Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid
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 <inline-formula> <math display="...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/4/3/124 |
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| author | Masoud Jabbari James McDonough Evan Mitsoulis Jesper Henri Hattel |
| author_facet | Masoud Jabbari James McDonough Evan Mitsoulis Jesper Henri Hattel |
| author_sort | Masoud Jabbari |
| collection | DOAJ |
| description | 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>δ</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−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>δ</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. |
| first_indexed | 2024-12-13T08:31:41Z |
| format | Article |
| id | doaj.art-9fbbaf3268f84f158577c5094156f40c |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-12-13T08:31:41Z |
| publishDate | 2019-07-01 |
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| record_format | Article |
| series | Fluids |
| spelling | doaj.art-9fbbaf3268f84f158577c5094156f40c2022-12-21T23:53:45ZengMDPI AGFluids2311-55212019-07-014312410.3390/fluids4030124fluids4030124Application of a Projection Method for Simulating Flow of a Shear-Thinning FluidMasoud Jabbari0James McDonough1Evan Mitsoulis2Jesper Henri Hattel3School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M13 9PL, UKDepartments of Mechanical Engineering and Mathematics, University of Kentucky, Lexington, KY 40506, USASchool of Mining Engineering and Metallurgy, National Technical University of Athens, 15780 Zografou, GreeceDepartments of Mechanical Engineering, Technical University of Denmark, Nils Koppels Allé, 2800 Kgs. Lyngby, DenmarkIn 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>δ</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−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>δ</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.https://www.mdpi.com/2311-5521/4/3/124lid-driven cavityprojection methodshear-thinningaspect ratio<i>Re</i> numbers |
| spellingShingle | Masoud Jabbari James McDonough Evan Mitsoulis Jesper Henri Hattel Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid Fluids lid-driven cavity projection method shear-thinning aspect ratio <i>Re</i> numbers |
| title | Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid |
| title_full | Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid |
| title_fullStr | Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid |
| title_full_unstemmed | Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid |
| title_short | Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid |
| title_sort | application of a projection method for simulating flow of a shear thinning fluid |
| topic | lid-driven cavity projection method shear-thinning aspect ratio <i>Re</i> numbers |
| url | https://www.mdpi.com/2311-5521/4/3/124 |
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