A Study on Shape-Dependent Settling of Single Particles with Equal Volume Using Surface Resolved Simulations

Abstract

A detailed knowledge of the influence of a particle’s shape on its settling behavior is useful for the prediction and design of separation processes. Models in the available literature usually fit a given function to experimental data. In this work, a constructive and data-driven approach is presented to obtain new drag correlations. To date, the only considered shape parameters are derivatives of the axis lengths and the sphericity. This does not cover all relevant effects, since the process of settling for arbitrarily shaped particles is highly complex. This work extends the list of considered parameters by, e.g., convexity and roundness and evaluates the relevance of each. The aim is to find models describing the drag coefficient and settling velocity, based on this extended set of shape parameters. The data for the investigations are obtained by surface resolved simulations of superellipsoids, applying the homogenized lattice Boltzmann method. To closely study the influence of shape, the particles considered are equal in volume, and therefore cover a range of Reynolds numbers, limited to [9.64, 22.86]. Logistic and polynomial regressions are performed and the quality of the models is investigated with further statistical methods. In addition to the usually studied relation between drag coefficient and Reynolds number, the dependency of the terminal settling velocity on the shape parameters is also investigated. The found models are, with an adjusted coefficient of determination of 0.96 and 0.86, in good agreement with the data, yielding a mean deviation below 5.5% on the training and test dataset.

Real-Time Modeling of Volume and Form Dependent Nanoparticle Fractionation in Tubular Centrifuges

“…Both smooth, convex shapes such as spheres, plates, cuboids and ellipsoids as well as more complex aggregated structures and rough surfaces are possible. An extensive overview of different form parameters found in the literature is listed in [41]. Barrett et al [42] mentions the three independent parameters form, roundness and surface texture one may consider for describing particle shape.…”

“…The consideration of multiple geometric particle properties by drag correlations in several ranges of Reynolds numbers is extensively studied and discussed in the literature [41,[48][49][50][51][52][53]. A recently published article by Trunk et al [41] compiles multiple drag correlations for non-spherical particles and provides additional information on the drag correlation approximation for Reynolds numbers outside the Stokes regime. In the context of this work the mathematical formulation of the corrected drag coefficient,…”

Modal analysis reveals imprint of snowflake shape on wake flow structures

“…Previous research has extensively studied the wake flow structures behind simple particle geometries such as spheres (Uhlmann and Dusek, 2014;Emadzadeh and Chiew, 2020), cylinders (Toupoint et al, 2019), disks (Field et al, 1997;Kim et al, 2018), planar polygons (Esteban et al, 2019), and polyhedra (Trunk et al, 2021;Gai and Wachs, 2024). Only a few studies have ventured into investigating the wake flow behind complex-shaped objects and the effect of shape features, such as shape porosity and sphericity, on drag and particle falling behavior (Nediç et al, 2015;Cummins et al, 2018;McCorquodale and Westbrook, 2020b).…”

Implicit propagation of directly addressed grids in lattice Boltzmann methods

“…Current high performance computation (HPC) setups combine different levels of parallelization and acceleration capabilities into one heterogeneous system. Simulations of transport phenomena using lattice Boltzmann methods (LBM) are a major application for HPC in for example, process engineering 1,2 . The lattice Boltzmann (LB) algorithm is commonly separated into a local and thus perfectly parallel collision step and a non‐local streaming step , both of which are applied to cells on a regular lattice.…”