A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow
In this paper, forces and torques on solid, non-spherical, orthotropic particles in Stokes flow are investigated by using a numerical approach on the basis of the Boundary Element Method. Different flow patterns around a particle are considered, taking into account the contributions of uniform, rota...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Journal of Marine Science and Engineering |
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| Online Access: | https://www.mdpi.com/2077-1312/10/3/369 |
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| author | Mitja Štrakl Matjaž Hriberšek Jana Wedel Paul Steinmann Jure Ravnik |
| author_facet | Mitja Štrakl Matjaž Hriberšek Jana Wedel Paul Steinmann Jure Ravnik |
| author_sort | Mitja Štrakl |
| collection | DOAJ |
| description | In this paper, forces and torques on solid, non-spherical, orthotropic particles in Stokes flow are investigated by using a numerical approach on the basis of the Boundary Element Method. Different flow patterns around a particle are considered, taking into account the contributions of uniform, rotational and shear flows, to the force and the torque exerted on the particle. The expressions for the force and the toque are proposed, by introducing translation, rotation and deformation resistance tensors, which capture each of the flow patterns individually. A parametric study is conducted, considering a wide range of non-spherical particles, determined by the parametric superellipsoid surface equation. Using the results of the parametric study, an approximation scheme is derived on the basis of a multivariate polynomial expression. A coefficient matrix for the polynomial model is introduced, which is used as a tunable parameter for a minimization problem, whereby the polynomials are fitted to the data. The developed model is then put to the test by considering a few examples of particles with different shapes, while also being compared to other, currently available solutions. On top of that, the full functionality of the model is demonstrated by considering an example of a pollen grain, as a realistic non-spherical particle. First, a superellipsoid, which best fits the actual particle shape, is found from the considered range. After that, the coefficients of the translation, rotation and deformation resistance tensors are obtained from the present model and compared to the results of other available models. In the conclusion, a superior accuracy of the present model, for the considered range of particles, is established. To the best of the authors knowledge, this is also one of the first models to extend the torque prediction capabilities beyond sphere and prolate particles. At the same time, the model was demonstrated to be simple to implement and very conservative with the computational resources. As such, it is suitable for large scale studies of dispersed two-phase flows, with a large number of particles. |
| first_indexed | 2024-03-09T19:34:58Z |
| format | Article |
| id | doaj.art-c7106f78210948628fcf8a224299f8ff |
| institution | Directory Open Access Journal |
| issn | 2077-1312 |
| language | English |
| last_indexed | 2024-03-09T19:34:58Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Marine Science and Engineering |
| spelling | doaj.art-c7106f78210948628fcf8a224299f8ff2023-11-24T01:57:34ZengMDPI AGJournal of Marine Science and Engineering2077-13122022-03-0110336910.3390/jmse10030369A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes FlowMitja Štrakl0Matjaž Hriberšek1Jana Wedel2Paul Steinmann3Jure Ravnik4Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, SloveniaFaculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, SloveniaInstitute of Applied Mechanics, Friedrich-Alexander Universität Erlangen-Nürnberg, Paul-Gordan-Str. 3, D-91052 Erlangen, GermanyInstitute of Applied Mechanics, Friedrich-Alexander Universität Erlangen-Nürnberg, Paul-Gordan-Str. 3, D-91052 Erlangen, GermanyFaculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, SloveniaIn this paper, forces and torques on solid, non-spherical, orthotropic particles in Stokes flow are investigated by using a numerical approach on the basis of the Boundary Element Method. Different flow patterns around a particle are considered, taking into account the contributions of uniform, rotational and shear flows, to the force and the torque exerted on the particle. The expressions for the force and the toque are proposed, by introducing translation, rotation and deformation resistance tensors, which capture each of the flow patterns individually. A parametric study is conducted, considering a wide range of non-spherical particles, determined by the parametric superellipsoid surface equation. Using the results of the parametric study, an approximation scheme is derived on the basis of a multivariate polynomial expression. A coefficient matrix for the polynomial model is introduced, which is used as a tunable parameter for a minimization problem, whereby the polynomials are fitted to the data. The developed model is then put to the test by considering a few examples of particles with different shapes, while also being compared to other, currently available solutions. On top of that, the full functionality of the model is demonstrated by considering an example of a pollen grain, as a realistic non-spherical particle. First, a superellipsoid, which best fits the actual particle shape, is found from the considered range. After that, the coefficients of the translation, rotation and deformation resistance tensors are obtained from the present model and compared to the results of other available models. In the conclusion, a superior accuracy of the present model, for the considered range of particles, is established. To the best of the authors knowledge, this is also one of the first models to extend the torque prediction capabilities beyond sphere and prolate particles. At the same time, the model was demonstrated to be simple to implement and very conservative with the computational resources. As such, it is suitable for large scale studies of dispersed two-phase flows, with a large number of particles.https://www.mdpi.com/2077-1312/10/3/369dragtorqueresistance tensorrotation tensorBoundary Element MethodStokes flow |
| spellingShingle | Mitja Štrakl Matjaž Hriberšek Jana Wedel Paul Steinmann Jure Ravnik A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow Journal of Marine Science and Engineering drag torque resistance tensor rotation tensor Boundary Element Method Stokes flow |
| title | A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow |
| title_full | A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow |
| title_fullStr | A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow |
| title_full_unstemmed | A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow |
| title_short | A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow |
| title_sort | model for translation and rotation resistance tensors for superellipsoidal particles in stokes flow |
| topic | drag torque resistance tensor rotation tensor Boundary Element Method Stokes flow |
| url | https://www.mdpi.com/2077-1312/10/3/369 |
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