Investigation of the structure of non-isothermal power-law fluid flow in an $\mathrm{L}$-shaped channel

O. A. Dyakova ; O. Yu. Frolov

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 58 (2019), pp. 71-83

Résumé

This paper is devoted to the investigation of a steady-state non-isothermal power-law fluid flow in a flat $\mathrm{L}$-shaped channel with account for viscous dissipation. Mathematical model of the flow includes the motion, continuity, and energy equations written using the dimensionless variables in a Cartesian coordinate system. The fluid rheological behavior is described by the Ostwald-de Waele power law with an exponential dependence of the consistency on temperature. The control volume method and the SIMPLE procedure are applied to solve the formulated problem numerically using the staggered computational grid. The effect of both power-law index and Reynolds and Brinkman numbers on the size of recirculation zones observed in the vicinity of internal and external angles of the $\mathrm{L}$-channel and on the size of two-dimensional flow regions is studied. It is found that the variation in the intensity of mechanical energy dissipation in a stream leads to a weak change in the flow pattern. Considering rising of the power-law index from the values providing pseudoplastic properties of the fluid to that providing dilatant properties, the size of recirculation zone in the vicinity of internal angle is found to tend to a constant value. With an increase in the power-law index, the two-dimensional flow region ahead of the stream turn increases and tends to a constant value, and after turn it decreases. The results obtained for a Newtonian fluid are in a good agreement with numerical and experimental data of other authors.

Détail

Keywords: flow, non-Newtonian fluid, $\mathrm{L}$-shaped channel, dissipative heating, numerical simulation, kinematics.
Mots-clés : viscous fluid

Bibliographie

[1] P. Naphon, S. Wongwises, “A review of flow and heat transfer characteristics in curved tubes”, Renewable and Sustainable Energy Reviews, 10:5 (2006), 463–490 | DOI

[2] R. K. Ojha, P. V. Joshi, “A Review of Fluid Flow and Heat Transfer Analysis on Curved Duct”, Proc. All India Conference on «Intelligent systems» in Mechanical and Mechatronics Engineering (April 25–26, 2014), 5.156–5.159 | DOI

[3] C. Rauwendaal, Polymer Extrusion, Hanser Gardner Publications, Munich

[4] G. B. Froyshteter, S. Yu. Danilevich, N. V. Radionova, Flow and heat transfer of non-Newtonian fluids in the pipes, Naukova dumka, Kiev, 1990

[5] M. Ghobadi, Y. S. Muzychka, “A Review of Heat Transfer and Pressure Drop Correlations for Laminar Flow in Curved Circular Ducts”, Heat Transfer Engineering, 37:10 (2016), 815–839 | DOI

[6] H. Soeberg, “Viscous flow in curved tubes-I. Velocity profiles”, Chem. Eng. Sci., 43:4 (1988), 855–862 | DOI

[7] K. H. Winters, “A bifurcation study of laminar flow in a curved tube of rectangular cross-section”, J. Fluid Mech., 180 (1987), 343–369 | DOI | Zbl

[8] W. Y. Soh, “Developing fluid flow in a curved duct of square cross-section and its fully developed dual solutions”, J. Fluid Mech., 188 (1988), 337–361 | DOI | Zbl

[9] B. Bara, K. Nandakumar, J. H. Masliyah, “An experimental and numerical study of the Dean problem: flow development towards two-dimensional multiple solutions”, J. Fluid Mech., 244 (1992), 339–376 | DOI

[10] M. Kawaguti, “Numerical Study of the Flow of a Viscous Fluid in a Curved Channel”, The Physics of Fluids, 12 (1969), II-101–II-104 | DOI | Zbl

[11] S. F. Tsai, T. W. H. Sheu, “Numerical exploration of flow topology and vortex stability in a curved duct”, Int. J. Numer. Meth. Engng., 71 (2007), 564–582 | DOI | Zbl

[12] E. I. Borzenko, O. A. Diakova, G. R. Shrager, “Studying the slip phenomenon for a viscous fluid flow in a curved channe”, Tomsk State University Journal of Mathematics and Mechanics, 2014, no. 2 (28), 35–44

[13] M. G. N. Perera, K. Walters, “Long-Range Memory Effects in Flows Involving Abrupt Changes in Geometry. Part I: Flows Associated With L-Shaped And T-Shaped Geometries”, J. Nonnewton. Fluid Mech., 2:1, 49–81 | DOI | MR | Zbl

[14] T. Cochrane, K. Walters, M. F. Webster, “Newtonian and non-Newtonian flow near a re-entrant corner”, J. Nonnewton. Fluid Mech., 10:1-2 (1982), 95–114 | DOI

[15] S. Chono, Y. Iemoto, “Generation of reverse flow of viscoelastic fluid upstream of re-entrant corner in two-dimensional L-shaped channel”, J. Rheol., 34:3 (1990), 295–308 | DOI

[16] S. Chono, Y. Iemoto, “Numerical simulation of viscoelastic flow in two-dimensional L-shaped channels”, J. Rheol., 36:2 (1992), 335–356 | DOI

[17] G. H. Wu, M. C. Lin, S. H. Ju, C. C. Wu, “Non-isothermal flow of a polymeric liquid through rounded L-channels”, Plastics, Rubber and Composites, 32:7 (2003), 297–305 | DOI

[18] M. Norouzi, M. H. Kayhani, M. R. H. Nobari, M. K. Demneh, “Convective Heat Transfer of Viscoelastic Flow in a Curved Duct”, Int. J. Mechanical and Mechatronics Engineering, 3:8 (2009), 921–927

[19] E. I. Borzenko, G. R. Shrager, “Non-isothermal steady flow of power-law fluid in a planar/axismetric channel”, Tomsk State University Journal of Mathematics and Mechanics, 2018, no. 52, 41–52 | DOI | MR

[20] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, New York, 1980 | Zbl