Drag coefficient for irregularly shaped grains: rotational dependence at various Reynolds numbers

Journal of Fluid Mechanics, vol. 994

Abstract

The nature and behaviour of the drag coefficient $C_D$ of irregularly shaped grains within a wide range of Reynolds numbers $Re$ is discussed. The morphology of the grains is controlled by their fractal description, and they differ in shape. Using computational fluid dynamics tools, the characteristics of the boundary layer at high $Re$ has been determined by applying the Reynolds-averaged Navier–Stokes turbulence model. Both grid resolution and mesh size dependence are validated with well-reported previous experimental results applied in flow around isolated smooth spheres. The drag coefficient for irregularly shaped grains is shown to be higher than that for spherical shapes, also showing a strong drop in its value at high $Re$ . This drag crisis is reported at lower $Re$ compared to the smooth sphere, but higher critical $C_D$ , demonstrating that the morphology of the particle accelerates this crisis. Furthermore, the dependence of $C_D$ on $Re$ in this type of geometry can be represented qualitatively by four defined zones: subcritical, critical, supercritical and transcritical. The orientational dependence for both particles with respect to the fluid flow is analysed, where our findings show an interesting oscillatory behaviour of $C_D$ as a function of the angle of incidence, fitting the results to a sine-squared interpolation, predicted for particles within the Stokes laminar regime ( $Re\ll 1$ ) and for elongated/flattened spheroids up to $Re=2000$ . A statistical analysis shows that this system satisfies a Weibullian behaviour of the drag coefficient when random azimuthal and polar rotation angles are considered.

Authors 3

1. Álvaro Vergara Aachen Institute of Geomechanics and Underground Technology Faculty of Civil Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute of Geomechanics and Underground Technology, Faculty of Civil Engineering, RWTH Aachen University, 52074 Aachen, Germany

2. Deheng Wei corresponding Aachen Institute of Geomechanics and Underground Technology Faculty of Civil Engineering

   RWTH Aachen University · The University of Sydney · Northeastern University

   Affiliation as printed

   Institute of Geomechanics and Underground Technology, Faculty of Civil Engineering, RWTH Aachen University, 52074 Aachen, Germany

   Key Laboratory of Ministry of Education on Safe Mining of Deep Mines, School of Resources and Civil Engineering, Northeastern University, Shenyang 110819, PR China

   School of Civil Engineering, The University of Sydney, NSW 2006, Australia

3. Raúl Fuentes Aachen Institute of Geomechanics and Underground Technology Faculty of Civil Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute of Geomechanics and Underground Technology, Faculty of Civil Engineering, RWTH Aachen University, 52074 Aachen, Germany