an efficient 3d fem model based on t-a formula for ... · formula for superconducting coated...
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An efficient 3D FEM model based on T-A formula for superconducting coated
conductors
Huiming Zhang, Min Zhang, Weijia Yuan
University of Bath, UK
June, 15-17, 2016
1
Outline
� Introduction
� Methodology
� Validation
� Application� TSTC coil
� Racetrack coil
� Reobel cable
2
Introduction
� Why do we need 3D models for 2G HTS?
� Assembled 2G HTS cables for high current applications� 3D modelling is crucial to guide design and optimisation
3
• Existing models for 3D FEM calculation:� A formula
�Convenient to implement (FlexPDE)
� H formula�Convenient to implement (COMSOL)
� T formula�Easy to impose transporting current
Challenges
4
� Current challenges facing large scale 3D modelling: �High aspect ratio�Complicated geometry�Non-linear E-J power law
� Can we combine the advantages of exiting formula to address the challenges?
�Easy to implement in FEM software�Easy to impose boundary conditions�Computationally efficient
YES, T - A formula
Extremely time consuming
Outline
� Introduction
� Methodology
� Validation
� Application� TSTC coil
� Racetrack coil
� Reobel cable
5
� Geometry
� HTS sheet � Air space
� Two assumptions� Sheet approximation� Ignore the parallel magnetic field component
� State variables� T (current vector potential) normal to Superconducting
sheet� T is also denoted as g in some other papers� A in Air space
T-A formula
6
J T= ∇ ×
Governing equation
J T= ∇ ×
yz y z
x z z x
x yy x
T n T n
J T n T n
T n T n
→ →
→ →
→ →
⋅ − ⋅
= ⋅ − ⋅ ⋅ − ⋅
0
| |
| |
n
c
J JE E
J J
=
0B n
E nt
→→ ∂ ⋅∇ × ⋅ + =
∂B A= ∇ ×
0A Jµ∇ × ∇ × =
Superconducting sheet
Air space
7
T – A formula
Imposing current
I JdS TdS Tds= = ∇ × =∫ ∫ ∫�
T2
x
yT=0
T=0
T1
1 2( )I T T d= −
8
T is normal to surface
1.
Outline
� Introduction
� Methodology
� Validation
� Application� TSTC coil
� Racetrack coil
� Reobel cable
9
Validation
� Magnetisation of thin disk� Dimension: R=10mm, thickness d =1µm� n=201, Jc = 1010A/m2
� Hc = Jc d� T=0 on the boundary of the disk
10
Validation
� Penetration depth & normalized magnetisation loss
11
1.
2.
Validation
� Current and field along radius direction
1.
2. 12
H = Hc
Validation
� Efficiency CPU: Intel i5 2400 Memory: 8 GB
13
Formula H T-A
Thickness 10µm 1µm
50
10
Outline
� Introduction
� Methodology
� Validation
� Application� TSTC coil
� Racetrack coil
� Reobel cable
14
Application-TSTC coil
5 strands TSTC cable coil
15
Application-TSTC coil
50 mT, 50 Hz16
J
Jc
� Magnetisation� width=5mm, thickness d =1µm� n=21, Jc = 1010A/m2
3 hours
Application-Racetrack coil
AC loss
| B |
17
� Current can be applied in complex geometry� Current distribution, magnetic field and loss
can be calculated
mT
W/m2
J
Jc
Application-Roebel
� Magnetisationof a full pitch Roebel cable� Dimension: length = 40mm, thickness d =1µm� n=21, Jc = 1010A/m2
18
Application-Roebel
19
20 mT, 50 Hz
Conclusions
� A new 3D FEM is presented
� Validated by analytical and FEM results
� Very efficient compared with existing models
• A powerful tool to model assembled 2G HTS cables
and magnets
20
Application-Roebel
22
twisted > untwisted
shielding in untwisted