Characteristics of a Particle’s Incipient Motion from a Rough Wall in Shear Flow of Herschel–Bulkley Fluid
A numerical simulation of the Herschel–Bulkley laminar steady state shear flow around a stationary particle located on a sedimentation layer was carried out. The surface of the sedimentation layer was formed by hemispheres of the same radius as the particle. The drag force, lift force, and torque va...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/9/3/65 |
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| author | Alexander Seryakov Yaroslav Ignatenko Oleg B. Bocharov |
| author_facet | Alexander Seryakov Yaroslav Ignatenko Oleg B. Bocharov |
| author_sort | Alexander Seryakov |
| collection | DOAJ |
| description | A numerical simulation of the Herschel–Bulkley laminar steady state shear flow around a stationary particle located on a sedimentation layer was carried out. The surface of the sedimentation layer was formed by hemispheres of the same radius as the particle. The drag force, lift force, and torque values were obtained in the following ranges: shear Reynolds numbers for a particle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>S</mi><mi>H</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>–</mo><mn>200</mn></mrow></semantics></math></inline-formula>, corresponding to laminar flow; power law index <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.6</mn><mo>–</mo><mn>1.0</mn></mrow></semantics></math></inline-formula>; and Bingham number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>n</mi><mo>=</mo><mn>0</mn><mo>–</mo><mn>10</mn></mrow></semantics></math></inline-formula>. A significant difference in the forces and torque acting on a particle in shear flow in comparison to the case of a smooth wall is shown. It is shown that the drag coefficient is on average 6% higher compared to a smooth wall for a Newtonian fluid but decreases with the increase in non-Newtonian properties. At the edge values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.6</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>n</mi><mo>=</mo><mn>10</mn></mrow></semantics></math></inline-formula>, the drag is on average 25% lower compared to the smooth wall. For a Newtonian fluid, the lift coefficient is on average 30% higher compared to a smooth wall. It also decreases with the increase in non-Newtonian properties of the fluid, but at the edge values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.6</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>n</mi><mo>=</mo><mn>10</mn></mrow></semantics></math></inline-formula>, it is on average only 3% lower compared to the smooth wall. Approximation functions for the drag, lift force, and torque coefficient are constructed. A reduction in the drag force and lifting force leads to an increase in critical stresses (Shields number) on the wall on average by 10% for incipient motion (rolling) and by 12% for particle detachment from the sedimentation bed. |
| first_indexed | 2024-04-24T18:16:49Z |
| format | Article |
| id | doaj.art-579346f92bba44aebc8260456ee2ede3 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-04-24T18:16:49Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-579346f92bba44aebc8260456ee2ede32024-03-27T13:38:23ZengMDPI AGFluids2311-55212024-03-01936510.3390/fluids9030065Characteristics of a Particle’s Incipient Motion from a Rough Wall in Shear Flow of Herschel–Bulkley FluidAlexander Seryakov0Yaroslav Ignatenko1Oleg B. Bocharov2OFS Technologies, 1st Krasnogvardeisky pr., 22, 123112 Moscow, RussiaBaker Hughes, Baker-Hughes-Straße 1, 29221 Celle, GermanyIWEP SB RAS, Molodezhnaya Str. 1, 656038 Barnaul, RussiaA numerical simulation of the Herschel–Bulkley laminar steady state shear flow around a stationary particle located on a sedimentation layer was carried out. The surface of the sedimentation layer was formed by hemispheres of the same radius as the particle. The drag force, lift force, and torque values were obtained in the following ranges: shear Reynolds numbers for a particle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>S</mi><mi>H</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>–</mo><mn>200</mn></mrow></semantics></math></inline-formula>, corresponding to laminar flow; power law index <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.6</mn><mo>–</mo><mn>1.0</mn></mrow></semantics></math></inline-formula>; and Bingham number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>n</mi><mo>=</mo><mn>0</mn><mo>–</mo><mn>10</mn></mrow></semantics></math></inline-formula>. A significant difference in the forces and torque acting on a particle in shear flow in comparison to the case of a smooth wall is shown. It is shown that the drag coefficient is on average 6% higher compared to a smooth wall for a Newtonian fluid but decreases with the increase in non-Newtonian properties. At the edge values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.6</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>n</mi><mo>=</mo><mn>10</mn></mrow></semantics></math></inline-formula>, the drag is on average 25% lower compared to the smooth wall. For a Newtonian fluid, the lift coefficient is on average 30% higher compared to a smooth wall. It also decreases with the increase in non-Newtonian properties of the fluid, but at the edge values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.6</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>B</mi><mi>n</mi><mo>=</mo><mn>10</mn></mrow></semantics></math></inline-formula>, it is on average only 3% lower compared to the smooth wall. Approximation functions for the drag, lift force, and torque coefficient are constructed. A reduction in the drag force and lifting force leads to an increase in critical stresses (Shields number) on the wall on average by 10% for incipient motion (rolling) and by 12% for particle detachment from the sedimentation bed.https://www.mdpi.com/2311-5521/9/3/65particlesedimentationrough surfaceshear flowHerschel–Bulkley fluiddrag force |
| spellingShingle | Alexander Seryakov Yaroslav Ignatenko Oleg B. Bocharov Characteristics of a Particle’s Incipient Motion from a Rough Wall in Shear Flow of Herschel–Bulkley Fluid Fluids particle sedimentation rough surface shear flow Herschel–Bulkley fluid drag force |
| title | Characteristics of a Particle’s Incipient Motion from a Rough Wall in Shear Flow of Herschel–Bulkley Fluid |
| title_full | Characteristics of a Particle’s Incipient Motion from a Rough Wall in Shear Flow of Herschel–Bulkley Fluid |
| title_fullStr | Characteristics of a Particle’s Incipient Motion from a Rough Wall in Shear Flow of Herschel–Bulkley Fluid |
| title_full_unstemmed | Characteristics of a Particle’s Incipient Motion from a Rough Wall in Shear Flow of Herschel–Bulkley Fluid |
| title_short | Characteristics of a Particle’s Incipient Motion from a Rough Wall in Shear Flow of Herschel–Bulkley Fluid |
| title_sort | characteristics of a particle s incipient motion from a rough wall in shear flow of herschel bulkley fluid |
| topic | particle sedimentation rough surface shear flow Herschel–Bulkley fluid drag force |
| url | https://www.mdpi.com/2311-5521/9/3/65 |
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