Thermal model for Nb3Sn Inner Triplet quadrupoles - 140 mm aperture option
Hervé Allain, R. van Weelderen (CERN)
4th September 2012
Overview• General aspect• Cases considered – proposed features• Coil insulations• Typical to be expected T-map for a coil with cooling
at 1.9 K up to 2.05 K• Parametric study•Main observations• Proposed features
Coil cooling principle•Heat from the coil area (green) and heat from the beam pipe (purple) combine in the annular space between beam pipe and coil and escape radially through the magnet “pole” towards the cold source “pole, collar and yoke” need to be “open”
•Heat Conduction mechanism in the coil packs principally via the solids, except for dedicated helium channels deliberately machined in the midplane
•Longitudinal extraction via the annular space is in superfluid helium, with T close to Tλ and with magnets up to 7 m long not reliable “pole, collar and yoke” need to be “open”
≥ 1.5 mm annular space
Superfluid helium cooling, 140 mm aperture, 2 cases considered:3.7 mm cold bore + 7 mm W inserts3.7 mm cold bore + 2 mm beam screen + 6 mm W absorbers
Proposed features
Feature Value comments
Annular gap 1.5 mm Safest choice for cooling and pressure rise due to quench
(to be verified)collar open 2 % Can be lower in steady state
Dynamic to be verifiedYoke open 2 % Can be lower in steady state
Dynamic to be verifiedTitanium piece open 4 % More investigation needed with the
real holesAluminium collar keys 4 % More investigation needed with the
real holesMidplane open
Beam screen actively cooled by helium channels
4 x 4.5 – 4.7 mm ID or8 x ~ 3.4 mm ID
estimated for ~ 400 W total
2 heat exchangers 68 mm ID calculated for ~ 500 W total
Some Materials thermal properties need to be measured
Naked coil in He II bath assumed for calculations to evaluate the best case
• Cable: 0.15 mm G-10 insulated
• 2-3-4 have been homogenized to form one mono layer
• Lack of some material thermal properties: need to be measured
2) 50 µm kapton + 25 µm stainless steel 50 % filled3) 200 µm G-104) 0.5 mm kapton
0.5 mm G-10
Inner coil layer Outer coil layerCold bore
Collars
2 3 4
1) 1.5 mm annular space1
0.5 mm G-10
Inner coil layer Outer coil layer
21 & 2: superfluid helium
1
Coil magnet configuration assumed for calculations
• Cable: 0.15 mm G-10 insulated
Energy deposition 2D map for Q1 at peak power
Courtesy of F. Cerutti and L. Salvatore
1) 3.7 mm cold bore + 7 mm W inserts 2) 3.7 mm cold bore + 6 mm W inserts + Beam Screen
Corresponding Energy deposition used for the model on the coil
Same heat load on the coil (~16 W/m)peak at 4.6 mW/cm3
Difference between 1 and 2: heat load on the cold bore -> 55.6 W/m2 for 1 and 6.8 W/m2 for 2
Absorbed by the heat exchanger
Simulated T-distribution
coils in a He II bath at 1.9 k coils in magnet configuration - HX at 1.9 kHe II channels in midplane (4 % open)
T He II midplane
Midplane He II channels closed 1 side open 2 sides open
T max (K) coils in a He II bath at 1.9 k 2.243 2.075 2.069
T max (K) coils in magnet configuration - HX at 1.9 k
3.265 2.396 2.377
ΔT (K) 1.022 0.321 0.308
Dangerous:T max He II midplane ~ 2.06 K
Too close to TLamda
Safe: T max He II midplane ~ 1.93 K~ Maximum effective
thermal conductivity of He II
Parametric study (1/2)
• Variation of the heat exchanger temperature• Midplane 4 % open, 2 sides open• Annular space: 1.5 mm
1.88 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 2.060
0.005
0.01
0.015
0.02
0.025
0.03ΔT max annular space
no beam screen, HeII channel 2 sides openbeam screen, He II channel 2 side openno beam screen, no He II channel
T heat exchanger
ΔT (K
)
1.88 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 2.060
0.05
0.1
0.15
0.2
0.25
0.3 ΔT max midplaneno beam screen, HeII channel 2 sides openbeam screen, He II channel 2 side openTlamda-Theat exchanger
T heat exchanger
ΔT (K
)
1.88 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 2.060.4
0.450.5
0.550.6
0.650.7
0.750.8
0.850.9
ΔT max on the coil
no beam screen, HeII channel 2 sides open
beam screen, He II channel 2 side open
no beam screen, no He II channel
T heat exchanger
ΔT (K
)
Parametric study (2/2)
• Variation of the midplane % open• 2 sides open• THX = 2.05 K• Annular space: 1.5 mm
He II -> He I in themidplane -> too dangerous
BS, if ≤ 2 % openno BS , if ≤ 3 % open
Remark:
3 4 5 6 7 8 9 10 110
0.02
0.04
0.06
0.08
0.1
0.12
0.14ΔT max midplane
no beam screenbeam screenDTlamda
% midplane open
ΔT (K
)
3 4 5 6 7 8 9 10 110.4320.4340.4360.438
0.440.4420.4440.4460.448 ΔT max on the coil
no beam screenbeam screen
% midplane open
ΔT (K
)
3 4 5 6 7 8 9 10 110
0.0005
0.001
0.0015
0.002
0.0025ΔT max annular space
no beam screenbeam screen
% midplane open
ΔT (K
)
Main ObservationsMidplane opened:
• Midplane open means He II channels in the midplane which communicate with the annular space and He II in space between laminations (NEED OF A WAY FOR THE HEAT TO GO TO THE HEAT EXCHANGER)
• Temperature field : 500 mK < Tmax coil – THX
• 7 mm W insert or 6 mm W insert + beam screen: • 1 side open Tmax HeII midplane over Tlamda (except for very low HX temperatures)
• 2 sides open assures functionality up to 2.05 K
• Safest choice: midplane > 7 % open (transits from He II to He I for Midplane ≤ 4 %)
• Caution: midplane taken open to He II homogeneously, more investigations needed with the real channels and experiments must be planned to assess the efficiency of the chosen geometry and design
Proposed featuresFeature Value comments
Annular gap 1.5 mm Safest choice for cooling and pressure rise due to quench
(to be verified)collar open 2 % Can be lower in steady state
Dynamic to be verifiedYoke open 2 % Can be lower in steady state
Dynamic to be verifiedTitanium piece open 4 % More investigation needed with the
real holesAluminium collar keys 4 % More investigation needed with the
real holesMidplane open 7 %
(≈ 35 µm for a 500 µm midplane spacing)
Assures functionality up to 2.05 KBeware of slit compression, actual size needs experimental validation
Beam screen actively cooled by helium channels
4 x 4.5 – 4.7 mm ID or8 x ~ 3.4 mm ID
estimated for ~ 400 W total
2 heat exchangers 68 mm ID calculated for ~ 500 W total
Some Materials thermal properties need to be measured
References1. “Investigation of Suitability of the Method of Volume Averaging for the
Study of Heat Transfer in Superconducting Accelerator Magnet Cooled by Superfluid Helium”, H. Allain, R. van Weelderen, B. Baudouy, M. Quintard, M. Prat, C. Soulaine, Cryogenics, Available online 14 July 2012.
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