CFD Simulation of Wet Fluidized Beds Using TFM with Variable Particle-Particle Restitution Coefficient

CFD
simulation of wet fluidized beds using TFM with variable particle-particle
restitution coefficient

Hanbin Zhong^a, Qingang Xiong^b,*,
Juntao Zhang^a, Yuqin Zhu^a, Shengrong Liang^a, Xinyu
Zhang ^a

^a School of
Chemistry and Chemical Engineering, Xi'an Shiyou University, Xi'an, Shaanxi 710065,
China

^b IT Innovation
Center, General Motors, Warren, MI 48092, USA

Abstract

For the wet fluidized
beds, the wet restitution coefficients are different with the particle-particle
restitution coefficients of dry particles, and affected by the liquid
viscosity, liquid layer thickness, and impact velocity. The two-fluid model
(TFM) is widely used in the CFD simulation of fluidized beds due to the
relatively low computational cost. However, a constant value for the particle-particle
restitution coefficient is normally used to describe the particle-particle
interaction in the simulation with TFM, while the previous reports indicated
that the predicted hydrodynamics were significantly affected by the value of
particle-particle restitution coefficient. Therefore, an advanced TFM with
variable particle-particle restitution coefficient was developed to describe
the actual wet restitution coefficients in the wet fluidized beds. The elastohydrodynamic
model proposed by Davis, et al. (Elastohydrodynamic rebound of spheres from
coated surfaces, J. Fluid Mech., 2002, 468, 107-109.) was used to calculate
the wet restitution coefficient based on the liquid viscosity, liquid layer
thickness, impact velocity, and particle properties. The hydrodynamics of the
dry and wet particles were predicted and compared with the experiments. The
effects of the liquid viscosity and liquid layer thickness were also
investigated.

Keywords:

Two-fluid
model; restitution coefficient; wet particle; fluidized bed; CFD

Details
on the relationship between the liquid viscosity and liquid layer thickness and
the effective wet restitution coefficients

Davis,
et al. (Elastohydrodynamic rebound of spheres from coated surfaces, J. Fluid
Mech., 2002, 468, 107-109.) have proposed an elastohydrodynamic model to
determine the wet restitution coefficient:

where e_dry
and e_wet are the dry and wet restitution coefficient,
respectively.

The
Stokes number is calculated by the following equation:

where m and r_p
are the particle mass and radius, respectively. V_c is the
impact velocity. μ_l is the liquid viscosity.

The
critical Stokes number St_c is given by:

where ε is
the
dimensionless elasticity parameter calculated as:

z₀
is the distance where the viscous forces become significant:

where d_l
is the liquid layer thickness.

Y_eff
is the effective Young’s modulus determined by:

where
ν₁ and ν₂ are Poisson’s ration
for the collision particle/plane, Y₁ and Y₂
are the effective Young’s modulus for the collision particle/plane.