Magnetic Convection and Exchange Flow in Reservoirs - numerical simulation of physics flows. Please refer to my publications, 2005-2010.

1. Four Hats of Math
Tomasz Bednarz
A/Professor | ACEMS + IFE @ QUT
PART #1/3

2. Who am I?
• A/Professor / Principal Research Fellow (ACEMS + IFE @ QUT)
• Earlier worked at (as):
• CSIRO (Research Team Leader, Leader in Computational Simulation Science TCP,
3D Visualisation Software Engineer).
• James Cook University (Senior Research Fellow).
• Kyushu University, Japan (PhD Candidate).
• Also worked as: IT projects manager, iPhone apps developer, NDS game
developer, demoscene coder and swapper, graphics designer, web developer.
• Education: Computational Physics, Interdisciplinary Engineering, MBAE.
• Also:
• Chair of Queensland IEEE Computer Society.
• Chair of Brisbane SIGGRAPH Chapter.
• Chair of Brisbane Khronos Group Chapter.
• ACM SIGGRAPH International Resources Committee.
• 125+ publications: http://www.researcherid.com/rid/A-7376-2011

3. Brisbane, Queensland, Australia

4. Couple of quick topics to cover
• Flying frogs and near zero gravity
• How to measure temperature/velocity non-invasively
• Tele-operating systems
• Human Computer Interaction experiments
• 360 degree panorama
• PDEs on GPU
• Cloud based image analysis toolbox
• Visualization and visual analytics
• Art + Science

5. Flying Frog Larry
and how to control gravity

6. Magnetic levitation
Diamagnetic levitation: Flying frogs and
floating magnets
Simon MD, Geim AK
JOURNAL OF APPLIED PHYSICS 87 (9):
6200-6204 Part 3 MAY 1 2000
Equivalent to Space Lab?

7. 2
2
2
2
B
B
f
m
m
m











Paramagnetic（χm>0) material is attracted to a magnet.
Diamagnetic（χm<0）material is repelled from a magnet.
g
B
g
B
force
gravi
force
mag
m
m
m









2
)
2
/
(
.
. 2
2




For oxygen gas, magnetic force is about 45 times of gravity force.
For water, magnetic force is about 1/3 of gravity force.
10-Tesla superconducting magnet has 400T2/m.
What is a magnetic force?

8. 8
Natural convection
Stable
stratification
Gravitational
unstable,
Conv. if Ra > Rac
Gravitational
stable,
Conv. if D  0
Convection modes in a cubic enclosure

9. 9
Magnetic buoyancy force
Magnetic body force acting on electrically non-conducting materials
Magnetic suceptibility of paramagnetic substances () is inversly
proportional to its absolute temperature q - Curie law.
Using Curie’s law we can obtain the magnetic force (similar to
Bousinessq approximation):
q < q0: attractive force
q > q0: repulsive force

10. 10
Thermochromic Liquid Crystals
 TLCs: smectic, nematic and choresteric phases
 Color-temperature play range: 0.5 - 20ºC
 The response time: 3ms, enough for typical thermal problems
 Particles diameter: 30-60 m
 Shelf-life time: 6 months
 Efficient: 50 litre tank needs only 65ml slurry
 Colours: red – orange – yellow – green – blue – violet

11. 11
Particle Image Thermometry
• Thermochromic Liquid Crystal
tracers
• Light sheet
• RGB (colour) images
• Image post-processing of TLC
patterns
• Quantitative, full-field information
about temperature field
PIT = NON-INVASIVE METHOD OF TEMPERATURE MEASUREMENT

12. 12
Hue vs temperature vs WB
0
60
120
180
240
300
360
18.9 19.9 20.9 21.9 22.9 23.9
temperature
hue
5200K
6000K
7000K
3000K
color temperature
of the camera
WB = White Balance of the Camera

13. 16th Australasian Fluid Mechanics Conference,
Gold Coast, 2-7 December 2007
13
19.6
20.6
21.6
22.6
23.6
19.6 20.6 21.6 22.6 23.6
Target Temperature
Temperature
Obtained
H (polynomial fitting 6th order)
18.8
19.8
20.8
21.8
22.8
23.8
18.8 19.8 20.8 21.8 22.8 23.8
Target Temperature
Temperature
Obtained
configuration 11
configuration 4
configuration 12
Calibrations
No. Input parameters Neurons in
layers
Activation functions Color bandwidth
[ºC]
Regression
coefficient
Mean absolute
error [ºC]
1 H polynomial fit 19.7 – 23.7 0.9962 0.0493
4 R, G, B 6, 6, 1 log, log, lin 19.7 – 23.7 0.9898 0.0733
11 R, G, B, H 20, 20, 1 log, log, log 19.7 – 23.7 0.9978 0.0319
12 R, G, B 3, 3, 1 log, log, log 18.9 – 24.2 0.9810 0.1129

14. Enclosure vs magnet position

15. 15
Magnetic field distribution

16. 16
Momentum equation
Continuity equation
Energy equation
Biot-Savart’s law
The non-dimensional parameters:
Governing equations

17. 0 Tesla 5 Tesla 10 Tesla
g
H
O
T
magnet

18. 18
Suppression of the convection
0 1 2 3 4 5
0
1
2
3
4
5
Nusselt
number
[-]
Magnetic induction in the center of the solenoid [T]
numerical results
experimental results

19. 19
Suppression of the convection
solenoid-1
solenoid-1
solenoid-2
solenoid-2
Fm
Fg
Fg
Fm
Xc = 7.28
6.84

20. Experimental results
Numerical results
(a) 0 [T], Dq = 3.44 [K] (b) 5 [T], Dq = 4.12 [K] (c) 10 [T], Dq = 5.27 [K]

21. Reservoirs
Exchange flows

22. Reservoir model
17
18
19
20
21
22
23
24
0 7 14 21 28 35 42 49 56 63 70
Time [min]
Temperature
[
o
C] a
b
c
d
e
f
g
h
i
j
k
Thermal forcing

23. Exchange Flows in Reservoirs – Cooling Case
• Water circulation in reservoirs is driven by thermal gradients changing
during day and night cycles.

24. 17
18
19
20
21
22
23
24
0 7 14 21 28 35 42 49 56 63 70
Time [min]
Temperature
[
o
C] a
b
c
d
e
f
g
h
i
j
k
Exchange Flows in Reservoirs – Diurnal Case
Pr = 6.82,
Gr = 3.52×104
Dt
PIV result
unsharp mask

25. (a)
(b)
(c)
(d)
(e)
(f)
(h)
(i)
(j)
(g)
(k)
17
18
19
20
21
22
23
24
0 7 14 21 28 35 42 49 56 63 70
Time [min]
Temperature
[
o
C]
a
b
c
d
e
f
g
h
i
j
k
PIT
Pr = 6.82 and Gr = 3.52 × 104
Isotherms are extracted from the colour
Images.

26. (a)
(b)
(c)
(d)
(e)
(f)
(h)
(i)
(j)
(g)
(k)
17
18
19
20
21
22
23
24
0 7 14 21 28 35 42 49 56 63 70
Time [min]
Temperature
[
o
C]
a
b
c
d
e
f
g
h
i
j
k
Streamlines

27. Numerical model
t [s]
T [K]
T 0
DT/2
DT/2
heating phase
cooling phase
P P
  







P
t
T


2
sin
5
.
0
5
.
0

28. Attic space
https://bitbucket.org/tomaszbednarz/hsmac-bfc-2d

29. • Transient flow:
Applications: scaling analysis
• Used to predict behaviour of the fluid flow for different cases.
• Approach: by comparing terms of governing equations.
https://bitbucket.org/tomaszbednarz/hsmac-bfc-2d

30. Gr = 1e7
t [s]
T [K]
T 0
DT/2
DT/2
heating phase
cooling phase
P P

31. OpenCL Fluid Solver