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

20

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]