Dynamic shape factor for particles of various shapes in the intermediate settling regime

There are a number of shape factors available in the literature to describe the deviation of non-spherical particles to spheres. Dynamic shape factor (χ) is the most suitable parameter for flow applications as it takes into account the dynamic properties of the non-spherical particles. In this study, dynamic shape factors for spheres, cubes, cuboids and cylinders settling in the transition regime (2 < Ret < 500) are determined experimentally. Wall effects on the terminal settling velocity are accounted based on literature models. χ for spheres and cubes are found to be constant with particle size when conventional wall effect models are followed. χ for cuboids and cylinders, on the other hand, are found to be a function of the particle characteristic length-to-column diameter ratio (l/D) and the particle aspect ratio (l/d). An empirical correlation is developed to estimate χ for both cuboids and cylinders settling in the intermediate regime. The correlation can provide a low average error of 3% for all the cuboids and cylinders used in this study.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Dynamic shape factor of various shapes in the transition regime are determined. ► χ for spheres and cubes are found to be 0.98 and 1.03, respectively. ► χ for spheres and cubes are constant with particle size when wall effect models are used. ► χ for cuboids and cylinders are found to be functions of l/D and l/d. ► An empirical correlation is developed to estimate χ for cuboids and cylinders.