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UNIVERSIDADE FEDERAL DO RIO DE JANEIRO Escola … · Flávio Goulart dos Reis Martins Felipe Sass,...
Transcript of UNIVERSIDADE FEDERAL DO RIO DE JANEIRO Escola … · Flávio Goulart dos Reis Martins Felipe Sass,...
Flávio Goulart dos Reis Martins
Felipe Sass, Rubens de Andrade Jr.
June 29th, 2018
Laboratório de Aplicação de SupercondutoresLaboratory for Applied Superconductivity
Universidade Federal do Rio de JaneiroFederal University of Rio de Janeiro
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
Presented last year...
Jointless loops made from REBCO tapes: Double Crossed Loop
04 / 28
1.1. Background
Intro
F. Martins, et al., “A novel magnetic bearing using 2G double crossed loops”. IEEE TAS, 2018
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
1.1. Background
Presented last year...
Jointless loops made from REBCO tapes: Double Crossed Loop
PMG
First Prototype DCL Coils20 double loops each
Levitation Tests and Simulations
Prototype SML Bearing
F. Martins, et al., “A novel magnetic bearing using 2G double crossed loops”. IEEE TAS, 2018
05 / 28Intro
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
Developed for substitute YBCO bulks in levitation...
1.2. Motivations
MagLev Cobra
SML Bearings
YBCO Bulk Cryostats
06 / 28Intro
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
Developed for substitute YBCO bulks in levitation...
1.2. Motivations
Actual Cryostat New Cryostat Concept
07 / 28Intro
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
... but today we glimpse more applications:
1.2. Motivations
TRANSPORTATION
ENERGY STORAGE
MACHINES
SFCLsMagLev Cobra
Cryostats
FlywheelRotational bearings
InductiveAir-coil type
Field Coils inGeneratorsand Motors
08 / 28Intro
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
1.3. Objectives
In this work, we intend to:
• Simulate DCL coils as SML bearings for the MagLev Cobra
• Analyze some design parameters to try to enhance the
(tape consumption)/(levitation force) ratio.
• Improve the simulation technique to better reproduce the
measured results in prototypes.
09 / 28Intro
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
2.1. Integral Equations Method
x
y
z
h
w
x
y
z
Jz(x,y,t) Kz(x,t)
H(x,y,t) H(x,t)
w
𝐾𝑧(𝑥, 𝑡) = න
−ℎ/2
ℎ/2
𝐽𝑧 𝑥, 𝑦, 𝑡 𝑑𝑦
R. Brambilla, et al., “Integral equations for the current density in thin conductors and their solution by the finite-element method”, IEEE TAS, 2008
Taking advantage of the tape’s geometry by considering
it a 1D current sheet: 𝐾𝑧(𝑥, 𝑡)
𝜕𝐻(𝑥, 𝑦, 𝑡)
𝜕𝑦= 0
𝜕𝐽𝑧(𝑥, 𝑦, 𝑡)
𝜕𝑦= 0
11 / 28Model
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
2.1. Integral Equations Method
The integral equation that solves 𝐾𝑧(𝑥, 𝑡):
𝐾𝑧 𝑥, 𝑡 =
𝜌𝐾𝑧 𝑥, 𝑡 = 𝜏 𝑎(𝑥, 𝑡) + 𝑏(𝑥, 𝑡) + 𝑐(𝑡)
Induced currents due to the external field variation
Induced currents due to the self-field variation
A term independent from x attributed to the current
constraint
𝜇0ℎ
𝜌න− Τ𝑤 2
𝑥
ሶ𝐻𝑒𝑥𝑡 𝜉, 𝑡 𝑑𝜉 + න− Τ𝑤 2
Τ𝑤 2 ൯ሶ𝐾𝑧(𝑢, 𝑡
2𝜋𝑙𝑛 𝑢 − 𝑥 𝑑𝑢 − න
− Τ𝑤 2
Τ𝑤 2 ൯ሶ𝐾𝑧(𝑢, 𝑡
2𝜋𝑙𝑛 𝑢 + Τ𝑤 2 𝑑𝑢
𝜌 =𝐸𝑐
𝐽𝑐(𝐵‖, 𝐵⊥)
𝐾𝑧(𝑥, 𝑡)
ℎ 𝐽𝑐(𝐵‖, 𝐵⊥)
𝑛−1 𝐽𝑐 𝐵‖, 𝐵⊥ =𝐽𝑐0
1 + ൗ𝑘𝐵‖2+ 𝐵
⊥
2 𝐵𝑐
𝑏
F. Grilli, et al., “Self-Consistent Modeling of the Ic of HTS Devices: How Accurate Models Really Need to Be?” IEEE TAS, 2014
12 / 28Model
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
2.2. Modelling the DCL Coils
The current continuity constraint:
A1
A2
B1
C1 D1
C2 D2
B2
න𝐴1
𝐾𝑧𝐴1𝑑𝑦 + න𝐴2
𝐾𝑧𝐴2𝑑𝑦 = 0
න𝐵1
𝐾𝑧𝐵1𝑑𝑦 + න𝐵2
𝐾𝑧𝐵2𝑑𝑦 = 0
න𝐶1
𝐾𝑧𝐶1𝑑𝑦 + න𝐶2
𝐾𝑧𝐶2𝑑𝑦 = 0
න𝐷1
𝐾𝑧𝐷1𝑑𝑦 + න𝐷2
𝐾𝑧𝐷2𝑑𝑦 = 0
x
y
z
13 / 28Model
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
INNERMOST → OUTTERMOST
LEFT → RIGHT
2.2. Modelling the DCL Coils
The current continuity constraint:
What makes the DCL coil different from conventional ones?
Concentric Rings Double Pancake
Double Crossed Loops
REBCO COIL CROSS-SECTION HOMOGENIZATION
Axissymetric current distribution
Can it be homogenized?
Discretize every tape nevertheless!
14 / 28Model
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
2.2. Modelling the DCL Coils
Integral Equations (IE) solved by Finite Elements (FE) method
1D and 2D coupling:
Drawback:neglects coil head effects
F. Grilli, et al., “Current Density Distribution in Multiple YBCO Coated Conductors by Coupled Integral Equations”, IEEE TAS, 2009
A1 1D Simulation
2D Simulation:Background
A1
A2
B1
C1 D1
C2 D2
B2
Current Continuity Constraint
A2 1D Simulation
B1 1D Simulation
B2 1D Simulation
C1 1D Simulation
C2 1D Simulation
D1 1D Simulation
D2 1D Simulation
SimulationsCoupling
15 / 28Model
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
2.3. Modelling the Magnets
Magnets displacement: Moving Mesh = TROUBLE!
Bypassed by splitting the simulatio in two:
Magnets Cross-section
Moving Mesh domain
x
y
z
Az1(x,t)Az2(y,t)
Az3(x,t)
Az4(y,t)
Az1(x,t)
x
y
z
Reduced Simulation
Az3(x,t)
Az4(y,t) DCL Coils Cross-section
Bo
un
dary:
Perfect Magn
etic Co
nd
ucto
r
to .txt files
to boundaries
16/ 28Model
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
Number of Xloops (N), inner width (w), stacking factor (d)
3.1. Design Parameters
4981
3014
1574
649319151
NF at 20 mm
(N / m)
F per DCL
(N / m / DCL)
2 151 75,5
5 319 63,8
10 649 64,9
25 1574 63,0
50 3014 60,3
100 4981 49,8
It’s not only about stacking the more tapes you could!
w
d
The more tapes, the more it
behaves like a bulk
18 / 28Results
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
3.1. Design Parameters
Number of Xloops (N), inner width (w), stacking factor (d)
wwwww
N = 25 Xloopsd = 0.4 mm
Lin
ear
Forc
e D
ensi
ty [
N/m
]
Position [mm]
Linear variatio
n...
No
n-l
inea
r ga
in!
The greater the flux linkage, the
greater the force.
w
d
19 / 28Results
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
3.1. Design Parameters
Number of Xloops (N), inner width (w), stacking factor (d)
Position [mm]
Lin
ear
Forc
e D
ensi
ty [
N/m
]
N = 25 Xloopsw = 12.5 mm
Linear variatio
n...
More significant than w increase,
however...
No
n-lin
ear gain!
... hysteresis increases too!
w
d
20 / 28Results
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
3.1. Design Parameters
Non-linear relations led to parametric simulations (54 variations).M
axim
um
Lin
ear
Forc
e D
ensi
ty @
20
mm
[N
/m]
Inner width (w) [mm]
+17%
+23%
+32%
Prototype coils:N = 25
w = 27.5 mm d = 0.2 mm
21 / 28Results
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
3.2. Simulations vs Measurements
Prototype tests: vertical displacement towards magnets in LN2
LOAD CELL
HOLDER
DCL COILS
PERMANENT MAGNET ARRAY
VER
TICA
L DISP
LAC
EMEN
T
2 DCL coils25 Xloops each11.125 m tape per coilSuperPower SF12050 (2012)
22 / 28Results
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
25 DCL prototype coil pair force characteristics
3.2. Simulations vs Measurements
Good agreement!
23 / 28Results
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
Trying improve the agreement...
3.2. Simulations vs Measurements
𝐽𝑐 𝐵‖, 𝐵⊥ =𝐽𝑐0
1 + ൗ𝑘𝐵‖2+ 𝐵
⊥
2 𝐵𝑐
𝑏
Lost the form fitting...
24 / 28Results
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
A simulation model for DCL coils is proposed and tested for
designing a SML bearing application.
• There are design variables that increase the levitation
force other than simply increasing the number of tapes.
• These variables effects are non-linear. Optimization
requires parametric simulations.
• The model does not match the values of the measured
force, but reproduce its behavior.
4. Conclusions
26 / 28Conclusions
29/06/2018Simulations of REBCO Tapes Double Crossed Loops Coils with Integral Equations MethodFlávio Goulart dos Reis Martins, D. Sc. [email protected]
Next steps (concerning simulations):
• Find a set of 𝐽𝑐 𝐵‖, 𝐵⊥ parameters (or even another
function) that allows a better reprodution of measured
results;
• Implement a 3D simulation to allow accounting for coil
head effects (leave Integral Equations?);
• Investigate other applications...
4. Conclusions
27 / 28Conclusions
Thank you for your atention!
Flávio Goulart dos Reis Martins
Laboratório de Aplicação de SupercondutoresLaboratory for Applied Superconductors
Universidade Federal do Rio de JaneiroFederal University of Rio de Janeiro