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-The particles re-focus from 4 to 2 (lateral or vertical) locations further downstream from measurements[1]:
-A lower particle concentration increases the rate of particle focusing and vice-versa:
0 , 0 0 , 1 0 , 2 0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 00 , 0
0 , 1
0 , 2
0 , 3
0 , 4
0 , 5
0 , 6
0 , 7
0 , 8
0 , 9
1 , 0
y /
L y
z / L z
• 3 2 p a r t i c l e s
Ellipsoids
Institute of Fluid Mechanics
Jesus Alvarez Sarro ([email protected])
The project was conducted at the TU Dresden, Germany
Motivation & Goals
• Numerical simulation of experiments performed by Di Carlo et al. (2007) [1]: spheres and ellipsoids
• Investigation of physical parameters involved in particle focusing, suggestions on possible improvements
• Statistical analysis of particle and flow behaviour
Method
• DNS, staggered Cartesian grid 2nd order in space
• Immersed Boundary Method (IBM) [3]
• 1) spherical particles 2) Red Blood Cells (RBC) modelled as ellipsoids in a square duct
• Collision: repulsive potential particle-particle/wall
Spheres:
- Experiments by [1] show that spheresconcentrate at locations in a square duct when the wall, Saffman (shear) and Magnus (rotation) effects are in balance.
Conclusions and outlook
• particle concentration affects rate of focusing
• spheres focus further from four to two locations
• there is a recirculation pattern happenning in the duct
• future simulations with ellipsoids should incorporate the recommendations given to increase physicality
References[1] Dino Di Carlo, Daniel Irimia, Ronald G. Tompkins, and Mehmet Toner, Continuous inertial focusing, ordering, and separation of particles in micro-channels, PNAS, 27 November 2007, Vol. 104, No. 48[2]-Lginglinh Shi, Tsorng-Whay Pan and Roland GloNumerical simulation of lateral migration of red blood cells in Poiseuille flowsInt. J. Numer. Meth. Fluids (2012), Vol. 68 Pp. [3] -Tobias Kempe, Jochen Fröhlich, An improved immersed boundary method with direct forcing for the simulation of particle laden flows, Journal of Computational Physics (2012) Vol. 231 Pp. 3663-3684
Master in Engineering, Final Year Project, Aero & Auto DepartmentLoughborough University, Loughborough, LE11 3TU, UK
Numerical Simulation of Modelled Blood Cells in a Viscous Flow Through a Duct
Computing time provided by ZIH, TU Dresden is greatfully acknowledged.
Fig. 1: Focusing locations [1] Fig. 7: Cross sectional comparison
ellipsoid-RBC (left), experimental focusing observed [1] (right)
N u m e r i c a l S i m u l a t i o n o f M o d e l l e d B l o o d C e l l s i n a V i s c o u s S h e a r F l o w t h r o u g h a S q u a r e
D u c t P r ä s e n t a t i o n s n a m e X Y Z
3 6
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 00 . 0
0 . 1
0 . 2
0 . 3
0 . 4
0 . 5
0 . 6
0 . 7
0 . 8
0 . 9
1 . 0
D i C a r l o M e a s u r i n g P o i n t : x / L y = 2 0 0
y /
L y
z / L z
• 3 6 p a r t i c l e s
Fig. 5: Particle location at X/Ly=200
X/Ly=200 X/Ly=400 X/Ly=600 X/Ly=1200
Fig. 2: Particles re-focus to 2 locations
Fig. 3: Location PDF, X/Ly=150-250
Part. conc. = 1% Part. conc. = 0.4% Part. conc. = 0.2%
yz
z
y
Fig. 8: Instantaneous particle location, X/Ly=200. Particles concentrate at a radius in the duct
Fig. 9: PDF location analysis, X/Ly=200 to X/Ly=500
Project supervisors:
- Prof. Dr. -Ing. habil. J. Fröhlich
- Dipl. -Hydrol. Berhard Vowinckel
- Dr. Adrian Spencer
-Blurred focusing obtained:
-Flow re-circulation as a result of particle focusing:
Fig. 4: Streamlines added on U contour background
-Higher particle concentration = more collisions and less focusing:
Fig. 10: Snapshot from simulation
Future Improvements:
- Simulation of deformable particles based on the spring model by Shi et al.[2]
- Exact RBC shape
- Higher collision damping
- Finer grid and increased simulation time
Focusing behaviour is Stokes number based:
2
0.73818( / 2)
m pk
y f
D US
L
ρνρ
= =
Fig. 6: Snapshot of further 2-point focusing Fig. 11: Ellipsoid rotational velocities
No rotation
Blured focusing
