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T. Salmi 1
QXF quench heater delay simulations
Tiina Salmi, 27.10.2015
T. Salmi 2
Outline• The main principles of the heater delay simulation code: CoHDA• CoHDA validation by comparison of simulated delays to measurements
– HQ01e, HQ02a-b, 11 T, HD3, LQ• Simulation of LHQ and SQXF delays• Possible reasons for the simulation uncertainties• Summary of the heater delays agreement with simulation• Description of a new code for computing current decay after a known distribution
of heater delays and propagation velocity• A case study for MQXF: The impact of heater delays distribution on hotspot
temperature• Summary of heater simulation status• References for more detailed information
T. Salmi 3
CoHDA: Code for Heater Delay Analysis
• Heat conduction from heater to the superconducting cable
• Quench when cable reaches Tcs(I,B)• Each coil turn considered separately
• Symmetric heater geometry: Model half of the heater period
• 2-D model (neglect turn-to-turn)• Uniform magnetic field in the
cable• Thermal network method• Model implementation verified in
comparison with COMSOL (Thanks to Juho Rysti, CERN)
PH coverage / 2
PH period/ 2
H e a t
y, radial (in cosθ)
z, axial
T. Salmi 4
0
10
20
30
40
50
0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
PH
del
ay [
ms]
Magnet current / SSL
C9 (1.9 K)
C9 (4.4 K)
C8 (4.4 K)
Simulation (1.9 K)
0
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
ms]
Magnet current / SSL
C20 (1.9 K)C20 (2.2 K)C20 (4.5 K)C20, 200 A/s (2.2 K)C20, 150 A/s (2.2 K)C20, HQ02b (1.9 K)C15 (1.9 K)C16 (1.9 K)Simulation (1.9 K)
CoHDA comparison with experimental data - OL
1. HQ01e, HQ02a-b, 11 T, HD3b: Outer layer (OL)– Above 50% of SSL: Nominal simulations typically within 20% of
measurement – Good agreement– Uncertainty larger at lower current– Comparable with experimental uncertainty
HQ01e outer layer HQ02a-b outer layer
Large difference btw coils 8 and 9. Suspected a defect in coil 8.
No signs of defects in HQ02 coils. The exp. variation suggests the minimum exp. uncertainty..
T. Salmi 5
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
ms]
Magnet current / SSL
Exp. (4.4 K)
Simulation (4.4 K)
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
ms]
Magnet current / SSL
Exp. (1.9 K)
Exp. (4.5 K)
Simulation (1.9 K)
0
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200
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300
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0 0.2 0.4 0.6 0.8 1
PH
del
ay [
ms]
Magnet current / SSL
Exp., HFU 2 (1.9 K)Exp, HFU 1+2 (1.9 K)Exp., HFU 2 (4.5 K)Exp., HFU1 (4.5 K)Exp., HFU1+2 (4.5 K)Simulation (1.9 K)
HD3 outer layer 11 T MBHSP01, 76 µm Kapton
11 T MBHSP01, 203 µm Kapton11 T MBHSP02
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
ms]
Magnet current / SSL
Exp. (1.9 K)
Exp. (4.5 K)
Simulation (1.9 K)
T. Salmi 6
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0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
PH
del
ay [
ms]
Magnet current / SSL
C9 (1.9 K)
C9 (4.4 K)
C8 (4.4 K)
Simulation (1.9 K)
0
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
ms]
Magnet current / SSL
HQ02a1
HQ02a2
HQ02b
Simulation (1.9 K)
CoHDA comparison with experimental data - IL
2. HQ01e, HQ02a-b, 11 T, HD3b: Inner layer (IL)– Above 50% of SSL: Nominal simulations within 10 ms or 40% of
measurement – Not good agreement…– At lower current simulation underestimates the delays– Experiment not fully understood either
• He bubbles?
HQ01e inner layer
HQ02a-b inner layer
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
ms]
Magnet current / SSL
Exp. (4.4 K)
Simulation (4.4 K)
HD3b inner layer
In HQ01 measured IL delays longer than OL. In HQ02 it was the contrary.
T. Salmi 7
HD3, HQ, and 11 T dipole heaters are all of uniform width
T. Salmi 8
CoHDA comparison with experimental data - LQ• In LQ also the wider segment participates in heating the cable• LQ simulation was done for the high field turn (2nd from the pole). Due to
asymmetry of heating station-wide segment connection 3 cases were simulated.• The simulation predicted too long delays in all cases. • Possible reasons why model not suitable: 1. short heating station requires more
detailed model of the cable structure, 2. non-uniform heating in the heater narrow segment must be simulated with more detail.
T. Salmi 9
The LHQ heaters• Two different heater layouts tested (only OL): ”pulse-wave” and ”LQ-style”• The measured delays with pulse-wave agree well with simulation• Simulation again overestimates the delay with ”LQ-style”. • Comsol simulations shows the non-uniform heater power distribution on the
heating segments.
T. Salmi 10
The SQXF-mirror, heaters in inner layer
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0 5000 10000 15000 20000
Del
ay (m
s)
Magnet current (A)
Heater delay on inner layer108 W/cm2217 W/cm2Meas. W 108 W/cm2 (by eye from the pdf)50 W/cm2Meas. With 50 W/cm2 (~ave)
• Measurement and simulation with 108 W/cm2 agree reasonably for Imag ≥ 13 kA • The low current regime and low heater power not captured in simulation.• Unlike in previous inner layer simulations, the simulation overestimates the delays
T. Salmi 11
Possible reasons for uncertainties with low current, low field, or low heater power
• Cable temperature increase slows down as heater power decreases and cable specific heat increases:– Small variations of Tcs have larger impact– Details of cooling and heat conduction
become more significant– Quench onset from voltage signals less clear
at low current – Current redistribution and heat generation
due to slow heating can occur (not modeled)• Magnetic field simulation important for Tcs –
Which field to use for each conductor?– I have used the field on coil surface (closest to the
protection heater), except for 11 T the maximum field because the field was significantly higher deeper in the cable
• Luckily, low current regime less critical for quench protection
0
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0 0.01 0.02 0.03 0.04Sim
ulat
ed c
able
max
. tem
p. (
K)
Time wrt. heater firing (s)
5 kA - 7th turn
14 kA - 4th turn
-0.03
-0.01
0.01
0.03
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0.07
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0.11
0.13
-0.08 -0.06 -0.04 -0.02 0
Vol
tage
(V
)
Time wrt. quench detection (s)
Fire PH (5 kA)
Quench onset (5 kA)
Quench onset (14 kA)
Fire PH (14 kA)
HQ01e voltage tap signals for a heater provoked quench at 5 kA and 14 kA.
Simulated temperature rise after heater activation.
T. Salmi 12
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
ms]
Magnet current / SSL
C20 (1.9 K)C20 (2.2 K)C20 (4.5 K)C20, 200 A/s (2.2 K)C20, 150 A/s (2.2 K)C20, HQ02b (1.9 K)C15 (1.9 K)C16 (1.9 K)Simul., criterion ASimul., criterion B
A possible conservative delay simulation criterion
• We need to add margin to the simulated heater delays for quench simulations• One option: Simulate delay time to the moment when cable Ic equals Imag. This
accounts for the temperature gradient in the cable cross-section.– Most of the measured delays on outer layer below this upper bound:
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0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
PH
del
ay [
ms]
Magnet current / SSL
C9 (1.9 K)
C9 (4.4 K)
C8 (4.4 K)
Simulation, criterion A
Simulation, criterion B
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
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Magnet current / SSL
Exp. (1.9 K)Exp. (4.5 K)Simulation, criterion ASimulation, criterion B
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
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Magnet current / SSL
Exp. (1.9 K)Exp. (4.5 K)Simulation, criterion ASimulation, criterion BHQ01e outer layer
HQ02a-b outer layer
11 T (MBHSP01) 11 T (MBHSP01)
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0 0.2 0.4 0.6 0.8 1
PH
del
ay [
ms]
Magnet current / SSL
Exp., HFU 2 (1.9 K)Exp, HFU 1+2 (1.9 K)Exp., HFU 2 (4.5 K)Exp., HFU1 (4.5 K)Exp., HFU1+2 (4.5 K)Simulation, criterion ASimulation, criterion B
Criterion A: Nominal simulaion, quench when cable Tmax = Tcs; Criterion B: Conservative criterion, quench when cable Ic = Imag.
11 T (MBHSP02)
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PH
del
ay [
ms]
Magnet current / SSL
Exp.Simulation, criterion ASimulation, criterion B
HD3 outer layer
T. Salmi 13
Summary of the heater delays• Outer layer heater delays typically within 20% of measurements, when above 50%
of SSL• Lower current has larger uncertainty• Uncertainties comparable with experimental uncertainty• Inner layer heater simulations have much larger uncertainty – but also the
experiments less well understood• LQ-style heater with short and complex shaped heating station not well simulated
with this model (simulation overestimates the delay)• The above simulations were for the high field region
• More analysis coming soon from comparison with the RMC tested at CERN (heater delays on high field and low field, AC-losses, current decay and NZPV)
T. Salmi 14
Coodi: Code for current decay computation based on known protection efficiency
Input: • For each turn:
– Heater delay, heating station length and period– Normal zone propagation velocity (between heating stations)– Magnetic field, Tcs
– Cable parametetrs• Magnet length, inductance vs. current, operating temperature, initial current• Initial normal zone length and location• Detection time, switches delays and external dump resistor
Each coil turn can have different heater delay and geometry (allows analysis of real heater geometres and delay distributions), different cables can be used to simulate graded coils.
The input delays and NZPV define the coil resistance development a priori. The code calculates the resistance at each time step, accounting for the different quenching times of the coil turns. The resistance drives the current decay. Temperature at the resistive coil turns and in the hotspot is calculated using the MIITs-concept at each time step. For each turn the heater covered segmentes and not-covered are treated separately.
T. Salmi 15
Area of insulated cable 35.61 mm2
Strand Cu /Nb3Sn ratio 1.15Voids fraction of bare cable 0.2Cable insulation thickness 0.145 mmWidth of cable 18.383 mmMid-thickness of cable 1.594 mmRRR 140 mmInter-layer insulation (G10) 0.5 mmInsulation between outer layer heater and collar
0.8 mm
Insulation between inner layer heater and bore
0.15 mm
Magnet length 7.2 m
Coil parameters*
A case study: What is the impact of different heater delay distributions?
* May not represent the latest design
Thanks to S. Izquierdo-Bermudez and V. Marinozzi for the field map.
T. Salmi 16
Simulated heater delay distributions, average delay in all cases 12.6 ms
0
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heat
er d
elay
(m
s)
Turn #
Case 6
Case 2
Case 3
Case 1
Case 4
Case 5
Case 1: CoHDA simulation with 150 W/cm2 peak power (τ = 50 ms), heater covers entire turn.Case 2: The average delay in every turn (12.6 ms).Case 3: The average delay for inner and outer layer.Case 4: A linear increase from 1 ms at turn #1 to 24 ms at turn #50. Case 5: A linear decrease from 24 ms at turn #1 to 1 ms at turn #50. Case 6: An exponential increase from 1 ms at turn #1 to 34 ms at turn #50.
• Detection time is 20 ms
Case Hotspot temperature (K)
1 2382 2413 2394 2335 2446 228
Entire turn quenches at the given delay time
Lower hotspot temperature when the quench starts faster in the high field region, even it means longer delay for low field region.
T. Salmi 17
0
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0 10 20 30 40 50
heat
er d
elay
(m
s)
Turn #
Case 6
Case 2
Case 3
Case 1
Case 4
Case 5
With 5 cm heating stations, 20 cm period
CaseHotspot
temperature with HS (K)
Hotspot temperature with
HS and average delay (K)
1 258 2682 261 2713 259 2694 253 2625 264 273 6 247 257
Heating station quenches at the given delay time, propagation between them at each time step
Entire turn quenches instantaneously, delay = heater delay + propagation time/2 (7.5 ms)
SS Cu
5 cm 15 cm
5 m/s 5 m/s
~ 20 K higher compared to covering entire turn~ 10 K higher compared with simulation with HS. Faster first delay, lower hotspot temperature…-> Better aim for short delay under HS.
T. Salmi 18
Summary of the heater modeling status• Heater delays for coil outer layers typically modeled well above 50% of SSL
– Uncertainty ~20% is comparable with experimental uncertainty• Lower currents and inner layer simulations have larger uncertainty
– Also the experimental uncertainty is larger• LQ-style heating stations require improvement to the model, because of non-
uniform heating in the heating station • More comparison with experiment foreseen in near future, and model development continues
• A code for computing magnet current decay and temperatures for different heater delay distributions was presented.
• A study was done to define what is a good criterion for heater layout optimization design– The result showed, that it is the best to aim at minimizing the delays to first
quenches, and to start the quenches in high field region• More detailed optimization needed, but in principle, better to put more
heating stations on high field region than low field.
T. Salmi 19
References for the details• T. Salmi et al., ”A novel computer code for modeling quench protection heaters in
high-field Nb3Sn accelerator magnets”, IEEE TAS 24(4), 2014 • T. Salmi et al., ”Analysis of uncertainties in protection heater delay time
measurements and simulations in Nb3Sn high-field accelerator magnets”,• T. Salmi, ”Optimization of Quench Protection Heater Performance in High-Field
Accelerator Magnets Through Computational and Experimental Analysis”, PhD Thesis, Tampere University of Technology, Finland
• T. Salmi et al., ”The impact of protection heaters delay distribution on the hotspot temperature”, Presented at MT-24.
