Solids holdup in flighted rotating drums: an experimental and simulation study

3. CFD simulation
Solid–gas two phase particle dynamics in a rotary dryer was simulated using the Eulerian Granular Multiphase Model. Thus, the flow was described using the Euler–Euler approach along with the Kinetic theory of granular flow.
3.1. Conservation of mass and momentum equations and drag model
The kinetic theory of granular flow, developed by Lun et al. [23], has been used to model the solid phase stress ( τ_s ). This theory is an



Fig. 2. Front view of the experimental apparatus.
extension of the classical kinetic theory of gases, and takes into account non-ideal particle–particle collisions and gas–particle drag.
Table 1 describes the main fundamental equations and the constitutive equations used in the granular formulation of the Euler–Euler approach.
In Table 1, θ_s is called granular temperature and can be considered as a measure of the particle velocity fluctuation. The terms , , V_f, α_S, α_f, C_D, R_er, ϕ_fS, k_θS, K_sf, g_0,SS, e_SS,and γ_θS are the solid velocity vector, fluid velocity vector, gas volume, solid volume fraction, gas volume fraction, drag coefficient, relative Reynolds number, energy exchange between gas and solid phase, energy diffusion coefficient, momentum exchange coefficient of gas–solid systems, radial distribution function, restitution coefficient and collisional dissipation of energy, respectively.
When the concentration of particles is high, instead of instant collisions, the contact between the particles is long–lasting and the particles slide over each other. Therefore, frictional viscosity (μ_s, _fric) must be added to the collisional viscosity (μ_s,col) and to the kinetics (μ_s,kin) to estimate the viscosity of the solid.
To estimate the frictional viscosity the Schaeffer's model was used [24]:
(18)
where P_S, I_2D and β are the solid pressure (Table 1), the second invariant of the deviatoric stress tensor and the angle of internal friction, respectively. The particle–particle internal angle of friction (β) is roughly the same as the experimentally determined static angle of repose. In this work the static angle of repose of particles was determined experimentally, as described in Section 2.
Table 1