Numerical Error in Weighting Function-Based Unsteady Friction Models for Pipe Transients
Publication: Journal of Hydraulic Engineering
Volume 132, Issue 7
Abstract
The accurate simulation of pressure transients in pipelines and pipe networks is becoming increasingly important in water engineering. Applications such as inverse transient analysis for condition assessment, leak detection, and pipe roughness calibration require accurate modeling of transients for longer simulation periods that, in many situations, requires improved modeling of unsteady frictional behavior. In addition, the numerical algorithm used for unsteady friction should be highly efficient, as inverse analysis requires the transient model to be run many times. A popular model of unsteady friction that is applicable to a short-duration transient event type is the weighting function-based type, as first derived by Zielke in 1968. Approximation of the weighting function with a sum of exponential terms allows for a considerable increase in computation speed using recursive algorithms. A neglected topic in the application of such models is evaluation of numerical error. This paper presents a discussion and quantification of the numerical errors that occur when using weighting function-based models for the simulation of unsteady friction in pipe transients. Comparisons of numerical error arising from approximations are made in the Fourier domain where exact solutions can be determined. Additionally, the relative importance of error in unsteady friction modeling and unsteady friction itself in the context of general simulation is discussed.
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Acknowledgments
The writers would like to acknowledge financial support from the Australian Research Council and a scholarship provided by the Australian Government for the second writer. Both sources of assistance are gratefully appreciated.
References
Gally, M., Güney, M., and Rieuford, E. (1979). “An investigation of pressure transients in viscoelastic pipes.” J. Fluids Eng., 101, 495–499.
Ghidaoui, M. S., and Mansour, S. (2002). “Efficient treatment of Vardy-Brown unsteady shear in pipe transients.” J. Hydraul. Eng., 128(1), 102–112.
Kagawa, T., Lee, I., Kitagawa, A., and Takenaka, T. (1983). “High speed and accurate computing method of frequency-dependent friction in laminar pipe flow for characteristics method.” Trans. Jpn. Soc. Mech. Eng., Ser. A, 49(447), 2638–2644 (in Japanese).
Pezzinga, G. (1999). “Quasi-2D model for unsteady flow in pipe networks.” J. Hydraul. Eng., 125(7), 676–685.
Schohl, G. A. (1993). “Improved approximate method for simulation frequency-dependent friction in transient laminar flow.” J. Fluids Eng., 115(3), 420–424.
Suzuki, K., Taketomi, T., and Sato, S. (1991). “Improving Zielke’s method of simulating frequency-dependent friction in laminar liquid pipe flow.” J. Fluids Eng., 113,(4) 569–573.
Trikha, A. K. (1975). “An efficient method for simulating frequency-dependent friction in transient liquid flow.” J. Fluids Eng., 97(1), 97–105.
Vardy, A. E., and Brown, J. M. (1995). “Transient, turbulent, smooth pipe friction.” J. Hydraul. Res., 33(4), 435–456.
Vardy, A. E., and Brown, J. M. (1996). “On turbulent, unsteady, smooth pipe friction.” Proc., 7th Int. Conf. on Pressure Surges and Fluid Transients in Pipelines and Open Channels, BHR Group, Harrogate, U.K., 289–311.
Vardy, A. E., and Brown, J. M. B. (2003). “Transient turbulent friction in smooth pipe flows.” J. Sound Vib., 259(5), 1011–1036.
Vardy, A. E., and Brown, J. M. B. (2004a). “Efficient approximation of unsteady friction weighting functions.” J. Hydraul. Eng., 130(11), 1097–1107.
Vardy, A. E., and Brown, J. M. B. (2004b). “Transient turbulent friction in fully-rough pipe flows.” J. Sound Vib., 270(1-2), 233–257.
Vardy, A. E., and Hwang, K.-L. (1991). “A characteristics model of transient friction in pipes.” J. Hydraul. Res., 29(5), 669–684.
Vítkovský, J. P., Stephens, M. L., Bergant, A., Lambert, M. F., and Simpson, A. R. (2004). “Efficient and accurate calculation of Zielke and Vardy-Brown unsteady friction in pipe transients.” Proc., 9th Int. Conf. on Pressure Surges, Vol. 2, BHR Group, Chester, U.K., 405–419.
Wylie, E. B., and Streeter, V. L. (1993). Fluid transients in systems, Prentice-Hall, Englewood Cliffs, N.J.
Zarzycki, Z. (1997). “Hydraulic resistance of unsteady turbulent liquid flow in pipes.” Water pipeline systems, BHR Group, The Hague, The Netherlands, 163–178.
Zarzycki, Z. (2000). “On weighting function for wall shear stress during unsteady turbulent pipe flow.” Proc., 8th Int. Conf. on Pressure Surges, BHR Group, The Hague, The Netherlands.
Zielke, W. (1968). “Frequency-dependent friction in transient pipe flow.” J. Basic Eng., 90(1), 109–115.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 132 • Issue 7 • July 2006
Pages: 709 - 721
Copyright
© 2006 ASCE.
History
Received: Mar 15, 2004
Accepted: Jun 15, 2005
Published online: Jul 1, 2006
Published in print: Jul 2006
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