Transient Friction in Pressurized Pipes. I: Investigation of Zielke’s Model
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Volume 137, Issue 5
Abstract
This paper investigates the well-known model for unsteady friction developed by Zielke in 1968. The model is based on weights of past local bulk accelerations and is analytically correct for laminar flow, but computationally demanding. Different models have been proposed using dynamic properties, typically based on instantaneous accelerations (IAB) that are more rapid in computational schemes. Unfortunately, they are not as accurate as Zielke’s model and fail to model certain types of transients. This paper points out that the water hammer transient is dominated by a periodicity varying along the pipe. Because of this, the unsteady friction calculated by the Zielke model is distributed nonuniformly along the pipe, and changes in the pipe length change the local unsteady friction. This phenomenon may explain why IAB models using calibrated coefficients to match experimental results have a large span in value for the reported coefficients. This paper will hopefully contribute to further work to find highly accurate and rapid models. The subject deserves to be brought up for discussion as a part of a total understanding of the problem.
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References
Adamkowski, A. (2006). “Experimental examination of unsteady friction models for transient pipe flow simulation.” J. Fluids Eng., 128(6), 1351–1363.
Axworthy, D. H., Ghidaoui, M. S., and McInnis, D. A. (2000). “Extended thermodynamics derivation of energy dissipation in unsteady pipe flow.” J. Hydraul. Eng., 126(4), 276–287.
Bergant, A., Simpson, A. R., and Vitkovsky, J. P. (2001). “Developments in unsteady pipe flow friction modelling.” J. Hydraul. Res., 39(3), 249–257.
Brunone, B., Golia, U. M., and Greco, M. (1995). “Effects of two-dimensionality on pipe transients modeling.” J. Hydraul. Eng., 121(12), 906–912.
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), 236–244.
Ghidaoui, M. S., Mansour, S. G. S., and Zhao, M. (2002). “Applicability of quasi-steady and axisymmetric turbulence models in water hammer.” J. Hydraul. Eng., 128(10), 917–24.
Ghidaoui, M. S., Zhao, M., McInnis, D. A., and Axworthy, D. H. (2005). “A review of water hammer theory and practice.” Appl. Mech. Rev., 58(1-6), 49–75.
Holmboe, E. L., and Rouleau, W. T. (1967). “Effect of viscous shear on transients in liquid lines.” J. Basic Eng., 89(1), 174–180.
Pezzinga, G. (1999). “Quasi-2D model for unsteady flow in pipe networks.” J. Hydraul. Eng., 125(7), 676–685.
Pezzinga, G. (2000). “Evaluation of unsteady flow resistances by quasi-2D or 1D models.” J. Hydraul. Eng., 126(10), 778–785.
Pothof, I. (2008). “A turbulent approach to unsteady friction.” J. Hydraul. Res., 46(5), 679–690.
Schohl, G. A. (1993). “Improved approximate method for simulating frequency-dependent friction in transient laminar flow.” J. Fluids Eng., 115(3), 420–424.
Silva-Araya, W. F., and Chaudhry, M. H. (1997). “Computation of energy dissipation in transient flow.” J. Hydraul. Eng., 123(2), 108–115.
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, 569–573.
Trikha, A. K. (1975). “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. B. (2003). “Transient turbulent friction in smooth pipe flows.” J. Sound Vib., 259(5), 1011–1036.
Vardy, A. E., and Brown, J. M. B. (2004). “Transient turbulent friction in fully rough pipe flows.” J. Sound Vib., 270(1-2), 233–257.
Vitkovsky, J. P. (2008). “Closure to ‘Systematic evaluation of one-dimensional unsteady friction models in simple pipelines’ by J. P. Vitkovsky, A. Bergant, A. R. Simpson, and M. F. Lambert.” J. Hydraul. Eng., 134(2), 284.
Vitkovsky, J. P., Bergant, A., Simpson, A. R., and Lambert, M. F. (2006). “Systematic evaluation of one-dimensional unsteady friction models in simple pipelines.” J. Hydraul. Eng., 132(7), 696–708.
Vitkovsky, J. P., Stephens, M., Bergant, A., Lambert, M. F., and Simpson, A. R. (2004). “Efficient and accurate calculations of Zielke and Vardy-Brown unsteady friction in pipe transients.” Proc., 9th Int. Conf. on Pressure Surges, BHR Group, Cranfield, Bedfordshire, UK, 405–419.
White, F. M. (2006). Viscous fluid flow, McGraw Hill, Boston.
Wylie, E. B., Streeter, V. L., and Shuo, L. (1993). Fluid transients in systems, Prentice Hall, Englewood Cliffs, NJ.
Zielke, W. (1968). “Frequency-dependent friction in transient pipe flow.” J. Basic Eng., 90, 109–115.
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Published In
Journal of Hydraulic Engineering
Volume 137 • Issue 5 • May 2011
Pages: 577 - 584
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Feb 9, 2009
Accepted: Apr 14, 2010
Published online: Apr 24, 2010
Published in print: May 1, 2011
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