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Quench Modelling Nb3Sn magnets: Longitudinal quench propagation
Susana Izquierdo Bermudez. 29-04-2014
Important because it determines the time needed to quench the whole magnet cross section
Important because it determines the time needed to detect a normal zone
Important because it defines the time needed to induce a distributed quench
11T and QXF are pushing the boundary of protection we need a good understanding of the dominating physics
Very different time and space scales
Different strongly coupled physics domains
Important dependence on very non-linear material properties
Longitudinal quench propagation
Heat transfer from heater to coil
Heat transfer within the coil
Let’s try to understand it bit by bit…
2
3
Models overviewROXIE QUENCH MODULE [Sch 2010]
Couples magnetic, electrical and thermal. First order thermal network (2D (XSec) + 1 (z*))
*Requires small element size (<1mm) in the longitudinal direction to converge in terms of longitudinal quench propagation velocity
SUPERMAGNET [Bot 2007]Built by different blocks with an unified interface for data exchange.
THEA [Bot 2010]Thermal, Hydraulic and Electric analysis of superconducting cablesAdaptive mesh tracking
HEATER [Bot 2010]FE heat conduction
POWER [Bot 2004]Electric network simulation of magnetic systems
Under the same assumptions…very close propagation velocity (not the case for Tmax!)
2 3 4 5 6 7 8 9 10 11 120
5
10
15
20
25THEA
B [T]
Que
nch
Prop
agati
on
Spee
d (m
/s)
T Mesh density
11T, I=11850 A
4
Modelling: Thermal Coupling𝜌𝐶𝑣 (𝑇 ,𝐵 ) 𝑑𝑇𝑑𝑡 =�̇� 𝑗𝑜𝑢𝑙𝑒+𝛻 ∙ (𝑘𝑇 (𝑇 ,𝐵)𝛻𝑇 )
[Gav 1992]
First Order Thermal Coupling
Higher Order Thermal Coupling
Hybrid model
Heat capacity Thermal resistanceCu+SC Insulation
Cp=Cpcond Cp=Cpcond+Cins
Option 1 Option 2
[ROXIE]
FE mesh (insulation)
Coupling
Conductor
5
Modelling: coupling heat conduction domainsHEATER : Heat conduction in the insulation is solved in 2D cross sections THEA: Thermal and Electrical analysis of the superconductor cable
Explicit coupling conditionally stable. Small heat capacity and large thermal conductance requires small time steps for the stability of the coupling
Heat flow from/to the insulationJoule heatingTemperature in the SC
Δz
2D quadrilateral elements with 4 nodes and first order shape function
Example: HEATER : Δz=20 mm tstep=[10-6 10-3] s THEA : Δz=0.3mm-100mm tstep=[10-7 10-4] s
6
5 10 15 20 25 300
10
20
30
40
50
60
70
t [ms]
T [K
]
Turn where quench starts
NetworkFE mesh
5 10 15 20 25 300
10
20
30
40
50
60
70
t [ms]
T [K
]
Adjacent Turn
NetworkHybrid
Modelling: Network model vs Hybrid model11T Cable, B = 11.3 T, I = 11850 AQuenched initiated in the middle turn of a stack of three cable
Network Model Hybrid Model DiffTmax @ t=30 ms [K] 66 68 3 %
Turn2Turn propagation (ms) 4 3 25 %
Longitudinal quench propagation velocity (m/s) 23 22 4%
0 5 10 15 20 25 300
1
2
3
4
5
t [ms]
Que
nche
d Le
ngth
[m]
NetworkHybrid
Negligible impact of the thermal coupling method on the longitudinal quench propagation
Preliminary results
Preliminary results
Preliminary results
7
Validation of the model
SMC 11T (H. Bajas): Pole turn @ 1.9 K I=12936 A (Bp=11.3 T) v= 27 m/s
SMC3 (H. Bajas): Pole turn @ 1.9 K & 4.4 K, I ≈ 11.5-14.2kA
MBHSM01 (G. Chlachidze): Outer layer mid-plane turn @ 4.5 K I ≈ 5-12kA
MBHSP01(G. Chlachidze): Inner layer pole turn @ 4.5 K I =73% v ~27 m/s
Available experimental data
HQ01d (M. Marchevsky)Training quenches. I = 14.3 kA v=11.4 m/s
I = 13.6 kA v=9.4 m/s
Experimental data
100 150 200 250 300 350 4000
5
10
15
20
25
30SMC3 (1.9K)SMC3 (4.4K)MBHSM01 (4.5K)MBHSP01 (4.5K)HQ01d (4.4K)SMC11T (1.9 K)HQ02b (4.4K)
Jop/(Tjoule-Top)1/2 [A/mm2/K0.5]
Mea
sure
d pr
opag
ation
vel
ocity
[m/s
]
𝑣 𝑎𝑑=𝐽 𝑜𝑝
(𝛾 𝐶 )𝑎𝑣 ( (𝜌𝑘)𝑎𝑣𝑇 𝑗𝑜𝑢𝑙𝑒−𝑇𝑜𝑝 )
1 /2
8
𝑣 𝑎𝑑 𝐽 𝑜𝑝(𝑇 𝑗𝑜𝑢𝑙𝑒−𝑇𝑜𝑝 )1/2
= = 0 5 10 15
0
1
2
3
4
5
6x 104
T [K]
Cp
[J/K
m3 ]
CuNb3SnDon’t forget that the material properties strongly depend
on the temperature and field, and change by several order of magnitudes!
9
Comparison to SMC measured data
8 9 10 11 12 13 14 150.05.0
10.015.020.025.030.035.040.045.050.0
SMC3 1.9 KConductor + Insulation
Only conductor
Experimental data
I [kA]
v (m
/s)
8 9 10 11 12 13 14 150.05.0
10.015.020.025.030.035.040.045.050.0
SMC3 4.2 KConductor + Insulation
Only conductor
Experimental data
I [kA]
v (m
/s)
Conductor onlyConductor + insulation
Measured longitudinal propagation velocities in SMC11T and SMC3 are close to numerical data when considering the heat capacity of insulation + conductor.
Remark: natural quenches in the high field region
Experimental data H. Bajas
10
Comparison to 11T measured data
The 11T mirror magnet tested at FNAL shows velocities ~2.5
times larger than the ones predicted by the model
I[kA]
Bpeak, OL mid-plane[T]
5 2.657 3.449 4.25
12 5.50
Spot heater test in the outer layer mid-plane turn
5 6 7 8 9 10 11 120.0
5.0
10.0
15.0
20.0
25.0MBHSM01 4.2 K
Only conductor
Conductor + Insulation
Experimental data
I [kA]
v (m
/s)
Experimental data G. Chlachidze
1112 13 14 15 16 17 18 19 20
1
10
100HF (only conductor)HF (Conductor + Insu-lation)LF (Only Conductor)LF (Conductor+Insulation)
I (kA)
v (m
/s)
Expected long. propagation QXF
T = 1.9 K
Field @ I=Inom=17.5kA
I (kA) Bp [T](HF: Pole turn IL)
Bp [T](LF: Mid plane turn OL)
12 8.5 3.414 9.8 4.116 11.1 4.918 12.4 5.720 13.7 6.5
Inom
12
REFERENCES• MATERIAL PROPERTIES
• [Man 2011] G. Manfreda, Review of ROXIE's Material Properties Database for Quench Simulation• [TD Note ----] TD Note 00-041, Material properties for quench simulation• [Dav ----] A. Davies, Material properties data for heat transfer modelling in Nb3Sn magnets
• EXPERIMENTAL DATA
• [Mar 2012] M. Marchevsky. Quench Performance of HQ01, a 120 mm Bore LARP Quadrupole for the LHC Upgrade
• MODELLING
• [Bot 2004] Power. User’s Guide. CryoSoft, Ver. 2.0; 2004• [Bot 2007] SuperMagnet. User’s Guide. CryoSoft, Ver. 1.0; 2007• [Bot 2010] Thea. User’s Guide. Cryosoft, Ver. 2.1; 2010• [Bot 2010] Heater. User’s Guide. Cryosoft, Ver. 2.0; 2010• [Bot 2013] L. Bottura, Magnet Quench 101, WAMSDO CERN 2013• [Gav 1992] A. Gavrilin, Cryogenics, 32 (1992), 390-393• [Rus 2008] S. Russenschuck. Field Computation for Accelerator Magnets• [Sch 2010] Numerical Calculation of Transient Field Effects in Quenching Superconducting Magnets. PhD
Thesis
Additional slides
14
Cable Data
DATA BEFORE REACTION# strands Strand diameter Cu/nCu Cable width Bare Cable Mid-Thickness Insulation thickness
- mm - mm mm mmSMC3 14 1.25 1.25 9.9 2.2 0.1
SMC 11T 40 0.7 1.25 14.99 1.305 0.1511T 40 0.7 1.15 14.7 1.25 0.15HQ 35 0.778 1.13 15.15 1.437 0.1QXF 40 0.85 1.13 18.15 1.525 0.15
15
Modelling: length scale
2 Principal directions: longitudinal and transverse
Longitudinal length scale: hundreds of mCable is a continuum “relatively easy” to solve with accurate (high order) and adaptive (front tracking) methods
Transverse length scale: mmHeat diffusion across the insulation
16
Modelling: time scale
• Heat flow• Heat flow from supports and structures 1 s• Heat flow in the coil winding 1 s• Heat flow along the cable 100 µs
• Electro-magnetics• Steady and transient coil currents 1 s• Steady and transient magnetics fields 1 s• Current distribution in the cable 1 ms• Steady and transient magnetization 10 µs
17
Conductor only
Conductor/insulation
Conductor+insulation
18
Network
FE mesh
19
Network vs Mesh. Joule heating
0 10 20 300
0.5
1
1.5
2
2.5
3
3.5 x 104
t [ms]
QJ
[W/m
]
Turn where quench starts
NetworkFE mesh
0 10 20 300
0.5
1
1.5
2
2.5
3 x 104
t [ms]
QJ
[W/m
]
Adjacent Turn
NetworkHybrid
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Material Properties
0 100 200 30010
-10
10-9
10-8
10-7
T [K]
Ele
ctric
al R
esis
itivi
ty [o
hm*m
]
Cu
CUDI&HugoMATPRONIST&Ezio&Cryosoft
0 100 200 30010
2
104
106
108
T [K]
Hea
t Cap
acity
[J/K
*m3]
Cu
CUDIMATPRONISTEzioHugoCryocomp
0 100 200 30010
0
102
104
106
108
T [K]
Hea
t Cap
acity
[J/K
*m3]
Nb3Sn
CUDIMATPROEzioHugoCryocomp
0 100 200 30010
0
102
104
106
108
T [K]
Hea
t Cap
acity
[J/K
*m3]
G10
NIST&HugoEzioCryocompFermilab
21
Material Properties
100
101
102
10310
-10
10-9
10-8
10-7
T [K]
Ele
ctric
al R
esis
itivi
ty [o
hm*m
]Cu
CUDI&HugoMATPRONIST&Ezio&Cryosoft
100
101
102
10310
2
104
106
108
T [K]
Hea
t Cap
acity
[J/K
*m3]
Cu
CUDIMATPRONISTEzioHugoCryocomp
100
101
102
10310
0
102
104
106
108
T [K]
Hea
t Cap
acity
[J/K
*m3]
Nb3Sn
CUDIMATPROEzioHugoCryocomp
100
101
102
10310
0
102
104
106
108
T [K]
Hea
t Cap
acity
[J/K
*m3]
G10
NIST&HugoEzioCryocompFermilab
22
Sensibility to material properties
Electrical ResistivityCopper Cu Nb3Sn G10CUDI (1) CUDI (1) CUDI (1)MATPRO (2) MATPRO (2) MATPRO(2)NIST (3) NIST (3) NIST (3)
Ezio (4) Ezio (4) Ezio (4)Hugo (5) Hugo (5)CRYOCOMP (6) CRYOCOMP (6) CRYOCOMP (6)
FERMILAB(7)
delta MIITs delta MIITs [%] Comments
1113 13.742113 14.27 0.53 3.863113 15.07 1.33 9.681213 13.74 0 0.001313 13.74 0 0.001413 13.76 0.02 0.151513 14.25 0.51 3.711613 13.65 -0.09 -0.661123 15 1.26 9.171143 15.12 1.38 10.041153 14.4 0.66 4.801163 14.99 1.25 9.101114 13.67 -0.07 -0.511116 14.13 0.39 2.841117 14.25 0.51 3.711553 14.90 1.16 8.44 (HugoMP)3666 16.78 3.04 22.11 (Cryocomp MP)3444 16.53 2.79 20.33 (Ezio MP)3323 16.45 2.71 19.73 (Susana MP)
Heat capacity
Electrical ResistivityCopper Cu Nb3Sn G10CUDI (1) CUDI (1) CUDI (1)MATPRO (2) MATPRO (2) MATPRO(2)NIST (3) NIST (3) NIST (3)
Ezio (4) Ezio (4) Ezio (4)Hugo (5) Hugo (5)CRYOCOMP (6) CRYOCOMP (6) CRYOCOMP (6)
FERMILAB(7)
CASE [resCu, CpCu,CpNb3Sn,CpG10]
MIITs for Tmax=300K
delta MIITs delta MIITs [%] Comments
1113 13.742113 14.27 0.53 3.863113 15.07 1.33 9.681213 13.74 0 0.001313 13.74 0 0.001413 13.76 0.02 0.151513 14.25 0.51 3.711613 13.65 -0.09 -0.661123 15 1.26 9.171143 15.12 1.38 10.041153 14.4 0.66 4.801163 14.99 1.25 9.101114 13.67 -0.07 -0.511116 14.13 0.39 2.841117 14.25 0.51 3.711553 14.90 1.16 8.44 (HugoMP)3666 16.78 3.04 22.11 (Cryocomp MP)3444 16.53 2.79 20.33 (Ezio MP)3323 16.45 2.71 19.73 (Susana MP)
?
For SMC-11T cable, MIITs to reach 300 K under adiabatic conditions vary from 14 to 17.5 depending on the material properties database
SMC 11T, B= 12T , RRR=100
23
Material Properties Cryosoft [1.9-15 K]
0 5 10 152
3
4
5
6
7
8 x 10-10
T [K]
Ele
ctric
al R
esis
itivi
ty C
u [
m]
RRR=50, B=2RRR=100, B=2RRR=50, B=12RRR=100, B=12
0 5 10 150
200
400
600
800
1000
1200
1400
1600
1800
T [K]
Ther
mal
Con
duct
ivity
Cu
[W/K
m]
RRR=50, B=2RRR=100, B=2RRR=50, B=12RRR=100, B=12
0 5 10 150
1
2
3
4
5
6 x 104
T [K]
Cp
[J/K
m3 ]
CuNb3Sn
0 5 10 152
3
4
5
6
7
8 x 10-10
T [K]
Ele
ctric
al R
esis
itivi
ty C
u [
m]
RRR=50, B=2RRR=100, B=2RRR=50, B=12RRR=100, B=12
0 5 10 150
200
400
600
800
1000
1200
1400
1600
1800
T [K]
Ther
mal
Con
duct
ivity
Cu
[W/K
m]
RRR=50, B=2RRR=100, B=2RRR=50, B=12RRR=100, B=12
0 5 10 150
1
2
3
4
5
6 x 104
T [K]
Cp
[J/K
m3 ]
CuNb3Sn
24
ROXIE Quench Module
Heat capacity: includes conductor + insulation
Thermal conductance and heat fluxes: Conductor without insulation. Uniform temperature in the conductor and linear temperature distribution in between them
Thermal network:
25
Current sharing and Joule heating
TTcsTop Tc
Iop
current in stabilizer
current in superconductor
TTcsTop Tc
26
Higher order thermal coupling for MBHSM01 (Supermagnet)
1. Spot heater provoked quench
3. Quench OL pole turn (t=29 ms)
4. OL fully quenched
Quench pole turn IL (longitudinal propagation)
Quench IL HF(transversal)
Quench IL LF(transversal)0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 0.160 0.180 0.200
0
50
100
150
200
250
300
Experimental points
OL mid plane
IL mid plane
IL pole
OL pole
OL mid plane
time (s)
T co
nduc
tor [
K]
Looking at the delays …• The first conductor that quenches thanks to the quench
heaters, quench at the measured delay: 29 ms (heater delay defined accordingly to satisfy this)
• All the OL quenches within ≈ 7 ms• Quench travels very fast from OL to IL thanks to the
longitudinal propagation (≈ 2 ms)• IL-OL delay due to transversal propagation is ≈ 20 ms in
the HF (Bp=9.5T) and about ≈25 ms in the LF (Bp=8.5T)
27
MBHSM01. Spot heater testMIITs T
MEASURED
TMAX ANALYTIC(B=5.5
RRR=100)
TMAX FIRST ORDER THERMAL
COUPING(ROXIE)
TMAX HIGHER ORDER THERMAL
COUPING(SUPERMAGNET)
8 92 82 88 7410 118 105 117 9912 142 136 156 13414 180 175 205 185
I = 12 kA
8 9 10 11 12 13 14507090
110130150170190210230250
T MEASURED T analyticT ROXIE T SuperMagnet
MIITs
Tmax
[K]