Comprehensive Modelling Study of Quench Behaviour of the NHMFL 32 T All-Superconducting Magnet System. Input Data and Methodology Aspects.

Transcription

1 Comprehensive Modelling Sudy of Quench Behaviour of he NHMFL 32 T All-Superconducing Magne Sysem. Inpu Daa and Mehodology Aspecs. Andrew V. Gavrilin & Huberus W. Weijers Naional High Magneic Field Laboraory (NHMFL), Florida Sae Universiy Tallahassee, Florida, USA Conribuions by: Dmyro V. Abraimov, W. Denis Markiewicz, David K. Hilon, Parick D. Noyes 5 h Inernaional Workshop on Numerical Modelling of High Temperaure Superconducors ( HTS Modelling 2016 ) Bologna, Ialy, June 15-17, 2016

2 .The 32 T Magne Sysem Key parameers: Cener field 32 T Clear bore 34 mm Ramp ime 1 hour Uniformiy 1 cm DSV Sored energy 8.3 MJ Expeced cycles/20 years 50,000 Operaing emperaure 4.2 K REBCO Nb 3 Sn NbTi 15 T / 250 mm bore LTS magne 17 T / 34 mm bore REBCO coils Separaely powered, simulaneously ramped

3 Ouline 1. Deails of a our approach o quench analysis. 2. Comparison wih quench es resuls. Wha inpu parameers can affec he simulaion resuls and o wha exen?

4 The 32T magne inser Each coil of he HTS inser consiss of double-pancakes (modules), co-wound wih alumina plaed sainless seel srips as he iner-urn insulaion and reinforcemen. The coils are conneced in series. SuperPower REBCO ape

5 Prooypes versus 32 T Parameer Prooypes 32 T Modules Operaing curren (defaul) 200 A 180 A Field consan 48 mt/a 94 mt/a B radial max 3.6 / 3.3 T 3.9 / 4.8 T L 1.6 H 16 H M wih ouser 4 H 22 H L ouser 194 H 194 H Max hoop sress 322 / 396 MPa 363 / 378 MPa Mid-plane sress -11 / -9 MPa -21 / -49 MPa Coil 20/70 or Coil 1 inner) & Coil 82/116 or Coil 2 (ouer)

6 REBCO Prooypes versus 32 T Prooype Coils ( Dual Coil Prooype ) 32 T Inner Coils 248 mm 34 mm Coil 2 6 modules Coil 1 6 modules 248 mm 34 mm 52 mm 320 mm Coil 2 36 modules Coil 1 20 modules

7 Module 1 disk 1 Facing Cooling spacer Imprins of G-10 spacer are visible as (edges of) dark radial bands 20/70 module 1 82/116 module 82/116 coil surface is noiceably flaer han 20/70 which was purchased wihou 32 T widh olerance spec

8 Proecion Heaer Design Epoxy Fiberglass G-10 Mechanical srengh Kapon Insulaion Heaer assembly Seel elemen Power, emperaure Kapon Insulaion

9 Proecion Heaer Locaions A heaer is fired by a curren pulse ~ 1 s long.

10 Thermal problem. Model equaion: hea conducance wih a source erm. He He ( A C + A C + A ( C + fγ C )) + 4 Pi ( ins) ( i) [ A QJ + A QAC ] + κi ( Ti )( T T ) i= 1 x - he coordinae along he spiral pah of wihin a given pancake. T = T ( x, ) he ape emperaure; he ape cross -secion area : A A A he ape copper marix cross - secion area; he cross -secion area of he insulaed ape hea capaciy : A also includes he hea capaciy of helium in he winding a consan pressure, f SC C SC ( T ) + A SC C SC is he helium proporion of The helium densiy γ ( T ) + A He p ins ( C he helium vaporizaion process. SC ins δ i ins = p A oher maerials of ins p + ( T ) + A T fγ + P 1(2) Q superconducing ape SC He p = x ( T ) C T Aκ x heaer ( T )), he insulaion in erms of [ W he ape, incl. haselloy subsrae, [ J / m] /( m volume. K)], ( T ) is considered emperaure dependen o mimic He p, + x Schemaic of a pancake ( disk ) ec.;

11 Thermal problem. Model equaion: hea conducance wih a source erm. ( He He A C + A C + A ( C + fγ C )) SC SC ins ins (in he superconducing areas) if p p any ) : T = x 4 P + [ + ] + ( ) i ( ins) ( i) A QJ A QAC κi ( Ti ) T T + P1(2) Q i= 1 δi The ape effecive longiudinal hermal conduciviy : Aκ = Aκ ( T, B); B T Aκ x heaer, [ W + / m] The heaing power densiy (index and Joule heaing, and AC loss A Q = A Q J + J A Q AC = = B( x, ); ( T ( x, ), I( ), B( x, )) + A Q AC ( T ( x, ), B( x, ), B( x, ), I( )) Deailed ime-varying disribuions of he magneic field componens wihin he coils are required.

12 Thermal problem. Model equaion. He He ( A C + A C + A ( C + fγ C )) + 4 Pi ( ins) ( i) [ A Q + A Q ] + κ ( T )( T T ) Pi ( T ) + R characerizing he qualiy of J ( T SC T ) AC copper marix and he insulaion. SC is he hermal conac resisance conac beween he superconducing ape ( x, ) is he hea flux densiy from he quench proecion heaers if i= 1 The ransverse hermal axial (disk - o - disk) and radial (urn - o - urn, wihin a disk) links : 4 i= 1 R Q ( i) C δ i heaer κ ( ins) i i ( i) C ( i) ins δ i any. ins i i p Heaer wih insulaion p T + P = x 1(2) Q T Aκ x heaer SS iner-urn insulaion, [ W + / m] Schemaic of winding cross-secion (fragmen). One module and a half of neighboring module are shown. x Iner-disk insulaion wihin a module (cooling spacer) Tape Finally, circui equaions are included.

13 Thermal problem. Model equaion: hea conducance wih a source erm. ( He He A C + A C + A ( C + fγ C )) SC SC ins ins B( x, ); p p T = x 4 P + [ + ] + ( ) i ( ins) ( i) A QJ A QAC κi ( Ti ) T T + P1(2) Q i= 1 δi The ape effecive longiudinal hermal conduciviy : Aκ = Aκ ( T, B); B = T Aκ x heaer, [ W + / m] We may disregard he longiudinal hea conducance, if he disribued heaers are used. A 3-elemen disribued proecion heaer is aached o a pancake of he inser coil 1 (he inner coil).

14 REBCO ape Ic-value. The REBCO criical curren dependence on he field and emperaure is much more complicaed; here exiss he dependence on he field angle as well: As can be inferred from he dependence, he criical curren value is exremely sensiive o he field angle value in he viciniy of peak (90 area). The fi funcions are obained for a paricular ape, SP-26. We apply his dependence o all he apes, albei using correcion coefficiens o mach he measured values. Numerous measuremens of he criical curren were made, and a pracical fi funcion was suggesed (@ 4.2K) (D.K. Hilon, A.V. Gavrilin and U.P. Trociewiz, Pracical fi funcions for ranspor criical curren versus field magniude and angle daa from (RE)BCO coaed conducors a fixed low emperaures and in high magneic fields, Superconducor Science and Technology, Volume 28, Number 7, 2015):

15 Criical curren calculaion. Temperaure dependence. To include he emperaure dependence, he criical curren was measured a several emperaures and he fi funcion coefficiens were found for each emperaure. The criical curren values a oher emperaures are calculaed by means of inerpolaion and exrapolaion.

16 Superconducing-normal ransiion modelling The process of superconducing-normal ransiion in a REBCO ape differs from ha in a LTSuperconducor. A new model is required. The index and Joule power densiy is calculaed using he following model : I If I < IC ( B, T, θ ), A QJ = I E, where E = E0 IC he criical curren crierion is 1 µ V / cm ( E = 1 µ V If I J I The resisive volage of a pancake (disk) V where l C ( B, T, θ ) and E ρ else (i.e., I A ρ A Q = I ( I I ) is he ape lengh wihin a given disk; he coil resisancev C C E I A ) : ( ) = E I, if I N C k = 1 E I V C 0 ( k ) D ρ < 0 A > 0, and A Q D J, ( ) = ( ), where = hen I l o n( T, I ) 2, / cm). ρ A Q, if E(, x) dx, n( T ) is measured. J A = I E; I C = 0. N is he oal number of disks in he coil.

17 Inser Coils Layou. Example. Differen conducors are used o wind pancakes (wih raher differen Icvalues). Despie he fac ha he leas-qualiy apes are used for he inernal modules, o quench hem by he heaers will no be easy.

18 Inser Coils Layou. Wha Ic-values are used? The superconducor comes in spools. Typically he Ic-value is measured a he ends of each spool in a high field a differen angles. We pick he minimal value. Is i a conservaive approach?.

19 Verificaion of he approach o quench analysis We esed he dual coil prooype in he acual ouser. The inser module volages and he inser curren were measured.

20 Quench es. Inser curren: 222 A (23T in he inser) Ouser curren: 214 A (12T in he ouser) The ouser is acively and passively proeced (false posiive in deecion). Quench iniiaion: all he inser heaers are fired simulaneously. ~ 1.2 s long pulse.

21 Quench es. The expeced sequence of quenching of he modules. Coil currens

22 Quench es. The real picure (he measured sequence of quenching) & he firs-cu simulaion. Coil 1. No agreemen?!

23 Quench es. The real picure (measuremens) & he firs-cu simulaion. Coil 1. Wha is a reason for so huge discrepancy? 1. The urns in he coils are no fully horizonally oriened (iling, dishing, ec.) due o he fac ha he apes are no fla, and so he il angle is no zero (may be ~1 and even larger). 2. The Ic-values we picked are no represenaive. Correcions are needed.

24 End o end relaive variaion of I c (4K; 17T; 18 o ) A 4.2K in-field more apes have relaive spread above 10% M4 apes have larger relaive spread Sandard deviaion 11.2% SD=10.1% SD=12.0% Digis above daa poins are SP run numbers D. Abraimov, NHMFL MRS, April 8, 2015, San Francisco, CA HTS Modelling, Bologna, Ialy, June 2016

25 Ic-value and il angle correcions. Coil 1. Mod 6 Mod 5 Mod 4 Mod 3 Mod 2 Mod 1 Ic-value change: 0% 0% +25% 25% 0% 0% -12% -13% 15% 15% 0% 0% New il angle: Each pancake consiss of wo secions. Le s decrease/ increase he Ic-magniudes and he il angles 0% 0% 20% 20% 0% 0% -28% -28% 15% 15% 0% 0% Z

26 Quench es. The real picure (measuremens) & he simulaion resul afer he correcions are made. Coil 1. The minor correcions wihin he limis can change he picure dramaically. The fiing is no perfec ye, bu i shows he phenomenon in all is glory. Wha he correcions change in erms of hospo emperaure and volage, which are of primary imporance and ineres o us?

27 Quench es. The real picure (measuremens) & he simulaion resul afer he correcions are made. Coil 1. The correcions do no resul in changes in he over-all proecedquench behavior in erms of he key characerisics of quench, if he proecion is effecive.

28 .. Conclusive remarks: 1. The REBCO ape Ic fi funcions are raher helpful and pracical. They describe he Ic-dependencies on he field and field angle adequaely. 2. The Ic-values should be measured a several values of high field and field angle and in several locaions o have an opporuniy o choose correc effecive values of Ic. 3. Noneheless, if he acive proecion is effecive, he inegral characerisics of quench are no so sensiive o he Ic-values and il angles of apes in he winding (if reasonable measured Ic-values are used and he il angles are kep wihin a realisic range). 4. We are acively using his approach for quench simulaion of he 32T magne, as he approach looks effecive.

29 I seems o be very much i, for now. Thank you!