Analysis of the quench propagation along Nb3SnRutherford cables with the THELMA code

G Manfreda1 F Bellina1 H Bajas2 J C Perez2

1Universita di Udine Via Delle Scienze 208 Udine Italy

2CERN TE Department Geneva Switzerland

2015 CHATS-AS Workshop Bologna Italy Sept 14 2015

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Summary

Introduction

The Rutherford cable models

geometricalelectromagnetic

The thermal model

The thermal model of the Rutherford cable

Analysis of the quench propagation in Short Model Coil 3

Conclusions

Acknowledgements

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Introduction

THELMA is a numerical analysis codedeveloped for the coupled thermaland electromagnetic analysis of cable-in-conduit conductors and joints

To model Nb3Sn Rutherford cables with THELMA

a new geometrical model has been implemented to describethe Rutherford cablesa new thermal model has also been implemented applicablethe Rutherford cables for the coupled electromagnetic-thermalanalysisa first validation of these models has been given by theanalysis of the quench longitudinal propagation velocity in theNb3Sn prototype coil SMC 3

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Introduction

THELMA is a numerical analysis codedeveloped for the coupled thermaland electromagnetic analysis of cable-in-conduit conductors and joints

To model Nb3Sn Rutherford cables with THELMA

a new geometrical model has been implemented to describethe Rutherford cablesa new thermal model has also been implemented applicablethe Rutherford cables for the coupled electromagnetic-thermalanalysisa first validation of these models has been given by theanalysis of the quench longitudinal propagation velocity in theNb3Sn prototype coil SMC 3

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Introduction

THELMA is a numerical analysis codedeveloped for the coupled thermaland electromagnetic analysis of cable-in-conduit conductors and joints

To model Nb3Sn Rutherford cables with THELMA

a new geometrical model has been implemented to describethe Rutherford cablesa new thermal model has also been implemented applicablethe Rutherford cables for the coupled electromagnetic-thermalanalysisa first validation of these models has been given by theanalysis of the quench longitudinal propagation velocity in theNb3Sn prototype coil SMC 3

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Introduction

THELMA is a numerical analysis codedeveloped for the coupled thermaland electromagnetic analysis of cable-in-conduit conductors and joints

To model Nb3Sn Rutherford cables with THELMA

a new geometrical model has been implemented to describethe Rutherford cablesa new thermal model has also been implemented applicablethe Rutherford cables for the coupled electromagnetic-thermalanalysisa first validation of these models has been given by theanalysis of the quench longitudinal propagation velocity in theNb3Sn prototype coil SMC 3

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Introduction

THELMA is a numerical analysis codedeveloped for the coupled thermaland electromagnetic analysis of cable-in-conduit conductors and joints

To model Nb3Sn Rutherford cables with THELMA

a new geometrical model has been implemented to describethe Rutherford cablesa new thermal model has also been implemented applicablethe Rutherford cables for the coupled electromagnetic-thermalanalysisa first validation of these models has been given by theanalysis of the quench longitudinal propagation velocity in theNb3Sn prototype coil SMC 3

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Rutherford cable geometrical model - I

Pa

u3

u2

s

x3

x2

x1

Ps

u3

u2

Pa

s

In THELMA the SC cableis a 3D objectcharacterised by itscurvilinear axis aroundwhich strands are built

OPs = OPa + x2u2 + x3u3

For a Rutherford cablex2(s) x3(s) correspond tothe cartesian coordinatesof a rectilinear cable whosestrand axes are describedanalytically as a set ofstraight and circumferencearc segments

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Rutherford cable geometrical model - I

Pa

u3

u2

s

x3

x2

x1

Ps

u3

u2

Pa

s

In THELMA the SC cableis a 3D objectcharacterised by itscurvilinear axis aroundwhich strands are built

OPs = OPa + x2u2 + x3u3

For a Rutherford cablex2(s) x3(s) correspond tothe cartesian coordinatesof a rectilinear cable whosestrand axes are describedanalytically as a set ofstraight and circumferencearc segments

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Rutherford cable model - II

Pictorial view of a curved segment of a 14 strands non-keystonedRutherford cable

Go to Rutherford geometrical model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA electromagnetic model of Rutherford cables

The THELMA distributed parameter electromagnetic (EM)cable model developed by Bologna University has been used

the model considers a non linear resistive-inductive networkand its unknowns are the strand current imbalances withrespect to the cable transport current uniformly distributed

along the cable each strand is divided into Nel longitudinalstrand elements suitably set according to the desired level ofspace resolution rArr no constraint from the cable band length

All the Rutherford cable strands are individually represented

Go to EM model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA electromagnetic model of Rutherford cables

The THELMA distributed parameter electromagnetic (EM)cable model developed by Bologna University has been used

the model considers a non linear resistive-inductive networkand its unknowns are the strand current imbalances withrespect to the cable transport current uniformly distributed

along the cable each strand is divided into Nel longitudinalstrand elements suitably set according to the desired level ofspace resolution rArr no constraint from the cable band length

All the Rutherford cable strands are individually represented

Go to EM model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA electromagnetic model of Rutherford cables

The THELMA distributed parameter electromagnetic (EM)cable model developed by Bologna University has been used

the model considers a non linear resistive-inductive networkand its unknowns are the strand current imbalances withrespect to the cable transport current uniformly distributed

along the cable each strand is divided into Nel longitudinalstrand elements suitably set according to the desired level ofspace resolution rArr no constraint from the cable band length

All the Rutherford cable strands are individually represented

Go to EM model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA electromagnetic model of Rutherford cables

The THELMA distributed parameter electromagnetic (EM)cable model developed by Bologna University has been used

the model considers a non linear resistive-inductive networkand its unknowns are the strand current imbalances withrespect to the cable transport current uniformly distributed

along the cable each strand is divided into Nel longitudinalstrand elements suitably set according to the desired level ofspace resolution rArr no constraint from the cable band length

All the Rutherford cable strands are individually represented

Go to EM model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Rutherford cable electrical resistances

In literature to describe the electrical resistances of a Rutherfordcable the cross-over Rc and the adjacent Ra resistances are used

Rc corresponds directly to the series of the THELMA spotresistances of the two strands

Rcij = Rsi + Rsj

Ra is associated to the length of the crossover between twostrands `a asymp `Tr(2(Nst minus 1) sinϕ) being Nst the number ofcable strands and is related to the THELMA distributedresistances

Raij = (Rdi + Rdj )`a

+ The THELMA contact resistances are determined from themodel of the cable DC resistance measurements

Go to THELMA electrical contact resistances details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Rutherford cable electrical resistances

In literature to describe the electrical resistances of a Rutherfordcable the cross-over Rc and the adjacent Ra resistances are used

Rc corresponds directly to the series of the THELMA spotresistances of the two strands

Rcij = Rsi + Rsj Ac

Ra is associated to the length of the crossover between twostrands `a asymp `Tr(2(Nst minus 1) sinϕ) being Nst the number ofcable strands and is related to the THELMA distributedresistances

Raij = (Rdi + Rdj )`a

+ The THELMA contact resistances are determined from themodel of the cable DC resistance measurements

Go to THELMA electrical contact resistances details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Rutherford cable electrical resistances

In literature to describe the electrical resistances of a Rutherfordcable the cross-over Rc and the adjacent Ra resistances are used

Rc corresponds directly to the series of the THELMA spotresistances of the two strands

Rcij = Rsi + Rsj Ac

Ra is associated to the length of the crossover between twostrands `a asymp `Tr(2(Nst minus 1) sinϕ) being Nst the number ofcable strands and is related to the THELMA distributedresistances

Raij = (Rdi + Rdj )`aAc

+ The THELMA contact resistances are determined from themodel of the cable DC resistance measurements

Go to THELMA electrical contact resistances details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Rutherford cable electrical resistances

In literature to describe the electrical resistances of a Rutherfordcable the cross-over Rc and the adjacent Ra resistances are used

Rc corresponds directly to the series of the THELMA spotresistances of the two strands

Rcij = Rsi + Rsj Ac

Ra is associated to the length of the crossover between twostrands `a asymp `Tr(2(Nst minus 1) sinϕ) being Nst the number ofcable strands and is related to the THELMA distributedresistances

Raij = (Rdi + Rdj )`aAc

+ The THELMA contact resistances are determined from themodel of the cable DC resistance measurements

Go to THELMA electrical contact resistances details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model

A brand-new thermal (TH) analysis model has been implemented

based on a lumped thermal network rArr unknowns nodestemperatures Tk and branches heat currents Φk

alternative to the original THELMA thermal-hydraulic modulewhich is focused on the CICC strand-helium heat exchange

general-purpose library of thermal components includingtemperature and heat current generators linear and non linearthermal conductances and capacitances

network equations written with the modified node approachand solved numerically in time domain

Go to TH module details Go to EM and TH modules coupling details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model

A brand-new thermal (TH) analysis model has been implemented

based on a lumped thermal network rArr unknowns nodestemperatures Tk and branches heat currents Φk

alternative to the original THELMA thermal-hydraulic modulewhich is focused on the CICC strand-helium heat exchange

general-purpose library of thermal components includingtemperature and heat current generators linear and non linearthermal conductances and capacitances

network equations written with the modified node approachand solved numerically in time domain

Go to TH module details Go to EM and TH modules coupling details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model

A brand-new thermal (TH) analysis model has been implemented

based on a lumped thermal network rArr unknowns nodestemperatures Tk and branches heat currents Φk

alternative to the original THELMA thermal-hydraulic modulewhich is focused on the CICC strand-helium heat exchange

general-purpose library of thermal components includingtemperature and heat current generators linear and non linearthermal conductances and capacitances

network equations written with the modified node approachand solved numerically in time domain

Go to TH module details Go to EM and TH modules coupling details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model

A brand-new thermal (TH) analysis model has been implemented

based on a lumped thermal network rArr unknowns nodestemperatures Tk and branches heat currents Φk

alternative to the original THELMA thermal-hydraulic modulewhich is focused on the CICC strand-helium heat exchange

general-purpose library of thermal components includingtemperature and heat current generators linear and non linearthermal conductances and capacitances

network equations written with the modified node approachand solved numerically in time domain

Go to TH module details Go to EM and TH modules coupling details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - I

Usually no forced-flow He cooling is present rArr thermal nonlinear conduction only is considered

in the cable both distributed and concentrated heat currentsare present

a mixed distributed and lumped model should therefore beconsidered

+ The discrete formulation of the thermal conduction has beenadopted with two staggered 1D complexes of cells

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - I

Usually no forced-flow He cooling is present rArr thermal nonlinear conduction only is considered

in the cable both distributed and concentrated heat currentsare present

a mixed distributed and lumped model should therefore beconsidered

+ The discrete formulation of the thermal conduction has beenadopted with two staggered 1D complexes of cells

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - I

Usually no forced-flow He cooling is present rArr thermal nonlinear conduction only is considered

in the cable both distributed and concentrated heat currentsare present

a mixed distributed and lumped model should therefore beconsidered

+ The discrete formulation of the thermal conduction has beenadopted with two staggered 1D complexes of cells

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - I

Usually no forced-flow He cooling is present rArr thermal nonlinear conduction only is considered

in the cable both distributed and concentrated heat currentsare present

a mixed distributed and lumped model should therefore beconsidered

+ The discrete formulation of the thermal conduction has beenadopted with two staggered 1D complexes of cells

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - II

Sk~Sk-1

~S1~ S2

~ Sk+1~

dual surfaces

dual volumes

strands elements

Nk Nk+1Nk-1N1 N2

sprimal nodes

V1~ Vk-1

~ Vk~ Vk+1

~V2~

the temperatures Tk are associated to the primal nodes Nk

the heat currents Φk are associated to the dual surfaces Skbetween adjacent dual volumes Vk

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - II

Sk~Sk-1

~S1~ S2

~ Sk+1~

dual surfaces

dual volumes

strands elements

Nk Nk+1Nk-1N1 N2

sprimal nodes

V1~ Vk-1

~ Vk~ Vk+1

~V2~

the temperatures Tk are associated to the primal nodes Nk

the heat currents Φk are associated to the dual surfaces Skbetween adjacent dual volumes Vk

Nk Nk+1Nk-1 Tk

Vk~

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - II

Sk~Sk-1

~S1~ S2

~ Sk+1~

dual surfaces

dual volumes

strands elements

Nk Nk+1Nk-1N1 N2

sprimal nodes

V1~ Vk-1

~ Vk~ Vk+1

~V2~

the temperatures Tk are associated to the primal nodes Nk

the heat currents Φk are associated to the dual surfaces Skbetween adjacent dual volumes Vk

Nk Nk+1Nk-1 Tk

Vk~

Nk Nk+1

Vk~

Nk-1

Sk~

Sk+1~

Φk Φk+1

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - III

j

iN j

k

N ik-1 N i

k N ik+1

To build the lumped network

the i-th strand primal mesh nodes correspond to the networknodes N i

k

each dual volume corresponds to a thermal capacitance C ik

each dual boundary surface corresponds to a longitudinalthermal conductance G l

kminus1k

losses are represented by heat current generators Pg ik

the inter-strand thermal conductances G i jk are also considered

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - III

Cik

j

iN j

k

N ik-1 N i

k

To build the lumped network

the i-th strand primal mesh nodes correspond to the networknodes N i

k

each dual volume corresponds to a thermal capacitance C ik

each dual boundary surface corresponds to a longitudinalthermal conductance G l

kminus1k

losses are represented by heat current generators Pg ik

the inter-strand thermal conductances G i jk are also considered

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - III

Cik

Glikk-1

j

iN j

k

N ik-1 N i

k

To build the lumped network

the i-th strand primal mesh nodes correspond to the networknodes N i

k

each dual volume corresponds to a thermal capacitance C ik

each dual boundary surface corresponds to a longitudinalthermal conductance G l

kminus1k

losses are represented by heat current generators Pg ik

the inter-strand thermal conductances G i jk are also considered

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - III

Cik

Glikk-1

Pgik

j

iN j

k

N ik-1 N i

k

To build the lumped network

the i-th strand primal mesh nodes correspond to the networknodes N i

k

each dual volume corresponds to a thermal capacitance C ik

each dual boundary surface corresponds to a longitudinalthermal conductance G l

kminus1k

losses are represented by heat current generators Pg ik

the inter-strand thermal conductances G i jk are also considered

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The thermal model of the Rutherford cable - III

Cik

Glikk-1

Gijk

Pgik

j

iN j

k

N ik-1 N i

k

To build the lumped network

the i-th strand primal mesh nodes correspond to the networknodes N i

k

each dual volume corresponds to a thermal capacitance C ik

each dual boundary surface corresponds to a longitudinalthermal conductance G l

kminus1k

losses are represented by heat current generators Pg ik

the inter-strand thermal conductances G i jk are also considered

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Model validation

Analysis of the quench longitudinalpropagation in Short Model Coil 3

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Short Model Coil 3

Short racetrack coilmade with Nb3Sndeveloped in theframe of the NextEuropean DipoleJoint ResearchActivity

Coil target magneticfield of 12 T on theconductor

Two double pancakecoils

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Short Model Coil 3

Short racetrack coilmade with Nb3Sndeveloped in theframe of the NextEuropean DipoleJoint ResearchActivity

Coil target magneticfield of 12 T on theconductor

Two double pancakecoils

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Short Model Coil 3

Short racetrack coilmade with Nb3Sndeveloped in theframe of the NextEuropean DipoleJoint ResearchActivity

Coil target magneticfield of 12 T on theconductor

Two double pancakecoils

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Short Model Coil 3 pancake

Each pancake is made of 21 turns divided into 3 groups of 172 and 2 turns

Rutherford cable

14 Nb3Sn PIT strands with a diameter of 125 mm nokeystoningcross-section 10 mm wide and 22 mm thick transpositionpitch 60 mm

IcSS =15400 A 42 K and 18500 A 19 K

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Short Model Coil 3 pancake

Each pancake is made of 21 turns divided into 3 groups of 172 and 2 turns

Rutherford cable

14 Nb3Sn PIT strands with a diameter of 125 mm nokeystoningcross-section 10 mm wide and 22 mm thick transpositionpitch 60 mm

IcSS =15400 A 42 K and 18500 A 19 K

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The Short Model Coil 3 pancake

Each pancake is made of 21 turns divided into 3 groups of 172 and 2 turns

Rutherford cable

14 Nb3Sn PIT strands with a diameter of 125 mm nokeystoningcross-section 10 mm wide and 22 mm thick transpositionpitch 60 mm

IcSS =15400 A 42 K and 18500 A 19 K

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Experimental set-up

voltage distribution along the coil conductor measured byeight voltage taps per pancake Go to voltage probes location details

magnetic field measured by a Hall probe

all probes the coil strain gauges and two spot heatersconnected by traces obtained with a technique similar to thatof printed boards

voltages along the conductor measured as differences betweenthese taps signals rArr 15 longitudinal voltage signals available

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Experimental set-up

voltage distribution along the coil conductor measured byeight voltage taps per pancake Go to voltage probes location details

magnetic field measured by a Hall probe

all probes the coil strain gauges and two spot heatersconnected by traces obtained with a technique similar to thatof printed boards

voltages along the conductor measured as differences betweenthese taps signals rArr 15 longitudinal voltage signals available

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Experimental set-up

voltage distribution along the coil conductor measured byeight voltage taps per pancake Go to voltage probes location details

magnetic field measured by a Hall probe

all probes the coil strain gauges and two spot heatersconnected by traces obtained with a technique similar to thatof printed boards

voltages along the conductor measured as differences betweenthese taps signals rArr 15 longitudinal voltage signals available

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Experimental set-up

voltage distribution along the coil conductor measured byeight voltage taps per pancake Go to voltage probes location details

magnetic field measured by a Hall probe

all probes the coil strain gauges and two spot heatersconnected by traces obtained with a technique similar to thatof printed boards

voltages along the conductor measured as differences betweenthese taps signals rArr 15 longitudinal voltage signals available

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Tests

The voltage data used for the model validation have beencollected 42 and 19 K with the coil fed with currentramps at 10 or 20 As

During training two plateau current values have beenreached at 95 and 92 of the load line respectively at 42and 19 K which correspond to 125 T on the conductor

The large majority of the quenches was detected in thestraight part of the innermost turn 13 cm long between taps102 and 72 located in the coil 1 lower layer

Go to voltage probes location details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Tests

The voltage data used for the model validation have beencollected 42 and 19 K with the coil fed with currentramps at 10 or 20 As

During training two plateau current values have beenreached at 95 and 92 of the load line respectively at 42and 19 K which correspond to 125 T on the conductor

The large majority of the quenches was detected in thestraight part of the innermost turn 13 cm long between taps102 and 72 located in the coil 1 lower layer

Go to voltage probes location details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Tests

The voltage data used for the model validation have beencollected 42 and 19 K with the coil fed with currentramps at 10 or 20 As

During training two plateau current values have beenreached at 95 and 92 of the load line respectively at 42and 19 K which correspond to 125 T on the conductor

The large majority of the quenches was detected in thestraight part of the innermost turn 13 cm long between taps102 and 72 located in the coil 1 lower layer

Go to voltage probes location details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Quench propagation velocity measurements

-01

0

01

02

03

04

05

-12 -8 -4 0

Voltagev[V

]

Time t [ms]

102-72

62-102

72-71

t1

t2

The propagation velocity wasmeasured with the Time-of-Flight(ToF) method using the voltagewaveform along one or three con-secutive coil segments

vToFq = dtaps(t1 + t2)

Measured quench propagation ve-locities along coil segment 72-102from tests at 42 and 19 K

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Quench propagation velocity measurements

-01

0

01

02

03

04

05

-12 -8 -4 0

Voltagev[V

]

Time t [ms]

102-72

62-102

72-71

t1

t2

The propagation velocity wasmeasured with the Time-of-Flight(ToF) method using the voltagewaveform along one or three con-secutive coil segments

vToFq = dtaps(t1 + t2)

5

10

15

20

25

11 12 13 14 15Longitudinalpropagationvelocity

v lq[m

s]

Transport current It [kA]

19 K42 K

Measured quench propagation ve-locities along coil segment 72-102from tests at 42 and 19 K

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA model of SMC3

Modelled part the 15 cm long coil straight part whichincludes the 72-102 coil segment

discretisation step along the cable 1 mm

TwenteITER SC strand scaling law

EM model boundary conditions at both ends strands fed byequal constant current generators with two polygons ofinter-strand resistances rArr current redistribution possible upto the ends

TH model boundary conditions adiabatic

quench triggered by a heat pulse (01 few mJ) applied to asingle strand in the highest field zone the cable middlelength

Go to THELMA SMC3 model details Go to SMC3 iron model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA model of SMC3

Modelled part the 15 cm long coil straight part whichincludes the 72-102 coil segment

discretisation step along the cable 1 mm

TwenteITER SC strand scaling law

EM model boundary conditions at both ends strands fed byequal constant current generators with two polygons ofinter-strand resistances rArr current redistribution possible upto the ends

TH model boundary conditions adiabatic

quench triggered by a heat pulse (01 few mJ) applied to asingle strand in the highest field zone the cable middlelength

Go to THELMA SMC3 model details Go to SMC3 iron model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA model of SMC3

Modelled part the 15 cm long coil straight part whichincludes the 72-102 coil segment

discretisation step along the cable 1 mm

TwenteITER SC strand scaling law

EM model boundary conditions at both ends strands fed byequal constant current generators with two polygons ofinter-strand resistances rArr current redistribution possible upto the ends

TH model boundary conditions adiabatic

quench triggered by a heat pulse (01 few mJ) applied to asingle strand in the highest field zone the cable middlelength

Go to THELMA SMC3 model details Go to SMC3 iron model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA model of SMC3

Modelled part the 15 cm long coil straight part whichincludes the 72-102 coil segment

discretisation step along the cable 1 mm

TwenteITER SC strand scaling law

EM model boundary conditions at both ends strands fed byequal constant current generators with two polygons ofinter-strand resistances rArr current redistribution possible upto the ends

TH model boundary conditions adiabatic

quench triggered by a heat pulse (01 few mJ) applied to asingle strand in the highest field zone the cable middlelength

Go to THELMA SMC3 model details Go to SMC3 iron model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA model of SMC3

Modelled part the 15 cm long coil straight part whichincludes the 72-102 coil segment

discretisation step along the cable 1 mm

TwenteITER SC strand scaling law

EM model boundary conditions at both ends strands fed byequal constant current generators with two polygons ofinter-strand resistances rArr current redistribution possible upto the ends

TH model boundary conditions adiabatic

quench triggered by a heat pulse (01 few mJ) applied to asingle strand in the highest field zone the cable middlelength

Go to THELMA SMC3 model details Go to SMC3 iron model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

The THELMA model of SMC3

Modelled part the 15 cm long coil straight part whichincludes the 72-102 coil segment

discretisation step along the cable 1 mm

TwenteITER SC strand scaling law

EM model boundary conditions at both ends strands fed byequal constant current generators with two polygons ofinter-strand resistances rArr current redistribution possible upto the ends

TH model boundary conditions adiabatic

quench triggered by a heat pulse (01 few mJ) applied to asingle strand in the highest field zone the cable middlelength

Go to THELMA SMC3 model details Go to SMC3 iron model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Comparison between measured and computed velocities

The quench propagation velocity vq has been studied as a functionof the cable transport current It at two initial temperatures T0 =19 (left) and 42 K (right)

0

5

10

15

20

25

30

0 3 6 9 12 15Longitudinalpropagationvelocity

vq(m

s)

Transport current It (kA)

ExperimentalSimulation

0

5

10

15

20

25

0 2 4 6 8 10 12 14Longitudinalpropagationvelocity

vq(m

s)

Transport current It (kA)

ExperimentalSimulation

The agreement is very good since the only model parameterchanged between the two cases is the initial temperaturewhile the magnetic field depends on the transport current

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Comparison between measured and computed velocities

The quench propagation velocity vq has been studied as a functionof the cable transport current It at two initial temperatures T0 =19 (left) and 42 K (right)

0

5

10

15

20

25

30

0 3 6 9 12 15Longitudinalpropagationvelocity

vq(m

s)

Transport current It (kA)

ExperimentalSimulation

0

5

10

15

20

25

0 2 4 6 8 10 12 14Longitudinalpropagationvelocity

vq(m

s)

Transport current It (kA)

ExperimentalSimulation

The agreement is very good since the only model parameterchanged between the two cases is the initial temperaturewhile the magnetic field depends on the transport current

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Further results - I

(Loading smc profile)

View of the strands temperature along the cable

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Further results - II

(Loading smc cross section)

View of the strands temperature in the cross-section where theheat pulse was applied and two close cross-sections

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Further results - III

08

09

1

11

12

-75 -5 -25 0 25 5 75

Adim

ension

alcu

rrenti(-)

Axial coordinate s (cm)

08

09

1

11

12

-75 -5 -25 0 25 5 75

Adim

ension

alcu

rrenti(-)

Axial coordinate s (cm)

08

09

1

11

12

-75 -5 -25 0 25 5 75

Adim

ension

alcu

rrenti(-)

Axial coordinate s (cm)

View of the strands adimensional currents along the cable atT0 = 42 K It = 14 kA Above left t = 03 ms above right

t = 1 ms below t = 25 ms after the disturbance

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Conclusions

A new THELMA model of the Rutherford cables has beendeveloped

This model makes use of the new THELMA thermal modelcoupled with the existing electromagnetic module

THELMA can analyse the Rutherford cable behavior at a verydetailed level showing electromagnetic and thermal diffusioneffects both along and among strands

+ For a first validation

The analysis of the quench longitudinal propagation in theNb3Sn prototype coil SMC3 has been presentedA very good correspondence is present between measured andcomputed values

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Conclusions

A new THELMA model of the Rutherford cables has beendeveloped

This model makes use of the new THELMA thermal modelcoupled with the existing electromagnetic module

THELMA can analyse the Rutherford cable behavior at a verydetailed level showing electromagnetic and thermal diffusioneffects both along and among strands

+ For a first validation

The analysis of the quench longitudinal propagation in theNb3Sn prototype coil SMC3 has been presentedA very good correspondence is present between measured andcomputed values

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Conclusions

A new THELMA model of the Rutherford cables has beendeveloped

This model makes use of the new THELMA thermal modelcoupled with the existing electromagnetic module

THELMA can analyse the Rutherford cable behavior at a verydetailed level showing electromagnetic and thermal diffusioneffects both along and among strands

+ For a first validation

The analysis of the quench longitudinal propagation in theNb3Sn prototype coil SMC3 has been presentedA very good correspondence is present between measured andcomputed values

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Conclusions

A new THELMA model of the Rutherford cables has beendeveloped

This model makes use of the new THELMA thermal modelcoupled with the existing electromagnetic module

THELMA can analyse the Rutherford cable behavior at a verydetailed level showing electromagnetic and thermal diffusioneffects both along and among strands

+ For a first validation

The analysis of the quench longitudinal propagation in theNb3Sn prototype coil SMC3 has been presentedA very good correspondence is present between measured andcomputed values

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Conclusions

A new THELMA model of the Rutherford cables has beendeveloped

This model makes use of the new THELMA thermal modelcoupled with the existing electromagnetic module

THELMA can analyse the Rutherford cable behavior at a verydetailed level showing electromagnetic and thermal diffusioneffects both along and among strands

+ For a first validation

The analysis of the quench longitudinal propagation in theNb3Sn prototype coil SMC3 has been presentedA very good correspondence is present between measured andcomputed values

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Conclusions

A new THELMA model of the Rutherford cables has beendeveloped

This model makes use of the new THELMA thermal modelcoupled with the existing electromagnetic module

THELMA can analyse the Rutherford cable behavior at a verydetailed level showing electromagnetic and thermal diffusioneffects both along and among strands

+ For a first validation

The analysis of the quench longitudinal propagation in theNb3Sn prototype coil SMC3 has been presentedA very good correspondence is present between measured andcomputed values

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Acknowledgements

The research leading to these results has received funding from theEuropean Commission under the Transnational Access activity ofthe FP7 Research Infrastructures project EUCARD-2 grantagreement no 312453

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Thanks for your attention

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Go to to Rutherford geometrical model Go to Rutherford geometrical model details

Go to EM model Go to EM model details

Go to Rutherford electrical contact resistances Go to contact resistances details

Go to TH module Go to TH module details Go to EM and TH modules coupling details

Go to voltage probes location details

Go to THELMA SMC3 model Go to SMC3 model details

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the Rutherford cable geometrical models

u3

u2

w

ltr

ϕ

ϕ

Keystoning can be takeninto account

The twisting angle ϕ usedfor both the in-plane andthe out-of-planetranspositions is

ϕ asymp tanminus1

ltr

2

(hmed +

w

cosα2

)

Return to Rutherford geometrical model Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the cable EM model

Different strand scaling laws are available

Strand cross-section rArr electrical parallel of the Cu stabilizerand the SC material

rCu

rSC

+ dU=Edl -

ACu

ASCdl

The following equation is numerically solved in terms of ISC

Ist = ISC +ACu

CuEc

(ISCIc

)n

Return to electromagnetic model Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the cable EM model

Different strand scaling laws are available

Strand cross-section rArr electrical parallel of the Cu stabilizerand the SC material

rCu

rSC

+ dU=Edl -

ACu

ASCdl

The following equation is numerically solved in terms of ISC

Ist = ISC +ACu

CuEc

(ISCIc

)n

Return to electromagnetic model Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the cable EM model

Different strand scaling laws are available

Strand cross-section rArr electrical parallel of the Cu stabilizerand the SC material

rCu

rSC

+ dU=Edl -

ACu

ASCdl

The following equation is numerically solved in terms of ISC

Ist = ISC +ACu

CuEc

(ISCIc

)n

Return to electromagnetic model Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the EM and TH contact resistances models

Ac

Ac

(a) (b)

In THELMA

(a) the spot Rs (Ω or KW) and

(b) the distributed Rd (Ωmiddotm orKmiddotmW)

contact resistances can be in-dividually assigned to the cablestrands

the cable geometry is scannedand the single localconductances are computed

The inter-strand specific EMconductances σij(sk) (Ωm)are computed as the averageconductance associated to lk

Return to Rutherford electrical contact resistances Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the EM and TH contact resistances models

Ac

Ac

(a) (b)

In THELMA

(a) the spot Rs (Ω or KW) and

(b) the distributed Rd (Ωmiddotm orKmiddotmW)

contact resistances can be in-dividually assigned to the cablestrands

ij lk

~

lk+1

~

s

sk sk+1the cable geometry is scannedand the single localconductances are computed

The inter-strand specific EMconductances σij(sk) (Ωm)are computed as the averageconductance associated to lk

Return to Rutherford electrical contact resistances Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the new THELMA TH model - I

The resulting system of algebraic-differential equations can bewritten as(

ATr Rth

Gth Ar

)(T

ΦΦΦ

)+

(0 0

Cth 0

)d

d t

(T

ΦΦΦ

)=

(Ti

ΦΦΦi

)

the equations are sorted by grouping the algebraic (a) anddifferential (d) equations

the system unknowns are grouped into differential variables(d) or simple algebraic (a) unknown quantities

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the new THELMA TH model - I

The resulting system of algebraic-differential equations can bewritten as(

ATr Rth

Gth Ar

)(T

ΦΦΦ

)+

(0 0

Cth 0

)d

d t

(T

ΦΦΦ

)=

(Ti

ΦΦΦi

)

the equations are sorted by grouping the algebraic (a) anddifferential (d) equations

the system unknowns are grouped into differential variables(d) or simple algebraic (a) unknown quantities

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the new THELMA TH model - I

The resulting system of algebraic-differential equations can bewritten as(

ATr Rth

Gth Ar

)(T

ΦΦΦ

)+

(0 0

Cth 0

)d

d t

(T

ΦΦΦ

)=

(Ti

ΦΦΦi

)

the equations are sorted by grouping the algebraic (a) anddifferential (d) equations

the system unknowns are grouped into differential variables(d) or simple algebraic (a) unknown quantities

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the new THELMA TH model - II

The final form of the system is(0 0

Fthd d 0

)d

d t

(Xa

Xd

)+

(Dth

aa Dthad

Dthd a Dth

d d

)(Xa

Xd

)=

(Ya

Yd

)

These two equation systems are obtained which are solved at eachiteration

Xa = Dthaa

minus1Ya minusUth

adXd

d

d tXd = Fth

d dminus1

Yd minusUthd aXa minusUth

d dXd

whereUth

ad = Dthaa

minus1Dth

ad Uthd a = Fth

d dminus1

Dthd a Uth

d d = Fthd d

minus1Dth

d d Return to the thermal module Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

EM and TH models coupling

The EM and the TH models are coupled in an explicit way Ateach adaptive time step a loop is followed

the currents and losses are computed by the EM module startingfrom the initial temperatures and currents

the temperatures are computed by the TH model starting from theinitial temperatures and the losses computed by the EM module

if necessary the timestep is adjusted on the basis of thetemperature variations

the final currents and temperatures are initial conditions for thefollowing time step

Return to the thermal module Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

EM and TH models coupling

The EM and the TH models are coupled in an explicit way Ateach adaptive time step a loop is followed

the currents and losses are computed by the EM module startingfrom the initial temperatures and currents

the temperatures are computed by the TH model starting from theinitial temperatures and the losses computed by the EM module

if necessary the timestep is adjusted on the basis of thetemperature variations

the final currents and temperatures are initial conditions for thefollowing time step

k-th time stepTH initialconditions

k-th time stepEM initialconditions

EM module

Return to the thermal module Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

EM and TH models coupling

The EM and the TH models are coupled in an explicit way Ateach adaptive time step a loop is followed

the currents and losses are computed by the EM module startingfrom the initial temperatures and currents

the temperatures are computed by the TH model starting from theinitial temperatures and the losses computed by the EM module

if necessary the timestep is adjusted on the basis of thetemperature variations

the final currents and temperatures are initial conditions for thefollowing time step

k-th time stepTH initialconditions

TH module

k-th time stepEM initialconditions

EM module

Return to the thermal module Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

EM and TH models coupling

The EM and the TH models are coupled in an explicit way Ateach adaptive time step a loop is followed

the currents and losses are computed by the EM module startingfrom the initial temperatures and currents

the temperatures are computed by the TH model starting from theinitial temperatures and the losses computed by the EM module

if necessary the timestep is adjusted on the basis of thetemperature variations

the final currents and temperatures are initial conditions for thefollowing time step

k-th time stepTH initialconditions

TH module

k-th time stepEM initialconditions

EM module

Return to the thermal module Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

EM and TH models coupling

The EM and the TH models are coupled in an explicit way Ateach adaptive time step a loop is followed

the currents and losses are computed by the EM module startingfrom the initial temperatures and currents

the temperatures are computed by the TH model starting from theinitial temperatures and the losses computed by the EM module

if necessary the timestep is adjusted on the basis of thetemperature variations

the final currents and temperatures are initial conditions for thefollowing time step

k-th time stepTH initialconditions

(k+1)-th time stepTH initialconditions

TH module

k-th time stepEM initialconditions

(k+1)-th time stepEM initialconditions

EM module

Return to the thermal module Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Voltage probes location details

Detail of the voltage probes location on the two layers of eachSMC3 coil Return to experimental set-up Return to tests Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the THELMA SMC3 model

TwenteITER SC strand scaling lawp q C Bc20max Tc0max Cn1 Cn2 ε0a εm

(T) (K) () ()05 2 2118middot1011 29452 16973 45062 4256 0286 0

applied strain εappl = minus02 and Ic degradation 163

n = 1 + r I sc = 1 + 220 I 047c (rescaled) Cu RRR=75 (NIST

model)

Rc = 1 mΩ and Ra = 94 microΩ rArr Rd = 104 nΩmiddotm andRs = 05 mΩ in THELMA

distributed thermal conductances (from NbTi)Gd = α T β = 0545 T 154 Wm middotKspot thermal conductance done by considering the stranddiameter

Return to THELMA SMC3 model Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the iron model of SMC3 - I

All the strandsof the modelledRutherford cablesegment are individ-ually represented

the rest of the coilis represented by asequence of solidblocks

+ However iron gives a non negligible contribution to the totalfield (up to 2 T)

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables

Details of the iron model of SMC3 - II

A ROXIE code 2Dmodel has been de-veloped to get theiron contribution

Return to THELMA SMC3 model Back to hub

G Manfreda F Bellina H Bajas J C Perez Quench propagation in Nb3Sn Rutherford cables