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

• Main Authors: Masoud Jabbari, James McDonough, Evan Mitsoulis, Jesper Henri Hattel
• Format: Article
• Language: English
• Published: MDPI AG 2019-07-01
• Series: Fluids
• Subjects: lid-driven cavity; projection method; shear-thinning; aspect ratio; <i>Re</i> numbers
• Online Access: https://www.mdpi.com/2311-5521/4/3/124

In this paper, a first-order projection method is used to solve the Navier&#8722;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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#948;</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> and Reynolds numbers <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mn>100</mn> <mo>,</mo> <mspace width="0.166667em"></mspace> <mn>400</mn> <mo>,</mo> <mspace width="0.166667em"></mspace> <mn>1000</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> 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&#8722;de Waele power-law model. Results show that, by decreasing <i>n</i> (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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics> </math> </inline-formula>, the behaviour is reversed and the main vortex shifts back towards the centre of the cavity. We moreover demonstrate that, for the deeper cavities, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#948;</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="0.166667em"></mspace> <mn>4</mn> </mrow> </semantics> </math> </inline-formula>, as the shear-thinning parameter <i>n</i> 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.