This PDF 1.5 document has been generated by TeX / MiKTeX pdfTeX-1.40.17, and has been sent on pdf-archive.com on 29/03/2017 at 14:54, from IP address 131.155.x.x.
The current document download page has been viewed 282 times.
File size: 141.65 KB (2 pages).
Privacy: public file
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
1 π
F~D0 = ~u|~u|CD ρ d2s
2 4
Where the drag coefficient is given by Holzer and Sommerfeld [1]:
CD =
16 1
3 1
8 1
0.4(− ln φ)0.2 1
p +
√ +√
3 + 0.4210
Re φk
Re φ
φ⊥
Re φ 4
Where
Re =
|~u|ds
ν
φ⊥ =
As,⊥
Ap,⊥
φk =
2As,k
Ap,tot − 2Ap,k
The drag force on a particle in presence of other particles is given according to Di Felice [2]:
F~D = F~D0 2−β
(1.5 − ln Re)2
β = 3.7 − 0.65 exp −
2
Ergun Equation
The pressure drop over a CFD cell is given by the Ergun equation [3]
~ 0 (1 − )2
~ 0 |U
~ 0 (1 − )
∆P
µU
ρ|U
= 150
+
1.75
L
(φds )2 3
φds 3
The total force on all particles in a cell is given by
Ftot,cell =
∆P
Vcell
L
The force on each particle is given by [4]
Fpart =
Ftot,cell
Vpart
∆P Vpart
= Ftot,cell
=
npart
Vcell (1 − )
L(1 − )
~ 0 (1 − )
~ 0 |U
~0
µU
Fpart
ρ|U
= 150
+
1.75
Vpart
(φds )2 2
φds 2
~ 0 we substitute ~u.
For µ we substitute νρ, for U
~uVpart ρ
ν(1 − )
F~part =
150
+ 1.75|u|
φds
φds
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 )
References
˜
1. HA¶lzer,
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.
2
dragmodels.pdf (PDF, 141.65 KB)
Use the permanent link to the download page to share your document on Facebook, Twitter, LinkedIn, or directly with a contact by e-Mail, Messenger, Whatsapp, Line..
Use the short link to share your document on Twitter or by text message (SMS)
Copy the following HTML code to share your document on a Website or Blog