Numerical Simulation of the Steady-State Herschel-Bulkley Fluid Flow in a Channel with Sudden Expansion

Abstract:

In this paper, the steady-state flow of non-Newtonian fluid in a planar channel with sudden expansion is investigated. The rheological behavior of this media is described by the Herschel-Bulkley model. To determine both steady-state velocity and pressure fields, a numerical algorithm based on the relaxation method and SIMPLE procedure is used.The mathematical problem statement includes three non-dimensional parameters: the Reynolds number, the Bingham number (non-dimensional viscoplasticity parameter), and the power-law index. The results of numerical simulation are obtained in a range of the Reynolds number 1 ≤ Re ≤ 40, Bingham number 0 ≤ Se ≤ 2, and power-law index 0.4 ≤ k ≤ 2 (for shear thinning, Newtonian, and shear thickening fluids).The distribution of the main fluid flow characteristics and localization of the two-dimensional region in an expansion zone is presented. The impact of main parameters of the problem on a dead zone distribution in the fluid flow is shown.

• Periodical: Key Engineering Materials (Volume 743)
• Pages: 474-479
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.743.474
• Online since: July 2017
• Authors: Efim Hegaj*, Evgeny Borzenko
• Keywords: Channel with Sudden Expansion, Dead Zone, Fluid Flow, Herschel-Bulkley Model, Numerical Simulation

References

[1] S.A. Patel, R.P. Chhabra. Steady flow of Bingham plastic fluids past an elliptical cylinder / Journal of Non-Newtonian Fluid Mechanics. 202 (2013) 32-53.

DOI: 10.1016/j.jnnfm.2013.09.006

[2] Ying-Hsin Wua, Ko-Fei Liu, Start-up flow of a Bingham fluid between two coaxial cylinders under a constant wall shear stress, Journal of Non-Newtonian Fluid Mechanics. 223 (2015) 116-121.

DOI: 10.1016/j.jnnfm.2015.06.002

[3] Yiolanda Damianou, Georgios C. Georgiou, Irene Moulitsas, Combined effects of compressibility and slip in flows of a Herschel–Bulkley fluid, Journal of Non-Newtonian Fluid Mechanics. 193 (2013) 89-102.

DOI: 10.1016/j.jnnfm.2012.09.004

[4] L.L. Ferras, A.M. Afonso, M.A. Alves, J.M. Nóbrega, O.S. Carneiro, F.T. Pinho, Slip flows of Newtonian and viscoelastic fluids in a 4: 1 contraction, Journal of Non-Newtonian Fluid Mechanics. 214 (2014) 28-37.

DOI: 10.1016/j.jnnfm.2014.09.007

[5] Fernanda B. Link, Sergio Frey, Roney L. Thompson, Mônica F. Naccache, Paulo R. de Souza Mendes, Plane flow of thixotropic elasto-viscoplastic materials through a 1: 4 sudden expansion, Journal of Non-Newtonian Fluid Mechanics. 220 (2015) 162-174.

DOI: 10.1016/j.jnnfm.2015.02.009

[6] Primoz Ternik, Planar sudden symmetric expansion flows and bifurcation phenomena of purely viscous shear-thinning fluids, Journal of Non-Newtonian Fluid Mechanics. 157 (2009) 15-25.

DOI: 10.1016/j.jnnfm.2008.09.002

[7] S. Dhinakaran, M.S.N. Oliveira, F.T. Pinho, M.A. Alves, Steady flow of power-law fluids in a 1: 3 planar sudden expansion, Journal of Non-Newtonian Fluid Mechanics. 198 (2013) 48-58.

DOI: 10.1016/j.jnnfm.2013.01.006

[8] Lober Hermany, Daniel Dall'Onder dos Santos, Sérgio Frey, Mônica F. Naccache, Paulo R. de Souza Mendes, Flow of yield-stress liquids through an axisymmetric abrupt expansion-contraction, Journal of Non-Newtonian Fluid Mechanics. 201 (2013) 1-9.

DOI: 10.1016/j.jnnfm.2013.07.002

[9] P. Coussot, Yield stress fluid flows: A review of experimental data, Journal of Non-Newtonian Fluid Mechanics. 211 (2014) 31-49.

DOI: 10.1016/j.jnnfm.2014.05.006

[10] M. Perez-Camacho, J.E. Lopez-Aguilar, F. Calderas, O. Manero, M.F. Webster, Pressure-drop and kinematics of viscoelastic flow through an axisymmetric contraction–expansion geometry with various contraction-ratios, Journal of Non-Newtonian Fluid Mechanics. 222 (2015).

DOI: 10.1016/j.jnnfm.2015.01.013

[11] Stephane Mossaz, Pascal Jay, Albert Magnin, Experimental study of stationary inertial flows of a yield-stress fluid around a cylinder, Journal of Non-Newtonian Fluid Mechanics. 189 (2012) 40-52.

DOI: 10.1016/j.jnnfm.2012.10.001

[12] G. Ovarlez, S. Cohen-Addad, K. Krishan, J. Goyon, P. Coussot, On the existence of a simple yield stress fluid behavior, Journal of Non-Newtonian Fluid Mechanics. 193 (2013) 68-79.

DOI: 10.1016/j.jnnfm.2012.06.009

[13] M. Maillard, J. Boujlel, P. Coussot, Flow characteristics around a plate withdrawn from a bath of yield stress fluid, Journal of Non-Newtonian Fluid Mechanics. 220 (2015) 33-43.

DOI: 10.1016/j.jnnfm.2014.08.001

[14] B.M. Smolskiy, Z.P. Shulman, V.M. Gorislavec, Reodinamika i teploobmen nelineino-vyazkoplastichnyh materialov, Nauka i Technika, Minsk, (1970).