0
Research Papers: Flows in Complex Systems

On the Propagation and Attenuation of Turbulent Fluid Transients in Circular Pipes

[+] Author and Article Information
E. M. Wahba

Mechanical Engineering Department,
Faculty of Engineering,
Alexandria University,
Alexandria 21544, Egypt
e-mail: emwahba@yahoo.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 2, 2015; final manuscript received August 24, 2015; published online October 14, 2015. Assoc. Editor: Olivier Coutier-Delgosha.

J. Fluids Eng 138(3), 031106 (Oct 14, 2015) (7 pages) Paper No: FE-15-1137; doi: 10.1115/1.4031557 History: Received March 02, 2015; Revised August 24, 2015

The attenuation of turbulent fluid transients in pipes is numerically investigated in the present study using one-dimensional (1D) and two-dimensional (2D) water hammer models. The method of characteristics (MOC) is used for the integration of the 1D model, while the semidiscretization approach and the fourth-order accurate Runge–Kutta method are used for the integration of the 2D model. The present results for a reservoir–pipe–valve system indicate that the damping of the transient is governed by a nondimensional parameter representing the ratio of the steady-state frictional head to the Joukowsky pressure head. Based on this parameter, the attenuation of the transient could be classified into three main categories. The first category is for values of the nondimensional parameter much smaller than unity, where attenuation of the transient is insignificant and line packing effects are negligible. The second category is for values of the parameter approaching unity, where the attenuation of the transient is significant and line packing results in a pressure rise at the valve that is slightly higher than the Joukowsky pressure rise. The third category is for values of the parameter much greater than unity, such as in long cross-country pipelines, where the transient is damped out within a few cycles and excessive line packing effects would result in a pressure rise at the valve that is significantly larger the Joukowsky pressure rise.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

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), pp. 236–244. [CrossRef]
Hino, M. , Masaki, S. , and Shuji, T. , 1976, “ Experiments on Transition to Turbulence in an Oscillatory Pipe Flow,” J. Fluid Mech., 75(2), pp. 193–207. [CrossRef]
Brunone, B. , and Berni, A. , 2010, “ Wall Shear Stress in Transient Turbulent Pipe Flow by Local Velocity Measurement,” J. Hydraul. Eng., 136(10), pp. 716–726. [CrossRef]
Wahba, E. M. , 2008, “ Modeling the Attenuation of Laminar Fluid Transients in Piping Systems,” Appl. Math. Modell., 32(12), pp. 2863–2871. [CrossRef]
Brunone, B. , Ferrante, M. , and Cacciamani, M. , 2004, “ Decay of Pressure and Energy Dissipation in Laminar Transient Flow,” ASME J. Fluids Eng., 126(6), pp. 928–934. [CrossRef]
Bergant, A. , Tijsseling, A. S. , Vítkovský, J. P. , Covas, D. I. C. , Simpson, A. R. , and Lambert, M. F. , 2008, “ Parameters Affecting Water-Hammer Wave Attenuation, Shape and Timing—Part 1: Mathematical Tools,” J. Hydraul. Res., 46(3), pp. 373–381. [CrossRef]
Bergant, A. , Tijsseling, A. S. , Vítkovský, J. P. , Covas, D. I. C. , Simpson, A. R. , and Lambert, M. F. , 2008, “ Parameters Affecting Water-Hammer Wave Attenuation, Shape and Timing—Part 2: Case Studies,” J. Hydraul. Res., 46(3), pp. 382–391. [CrossRef]
Ghidaoui, M. S. , Mansour, S. G. , and Zhao, M. , 2002, “ Applicability of Quasi-Steady and Axisymmetric Turbulence Models in Water Hammer,” J. Hydraul. Eng., 128(10), pp. 917–924. [CrossRef]
Wang, X. J. , Lambert, M. F. , Simpson, A. R. , Liggett, J. A. , and Vitkovsky, J. P. , 2002, “ Leak Detection in Pipelines Using the Damping of Fluid Transients,” J. Hydraul. Eng., 128(7), pp. 697–711. [CrossRef]
Kim, S. H. , Zecchin, A. , and Choi, L. , 2014, “ Diagnosis of a Pipeline System for Transient Flow in Low Reynolds Number With Impedance Method,” J. Hydraul. Eng., 140(12), p. 04014063. [CrossRef]
Zielke, W. , 1968, “ Frequency-Dependent Friction in Transient Pipe Flow,” ASME J. Fluids Eng., 90(1), pp. 109–115.
Szymkiewicz, R. , and Mitosek, M. , 2013, “ Alternative Convolution Approach to Friction in Unsteady Pipe Flow,” ASME J. Fluids Eng., 136(1), p. 011202. [CrossRef]
Brunone, B. , Golia, U. M. , and Greco, M. , 1995, “ Effects of Two-Dimensionality on Pipe Transients Modeling,” J. Hydraul. Eng., 121(12), pp. 906–912. [CrossRef]
Vardy, A. E. , and Hwang, K. L. , 1993, “ A Weighting Function Model of Transient Turbulent Pipe Friction,” J. Hydraul. Res., 31(4), pp. 533–548. [CrossRef]
Vardy, A. , and Brown, J. , 2004, “ Efficient Approximation of Unsteady Friction Weighting Functions,” J. Hydraul. Eng., 130(11), pp. 1097–1107. [CrossRef]
Storli, P. T. , and Nielsen, T. K. , 2010, “ Transient Friction in Pressurized Pipes. II: Two-Coefficient Instantaneous Acceleration-Based Model,” J. Hydraul. Eng., 137(6), pp. 679–695. [CrossRef]
Wahba, E. M. , 2006, “ Runge–Kutta Time-Stepping Schemes With TVD Central Differencing for the Water Hammer Equations,” Int. J. Numer. Methods Fluids, 52(5), pp. 571–590. [CrossRef]
Nathan, G. K. , Tan, J. K. , and Ng, K. C. , 1988, “ Two‐Dimensional Analysis of Pressure Transients in Pipelines,” Int. J. Numer. Methods Fluids, 8(3), pp. 339–349. [CrossRef]
Mitra, A. K. , and Rouleau, W. T. , 1985, “ Radial and Axial Variations in Transient Pressure Waves Transmitted Through Liquid Transmission Lines,” ASME J. Fluids Eng., 107(1), pp. 105–111. [CrossRef]
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., 138(2), pp. 154–166. [CrossRef]
Meniconi, S. , Duan, H. F. , Brunone, B. , Ghidaoui, M. S. , Lee, P. J. , and Ferrante, M. , 2014, “ Further Developments in Rapidly Decelerating Turbulent Pipe Flow Modeling,” J. Hydraul. Eng., 140(7), p. 04014028. [CrossRef]
Pezzinga, G. , 1999, “ Quasi-2D Model for Unsteady Flow in Pipe Networks,” J. Hydraul. Eng., 125(7), pp. 676–685. [CrossRef]
Vardy, A. E. , and Hwang, K. L. , 1991, “ A Characteristics Model of Transient Friction in Pipes,” J. Hydraul. Res., 29(5), pp. 669–684. [CrossRef]
Silva-Araya, W. F. , and Chaudhry, M. H. , 1997, “ Computation of Energy Dissipation in Transient Flow,” J. Hydraul. Eng., 123(2), pp. 108–115. [CrossRef]
Zhao, M. , and Ghidaoui, M. S. , 2006, “ Investigation of Turbulence Behavior in Pipe Transient Using a k–∊ Model,” J. Hydraul. Res., 44(5), pp. 682–692. [CrossRef]
Riasi, A. , Nourbakhsh, A. , and Raisee, M. , 2013, “ Energy Dissipation in Unsteady Turbulent Pipe Flows Caused by Water Hammer,” Comput. Fluids, 73, pp. 124–133. [CrossRef]
Wahba, E. M. , 2009, “ Turbulence Modeling for Two-Dimensional Water Hammer Simulations in the Low Reynolds Number Range,” Comput. Fluids, 38(9), pp. 1763–1770. [CrossRef]
Vardy, A. E. , Brown, J. M. B. , He, S. , Ariyaratne, C. , and Gorji, S. , 2015, “ Applicability of Frozen-Viscosity Models of Unsteady Wall Shear Stress,” J. Hydraulic Eng., 141(1), p. 04014064. [CrossRef]
Shamloo, H. , and Mousavifard, M. , 2015, “ Turbulence Behaviour Investigation in Transient Flows,” J. Hydraul. Res., 53(1), pp. 83–92. [CrossRef]
Ghidaoui, M. S. , Zhao, M. , McInnis, D. A. , and Axworthy, D. H. , 2005, “ A Review of Water Hammer Theory and Practice,” ASME Appl. Mech. Rev., 58(1), pp. 49–76. [CrossRef]
Wylie, E. B. , and Streeter, V. L. , 1993, Fluid Transients in Systems, Prentice Hall, Upper Saddle River, NJ.
Baldwin, B. S. , and Lomax, H. , 1978, “ Thin-Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA Paper No. 78-257.
Bergant, A. , Vítkovský, J. , Simpson, A. R. , and Lambert, M. , 2001, “ Valve Induced Transients Influenced by Unsteady Pipe Flow Friction,” 10th International Meeting of the Work Group on the Behaviour of Hydraulic Machinery under Steady Oscillatory Conditions, pp. 12–23.
Marcinkiewicz, J. , Adamowski, A. , and Lewandowski, M. , 2008, “ Experimental Evaluation of Ability of Relap5, Drako®, Flowmaster2 and Program Using Unsteady Wall Friction Model to Calculate Water Hammer Loadings on Pipelines,” Nucl. Eng. Des., 238(8), pp. 2084–2093. [CrossRef]
Warda, H. , Haddara, S. , and Wahba, E. , 2014, “ Fluid Hammer and Fatigue Analysis for Oil Transport Pipelines With Peak Points,” ASME Paper No. PVP2014-28070.
American Society of Mechanical Engineers, 2009, Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer, ASME, New York.
Kaplan, M. , Streeter, V. L. , and Wylie, E. B. , 1967, “ Computation of Oil Pipeline Transients,” ASCE J. Pipeline Div., 93(3), pp. 59–71.

Figures

Grahic Jump Location
Fig. 1

Grid independence study for the pressure transient at the valve for test case (a)

Grahic Jump Location
Fig. 2

Grid independence study for the pressure transient at the midpoint for test case (a)

Grahic Jump Location
Fig. 3

Validation of the numerical procedure—pressure transient at the valve for test case (a)

Grahic Jump Location
Fig. 4

Validation of the numerical procedure—pressure transient at the midpoint for test case (a)

Grahic Jump Location
Fig. 5

Comparison of the attenuation of the transient at the valve for test cases (a) and (b)

Grahic Jump Location
Fig. 6

Comparison of the attenuation of the transient at the midpoint for test cases (a) and (b)

Grahic Jump Location
Fig. 7

Parametric study for the attenuation of the transient at the valve for test case (a)

Grahic Jump Location
Fig. 8

Parametric study for the attenuation of the transient at the midpoint for test case (a)

Grahic Jump Location
Fig. 10

Parametric study for the attenuation of the transient at the midpoint for test case (b)

Grahic Jump Location
Fig. 9

Parametric study for the attenuation of the transient at the valve for test case (b)

Grahic Jump Location
Fig. 11

Pressure transient at the valve for test case (c)

Grahic Jump Location
Fig. 12

Line packing as a function of the nondimensional parameter λ

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In