2.1. Particle phase modeling

 

2.1.1. Translational and rotational motion of a particle

In the frame of the DEM, all particles within the computational domain are tracked in a Lagrangian way, by solving explicitly Euler's first and second laws, that govern translational and rotational particle motion, respectively:

(2–1)

(2–2)

where is the particle mass, is the gravitational acceleration vector, is the contact force that accounts for particle-particle and particle-wall interactions, is the angular velocity vector, is its moment of inertia tensor and is the net torque generated by tangential forces that causes the rotation of the particle.

Due to the fluid interaction, two additional terms appear when comparing with a pure DEM simulation: is the additional force accounting for the interaction with the fluid phase and is the additional torque due to the fluid phase velocity gradient, whose calculations are further described in section Particle-fluid interaction forces.

 

2.1.2. Energy balance in a particle

If the thermal model is activated, an additional equation for the energy balance is solved along with the equations governing the motion of the particle. In the current implementation, the particle temperature is assumed to be uniform, i.e., no radial or circumferential temperature variation is admitted. This approximation is reasonable for small or highly conductive particles.

Note:  For more information on the thermal model used in Rocky, refer to the Rocky Technical Manual.

The temperature variation of a particle can be obtained over time according to the differential equation:

(2–3)

where is the specific heat of the particle material and is the total particle heat transfer rate.

This heat transfer rate accounts for the heat transfer that occurs during the contact with other particles or walls, , and the convective heat transfer between particle and fluid phase, , according to the expression:

(2–4)

The convective heat transfer between particle and fluid is calculated by assuming a lumped capacitance system (Bi < 0.1) and using one of many correlations available in the literature for dense particulate systems. The convective fluid-particle heat transfer calculation is described in section Heat transfer between fluid and particle.