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