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Effect of particle angularity on flow regime transitions and segregation of bidisperse blends in a rotating drum

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Abstract

Granular segregation is a phenomenon that occurs when mixing different-sized particles. This work aims at comparing the segregation pattern and intensity in a bidisperse blend of spherical, cubic and icosahedral particles with a size ratio of 1.5 in a rotating drum. A model based on the discrete element method is used to simulate the flow of particles at rotational speeds ranging from 15 RPM to 115 RPM. This model is validated for monodisperse cubic particles. Segregation is shown to decrease with increasing particle shape angularity for a given rotational speed as long as the flow remains in the same regime. For all three shapes, the same sequence of segregation pattern occurs as the rotational speed increases (from a classic core segregation to a mixed state, and then to inverse segregation), but the speed thresholds for the transitions are shape-dependent and linked to the total kinetic energy of particles, as evidenced by a proposed apparent Froude number. The slip at the wall and the ability to spin explain why rounder shapes are less efficient to transfer kinetic energy from the wall into translational motion of the particles. This triggers regime transitions at higher rotational speeds for rounder particles, but at the same apparent Froude numbers. The transitions between cascading and cataracting, and between cataracting and centrifuging, occur at \(Fr_\mathrm{{app}}\approx 0.20\) and 0.35, respectively, regardless of the particle shape.

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Abbreviations

D :

: drum diameter (m)

\(d_p\) :

: particle diameter (sphere) (m)

\(e_n\) :

: coefficient of restitution (–)

f :

: drum filling degree (%)

\(\mathbf {F_{c,ij}}\) :

: contact force between particles i and j (N)

\(\mathbf {F_{nc,ik}}\) :

: non-contact force between particles i and k (N)

\(\mathbf {F_{g,i}}\) :

: gravitational force acting on particle i (N)

\(\mathbf {F_{i,f}}\) :

: interaction force between particle i and a fluid f (N)

\(\mathbf {F_{c,iw}}\) :

: contact force between particles i and the wall (N)

Fr :

: Froude number (−)

\(Fr_\mathrm{{app}}\) :

: apparent Froude number (−)

\({\varvec{g}}\) :

: gravitational acceleration (9.81 \(\mathrm {m/s}^2\))

h :

: active layer thickness (m)

\(I_i\) :

: inertia of particle i (\(\mathrm {kg}\!\cdot \!\mathrm{{m}}^2\))

\(I_{seg}\) :

: segregation index (−)

\(k_n\) :

: numerical stiffness (\(\mathrm{Pa}\!\cdot \!\mathrm{m}\))

L :

: drum length (m)

\(l_p\) :

: cube or icosahedron edge length (m)

\(m_i\) :

: mass of particle i

N :

: total number of particles in the system (−)

r :

: particle radius (sphere) (m)

R :

: drum radius (m)

\({\varvec{R_j}}\) :

: vector pointing between the center of mass of particle i and the contact point with particle j (m)

\({\varvec{R_w}}\) :

: vector pointing between the center of mass of particle i and the contact point with the wall (m)

t :

: time (s)

\(T_C\) :

: contact duration (s)

\({\varvec{T_{ij}}}\) :

: torque calculated between particles i and j in contact (\(\mathrm {N}\!\cdot \!\mathrm {m}\))

\(\mathbf {v_i}\) :

: translational total velocity of particle i (m/s)

\(V_\mathrm{{cell}}\) :

: volume of the cell (\(\mathrm {m}^3\))

\(V_{p,\mathrm {cell}}\) :

: volume occupied by particles in the cell (\(\mathrm {m}^3\))

\(\overline{v_w}\) :

: dimensionless mean velocity at the wall (m/s)

x :

: mass concentration (kg/kg)

\(\Delta t\) :

: time step (s)

\(\theta \) :

: dynamic angle of repose (\(^\circ \))

\(\lambda _i\) :

: weighting coefficient (−)

\(\mu _C\) :

: sliding friction coefficient (−)

\(\mu _r\) :

: rolling friction coefficient (−)

\(\rho \) :

: density (\(\mathrm{kg}\!/\!\mathrm{m}^3)\)

\(\sigma \) :

: standard deviation (\(\mathrm{kg}\!/\mathrm{kg}\))

\({\varvec{\omega }}\) :

: rotational speed of the drum (\(\mathrm{rad}/\mathrm{s}\))

\({\varvec{\omega _i}}\) :

: angular velocity of particle i (\(\mathrm{rad}/\mathrm{s}\))

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Acknowledgements

The authors thank Calcul Quebec, Compute Canada and the Natural Sciences and Engineering Research Council of Canada for computational resources and funding. The authors also gratefully acknowledge financial support from the Simulation-based Engineering Science (Genie Par la Simulation) program funded through the CREATE program of the Natural Sciences and Engineering Research Council of Canada. Special thanks to Prof. Balmforth (UBC) for the use of the rotating drum and to Dr. Daniel Rakotonirina for introducing and helping understand Grains3D, even remotely.

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Authors and Affiliations

  1. Research Unit for Industrial Flow Processes (URPEI), Department of Chemical Engineering, Polytechnique Montreal, PO Box 6079, H3C 3A7, Stn Centre-Ville, Montreal, QC, Canada

    Christine Beaulieu, David Vidal, Carine Niyonkuru & François Bertrand

  2. Process Engineering Advanced Research Lab (PEARL), Department of Chemical Engineering, Polytechnique Montreal, PO Box 6079, H3C 3A7, Stn Centre-Ville, Montreal, QC, Canada

    Jamal Chaouki

  3. Department of Chemical and Biological Engineering, University of British Columbia, 2360, BC V6T 1Z3, East Mall, Vancouver, Canada

    Anthony Wachs

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  1. Christine Beaulieu
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  2. David Vidal
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Correspondence to Christine Beaulieu.

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Beaulieu, C., Vidal, D., Niyonkuru, C. et al. Effect of particle angularity on flow regime transitions and segregation of bidisperse blends in a rotating drum . Comp. Part. Mech. 9, 443–463 (2022). https://doi.org/10.1007/s40571-021-00421-1

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