wahba, E. M. , 2016, “ On the Propagation and Attenuation of Turbulent Fluid Transients in Circular Pipes,” ASME J. Fluids Eng., 138(3), p. 031106. [CrossRef]
Meniconi, S. , Duan, H. F. , Brunone, B. , Ghidaoui, M. S. , Lee, P. J. , and Ferrante, M. , 2014, “ Further Development in Rapidly Decelerating Turbulent Pipe Flow Modeling,” ASCE J. Hydraulic Eng., 140(7), p. 04014028. [CrossRef]
Bergant, A. , Tijsseling, A. S. , Vitkovsky, J. P. , Covas, D. I. C. , Simpson, A. R. , and Lambert, M. F. , 2008, “ Parameters Affecting Water Hammer Wave Attenuation, Shape, and Timing—Part 2: Case Studies,” IAHR J. Hydraulic Res., 46(3), pp. 382–391. [CrossRef]
Brunone, B. , Karney, B. W. , Mecarelli, M. , and Ferrante, M. , 2000, “ Velocity Profiles and Unsteady Pipe Friction in Transient Flow,” J. Water Resour. Plann. Manage., 126(4), pp. 236–244. [CrossRef]
Ghidaoui, M. S. , Mansour, S. G. S. , and Zhao, M. , 2002, “ Applicability of Quasi-Steady and Axisymmetric Turbulence Models in Water Hammer,” ASCE J. Hydraulic Eng., 128(10), pp. 917–924. [CrossRef]
Brunone, B. , Ferrante, M. , and Cacciamani, M. , 2004, “ Decay of Pressure and Energy Dissipation in Laminar Transient Flow,” ASME J. Fluids Eng., 126(11), pp. 928–934. [CrossRef]
Jung, B. S. , Karney, B. W. , Boulos, P. F. , and Wood, D. J. , 2007, “ The Need for Comprehensive Transient Analysis of Distribution Systems,” J. AWWA, 99(1), pp. 112–123.
Wood, D. J. , Lingireddy, S. , Boulos, P. F. , Karney, B. W. , and McPherson, D. L. , 2005, “ Numerical Methods for Modeling Transient Flows in Distribution Systems,” J. AWWA, 97(7), pp. 104–115.
Meniconi, S. , Brunone, B. , Ferrante, M. , Capponi, C. , Carrettini, C. A. , Chiesa, C. , Segalini, D. , and Lanfranchi, E. A. , 2015, “ Anomaly Pre-Localization in Distribution-Transmission Mains by Pump Trip: Preliminary Field Tests in the Milan Pipe System,” J. Hydroinf., 17(3), pp. 377–389. [CrossRef]
Ludwig, M. , and Johnson, S. P. , 1950, “ Prediction of Surge Pressures in Long Oil Transmission Lines,” Proc. API Div. Transp., 30(5), pp. 62–70.
Leslie, D. J. , and Tijsseling, A. S. , 2000, “ Traveling Discontinuities in Waterhammer Theory – Attenuation Due to Friction,” BHR Group 2000 Pressure Surges, Apr. 12–14, The Hague, The Netherlands, pp. 323–335.
Gibson, A. H. , 1948, Hydraulics and Its Applications, 4th ed., Constable and Company, Ltd., London.
McNown, J. S. , 1950, “ Surges and Water Hammer,” Proceedings of the Fourth Hydraulic Conference, Iowa Institute of Hydraulic Research, Jun. 12–15, H. Rouse , ed., Wiley, New York, Chapter VII.
Ellis, J. , 2008, Pressure Transients in Water Engineering, Thomas Telford Publishing, London.
Liou, C. P. , 1993, Pipeline Variable Uncertainties and Their Effects on Leak Detectability, American Petroleum Institute, Washington, DC.

Figures

Grahic Jump Location
Fig. 1

Head and velocity profiles at two instants in a frictionless pipe

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

Dimensionless head at the valve showing different amounts of line packing

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In