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 Full-text PDF
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.
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-, 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.
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.
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.
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.
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.
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.
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.
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.