Investigating the Effect of Reynolds Number on Non-Newtonian Fluid-Hammer in Laminar Flow

Document Type : Original Article

Authors

1 Civil Eng., Lamei Gorgani higher Edu. Inst. Gorgan,Golestan, Iran

2 Civil Eng., Shahrood univ. of tech.

3 Mechanical Eng., Shahrood univ. of tech.,Shahrood, Iran

4 Civil Eng., Golestan university, Golestan, Iran

Abstract

In the present study, the sensitivity of the behavior of an Upper-Convected-Maxwell polymer and an Oldroyd-B fluid are compared to a Newtonian fluid. The governing equations are the Navier - Stokes equations and viscoelastic fluid equations. These equations are non-dimensionalized and it is found that Reynolds and Mach numbers are only the dimensionless parameters that exists in all three mentioned fluids. The viscosity of fluids as a friction factor causes that Reynolds number and its changes play an important role in the oscillations and also the attenuation of the fluid transient during Fluid hammer phenomenon. The numerical method used is a two-step variant of the Lax-Friedrichs (LxF) method. The results show that the viscoelastic properties of fluids, such as the non-linear relationship of stress and strain, relaxation time and …, reduce their variability compared to Newtonian fluid. Finally, the maximum sensitivity to Reynolds variations in Newtonian fluid and the minimum amount is observed in the Upper-Convected-Maxwell polymer that there are strong viscoelastic properties in its equations.

Keywords

References

  1. Mora, S., Manna, M. “From viscous fingering to elastic instabilities”, Non-Newtonian Fluid Mechanics, Vol. 173, pp. 30-39, 2012.##
  2. Poole, R. J., Alves, M. A., Oliveira, P. J., and Pinho, F. T. “Plane sudden expansion flows of viscoelastic liquids”, Non-Newtonian Fluid Mechanics, Vol. 146, pp. 79–91, 2007.##
  3. Abbas Nejad, A., Norouzi, M., and Talebi, Z. “Investigation of Pulsatile Blood Flow Interaction with a Viscoelastic Artery and Its Effect on Atherosclerosis”, Fluid Mechanics and Aerodynamics  Journal, Imam Hossein University,  Vol. 3, No. 4, pp. 1-16, 2015.##
  4. Jalali, A. and Kayhani, M.H. “Numerical Simulation of Viscoelastic Developing Flow and Heat Transfer in a Rectangular Duct”, Fluid Mechanics and Aerodynamics  Journal, Imam Hossein University,  Vol. 1, No. 2, pp. 41-54, 2012.##
  5. Keyhanpour, M. and Ghasemi, M. “Numerical Analysis of Heat and Mass Transfer of Magnetic Nanoparticles in a Non-Newtonian Blood Flow under Influence of Magnetic Field”, Fluid Mechanics and Aerodynamics  Journal, Imam Hossein University,  Vol. 7, No. 1, pp. 19-31, 2017.##
  6. Keramat, A., Tijsseling, A. S. “Waterhammer with column separation, fluid-structure interaction and unsteady friction in a viscoelastic pipe”. In: International Conference on Pressure Surges, Lisbon, Portugal, (2012).##
  7. Hadj-Taïeb, L., Hadj-Taïeb, E. “Numerical simulation of transient flows in viscoelastic pipes with vapor cavitation”, International Journal of Modelling and Simulation, Vol. 29, No. 2, pp. 206–213, 2009.##
  8. Keramat, A., Tijsseling, A.S., Hou, Q. and Ahmadi, A. “Fluid-structure interaction with pipe-wall viscoelasticity during water hammer”, Journal of Fluids and Structures, Vol. 28, No. 5, pp. 434–455, 2012.##
  9. Wiggert, D. and Tijsseling, A. S. “Fluid transients and fluid-structure interaction in flexible liquid-filled piping”, Applied Mechanics Reviews, Vol. 54, No. 5, pp. 455–481, 2001.##
  10. Tijsseling, A.S. and Vardy, A.E. “Time scales and FSI in oscillatory liquid-filled pipe flow”. BHR Group, Proc. of the 10th Int. Conf. on Pressure Surges (Editor S Hunt), P553, Edinburgh, United Kingdom, (2008).##
  11. Ahmadi, A., and Keramat, A. “Investigation of fluid-structure interaction with various types of Junction coupling”, Journal of Fluid and Structures, Vol. 26, No. 7-8, pp. 1123-1141, 2010.##
  12. Korbar; R., Virag, Z., and Šavar,  M. “Truncated Method of Characteristics for Quasi-Two- Dimensional Water Hammer Model”, J. Hydraul. Eng., Vol. 140, No. 6, pp. 04014013-1: 04014013-7, 2015.##
  13. Tijsseling, S. and Bergant, A. “Meshless computation of water hammer”, Proc. 2nd IAHR International meeting of the workgroup on cavitation and dynamic problems in hydraulic machinery and systems, Timisoara, Romania, 2007.##
  14. Shamloo, H., Norooz, R. and Mousavifard, M. “A review of one-dimensional unsteady friction models for transient pipe flow”, Proc. The Second National Conference on Applied Research in Science and Technology, Faculty of Science, Cumhuriyet University, 2015.##
  15. Zielke, W. “Frequency- Dependent Friction in Transient Pipe flow”, Basic Engineering, Vol. 90, No. 1, pp. 109-1338, 1968.##
  16. Vardy, A. and Brown, J. “Efficient approximation of unsteady friction weighting functions”, Hydraulic Engineering, Vol. 130, No. 11, pp. 1097-1107, 2004.##
  17. Wahba, E.M. “Non-Newtonian fluid hammer in elastic circular pipes: Shear-thinning and shear-thickening effects”, Non-Newtonian Fluid Mechanics, Vol. 198, No. 10, pp. 24-30, 2013.##
  18. Majd, A., and Ahmadi, A. “Investigation of non-Newtonian fluid effects during transient flows in a pipeline”, Journal of Mechanical Engineering, Vol. 62, No. 2, pp. 105-115, 2016.##
  19. Bird, R. B., Armstrong, R. and Hassager, O. “Dynamics of Polymeric Liquids”. Vol. 1: Fluid Mechanics, Wiley, 1987.##
  20. Wahba, E.M. “Runge–Kutta time-stepping schemes with TVD central differencing for the water hammer equations”, Numerical Methods in Fluids, Vol. 52, No. 5, pp.571-590, 2006.##
  21. Ghidaoui, M.S., Zhao, M., McInnis, D.A. and Axworthy, D.H. “A review of water hammer theory and practice”, Applied Mechanics, Vol. 58, No. 49, pp. 49-76, 2005.#
  22. Streeter, V.L., and Lai, C. “Waterhammer Analysis Including Fluid Friction”, Second Edition, American Society of Civil Engineers, 1993.##
  23. Shampine, L.F. “Two-step Lax-Friedrichs method”, Applied Mathematics Letters, Vol. 18, No. 10, pp. 1134-1136.##
  24. Khalighi, F., Ahmadi, A. and Keramat, A. “Investigation of Fluid-Structure Interaction by Explicit Central Finite Difference Methods”, International Journal of Engineering journal, Vol. 29, No. 5, pp. 590-598, 2016.##
  25. Holmboe, E.L., Rouleau, W.T. “The effect of viscous shear on transients in liquid lines”, Basic Engineering, Vol. 89, No. 1, pp. 174–180, 1967.##
  26. Mandani, S., Norouzi, M. and Shahmardan, M.M. “An experimental investigation on impact process of Boger drops onto solid surfaces”, Korea-Australia Rheology J., Vol. 30, No. 2, pp. 99–108, 2018.##

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History

  • Receive Date: 24 July 2019
  • Revise Date: 01 November 2019
  • Accept Date: 23 June 2020
  • Publish Date: 20 February 2020

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