Simple Particle Model for Low-Density Granular Flow Interacting with Ambient Fluid
To understand the time evolutions of frontal speed and shape in a low-density granular flow, we propose a simple particle model. This model solves the equation of motion for each particle and simulates the time evolution of low-density granular flow. Spherical particles constituting a low-density gr...
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| Format: | Article |
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MDPI AG
2020-02-01
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| Series: | Geosciences |
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| Online Access: | https://www.mdpi.com/2076-3263/10/2/69 |
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| author | Hirofumi Niiya Akinori Awazu Hiraku Nishimori |
| author_facet | Hirofumi Niiya Akinori Awazu Hiraku Nishimori |
| author_sort | Hirofumi Niiya |
| collection | DOAJ |
| description | To understand the time evolutions of frontal speed and shape in a low-density granular flow, we propose a simple particle model. This model solves the equation of motion for each particle and simulates the time evolution of low-density granular flow. Spherical particles constituting a low-density granular flow slide on a slope at a steeper angle than the angle of repose. The particle motion is determined based on three forces: gravity as the driving force, repulsive force due to particle collision, and drag force due to the particle interaction through the ambient fluid. Two-dimensional numerical simulations of this model are conducted on the slope: the <i>x</i>−<i>y</i> plane parallel to the slope and the <i>x</i>−<i>z</i> plane perpendicular to the slope. In the <i>x</i>−<i>y</i> plane, particles aggregate at the moving front of the granular flow, and subsequently, flow instability occurs as a wavy pattern. This flow pattern is caused by the interparticle interaction arising from the drag force. Additionally, a vortex convection of particles is formed inside the aggregations. Simultaneously, particle aggregation is also found at the moving front of the granular flow in the <i>x</i>−<i>z</i> plane. The aggregation resembles a head−tail structure, where the frontal angle against the slope approaches 60<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mo>∘</mo> </msup> </semantics> </math> </inline-formula> from a larger angle as time progresses. Comparing the numerical result by varying the particle size reveals that the qualitative dynamics of the granular flow are independent of particle size. Although the model is not realistic, our study presents a new particle-based approach that elucidates the dynamics of low-density granular flow. |
| first_indexed | 2024-12-21T18:20:20Z |
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| language | English |
| last_indexed | 2024-12-21T18:20:20Z |
| publishDate | 2020-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Geosciences |
| spelling | doaj.art-ee89ef67ee024bf9a5208d644d2b2cb92022-12-21T18:54:34ZengMDPI AGGeosciences2076-32632020-02-011026910.3390/geosciences10020069geosciences10020069Simple Particle Model for Low-Density Granular Flow Interacting with Ambient FluidHirofumi Niiya0Akinori Awazu1Hiraku Nishimori2Center for Transdisciplinary Research, Niigata University, 8050 Ikarashi-nino-cho, Nishi-ku, Niigata 950-2181, JapanDepartment of Mathematical and Life Sciences, Hiroshima University, 1-3-1, Kagamiyama, Higashi-Hiroshima 739-8526, JapanDepartment of Mathematical and Life Sciences, Hiroshima University, 1-3-1, Kagamiyama, Higashi-Hiroshima 739-8526, JapanTo understand the time evolutions of frontal speed and shape in a low-density granular flow, we propose a simple particle model. This model solves the equation of motion for each particle and simulates the time evolution of low-density granular flow. Spherical particles constituting a low-density granular flow slide on a slope at a steeper angle than the angle of repose. The particle motion is determined based on three forces: gravity as the driving force, repulsive force due to particle collision, and drag force due to the particle interaction through the ambient fluid. Two-dimensional numerical simulations of this model are conducted on the slope: the <i>x</i>−<i>y</i> plane parallel to the slope and the <i>x</i>−<i>z</i> plane perpendicular to the slope. In the <i>x</i>−<i>y</i> plane, particles aggregate at the moving front of the granular flow, and subsequently, flow instability occurs as a wavy pattern. This flow pattern is caused by the interparticle interaction arising from the drag force. Additionally, a vortex convection of particles is formed inside the aggregations. Simultaneously, particle aggregation is also found at the moving front of the granular flow in the <i>x</i>−<i>z</i> plane. The aggregation resembles a head−tail structure, where the frontal angle against the slope approaches 60<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mo>∘</mo> </msup> </semantics> </math> </inline-formula> from a larger angle as time progresses. Comparing the numerical result by varying the particle size reveals that the qualitative dynamics of the granular flow are independent of particle size. Although the model is not realistic, our study presents a new particle-based approach that elucidates the dynamics of low-density granular flow.https://www.mdpi.com/2076-3263/10/2/69granular avalanchesmathematical modelingparticle modelnumerical simulationpattern formation |
| spellingShingle | Hirofumi Niiya Akinori Awazu Hiraku Nishimori Simple Particle Model for Low-Density Granular Flow Interacting with Ambient Fluid Geosciences granular avalanches mathematical modeling particle model numerical simulation pattern formation |
| title | Simple Particle Model for Low-Density Granular Flow Interacting with Ambient Fluid |
| title_full | Simple Particle Model for Low-Density Granular Flow Interacting with Ambient Fluid |
| title_fullStr | Simple Particle Model for Low-Density Granular Flow Interacting with Ambient Fluid |
| title_full_unstemmed | Simple Particle Model for Low-Density Granular Flow Interacting with Ambient Fluid |
| title_short | Simple Particle Model for Low-Density Granular Flow Interacting with Ambient Fluid |
| title_sort | simple particle model for low density granular flow interacting with ambient fluid |
| topic | granular avalanches mathematical modeling particle model numerical simulation pattern formation |
| url | https://www.mdpi.com/2076-3263/10/2/69 |
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