UNIVERSIDADE FEDERAL DO RIO DE JANEIRO Escola … · Flávio Goulart dos Reis Martins Felipe Sass,...

Good Afternoon!

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

1. Introduction

Research background

Motivations

Objectives

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


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


Developed for substitute YBCO bulks in levitation...

1.2. Motivations

MagLev Cobra

SML Bearings

YBCO Bulk Cryostats

06 / 28Intro


Developed for substitute YBCO bulks in levitation...

1.2. Motivations

Actual Cryostat New Cryostat Concept

07 / 28Intro


... 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


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

2. Numerical Modelling

Integral Equations Method

Modelling the DCL Coils

Modelling the Magnets


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


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


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


INNERMOST → OUTTERMOST

LEFT → RIGHT


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



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


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

3. Results

Analyzing Design Parameters

Comparing Simulations to Measurements


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




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




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



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


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


25 DCL prototype coil pair force characteristics


Good agreement!

23 / 28Results


Trying improve the agreement...


𝐽𝑐 𝐵‖, 𝐵⊥ =𝐽𝑐0

1 + ൗ𝑘𝐵‖2+ 𝐵

⊥

2 𝐵𝑐

𝑏

Lost the form fitting...

24 / 28Results

4. Conclusions


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


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

[email protected]

Laboratório de Aplicação de SupercondutoresLaboratory for Applied Superconductors

Universidade Federal do Rio de JaneiroFederal University of Rio de Janeiro

UNIVERSIDADE FEDERAL DO RIO DE JANEIRO Escola … · Flávio Goulart dos Reis Martins Felipe Sass,...

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