thermo-mechanical 3d model of the 11t magnet
TRANSCRIPT
Thermo-mechanical 3D model of the 11T magnet
11T Task Force - Team 1:
Cédric Garion, Marco Morrone, Jérôme Harray, Fabrice Santangelo
TE-VSC-DLM 03/06/2021
Outline
• Aim of the model
• General considerations
• Input• Geometry
• Material properties
• Contacts
• Mesh and coordinate systems
• Sub-modelling
• Loading phases• Pre-stress of the coil
• Shell welding
• Bullet loading
• Cool-down
• CFD coupling for transient study
• Quasi-static study
• Powering
• Visual inspection of a tested coil
• Conclusions
• Next steps2
Aim of the model
• Understand the overall behaviour of the 11 T series magnet, in particular
in the connection side during the thermal and powering cycles;
• Validation of the loading phases via available measurements;
• Assess the transfer of the E.M. longitudinal force within the structure;
• Identify critical areas during thermal and powering cycles.
Not aiming at
• Precise study of the complex collaring phase;
• Local stress distribution in the cable.
3
General considerations for the modelling
of the 11 T series magnet
During CD:
• No longitudinal interaction between the yoke and the shell
• Shell is in tension and interact directly with the coil
𝛼𝑠ℎ𝑒𝑙𝑙 > 𝛼𝑐𝑜𝑖𝑙
1. The 98 % packing factor of the yoke can take the
differential thermal contraction between the yoke and the
shell (2% free >> differential thermal contraction -0.9E-3);
2. Yoke and shell ends are independent (the shell can
contract more than the yoke);
3. The laminar structures (yoke, collars, central lamination)
are modelled as transversally isotropic bulk material;
4. The azimuthal and radial stiffness of the collars is halved
due to alternating plates holding the keys.
CD
Coil contracts less than the shell
Loading of the bullets
Shell
End
pla
te
CoilCollar
Yoke
Integrated thermal contraction: 2.05E-3Packing factor: 98%
Integrated thermal contraction: -2.7E-3
Integrated thermal contraction: -2.71E-3
Integrated thermal contraction: -2.95E-3
4
Geometry
2875 mm
End
plateYoke (bulk)Kawasaki
(bulk)
Central lamination (bulk)
918 mm1862 mm
Detailed coilEquivalent coil (bulk)
A quarter of half a magnet, connection side, is modelled by adopting some simplifications :
75mm2474 mm 306 mm
End plate
Half moonCollar
Coil
Shell
Weld
Bullets
Transversal cross-sections:
5
Saddle
Cables (bulk)
Spacers
Pole
Wedges
No gap with
winding key
Winding key
Saddle
Cables (bulk)
Spacers
Pole
Wedges
Insulation layer
Loading plate
0.5 mm gap between wedge
and spacersLayer jump
Geometry
Outer and inner coils:
6
Material properties
Yoke - central laminations
(Magnetil)
Transversely isotropic
ET=210 GPa
EL=0 GPa
GL-T=2.1 GPa
νT= 0.3
νL-T = 0
CTE= -2.05E-3
Austenitic yoke
(KHMN30L-Kawasaki steel)
Transversely isotropic
ET=210 GPa
EL=0 GPa
GL-T=0.59 GPa
νT= 0.3
νL-T = 0
CTE= -1.85 E-3
Shell
(316 LN)
Isotropic
E=210 GPa
ν= 0.3
CTE= -2.95E-3
Collar
(X8CrMnNiN19-11-6)
Transversely isotropic
ET=101 GPa
EL=0 GPa
GL-T=8.62 GPa
νT= 0.33
νL-T = 0
CTE= -2.7 E-3
Coil
(composite)
Equivalent
E=105 GPa
νT= 0.3
CTE= -2.71E-3
Saddle
(G11)
Orthotropic
E_r=15.9 GPa
E_θ=24 GPa
E_z=23.2 GPa
ν= 0.21
CTE_r= -7E-3
CTE_ θ=-2.5E-3
CTE_ z=-2.5E-3
Spacers –Winding key
(316 L)
Isotropic
E=206 GPa
ν= 0.3
CTE= -3E-3
End plate
(316 L)
Isotropic
E=206 GPa
ν= 0.3
CTE= -3E-3
Material properties at 4 K. Coefficient of Thermal Expansion (CTE) integrated from 300 K to 4 K.
[1] [2] [3] [4]
[5] [6] [4] [7] [7.1]
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Material properties
Pole
(Ti 6Al-4V)
Isotropic
E=127 GPa
ν= 0.3
CTE= -1.74E-3
Wedge
(ODS-Copper "Glidcop" )
Isotropic
E=93 GPa
ν= 0.3
CTE= -3.07E-3
Loading plate
(316 L)
Isotropic
E=206 GPa
ν= 0.3
CTE= -2.94E-3
Insulation layer
(kapton)
Isotropic
E=8.96 GPa
ν= 0.34
CTE= -12E-3
Cable block
(Nb3Sn)
Orthotropic
ν= 0.3
E_long. = 95 GPa
E_rad. = 80 GPa
E_azim. = 31 GPa
[4]
[10][11]
[8]
[9]
Material properties at 4 K. Coefficient of Thermal Expansion (CTE) integrated from 300 K to 4 K.
CTE_long. = -2.8E-3
CTE_rad. = -2.5E-3
CTE_azim. = -2.5E-3
[11.1][10.1]
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Contacts
Frictionless contact
Frictional contact (μ=0.2)
Winding key-pole
Bulk coil-pole
Bulk coil
Yoke - collar
Collar - coil
Lateral surfaces pole - coil
Shell-Yoke
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Mesh and coordinate systems
Two cylindrical coordinate systems are used to assign
the material properties. One centred in the coil (red)
and the other at the centre of the magnet (blue).
A curvilinear system is adopted to better distribute the
Lorentz force and to account for the curvature of the cable
in the material properties.
Around 200 k quadratic elements (tetrahedral type) are used.
The average quality element is 0.55*. The sub modelling technique
is used to refine the mesh in the areas of interest.
*Comsol recommends to have an
average quality as of 0.5.10
Sub-modelling
The submodelling technique is implemented in the model to have a better mesh and then higher stress/strain
resolution in critical areas. However there are some underlying assumptions when using submodels:
• The global model is accurate enough to give correct displacements on the boundary to the submodel.
• The improvements introduced in the submodel are so small that they do not introduce significant changes in
stiffness on the global level. Given this, it could still be possible to introduce a nonlinear material locally in the
submodel.
Coil
Sub-model
Full model
Full model
Full model
Head
Sub-model
Layer Jump
Sub-model
Boundary displacement
of the main model needs to be
assigned to each submodel-surface
11
Loads are applied in sequential steps:
Loading phases
Prestress in the coil
(variable excess up to 0.3 mm at the interface
pole/coil)
Shell welding
(0.6 mm pull on the shell)
Bullet loading
(offset at the interface end-plate bullets)
Cooldown (2 options)
1) transient decrease from 300K 4K by means of CFD analysis.
Ideal to assess mechanical behaviour during the cool-down;
2) quasi-static uniform decrease from 300K 4K by means of integrated thermal strains ΔL/L.
Powering
(440 kN axial load/aperture shared between
inner/outer coils)
0.6 mm
0.3 mm
excess
45 kN
F_axial
12
13
Prestress of the coil (variable excess up to 0.3 mm at the interface pole/coil)
Radial stress [MPa]
Azimuthal stress [MPa]
0 mm
0.15 mm
0.3 mm
The excess is set as a contact offset between the pole and the
loading plate. It is variable along the pole.
Peak stress mid-plane = 140 MPa as measured in https://ieeexplore.ieee.org/document/8642408 by Task Force 1.
New measurements are being carried out by Task Force 2 - team 4 (https://indico.cern.ch/event/1037106/)
Shell welding(0.6 mm pull on the shell)
Radial stress [MPa]
Azimuthal stress [MPa]
Strain gauges mounted
at the level of the busbars
(Table 8, p.14): https://iopscience.iop.org/article/10.1088/1361-6668/ab1f39/pdf
The shell is pulled by 0.6 mm.
This reproduces the stress measured during this operation.
220 – 230 MPa
Vs 250 MPa (measured)
230 360FEM 130
14
Courtesy E. Gautheron
Bullet loading (calibrated offset in the bullet)
A calibrated offset between the end plate and the bullets is used
to assign the axial prestress. This offset is kept constant during
the other phases, engaging the shell with the coil.
The force transferred via the bullet is 40 kN.
This corresponds to the measured force at RT (red bar in the bar chart).
Longitudinal stress [MPa]
The coil is free to move
axially during the collaring
and welding phases.
Longitudinal stress [MPa]
Courtesy E. Gautheron
15
Flexible structure
Simplification of the flow in 1-DThermal model
CFD-THERMAL coupling
Transient local
temperature field
during cool down
Helium flow
properties
Transient and steady state
overall behaviour and local
stress/strain fields
Thermo-mechanical model
with submodelling
Results shall be compared with local and overall measures (temperature, strain, forces,…)
Thermal properties (T)
Thermal mechanical properties (T)
1) transient decrease from 300K 4K by means of CFD analysis.
Ideal to assess mechanical behaviour during the cool-down;
2) quasi-static uniform decrease from 300K 4K by means of integrated thermal strains ΔL/L.
Cooldown
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2 X
dhyd ≈ 23 mmm = 5g/s (10%)
Ø60mmm = 20 g/s (40%)
Total flow: 50 g/sP=3.5 bara
1
2a
3b
2b
4 X
dhyd ≈ 18 mmm = 5.0 g/s (10%)
• The CFD calculation is simplified in a 1-D approximated flow. Advection is considered (No NS/RANS equations
computed);
• The convective heat coefficient is automatically calculated through analytical formulations;
• The input parameters are: pipe shape & dimensions, friction model for pressure loss, inlet pressure, temperature,
tangential velocity, mass flow rate.
• The thermal physics (heat equation) is coupled with the CFD physics to account for the convective heat flux;
• Temperature dependence of material properties is accounted.
• Measured Inlet temperature is used as input of the model.
• Symmetry conditions are used.
Temperature profile at the inlet as input
Cooling channels for the CFD modelMass flow distribution
1) transient decrease from 300K 4K by means of CFD analysis.
Ideal to assess mechanical behaviour during the cool-down;
2) quasi-static uniform decrease from 300K 4K by means of integrated thermal strains ΔL/L.
Cooldown
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Instrumented S2
Test 25.08.20 to 150K
CD config:
ሶ𝑚=50 g/s
Tgas_out-Tgas_in = 30K
Temperatures obtained by simulations are in good agreement
with measurements.
• maximum temperature difference between the
measurements and simulations is below 3% for the main
cooling channel.
• Maximum difference simulation/measurement of 9 % is
obtained on the shell.
Main results:
• Temperature gradient in helium along main cooling channel around 13 K.
• Longitudinal temperature gradient in the
structure around 20 K.
• Radial average temperature difference in the
magnet structure around 5K.
• Collar temperature at CS always lower than
coil temperature.
• The CFD-thermal model and cooldown test
on an instrumented magnet do not exhibit any
specific issue or critical areas related to the
cooldown transient.Average temperature difference on CS Average temperature difference on NCS side
Comparaison measurement/simulation of the
inlet and outlet temperatures
1) transient decrease from 300K 4K by means of CFD analysis.
Ideal to assess mechanical behaviour during the cool-down;
2) quasi-static uniform decrease from 300K 4K by means of integrated thermal strains ΔL/L.
Cooldown
18
Flexible structure
Thermo-mechanical model
Thermal mechanical properties (4K)
Integrated thermal strain
Steady state overall
behavior and local
stress/strain fields
1) transient decrease from 300K 4K by means of CFD analysis.
Ideal to assess mechanical behaviour during the cool-down;
2) quasi-static uniform decrease from 300K 4K by means of integrated thermal strains ΔL/L.
Cooldown
This approach is used for the 11 T cool-down behaviour shown in this presentation.
19
Cool-down(uniform cool-down)
Longitudinal stress [MPa]
Tensile stress appears at the interface between:
1) pole and the winding key (layer jump),
2) wedges-spacers,
3) cable-saddle.
In these areas cracks might propagate.
Mismatch CTE pole-cable
Stress concentration wedge-spacer
Saddle-cable
Layer jump
100 MPa
20
Longitudinal stress [MPa]Longitudinal stress [MPa]
The forces in the 4 bullet gauges after cool-down is
180 kN.
The one measured in the double aperture magnet
varies between 150 kN and 180 kN (see red circles).
Longitudinal stress [MPa]Courtesy E. Gautheron
Cool-down(uniform cool-down)
(longitudinal cut)
Mismatch CTE saddle-coil induces
some bending
Tensile stress for the wedges due to
a high CTE.
Compression stress for the pole due
to a low CTE.
90 MPa 21
Powering(440 kN axial load/aperture shared between inner/outer layers)
Longitudinal stress [MPa]
Layer jump
Analytical force
distribution
Integrated axial
force=440kN/aperture
Stress concentration
wedge-spacer
90 MPa
22
Longitudinal stress [MPa]
The forces in the 4 bullet gauges after powering is
380 kN, corresponding to 45 % of the powering force
transferred to the bullets.
The ratio measured in the double aperture magnet is
around 40 % (see red circles).
Courtesy E. Gautheron
Powering(440 kN axial load/aperture shared between inner/outer layers)
Longitudinal stress [MPa]
(longitudinal cut)
Light tensile stress in some areas of
the cable due to the longitudinal
force (10-25 MPa)
23
Visual inspection of a tested coil (G03)
24
Magnet testing
After impregnation After de-collaring
CS
Top picture coil orientation
Courtesy F. Savary @ 78th Meeting of the HL-LHC TCC
25
Magnet testing
After impregnation After de-collaring
CS
Top picture coil orientation
Crack initiation
Courtesy F. Savary @ 78th Meeting of the HL-LHC TCC
Visual inspection of a tested coil (G03)
Courtesy F. Savary @ 78th Meeting of the HL-LHC TCC
26
Magnet testing
After impregnation After de-collaring
CS
Top picture coil orientation
Interface
Interface
Visual inspection of a tested coil (G03)
Flexible structure
Conclusions
• A 3D CFD-thermal-mechanical model of the 11T has been developed and
is available. Most of the thermal mechanical materials properties have been
confirmed or re-evaluated.
• The CFD-thermal model and cooldown test on an instrumented magnet do not
exhibit any specific issue or critical areas related to the cooldown transient. The
30K temperature difference (inlet/outlet) is appropriated for the cooling of the
11T magnet.
• The model allows a much deeper understanding of the overall thermal
mechanical behaviour of the magnet. Results of the overall behaviour are in
rather good agreement with measurements.
• The transition between the curved and straight parts of the coils seems to be
the most critical. It cumulates:
• Effect of the thermal contraction mismatch between the Ti pole and the coil.
• Powering longitudinal force not fully transferred to the mechanical structure
due to a soft longitudinal support (saddle).
• Geometrical singularities.
27
Flexible structure
Next steps
• Refine the thermal-mechanical model:
• Implement a kinematic hardening model to account for the non-linearitiy of the
cable as recently measured by team 7 (EDMS 2572505);
• Study mitigation solutions.
• Effect of the thermal contraction mismatch between the Ti pole and the coil
gap pole/winding key,…?
• Powering longitudinal force not fully transferred to the mechanical structure
due to a soft longitudinal support (saddle) stiffer support, additional
features,…?
• The experience gained in the 11 T modelling can be shared with the MQXF team
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Material references:
[2] M. Fukuhara and A. Sanpei, ISIJ International, vol 33(4), p508 (1993) and J.A. Rayne and B.S. Chandrasekhar, Physical Review, v122, p1714 (1961)[2.1] F. Bertinelli et al., Production of Low-Carbon Magnetic Steel for the LHC Superconducting Dipole and Quadrupole Magnets, LHC Procer report 298, 2006.
[4] S.S. Lee, U-S. Min, B. Ahn and S.H. Yoo, J. Materials Science, v33, p687 (1998); and H.M. Ledbetter, J. of Applied Physics, v52 no. 3, March (1981)
[5] Bertinelli, F., Fudanoki, F., Komori, T., Peiro, G., & Rossi, L. (2006). Production of austenitic steel for the LHC superconducting dipole magnets. IEEE transactions on applied superconductivity, 16(2), 1773-1776.
[3] Ozaki, Y., Furukimi, O., Kakihara, S., Shiraishi, M., Morito, N., & Nohara, K. (2002). Development of non-magnetic high manganese cryogenic steel for the construction of LHC project's superconducting magnet. IEEE transactions on applied superconductivity, 12(1), 1248-1251.
[6] C. Garion, M. Morrone. 3D Thermal mechanical behavior of the 11T cold mass during cool down. Technical Note in progress
[7] O. Sacristan, G11 – Mechanical characterisation at 77 K. CERN, EDMS_2447618, 2021.[7.1] M.B. Kasen, G.R. MacDonald, D.H. Beekman, and R.E. Schramm, Mechanical, electrical, and thermal characterizationof G-10CR and G-11CR glass cloth/epoxy laminates between room temperature and 4 K, in Advances in Cryogenic Engineering, Vol. 26, (Plenum, New York, 1980).
[8] AF Clark. Advances in Cryogenic Engineering Materials, volume 26. Springer Science & Business Media, 2012
[9] RMI Titanium Co., 1000 Warren Ave., Niles Ohio, 44446, USA and NIST, Physical and Chemical Properties Division, Cryogenics Technologies Group at http://cryogenics.nist.gov/
[11] Wolf, F., Lackner, F., Hofmann, M., Scheuerlein, C., Schoerling, D., & Tommasini, D. (2019). Effect of epoxy volume fraction on the stiffness of Nb 3 Sn Rutherford cable stacks. IEEE Transactions on Applied Superconductivity, 29(5), 1-6.
[10] Scheuerlein, C., Lackner, F., Savary, F., Rehmer, B., Finn, M., & Uhlemann, P. (2016). Mechanical properties of the HL-LHC 11 T Nb 3 Sn magnet constituent materials. IEEE Transactions on Applied Superconductivity, 27(4), 1-7. ONLY R.T. DATA
[1] Sgobba, S., Kumpula, M., Liimatainen, J., & Savary, F. (2000). A powder metallurgy austenitic stainless steel for application at very low temperatures (No. CERN-EST-2000-008-SM).[1.1] J.P. Arnaud, inox 316LN – SPT1 – LX15/TX15, Thermal expansion, NOTE SBT/CT14-47, CEA-GRENOBLE, 2017.
[10.1] J.P. Arnaud, ODS Copper Discup C3/30 thermal expansion, NOTE SBT/CT12-28, CEA-GRENOBLE, 2012.
[11.1] Kriboo et al., Dilatation of impregnated coil samples, Nov. 2019, CRG report.
30
Courtesy O. Sacristan, M. Guinchard
10 stacks cables have been measured by the team 7 in the 3 directions at 293 K and 77 K (May 2021).
The axial behaviour of the cable needs further testing due to a large spread.
The Armstrong-Frederik hardening model is being implemented in Comsol to reproduce the measured behaviour of the
conductors.
Armstrong-Frederik
hardening model
For illustration only
31