master thesis presentation: numerical simulation of modelled blood cells in a viscous flow through a...
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This presentation was held in was my master thesis presentation,TRANSCRIPT
Numerical Simulation of Modelled Blood Cells in Viscous Flow
Master Thesis Presentation, TU Dresden, 31.07.2012
Fakultätsname XYZ Fachrichtung XYZ Institutsname XYZ, Professur XYZ
Jesus Alvarez Sarro
Institute of Fluid Mechanics, TU Dresden
2
Simulation of Blood Cells
http://www.preventing-a-heart-attack.com/what-is-blood.htmlPhoto credit: Annie Cavanagh
Photo credit: Edwin L. Steele Laboratory
3
I Introduction
II Methodology
III Hydrodynamic Effects
IV Simulation with Spheres
V Simulation with Ellipsoids
VI Discussion
4
Di Carlo et al. (2007) Experimental Results: Spheres
[Di Carlo et al.]
[Di Carlo et al.
[Di Carlo et al.]
Inlet
y
z
5
Di Carlo et al. (2007) experimental results: Ellipsoids
[Di Carlo et al. 2007]
Experimental Findings
Numerical Simulation
6
I Introduction
II Methodology
III Hydrodynamic Effects
IV Simulation with Spheres
V Simulation with Ellipsoids
VI Discussion
7
Grid Generation
D / h: 8, 12, 16
Reynolds Number: 1, 10, 50, 100
-> Determine optimal mesh size:
Higher Reynolds numbers
Higher velocity gradients
Higher resolution required
Higher Computational Power Required
More accurate solution
8
Grid Generation
Summary of drag and lift forces and coefficients
4.6
4.7
4.8
4.9
5
Cd
Dra
g C
oe
ffici
en
t Cd
D/dx=8 D/dx=12 D/dx=16 Zeng et al. 4.6
4.7
4.8
4.9
5
CdD
rag
Co
effic
ien
t C
d
D/dx=8 D/dx=12 D/dx=16 Zeng et al.
ω=0
(2005)
9
U-velocity cross-sectional profile
0 1 2 3 4 5 6 7 8-0,2
0,0
0,2
0,4
0,6
0,8
1,0
1,2Re = 10
D/h=8
D/h=12
D/h=16
yp / D
U v
elo
city
10
V-velocity cross-sectional profile
0 1 2 3 4 5 6 7 8
-0,15
-0,1
-0,05
0
0,05
0,1
0,15Re = 10
D/h=8
D/h=12
D/h=16
yp / D
V v
elo
city
11
Grid Generation
12
I Introduction
II Methodology
III Hydrodynamic effects
IV Simulation with Spheres
V Simulation with Ellipsoids
VI Discussion
13
Lift Forces on Particle
Wall Effect Shear Flow (Saffmann Effect)
Particle Rotation (Magnus Effect) Velocity/Pressure Difference
14
Effects on Pressure
Wall Effect Shear Flow (Saffmann Effect)
Particle Rotation (Magnus Effect) Velocity/Pressure Difference
x
y
ppref
ppref
ppref
ppref
free slip conditionfree slip condition
no slip condition
particle allowed to rotate
ellipsoidal shape
15
Lift Forces on Particle: (U) velocity plots
Wall Effect Shear Flow (Saffmann Effect)
Particle Rotation (Magnus Effect) Velocity/Pressure Difference
x
y
16
Lift Forces on Particle: (V) velocity plots
Wall Effect Shear Flow (Saffmann Effect)
Particle Rotation (Magnus Effect) Velocity/Pressure Difference
17
Lift coefficients on spheres
18
Lift force comparison: Spheres and Ellipsoid
19
I Introduction
II Methodology
III Hydrodynamic Effects
IV Simulation with Spheres
V Simulation with Ellipsoids
VI Discussion
No Slip
20
Basic Configuration
x
y
Lx = 1024h
Lz = 90h
Ly = 90h
No Slip
Periodic Periodic
D/h=16z
21
Configuration Variants: Particle Concentration
Di Carlo et al. (2007) : Particle Wt/Vol = 0.1% - 1%
-> Simulation: No. Particles ~ 4 – 36
Segre and Silberberg (1962) & Di Carlo et al. (2007):
„Particle concentration does not influence particle focusing“
Numerical Simulation:
„Particle concentration does influence particle focusing location and time to focusing“
22
•4 particles per plane:
•Ramdomly inserted within sub-planes
•No contact particle - particle/wall
Particle Insertion
x
y
• Allows for more inserted particles
•Observe particle self orderingz
•1 particle per plane:
•Ramdomly inserted within plane
•No contact between particles & wall
23
Particle trajectory after initial focusing
y /
L y
z / Lz
24
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
Di Carlo et al. (2007) measuring point: x/Ly = 200
y /
L y
z / Lz
•36 particles
25
Particle focusing after Di Carlo measurement
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
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
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
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 / Lz
y /
L y
z / Lz
y /
L y
z / Lz
y /
L y
z / Lz
x/Ly =400 x/Ly =600
x/Ly =800 x/Ly =1230
focusing location
also possible
26
Statistical Analysis: x/Ly=150 x/Ly=250
Lz
z
y
Particle concentration: 1%
27
Statistical Analysis: x/Ly=1180 x/Ly=1280
LzLz
z
y
28
Statistical Analysis: x/Ly=150 x/Ly=250
Particle concentration: 1% Particle concentration: 0.2%Particle concentration: 0.4%
29
y-axis velocity (V) plot
v/ub
y /
L y
z / Lz
30
z-axis velocity (W) plot
w/ub
y /
L y
z / Lz
31
Particle – particle distance
x/Ly =400 x/Ly =600
x/Ly =800 x/Ly =1230
32
Movie: Pressure changes due to particles
33
I Introduction
II Methodology
III Hydrodynamic Effects
IV Simulation with Spheres
V Simulation with Ellipsoids
VI Discussion
34
Configuration: Re-scaling of Parameters
Micro-scale not supported by software. Re-scaling:
Di Carlo et al. (2007) : Blood Dilution = 0.5% - 5% (sel. 2%)
Blood cells modelled as rigid disks (Shi et al. 2010)
a=c
b b/h = 8
REc=U m D h
ν=60 Skb=
D2U mρp
18(Dh /2) νρ f
=0.018 gresc=g⋅Ly
2⋅U m2 =1.7⋅10−4
35
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 / Lz
•32 particles
Instantaneous particle location at Di Carlo et al. (2007) at measurement point x/Lx=200
36
Statistical Focusing for Ellipsoids: x/Ly =200 x/Ly =500
Less focused than spheres
Agreement with experiments
•shape
•particle concentration
•collisions
37
Particle – particle center-point distance
Slight particle self ordering
38
Movie - Ellipsoids
39
Mean streamwise velocity (U) plot
40
I Introduction
II Methodology
III Hydrodynamic Effects
IV Simulation with Spheres
V Simulation with Ellipsoids
VI Summary and Discussion
Summary
• Grid study
• Description of effects inducing focusing
• Successfully simulated spheres in a duct
• Noted the influence of particle concentration on focusing
• Noted that spheres focus to 2 locations further downstream
• Analysis of physical parameters in the duct:
• Re-circulation, velocity profiles, particle-particle distance
• Attempted simulation with ellipsoids: only slight focusing observed
• Grid size, particle concentration, collision model, insertion
conditions, longer simulations, higher Stokes number?
41
Thank you
Any Questions?
42
43
Appendices
44
Effects on Pressure
Wall Effect Shear Flow (Saffmann Effect)
Particle Rotation (Magnus Effect) Velocity/Pressure Difference
x
y
45
Lift Forces on Particle: Tecplot
Wall Effect Shear Flow (Saffmann Effect)
Particle Rotation (Magnus Effect) Velocity/Pressure Difference
x
y
46
Strömungen berechnen
Boundary conditions
Free slip
du/dy=0
v=0
No slip
u=0
47
48
Grid Generation
Summary of drag and lift forces and coefficients
4.6
4.7
4.8
4.9
5
Cd
Dra
g C
oe
ffici
en
t Cd
D/dx=8 D/dx=12 D/dx=16 Zeng et al.
4.6
4.7
4.8
4.9
5
CdD
rag
Co
effic
ien
t C
d
D/dx=8 D/dx=12 D/dx=16 Zeng et al.
49
Grid Generation: drag & lift forces & coefficients
Summary of drag and lift forces and coefficients
50
Drag coefficients on spheres
51
y-axis velocity (V) plot
v/ub
y /
L y
z / Lz
52
Bernoulli´s Principle
21Constant
2 sv Pρ + ≈
53
Grid Generation: U velocity plots
0 1 2 3 4 5 6 7 8
-4
-2
0
2
4
6
8
10
12Re = 100
D8
D12
D16
yp / D
U v
elo
city
0 1 2 3 4 5 6 7 8
-2
-1
0
1
2
3
4
5
6Re = 50
D8
D12
D16
yp / D
U v
elo
city
0 1 2 3 4 5 6 7 8
-0,2
0,0
0,2
0,4
0,6
0,8
1,0
1,2Re = 10
D8
D12
D16
yp / D
U v
elo
city
0 1 2 3 4 5 6 7 8
-0,02
0,00
0,02
0,04
0,06
0,08
0,10
0,12Re = 1
D8
D12
D16
yp / D
U v
elo
city
54
Grid Generation: V velocity plots
0 1 2 3 4 5 6 7 8
-0,006
-0,004
-0,002
0
0,002
0,004
0,006Re = 1
D8
D12
D16
yp / D
V v
elo
city
0 1 2 3 4 5 6 7 8
-0,15
-0,1
-0,05
0
0,05
0,1
0,15Re = 10
D8
D12
D16
yp / D
V v
elo
city
0 1 2 3 4 5 6 7 8
-1
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
0,8
1Re = 50
D8
D12
D16
yp / D
V v
elo
city
0 1 2 3 4 5 6 7 8
-2,5
-2
-1,5
-1
-0,5
0
0,5
1
1,5
2
2,5Re = 100
D8
D12
D16
yp / D
V v
elo
city
55
Advantages & Disadvantages of Numerical Simulations
++ _ _
•More data obtained
•Possibility of effect isolation
•Does not disturb the flow
•No experimental set up needed
•Possibility of simulating non physical parameters
•Great Computational Power
•Long time
•May not represent reality exactly
56
= 1024h (Long)
Configuration Variants: Length
x
y
z
• increased simulation time
Lz
Ly
Lx
• more particles -> more statistical data
Ly
Lz
= 512h (Short)
57
•1 particle per plane:
•Ramdomly inserted within plane
•No contact between particles & wall
Configuration Variants: Particle Insertion 1
x
y
•Variable inter-plane distance
z
58
Grid Configuration
D
h
D / h = 2
h
D / h = 8D
59
Grid Configuration
Ny
Nx
Nz
x
y•Same grid size in all directions: δx= δy= δz= h
z