A model for translation and rotation resistance tensors for superellipsoidal particles in Stokes flow

Štrakl, M., Hriberšek, M., Wedel, J., Steinmann, P. and Ravnik, J. (2022) A model for translation and rotation resistance tensors for superellipsoidal particles in Stokes flow. Journal of Marine Science and Engineering, 10(3), 369. (doi: 10.3390/jmse10030369)

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Abstract

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.

Item Type:Articles
Additional Information:Funding: Deutsche Forschungsgemeinschaft (project STE 544/58), Slovenian Research Agency (research core funding No. P2-0196).
Keywords:Drag, torque, resistance tensor, rotation tensor, Boundary Element Method, Stokes flow, non-spherical, particle.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Štrakl, M., Hriberšek, M., Wedel, J., Steinmann, P., and Ravnik, J.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Journal of Marine Science and Engineering
Publisher:MDPI
ISSN:2077-1312
ISSN (Online):2077-1312
Published Online:04 March 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Journal of Marine Science and Engineering 10(3): 369
Publisher Policy:Reproduced under a Creative Commons License

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