Transcript Susana Izquierdo Bermudez. 29-04-2014 11T and QXF are pushing the boundary of protection  we need a good understanding of the.

Susana Izquierdo Bermudez. 29-04-2014
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
Let’s try to understand it bit by bit…
Longitudinal quench propagation
Heat transfer within the coil
Important because it determines the
time needed to detect a normal zone
Important because it determines
the time needed to quench the
whole magnet cross section
Heat transfer from heater to coil
Important because it defines the time
needed to induce a distributed quench
2
Models overview
ROXIE QUENCH MODULE [Sch 2010]
Couples magnetic, electrical and thermal.
First order thermal network (2D (XSec) + 1 (z*))
SUPERMAGNET [Bot 2007]
Built by different blocks with an unified
interface for data exchange.
THEA [Bot 2010]
Thermal, Hydraulic and Electric analysis of
superconducting cables
Adaptive mesh tracking
*Requires small element size (<1mm) in the
longitudinal direction to converge in terms of
longitudinal quench propagation velocity
T
Quench Propagation
Speed (m/s)
Under the same assumptions…very close
propagation velocity (not the case for Tmax!)
Mesh
density
25
THEA
ROXIE
20
HEATER [Bot 2010]
FE heat conduction
15
10
POWER [Bot 2004]
5
Electric network simulation of magnetic systems
11T, I=11850 A
0
2
7
B [T]
12
3
Modelling: Thermal Coupling
𝜌𝐶𝑣 𝑇, 𝐵
First Order
Thermal Coupling
𝑑𝑇
= 𝑄 𝑗𝑜𝑢𝑙𝑒 + 𝛻 ∙ (𝑘 𝑇 (𝑇, 𝐵)𝛻𝑇)
𝑑𝑡
Higher Order
Thermal Coupling
Hybrid model
[Gav 1992]
Option 1
Cp=Cpcond
Option 2
Cp=Cpcond+Cins
FE mesh
(insulation)
Conductor
Coupling
[ROXIE]
Cu+SC
Insulation
Heat capacity
Thermal resistance
4
Modelling: coupling heat conduction domains
HEATER : Heat conduction in the insulation is solved in 2D cross sections
THEA: Thermal and Electrical analysis of the superconductor cable
Δz
2D quadrilateral elements with 4 nodes
and first order shape function
Explicit coupling  conditionally stable. Small heat capacity and large thermal
conductance requires small time steps for the stability of the coupling
Example: HEATER : Δz=20 mm
THEA
: Δz=0.3mm-100mm
Temperature in the SC
tstep=[10-6 10-3] s
tstep=[10-7 10-4] s
Joule heating
Heat flow from/to the insulation
5
Modelling: Network model vs Hybrid model
11T Cable, B = 11.3 T, I = 11850 A
Quenched initiated in the middle turn of a stack of three cable
Network Model Hybrid Model
Tmax @ t=30 ms [K]
66
68
3%
Turn2Turn propagation (ms)
4
3
25 %
Longitudinal quench propagation velocity (m/s)
23
22
4%
Turn where quench starts
Adjacent Turn
70
70
Network
Hybrid
60
60
50
50
40
40
2
1
0
0
Preliminary
results
5
10
15
t [ms]
20
25
30
T [K]
3
T [K]
Quenched Length [m]
Network
Hybrid
Network
FE mesh
5
4
Diff
30
30
20
20
10
10
Preliminary
results
0
5
10
15 20
t [ms]
25
Preliminary
results
30
0
5
10
15 20
t [ms]
Negligible impact of the thermal coupling method on the
longitudinal quench propagation
25
6
30
Validation of the model
Available experimental data
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
HQ01d (M. Marchevsky)
Training quenches. I = 14.3 kA
I = 13.6 kA
MBHSP01(G. Chlachidze):
Inner layer pole turn @ 4.5 K I =73%
v ~27 m/s
MBHSM01 (G. Chlachidze):
Outer layer mid-plane turn @ 4.5 K
I ≈ 5-12kA
v=11.4 m/s
v=9.4 m/s
7
Measured propagation velocity [m/s]
Experimental data
30
𝑣𝑎𝑑
25
𝐽𝑜𝑝
𝜌𝑘 𝑎𝑣
=
𝛾𝐶 𝑎𝑣 𝑇𝑗𝑜𝑢𝑙𝑒 − 𝑇𝑜𝑝
𝑣𝑎𝑑~
20
𝐽𝑜𝑝
𝑇𝑗𝑜𝑢𝑙𝑒 − 𝑇𝑜𝑝
SMC3 (1.9K)
SMC3 (4.4K)
MBHSM01 (4.5K)
MBHSP01 (4.5K)
HQ01d (4.4K)
SMC11T (1.9 K)
HQ02b (4.4K)
1/2
1/2
15
10
5
0
100
150
200
250
300
350
Jop/(Tjoule-Top)1/2 [A/mm2/K0.5]
4
6
x 10
5
Cp [J/Km3]
Don’t forget that the material properties strongly depend
on the temperature and field, and change by several order
of magnitudes!
400
Cu
Nb3Sn
4
3
2
1
𝜌= 𝜌 𝑇, 𝐵, 𝑅𝑅𝑅
𝑘= 𝑘 𝑇, 𝐵, 𝑅𝑅𝑅
𝐶𝑝 = 𝐶𝑝(𝑇, 𝑇𝑐, 𝐵)
0
0
5
10
T [K]
8
15
Comparison to SMC measured data
Conductor + insulation
Conductor only
Measured longitudinal propagation velocities in SMC11T and SMC3 are close to
numerical data when considering the heat capacity of insulation + conductor.
50.0
45.0
40.0
35.0
30.0
25.0
20.0
15.0
10.0
5.0
0.0
SMC3 4.2 K
Conductor + Insulation
Only conductor
Experimental data
v (m/s)
v (m/s)
SMC3 1.9 K
8
9
10
11
12
I [kA]
13
14
15
50.0
45.0
40.0
35.0
30.0
25.0
20.0
15.0
10.0
5.0
0.0
Conductor + Insulation
Only conductor
Experimental data
8
9
10
11
12
13
14
15
I [kA]
Experimental data H. Bajas
Remark: natural quenches in the high field region
9
Comparison to 11T measured data
Spot heater test in the outer layer mid-plane turn
I
[kA]
5
7
9
12
Bpeak, OL mid-plane
[T]
2.65
3.44
4.25
5.50
MBHSM01 4.2 K
The 11T mirror magnet tested
at FNAL shows velocities ~2.5
times larger than the ones
predicted by the model
v (m/s)
25.0
Only conductor
20.0
Conductor + Insulation
15.0
Experimental data
10.0
5.0
0.0
5
7
I [kA]
9
11
Experimental data G. Chlachidze
10
Expected long. propagation QXF
I (kA)
12
14
16
18
20
Bp [T]
Bp [T]
(HF: Pole turn IL) (LF: Mid plane turn OL)
8.5
9.8
11.1
12.4
13.7
3.4
4.1
4.9
5.7
6.5
Field @ I=Inom=17.5kA
100
HF (only conductor)
HF (Conductor + Insulation)
LF (Only Conductor)
v (m/s)
LF (Conductor+Insulation)
10
T = 1.9 K
1
12
13
14
15
16
I (kA)
17
18
Inom
19
20
11
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
12
Cable Data
DATA BEFORE REACTION
# strands Strand diameter Cu/nCu Cable width Bare Cable Mid-Thickness
mm
mm
mm
14
1.25
1.25
9.9
2.2
SMC3
40
0.7
1.25
14.99
1.305
SMC 11T
11T
40
0.7
1.15
14.7
1.25
HQ
35
0.778
1.13
15.15
1.437
QXF
40
0.85
1.13
18.15
1.525
Insulation thickness
mm
0.1
0.15
0.15
0.1
0.15
14
Modelling: length scale
2 Principal directions:
longitudinal and transverse
Longitudinal  length scale: hundreds of m
Cable is a continuum “relatively easy” to solve
with accurate (high order) and adaptive (front
tracking) methods
Transverse  length scale: mm
Heat diffusion across the insulation
15
Modelling: time scale
•
Heat flow
•
•
•
•
Heat flow from supports and structures
Heat flow in the coil winding
Heat flow along the cable
1s
1s
100 µs
Electro-magnetics
•
•
•
•
Steady and transient coil currents
Steady and transient magnetics fields
Current distribution in the cable
Steady and transient magnetization
1s
1s
1 ms
10 µs
16
Conductor only
Conductor
/insulation
Conductor
+insulation
17
Network
FE mesh
18
Network vs Mesh. Joule heating
3.5
4
x 10 Turn where quench starts
3
4
3
x 10
Adjacent Turn
Network
Hybrid
Network
FE mesh
2.5
2.5
2
QJ [W/m]
QJ [W/m]
2
1.5
1.5
1
1
0.5
0.5
0
0
10
20
t [ms]
30
0
0
10
20
30
t [ms]
19
Material Properties
Cu
-7
-8
-9
10
CUDI&Hugo
MATPRO
NIST&Ezio&Cryosoft
Heat Capacity [J/K*m3]
Electrical Resisitivity [ohm*m]
10
10
-10
10
Cu
8
10
0
6
10
CUDI
MATPRO
NIST
Ezio
Hugo
Cryocomp
4
10
2
100
200
10
300
0
100
T [K]
Nb3Sn
8
Heat Capacity [J/K*m3]
Heat Capacity [J/K*m3]
10
6
10
4
10
CUDI
MATPRO
Ezio
Hugo
Cryocomp
2
10
0
0
300
G10
8
10
10
200
T [K]
6
10
4
10
NIST&Hugo
Ezio
Cryocomp
Fermilab
2
10
0
100
200
T [K]
300
10
0
100
200
300
T [K]
20
Material Properties
Cu
10
10
CUDI&Hugo
MATPRO
NIST&Ezio&Cryosoft
-8
10
-9
10
-10
10
Cu
8
Heat Capacity [J/K*m3]
Electrical Resisitivity [ohm*m]
-7
CUDI
MATPRO
NIST
Ezio
Hugo
Cryocomp
6
10
4
10
2
0
10
1
2
10
10
10 0
10
3
10
1
T [K]
10
Heat Capacity [J/K*m3]
Heat Capacity [J/K*m3]
3
10
G10
8
10
6
10
4
CUDI
MATPRO
Ezio
Hugo
Cryocomp
10
2
10
0
10 0
10
10
T [K]
Nb3Sn
8
2
10
6
10
4
10
NIST&Hugo
Ezio
Cryocomp
Fermilab
2
10
0
1
2
10
10
T [K]
3
10
10 0
10
1
2
10
10
3
10
T [K]
21
Sensibility to material properties
SMC 11T, B= 12T , RRR=100
Electrical Resistivity
Copper
Electrical
CUDI (1) Resistivity
Copper
MATPRO (2)
(1)
CUDI
NIST (3)
MATPRO (2)
NIST (3)
CASE
[resCu, CpCu,CpNb3Sn,CpG10]
CASE
1113
[resCu, CpCu,CpNb3Sn,CpG10]
2113
1113
3113
2113
1213
3113
1313
1213
1413
1313
1513
1413
1613
1513
1123
1613
1143
1123
1153
1143
1163
1153
1114
1163
1116
1114
1117
1116
1553
1117
3666
1553
3444
3666
3323
3444
3323
Cu
CUDI (1)
Cu
MATPRO (2)
(1)
CUDI
NIST (3)
MATPRO
Ezio (4) (2)
NIST
Hugo(3)
(5)
(4)
Ezio
CRYOCOMP
(6)
Hugo (5)
CRYOCOMP (6)
MIITs
for Tmax=300K
MIITs 13.74
for Tmax=300K
14.27
13.74
15.07
14.27
13.74
15.07
13.74
13.74
13.76
13.74
14.25
13.76
13.65
14.25
15
13.65
15.12
15
14.4
15.12
14.99
14.4
13.67
14.99
14.13
13.67
14.25
14.13
14.90
14.25
16.78
14.90
16.53
16.78
16.45
16.53
16.45
Heat capacity
Nb3Sn
capacity
Heat(1)
CUDI
Nb3Sn
MATPRO(2)
CUDI (1)
MATPRO(2)
Ezio (4)
Hugo (5)
(4)
Ezio
CRYOCOMP
(6)
Hugo (5)
CRYOCOMP (6)
G10
G10
NIST (3)
Ezio (4)
NIST (3)
(4)
Ezio
CRYOCOMP
(6)
FERMILAB(7)
CRYOCOMP (6)
FERMILAB(7)
?
delta MIITs
delta MIITs [%]
Comments
delta MIITs
0.53
1.33
0.53
0
1.33
0
0
0.02
0
0.51
0.02
-0.09
0.51
1.26
-0.09
1.38
1.26
0.66
1.38
1.25
0.66
-0.07
1.25
0.39
-0.07
0.51
0.39
1.16
0.51
3.04
1.16
2.79
3.04
2.71
2.79
2.71
delta MIITs [%]
3.86
9.68
3.86
0.00
9.68
0.00
0.00
0.15
0.00
3.71
0.15
-0.66
3.71
9.17
-0.66
10.04
9.17
4.80
10.04
9.10
4.80
-0.51
9.10
2.84
-0.51
3.71
2.84
8.44
3.71
22.11
8.44
20.33
22.11
19.73
20.33
19.73
Comments
(HugoMP)
(Cryocomp MP)
(HugoMP)
(Ezio MP)
(Cryocomp
(Susana MP)MP)
(Ezio MP)
(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
22
Material Properties Cryosoft [1.9-15 K]
-10
4
6
5
4
Thermal Conductivity Cu [W/Km]
RRR=50, B=2
RRR=100, B=2
RRR=50, B=12
RRR=100, B=12
Electrical Resisitivity Cu [ m]
1400
1200
RRR=50, B=2
RRR=100, B=2
RRR=50, B=12
800 RRR=100, B=12
1000
600
400
1400
1200
1000
800
600
T [K]
2
15 0
0
0 5
x 10
Cu
Nb3Sn
5
4
4
3
3
2
2
1
1
400
200
10
6
CuB=2
RRR=50,
Nb3Sn
RRR=100,
B=2
5RRR=50, B=12
RRR=100, B=12
1600
3
5
6
Cp [J/Km3]
7
RRR=50, B=2
RRR=100, B=2
RRR=50, B=12
RRR=100, B=12
Thermal Conductivity Cu [W/Km]
1600
1800
4
x 10
Cp [J/Km3]
x 10
8
1800
200
5 10
T [K]
T [K]
10 15
0
15 0
0
0 5
5 10
T [K]
T [K]
10 15
0
15 0
5
10
T [K]
23
ROXIE Quench Module
Thermal network:
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
24
Current sharing and Joule heating
I st = I op - I c
Iop
current in
stabilizer
I sc = I c
Top
ì0
ïï
T - Tcs
q¢J¢¢ = íq¢J¢¢max
Tc - Top
ï
ïîq¢J¢¢max
Tcs
Tc
for T < Tcs
for Tcs < T < Tc
for T > Tc
current in
superconductor
T
q¢J¢¢max
q¢J¢¢max =
Top
2
hst I op
Ast A
Tcs
Tc
25
T
Higher order thermal coupling for MBHSM01
(Supermagnet)
Quench pole turn IL
(longitudinal propagation)
T conductor [K]
300
250
Experimental
points
OL mid plane
200
IL mid plane
3. Quench OL pole turn
(t=29 ms)
IL pole
150
OL pole
100
Quench IL HF
(transversal)
OL mid plane
50
0
0.000
0.050
0.100
time (s)
0.150
0.200
4. OL fully
quenched
Quench IL LF
(transversal)
1. Spot heater provoked quench
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)
26
MBHSM01. Spot heater test
I = 12 kA
MIITs
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
74
10
118
105
117
99
12
142
136
156
134
14
180
175
205
185
250
Tmax [K]
200
T MEASURED
T analytic
T ROXIE
T SuperMagnet
150
100
50
8
9
10
11
MIITs
12
13
14
27