Further Developments in Rapidly Decelerating Turbulent Pipe Flow Modeling
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 7
Abstract
In the last two decades, energy dissipation in unsteady-state pressurized pipe flow has been examined by various authors, where the instantaneous wall shear stress is split into a quasi-steady and an unsteady shear stress component. The focus of most past studies is on formulating expressions for the unsteady wall shear stress, but there has been less work on the key parameters governing the dominance of unsteady friction in transient flows. This paper derives an expression for the head envelope damping for turbulent flows in smooth and rough pipes and provides new and carefully measured field data for the initial (i.e., pretransient) Reynolds number, , that ranges from 97,000 to 380,000. The analytical solutions is derived on the basis of one-dimensional (1D) water hammer equations in which the unsteady component is represented by existing convolutional unsteady friction formulas for both smooth and rough turbulent subregimes. The analytical solution is used to formulate general, encompassing and theoretically-based dimensionless parameters to assess the importance of unsteady friction in comparison to the quasi-steady component. In addition, the analytical solution furnishes the similitude relations that allowed the damping behavior from existing laboratory tests, the field tests conducted as part of this research, and the weighting function-based (WFB) models to be investigated and compared in a coherent manner in a single graph. The analysis confirms that the magnitude of has a significant impact on the damping for transients generated by flow stoppage. In addition, the results show that convolutional unsteady friction model that uses the frozen eddy viscosity hypothesis and has accuracy that decreases with time. An improvement for this shortcoming is proposed and verified and involves the use of the instantaneous Reynolds number in lieu of the pretransient Reynolds number in the evaluation of the WFB models. The result is a modified unsteady friction model that provides improved matches for both laboratory and field data compared with the original model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research has been supported by: (1) the Italian Ministry of Education, University and Research under the Projects of Relevant National Interest “Advanced analysis tools for the management of water losses in urban aqueducts”, and “Tools and procedures for an advanced and sustainable management of water distribution systems”; (2) the Hong Kong Research Grant Council under the projects numbers 612511 and 612910; and (3) the Royal Society of New Zealand with Marsden Grant UOC1153.
References
Adamkowski, A., and Lewandowski, M. (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., 276–287.
Bergant, A., Simpson, A. R., and Vitkovsky, J. (2001). “Developments in unsteady pipe flow friction modelling.” J. Hydraul. Res., 39(3), 249–257.
Brunone, B., Ferrante, M., and Cacciamani, M. (2004). “Decay of pressure and energy dissipation in laminar transient flow.” J. Fluids Eng., 126(6), 928–934.
Brunone, B., Ferrante, M., and Calabresi, F. (2001). “High Reynolds number transients in a pump rising main. Field tests and numerical modeling.” Proc., 4th Int. Conf. Water Pipeline Systems, A. Lowdon, ed., BHR Group, York, U.K., 339–348.
Brunone, B., Ferrante, M., and Calabresi, F. (2002). “Discussion of “Evaluation of unsteady flow resistances by quasi-2D or 1D models”, by G. Pezzinga.” J. Hydraul. Eng., 646–647.
Brunone, B., and Golia, U. M. (2008). “Discussion of “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., 282–284.
Brunone, B., Golia, U. M., and Greco, M. (1991). “Some remarks on the momentum equations for fast transients.” E. Cabrera and M. Fanelli, eds., Proc., Int. Meeting on Hydraulic Transients with Column Separation, 9th Round Table, Universidad Politecnica de Valencia, Valencia, Spain, 140–148.
Brunone, B., Golia, U. M., and Greco, M. (1995). “Effects of two-dimensionality on pipe transients modelling.” J. Hydraul. Eng., 906–912.
Duan, H. F., Ghidaoui, M. S., Lee, P. J., and Tung, Y. K. (2010). “Unsteady friction and visco-elasticity in pipe fluid transients.” J. Hydraul. Res., 48(3), 354–362.
Duan, H. F., Ghidaoui, M. S., Lee, P. J., and Tung, Y. K. (2012). “Relevance of unsteady friction to pipe size and length in pipe fluid transients.” J. Hydraul. Eng., 154–166.
Ghidaoui, M. S., and Mansour, S. (2002). “Efficient treatment of the Vardy-Brown unsteady shear in pipe transients.” J. Hydraul. Eng., 102–112.
Ghidaoui, M. S., Mansour, S. G. S., and Zhao, M. (2002). “Applicability of quasisteady and axisymmetric turbulence models in water hammer.” J. Hydraul. Eng., 917–924.
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), 49–76.
He, S., Ariyaratne, C., and Vardy, A. E. (2011). “Wall shear stress in accelerating turbulent pipe flow.” J. Fluid Mech., 685, 440–460.
He, S., and Jackson, J. D. (2000). “A study of turbulence under conditions of transient flow in a pipe.” J. Fluid Mech., 408, 1–38.
Holmboe, E. L., and Rouleau, W. T. (1967). “The effect of viscous shear on transients in liquid lines.” J. Basic Eng., 89(1), 174–180.
Mitosek, M., and Szymkiewicz, R. (2012). “Wave damping and smoothing in the unsteady pipe flow.” J. Hydraul. Eng., 619–628.
Pezzinga, G. (2009). “Local balance unsteady friction model.” J. Hydraul. Eng., 45–56.
Stephens, M., Simpson, A. R., Lambert, M. F., and Vítkovsky, J. P. (2005). “Field measurement of unsteady friction effects in a trunk transmission pipeline.” Proc,. Int. Conf. of 7th Annual Symp. on Water Distribution Systems Analysis, ASCE, Reston, VA.
Storli, P.-T., and Nielsen, T. K. (2011a). “Transient friction in pressurized pipes. ii: two-coefficient instantaneous acceleration-based model.” J. Hydraul. Eng., 679–695.
Storli, P.-T., and Nielsen, T. K. (2011b). “Transient friction in pressurized pipes III: Investigation of the EIT model based on position-dependent coefficient approach in MIAB model.” J. Hydraul. Eng., 1047–1053.
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. B. (1995). “Transient, turbulent, smooth pipe friction.” J. Hydraul. Res., 33(4), 435–456.
Vardy, A. E., and Brown, J. M. B. (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. (2004). “Transient turbulent friction in fully rough pipe flows.” J. Sound Vib., 270(1–2), 233–257.
Vardy, A. E., and Brown, J. M. B. (2010). “Influence of time-dependent viscosity on wall shear stresses in unsteady pipe flows.” J. Hydraul. Res., 48(2), 225–237.
Vitkovský, J., Stephens, M., Bergant, A., Simpson, A., and Lambert, M. (2006). “Numerical error in weighting function-based unsteady friction models for pipe transients.” J. Hydraul. Eng., 709–721.
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, Netherlands, 529–543.
Zhao, M., Ghidaoui, M. S., and Kolyshkin, A. A. (2007). “Perturbation dynamics in unsteady pipe flows.” J. Fluid Mech., 570, 129–154.
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 140 • Issue 7 • July 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 21, 2013
Accepted: Jan 28, 2014
Published online: Mar 19, 2014
Published in print: Jul 1, 2014
Discussion open until: Aug 19, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.