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Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid

1
School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M13 9PL, UK
2
Departments of Mechanical Engineering and Mathematics, University of Kentucky, Lexington, KY 40506, USA
3
School of Mining Engineering and Metallurgy, National Technical University of Athens, 15780 Zografou, Greece
4
Departments of Mechanical Engineering, Technical University of Denmark, Nils Koppels Allé, 2800 Kgs. Lyngby, Denmark
*
Author to whom correspondence should be addressed.
Fluids 2019, 4(3), 124; https://doi.org/10.3390/fluids4030124
Received: 29 May 2019 / Revised: 1 July 2019 / Accepted: 3 July 2019 / Published: 8 July 2019
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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Abstract

In this paper, a first-order projection method is used to solve the Navier–Stokes equations numerically for a time-dependent incompressible fluid inside a three-dimensional (3-D) lid-driven cavity. The flow structure in a cavity of aspect ratio δ = 1 and Reynolds numbers ( 100 , 400 , 1000 ) is compared with existing results to validate the code. We then apply the developed code to flow of a generalised Newtonian fluid with the well-known Ostwald–de Waele power-law model. Results show that, by decreasing n (further deviation from Newtonian behaviour) from 1 to 0.9, the peak values of the velocity decrease while the centre of the main vortex moves towards the upper right corner of the cavity. However, for n = 0.5 , the behaviour is reversed and the main vortex shifts back towards the centre of the cavity. We moreover demonstrate that, for the deeper cavities, δ = 2 , 4 , as the shear-thinning parameter n decreased the top-main vortex expands towards the bottom surface, and correspondingly the secondary flow becomes less pronounced in the plane perpendicular to the cavity lid. View Full-Text
Keywords: lid-driven cavity; projection method; shear-thinning; aspect ratio; Re numbers lid-driven cavity; projection method; shear-thinning; aspect ratio; Re numbers
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Jabbari, M.; McDonough, J.; Mitsoulis, E.; Hattel, J.H. Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid. Fluids 2019, 4, 124.

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