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.
Highlights
Multiphase flows with non-spherical particles are being extensively researched in recent years, by authors from numerous fields of engineering and science
The models of shape dependant translation, rotation and deformation resistance tensor components are based on the conducted parametric study, where we investigate approximately 5.4 · 103 superellipsoidal particles, which are obtained from the following range for the superellipsoidal parameters: λ1 = [1, 11], λ2 = [1, 11], e1 = [0.2, 1.8] and e2 = [0.2, 1.8]
Due to the nature of the problem, we employ the Boundary Element Method (BEM) approach, which is proven to be superior in terms of computational cost and accuracy for the proposed problem set-up, as it enables a direct evaluation of the boundary tractions, leading to excellent accuracy of computed forces and torques acting on a particle
Summary
Multiphase flows with non-spherical particles are being extensively researched in recent years, by authors from numerous fields of engineering and science. With significant development of computational methods, one of the greatest challenges still remains in tackling industrial level simulations This follows from a fact that they are frequently associated with complex carrier fluid flow fields and a large number of dilutely distributed, non-spherical particles. Problems of this nature are usually treated by using the Euler-Lagrangian approach, based on the point-particle assumption, which is valid for particle sizes much lower than the Kolmogorov length scale of the flow. Such an approach relies on using a model for the prediction of the particle-fluid interaction, instead of using the computationally expensive direct approach. Examples that can be found in the literature range from the studies of volcanic ash transport in the atmosphere [30,31], as well as investigations of ice crystal trajectories in an aircraft turbofan compressor [32], to simulating the formation of polymer particles in a downer reactor [33]
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