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Drag models for the spherocylinder CFDEM model
In this document, ~u is used to denote the relative velocity between particle and fluid.
~u = ~uf − ~up
Holzer and Sommerfeld, Di Felice
The drag force on a single particle is given by
F~D0 = ~u|~u|CD ρ d2s
Where the drag coefficient is given by Holzer and Sommerfeld :
0.4(− ln φ)0.2 1
3 + 0.4210
Re φ 4
Ap,tot − 2Ap,k
The drag force on a particle in presence of other particles is given according to Di Felice :
F~D = F~D0 2−β
(1.5 − ln Re)2
β = 3.7 − 0.65 exp −
The pressure drop over a CFD cell is given by the Ergun equation 
~ 0 (1 − )2
~ 0 |U
~ 0 (1 − )
(φds )2 3
The total force on all particles in a cell is given by
The force on each particle is given by 
Vcell (1 − )
L(1 − )
~ 0 (1 − )
~ 0 |U
(φds )2 2
~ 0 we substitute ~u.
For µ we substitute νρ, for U
ν(1 − )
In order to decide which drag model to use, the minimum of the Holzer & Sommerfeld / Di Felice
and the Ergun drag is taken. This ensures that the Ergun drag is used in dense regions.
F~D = min(F~D,H&Z/DF , F~D,Ergun )
A., & Sommerfeld, M. (2008). New simple correlation formula for the drag coefficient of
non-spherical particles. Powder Technology, 184(3)
2. Di Felice, R. (1994). The voidage function for fluid-particle interaction systems. International
Journal of Multiphase Flow, 20(I)
3. Ergun, S. (1952). Fluid flow through packed columns. Chem. Eng. Prog., 48
4. Gidaspow, D. (1994). Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. London: Academic Press Inc.
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