thermo-mechanical 3d model of the 11t magnet

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



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)


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)


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]

7

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]

8

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

9

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/)

https://ieeexplore.ieee.org/document/8642408

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

https://iopscience.iop.org/article/10.1088/1361-6668/ab1f39/pdf

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.



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)




Cooldown

16

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




Cooldown

17

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




Cooldown

18

Flexible structure

Thermo-mechanical model

Thermal mechanical properties (4K)

Integrated thermal strain

Steady state overall

behavior and local

stress/strain fields




Cooldown

This approach is used for the 11 T cool-down behaviour shown in this presentation.

19

Cool-down(uniform cool-down)


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)


Layer jump

Analytical force

distribution

Integrated axial

force=440kN/aperture

Stress concentration

wedge-spacer

90 MPa

22


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).


Powering(440 kN axial load/aperture shared between inner/outer layers)


(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


CS


Crack initiation




26

Magnet testing


CS


Interface

Interface


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

28

Flexible structure

Back slides

29

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

thermo-mechanical 3d model of the 11t magnet

Documents