Modeling of an Upper-Convected-Maxwell Fluid Hammer Phenomenon in Pipe System

Document Type : Research Article

Authors

1 Civil Engineering, Shahrood University of Technology, Shahrood, Iran

2 Mechanic Engineering, Shahrood University of Technology, Shahrood, Iran

3 Civil Engineering, Golestan University, Gorgan, Iran

Abstract

 In this paper, the occurrence of water hammer phenomenon is examined in a situation that instead of water, an upper-convected-Maxwell fluid flows in a pipe system. This phenomenon is called an upper-convected-Maxwell fluid hammer. This expression relates to transients of Maxwell fluid caused by the sudden alteration in the conditions of flow. Upper-convected-Maxwell fluids are a kind of non-Newtonian viscoelastic fluids. The system studied is a valve-horizontal pipe and reservoir. The equations representing the conservation of mass and momentum govern the transitional flow in the pipe system. The numerical method used is a two-step variant of the Lax-Friedrichs method. Firstly, the non-dimensional form of governing equations is defined, then, the effect of Deborah and Reynolds numbers on pressure historic is investigated. The results revealed that increasing Deborah number, indicating the elasticity of the polymer, increases the oscillation height and consequently attenuation time of the transient flow becomes longer. It was also found that in low Reynolds, in a Newtonian fluid, line packing phenomenon effect is observed only at the first time period but in upper convected Maxwell fluid the effect of this phenomenon continues to more time periods and damping time becomes longer.

Keywords

Main Subjects

References

[1] M.S. Ghidaoui, M. Zhao, D.A. McInnis, D.H. Axworthy, A review of water hammer theory and practice, Applied Mechanics Reviews, 58(1) (2005) 49-76.
[2] E.B. Wylie, V.L. Streeter, L. Suo, Fluid transients in systems, Prentice Hall Englewood Cliffs, NJ, 1993.
[3] W. Zielke, Frequency-dependent friction in transient pipe flow, Journal of basic engineering, 90(1) (1968) 109-115.
[4] A.E. Vardy, K.-L. Hwang, A characteristics model of transient friction in pipes, Journal of Hydraulic Research, 29(5) (1991) 669-684.
[5] A. Bergant, A. Ross Simpson, J. Vìtkovsk, Developments in unsteady pipe flow friction modelling, Journal of Hydraulic Research, 39(3) (2001) 249-257.
[6] B. Brunone, U. Golia, M. Greco, Some remarks on the momentum equation for fast transients, in: Proc. Int. Conf. on Hydr. Transients With Water Column Separation, 1991, pp. 201-209.
[7] M. Brunelli, Two-dimensional pipe model for laminar flow, Journal of fluids engineering, 127(3) (2005) 431-437.
[8] H. SHAMLOO, R. NOROOZ, M. MOUSAVIFARD, A review of one-dimensional unsteady friction models for transient pipe flow, Fen Bilimleri Dergisi (CFD), 36(3) (2015).
[9] A.E. Vardy, J.M. Brown, Transient, turbulent, smooth pipe friction, Journal of Hydraulic Research, 33(4) (1995) 435-456.
[10] A.K. Trikha, An efficient method for simulating frequency-dependent friction in transient liquid flow, Journal of Fluids Engineering, 97(1) (1975) 97-105.
[11] M. Zhao, Numerical solutions of quasi-two-dimensional models for laminar water hammer problems, Journal of Hydraulic Research, 54(3) (2016) 360-368.
[12] E. Wahba, Non-Newtonian fluid hammer in elastic circular pipes: Shear-thinning and shear-thickening effects, Journal of Non-Newtonian Fluid Mechanics, 198 (2013) 24-30.
[13] S. Mora, M. Manna, From viscous fingering to elastic instabilities, Journal of Non-Newtonian Fluid Mechanics, 173 (2012) 30-39.
[14] M. Darwish, J. Whiteman, M. Bevis, Numerical modelling of viscoelastic liquids using a finite-volume method, Journal of non-newtonian fluid mechanics, 45(3) (1992) 311-337.
[15] K. Missirlis, D. Assimacopoulos, E. Mitsoulis, A finite volume approach in the simulation of viscoelastic expansion flows, Journal of non-newtonian fluid mechanics, 78(2-3) (1998) 91-118.
[16] R. Poole, M. Alves, P.J. Oliveira, F.T.d. Pinho, Plane sudden expansion flows of viscoelastic liquids, Journal of Non-Newtonian Fluid Mechanics, 146(1-3) (2007) 79-91.
[17] R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of polymeric liquids. Vol. 1: Fluid mechanics, (1987).
[18] E. Wahba, Modelling the attenuation of laminar fluid transients in piping systems, Applied Mathematical Modelling, 32(12) (2008) 2863-2871.
[19] E. Wahba, Runge–Kutta time-stepping schemes with TVD central differencing for the water hammer equations, International journal for numerical methods in fluids, 52(5) (2006) 571-590.
[20] J.C. Maxwell, The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862, CUP Archive, 1990.
[21] L.F. Shampine, Two-step Lax–Friedrichs method, Applied Mathematics Letters, 18(10) (2005) 1134-1136.
[22] F. Khalighi, A. Ahmadi, A. Keramat, Investigation of Fluid-structure Interaction by Explicit Central Finite Difference Methods, Int. J. Eng. Trans. B Appl, 29 (2016) 590-598.
[23] E. Holmboe, W. Rouleau, The effect of viscous shear on transients in liquid lines, Journal of Basic Engineering, 89(1) (1967) 174-180.
[24] S. Mandani, M. Norouzi, M.M. Shahmardan, An experimental investigation on impact process of Boger drops onto solid surfaces, Korea-Australia Rheology Journal, 30(2) (2018) 99-108.
AUT Journal of Mechanical Engineering
Volume 4, Issue 1
Winter 2020
Pages 31-40

Files

Share

How to cite

Statistics