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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Multiple scales analysis of water hammer attenuation


Authors: S. Y. Han, D. Hansen and G. Kember
Journal: Quart. Appl. Math. 69 (2011), 677-690
MSC (2000): Primary 76M99; Secondary 76M45
Published electronically: July 7, 2011
MathSciNet review: 2893995
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Abstract | References | Similar Articles | Additional Information

Abstract: A multiple scales analysis is used to construct a uniformly accurate approximation to water hammer pressure wave attenuation that is initiated by a sudden valve opening. The method of analysis is well suited to the study of a water hammer that possesses several time scales and is applied to a mild generalization of the classical equations. It should prove useful for finding attenuation curves when effects such as unsteady friction and fluid-structure interaction are added. The analytical results are numerically verified using the method of characteristics.


References [Enhancements On Off] (What's this?)

  • 1. Fathi M. Allan and Kamel Al-Khaled, An approximation of the analytic solution of the shock wave equation, J. Comput. Appl. Math. 192 (2006), no. 2, 301–309. MR 2228815, http://dx.doi.org/10.1016/j.cam.2005.05.009
  • 2. A. S. Tijsseling and A. E. Vardy, Time scales and fsi in unsteady liquid-filled pipe flow, BHR Group, Proc. of the 9th Int. Conf. on Pressure Surges (Editor S. J. Murray), 2004, pp. 135-150.
  • 3. -, Time scales and fsi in oscillatory liquid-filled pipe flow, BHR Group, Proc. of the 10th Int. Conf. on Pressure Surges (Editor S. Hunt), 2008, pp. 553-568.
  • 4. A. Bergant, A. S. Tijsseling, J. P. Vitkovsky, D. I. C. Covas, A. R. Simpson, and M. F. Lambert, Parameters affecting water-hammer wave attenuation, shape, and timing part i: Mathematical tools, IAHR J. of Hydraulic Research 46(3) (2008), 373-381.
  • 5. -, Parameters affecting water-hammer wave attenuation, shape, and timing part ii: Case studies, IAHR J. of Hydraulic Research 46(3) (2008), 382-391.
  • 6. G. C. F. M. R. de Prony Baron, Recherches physico-mathematiques sur la theorie du mouvement des eaux courantes (1804).
  • 7. M. S. Ghidaoui and A. A. Kolyshkin, Stability analysis of velocity profiles in water hammer flows, ASCE J. of Hydraulic Engineering 127(6) (2001), 499-511.
  • 8. G. O. Brown, The history of the Darcy-Weisbach equation for pipe flow resistance, Proceedings of the 150th Anniversary Conference of ASCE (Editors J. Rogers and A. Fredrich), 2002, pp. 34-43.
  • 9. D. Hansen, V. K. Garga, and D. R. Townsend, Selection and application of a 1-d non-Darcy flow equation for 2-d flow through rockfill embankments, Can. Geotechnical J. 32(2) (1995), 223-232.
  • 10. D. J. Leslie and A. S. Tijsseling, Travelling discontinuities in waterhammer theory: attenuation due to friction, BHR Group, Proc. of the 8th Int. Conf. on Pressure Surges (Editor A. Anderson), 2000, pp. 323-335.
  • 11. A. S. Leon, M. S. Ghidaoui, A. R. Schmidt, and M. H. Garcia, Efficient second-order-accurate shock-capturing scheme for modelling one and two-phase water hammer flows, ASCE J. of Hydraulic Engineering 134(7) (2008), 970-983.
  • 12. L. F. Moody, Friction factors for pipe flow, Transactions of American Society of Mechanical Engineers 66(8) (1944), 671-678.
  • 13. A. M. A. Sattar, A. R. Dickerson, and M. H. Chaudhry, Wavelet-Galerkin solution to the water hammer equations, ASCE J. of Hydraulic Engineering 134(4) (2009), 283-295.
  • 14. A. S. Tijsseling, Fluid-structure interaction in liquid-filled pipe systems, J. of Fluids and Structures 10 (1996), 109-146.
  • 15. W. Driedger, Controlling centrifugal pumps, Hydrocarbon Processing 74(7) (1995), 43-49.
  • 16. X. Q. Wang, J. G. Sun, and W. T. Sha, Transient flows and pressure waves in pipes, Journal of Hydrodynamics 7(2) (1995), 51-59.
  • 17. D. H. Wilkinson and E. M. Curtis, Water hammer in a thin-walled pipe, Proc. $ 3$rd Int. Conf. on Pressure Surges, 1980, pp. 221-240.
  • 18. E. B. Wylie and V. L. Streeter, Fluid transients in systems, Prentice-Hall, Englewood Cliffs, NJ, 1993.

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Additional Information

S. Y. Han
Affiliation: Worley-Parsons Canada, 400-10201 Southport Rd. SW, Calgary, Alberta, Canada, T2W 4X9
Email: Sang-Yoon.Han@WorleyParsons.com

D. Hansen
Affiliation: Department of Civil and Resource Engineering, Dalhousie University, 1360 Barrington St., Halifax, NS, Canada, B3J 1Z1
Email: David.Hansen@dal.ca

G. Kember
Affiliation: Department of Engineering Mathematics, Dalhousie University, 1340 Barrington St., Halifax, NS, Canada, B3J 1Y9
Email: Guy.Kember@dal.ca

DOI: http://dx.doi.org/10.1090/S0033-569X-2011-01258-9
PII: S 0033-569X(2011)01258-9
Received by editor(s): March 2, 2010
Published electronically: July 7, 2011
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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