Use of COMSOL Multiphysics in the Design of an HTS Insert ...€¦ · LTS 137 A HTS 400 A Center: n...
Transcript of Use of COMSOL Multiphysics in the Design of an HTS Insert ...€¦ · LTS 137 A HTS 400 A Center: n...
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Use of FEM in the Design of an HTS Insert Coil for a High Field NMR Magnet
Ernesto S. Bosque HTS NMR Magnet Projects, ASC, NHFML
2 October 2014 – Post Doc Seminar
U.P. Trociewitz, D.S. Davis, P. Chen, D.K. Hilton, S. Miller, G.E. Miller, C.L. English, D.C. Larbalestier, I. Litvak, W.W. Brey, T.A. Cross, L. Frydman
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Platypus: An HTS NMR Magnet System
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‘As Designed’ Magnetic Field Analysis
2D-axisymmetric geometry • Low Temperature Superconductor (LTS)
NbTi and Nb3Sn
• High Temperature Superconductor (HTS) Bi2212 round wire
Magnetic Fields (mf) interface: • General PDEs
∇ × H = Je B = ∇ × A
• Current (I) to coils LTS 137 A HTS 400 A Center: n =179, m =18 Compensation: n = 46, m = 3 with Jw defined as I . m . n/area
• Far field evaluated with perfect conductor
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‘As Designed’ Magnetic Field Maps (LTS)
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‘As Designed’ Magnetic Field Maps (LTS)
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‘As Designed’ Magnetic Field Maps (LTS)
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‘As Designed’ Magnetic Field Maps (LTS)
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‘As Designed’ Magnetic Field Maps (LTS)
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‘As Designed’ Magnetic Field Maps (HTS)
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‘As Designed’ Magnetic Field Maps (HTS)
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‘As Designed’ Magnetic Field Maps (all)
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‘As Designed’ Total Magnetic Field Map
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High Homogeneity Requirement
Bz(0,0) – Bz(0,5) Bz(0,0)
h [ppm] = 1e6
B(0,0) [T] B(0,5mm) [T] h [ppm] 1.954739 1.954688 2.027699 2.027614 2.766974 2.766788 3.923075 3.922821 5.748768 5.748296
16.421254 16.420207 63.7877 6.577521 6.576254 0.226399 0.228721 6.803920 6.804975 -155.1064
23.225174 23.225182 -0.3383
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Concern of Mandrel Magnetization
Magnetization (M) vs field strength (H) data collected by Jun Lu and fits provided by David Hilton.
H ≡ (1/μ0 . B - M)
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Mandrel Magnetization
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Concern of Thermal Contraction 2D-axisymmetric • Active domains highlighted • Material List:
1. Inconel 600 2. Alumina 3. Stycast 1266 4. G-10
Thermal Stress (tc) interface: • General PDEs
-∇∙σ = FV ρCpu ∙ ∇T = ∇∙(k∇T) + Q
• Initial temperature T = 300 K
• Final temperature T = 4.2 K (everywhere)
• Fixed constraint at bottom of bore tube u = 0
Moving Mesh (ale) interface: To keep track of all geometric deformations.
Map of von Mises Stress [MPa]
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‘As Designed’ Total Field
23.185
23.190
23.195
23.200
23.205
23.210
23.215
23.220
23.225
23.230
-50 -30 -10 10 30 50
Mag
netic
Flu
x D
ensi
ty [T
]
Position Relative to LTS Outsert Center [mm]
As Designed: No Thermal Contraction
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Thermal Contraction Compensation
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Field of Thermally Contracted ‘As Designed’
23.185
23.190
23.195
23.200
23.205
23.210
23.215
23.220
23.225
23.230
-50 -30 -10 10 30 50
Mag
netic
Flu
x D
ensi
ty [T
]
Position Relative to LTS Outsert Center [mm]
As Designed: No Thermal Contraction
As Designed: Thermally Contracted
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Compensated Thermal Contraction
23.185
23.190
23.195
23.200
23.205
23.210
23.215
23.220
23.225
23.230
-50 -30 -10 10 30 50
Mag
netic
Flu
x D
ensi
ty [T
]
Position Relative to LTS Outsert Center [mm]
As Designed: No Thermal ContractionAs Designed: Thermally ContractedCompensated Design
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Stress Analysis of Platypup (Stress Test Coil)
2D-axisymmetric • Stress coil
1.3 mm round wire ~10% of Platypus height
• Material List: 1. Inconel 600 2. Alumina 3. Silver 4. Stycast 1266
• Assume good epoxy impregnation • Three step process:
First run thermal contraction to determine pre compression Then run magnetic field analysis using Je of each wire Finally, run structural mechanics with Lorentz body force on wires
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Exaggerated Thermal Stress Map
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Thermal Stress Analysis Deconstructed
Rad
ial S
tres
s A
xial
Str
ess
Tension Compression
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Coefficients of Thermal Contraction (alpha)
Axial Tension
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Step 2: Apply Current to Deformed Geometry Magnetic Fields (mf) interface: • Current (I) to coils 400 A
Coil: n =15, m =18 with Je defined as I/area
• Far field evaluated with perfect conductor
• Platypup modeled as an insert in the LTS magnet the finished coil will be put into
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Magnetic Field Calculation
Lorentz Body Force = J × B
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Step 3: Structural Analysis Solid Mechanics (solid) interface: • General PDE
-∇∙σ = FV
• Body force defined from magnetic field analysis: FV = J x B
• Fixed Constraint at bottom of bore tube.
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Final Stress Analysis Deconstructed
Rad
ial S
tres
s A
xial
Str
ess
Tension Compression
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Radial Tension ~ Wire Tension
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Summary COMSOL Multiphysics has been extensively used to model the HTS NMR Magnet System
• Preliminary magnetic field analyses agree well with analytical field calculations done prior to the onset of numerical modeling.
• Volumetric magnetization shown to have an appreciable effect on the homogeneity of the produced field.
• Thermal contraction of the Platypus design needs to be fully understood to achieve the ~1 ppm field homogeneity target.
• A three step approach: thermal stress magnetic field analysis structural mechanics provides insight to the true stress experienced by each winding in the winding pack.