Fast 2D Simulation of Superconductors: a Multiscale ... - Comsol

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Nov 15, 2013 (3 years and 7 months ago)

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Fast 2D Simulation of Superconductors: 
a Multiscale Approach
Victor M. Rodriguez‐Zermeno
1, Mads P. Sørensen
1, Niels Falsig Pedersen
2, Nenad 
Mijatovic
2
and Asger B. Abrahamsen
3
1
2
3
Presented at the COMSOL Conference 2009 Milan
Motivation
PhD Project: Computation of Superconducting Wind 
Turbine Generators.
Wire architecture
4.5 mm
0.2 mm
Substrate
Stabilizer coating
Substrate
Superconducting
layer ~ 1 μm
Solder
Governing equation
E‐J relationship in Superconductors
c
EE
/
1.5
c
/
1.0
0.5
00
05
10
15
0.0
c
J
J
/
0
.
0
0
.
5
1
.
0
1
.
5
c
Use of COMSOL
Conditions and Restrictions
Using Free Meshes
17150 elements in the Superconducting region
Using Mapped Meshes
Only 150 elements!
Calculation of AC losses
Results
Validation of Results
* R. Brambillaet al2008Supercond. Sci. Technol.21105008 (8pp)
Computing Time
* R. Brambillaet al2008Supercond. Sci. Technol.21105008 (8pp)
Externally applied field and current
MagneticFieldIntensity(peakvalue
shown)forathinsuperconductor
whenasinusoidalMagneticFieldof
2
T
(
1
6
3
A/)
i
lid
2
m
T
(
~
1
.
6
e
3
A/
m
)
i
sapp
li
e
d
.
Noexternalcurrentapplied.
Externalcurrentapplied
(80%criticalcurrent).
Interaction among several thin conductors
Top:Silver,noexternalcurrent.Center:superconducting,imposedACtransportcurrent
(
0.9I
c
,
50Hz
)
.Bottom:su
p
erconductin
g,
noexternaltrans
p
ortcurrent.Noticehowthe
(
,
)
pg,
p
fieldisexpelledfromthebottomconductor.
Stack of tapes
AC
electric
currents
(
0
9
Ic
50
Hz
in
phase)
are
applied
to
a
stack
of
15
coated
AC
electric
currents
(
0
.
9
Ic
,
50
Hz
,
in
phase)
are
applied
to
a
stack
of
15
coated
conductors.Magneticfieldstrengthat0phase(left)andatpeakvalue(right).A
substratewitharelativepermeabilityof50wasconsidered.Theinsertshowsthe
thicknessofthedifferentlayers.
AC losses in a stack of tapes
InstantaneousAClossesinthepreviousstackoftapes(bothphasesareshowninthe
insert).Considertapestobeenumeratedfromthetop.Observethatthehigherlosses
areexperiencedbythecentralconductors.Also,noticethatthetopconductors(tapes1,
2
d
3
)
i
l
l
h
hi
b
(
d
3
)
2
an
d
3
)
exper
i
ence
l
ess
l
osst
h
ant
h
e
ir
b
ottomcounterparts
(
tapes15,14an
d
1
3
)
.
Conclusions
Usemappedmeshesandspecifically,useoflargeaspectratioelements,
providesaconsiderableincreaseinthecomputingspeedforcalculationof
AClossesinsu
p
erconductors.Numericalsimulationswere
p
erformed
p
p
showingadecreaseof2to3ordersofmagnitudeinthecomputingtime
whencomparedwithother2Dsimulationwerenomappedmeshesare
used.
Th
ti
t
dli
il
liti
hil
i
l
t
Th
e
ti
mespen
t
mo
d
e
li
ngeverys
i
ng
l
eapp
li
ca
ti
onw
hil
eus
i
ng
l
argeaspec
t
ratioelementsdoesnotdependheavilyinthenumberofconductorsand
offers“similar”computingtimethanthe1Dformulation.Therefore,the
workpresentedhereoffersafastertimetosolutionstrategyfor
calculating
AC
losses
calculating
AC
losses
.
Finally,theeasetosetaproblemusingtheproposedformulationmakes
itpossibletothinkoffurtherapplicationssuchassuperconductingcoils,
andinductionmachiner
y,
amon
g
othersinthenearfuture.
y,
g
Thank You!
Thank You!
References
1.Superconductor, American.Superconductor Motors & Generators. [Online] [Cited: September 1, 2009.]
http://www.amsc.com/products/motorsgenerators/index.html
.
2.5 MW High Temperature Superconductor Ship Propulsion Motor Design and Test Results. Eckels, P. W., Snitchler, G.Naval Engineers
Journal, Vol. 117, No. 4. (2005), pp. 31-36.
3.Basic concepts, status, opportunities, and challenges of electrical machines utilizing high-temperature superconducting (HTS) windings. J
Frauenhofer, J Grundmann, G Klaus and W Nick.2008, 8th European Conference on Applied Superconductivity (EUCAS 2007) J. Phys.:
Conf. Ser. 97 012189.
4.Numerical analysis of high-temperature superconductors with the critical-state model. Farinon, S. Fabbricatore, P. Gomory, F. Greco, M.
SilE
IEEETiAlidSdiiJ2005Vl15I2P32867
2870
S
e
il
er,
E
.
IEEE

T
ransact
i
ons on
A
pp
li
e
d

S
upercon
d
uct
i
v
i
ty
J
une
2005
,
V
o
l
ume:
15
,
I
ssue:
2
,
P
art
3
, pages:
2867
-
2870
.
5."Numerical Evaluation of AC Losses in HTS Wires With 2D FEM Formulated by Self Magnetic Field". Kazuhiro Kajikawa, Toshihiro
Hayashi, Ryoji Yoshida, Masataka Iwakuma, and Kazuo Funaki,.IEEE TRANS. ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO.
2, JUNE 2003.
6.AC losses in high-temperature superconductors: revisiting the fundamentals of the loss modelling. Lahtinen, Jaakko Paasi and Markku.
Physica C: Superconductivity Volume 310, Issues 1-4, December 1998, Pages 57-61.
7.Numerical modelings of superconducting wires for AC loss calculations. Naoyuki Amemiya, Shun-ichi Murasawa, Nobuya Banno and
Kengo Miyamoto.Physica C: Superconductivity Volume 310, Issues 1-4, December 1998, Pages 16-29.
8.“Development of an edge-element model for AC loss computation of high-temperature superconductors”. R. Brambilla, F. Grilli, and L.
Martini.Superconductor Science and Technology, vol. 20, pp. 16–24, 2007.
9.ACDC Module/Model Library/Superconducting wire. FILES, COMSOL DOCUMENTATION.
10.Inte
g
ral e
q
uations
f
or the current densit
y
in thin conductors and their solution b
y
the
f
inite-element method. Roberto Brambilla
,
Francesco
gqfyyf
,
Grilli, Luciano Martini and Frédéric Sirois. Superconductor Science and Technology (2008) Volume 21, Number 10.