1. TS Cool Down Studies TSu Unit Coils (24-25) N. Dhanaraj and E. Voirin Tuesday, 10 March 2015 Reference: Docdb No:5217 1

2. Introduction Goal: Perform a cool down analysis on the TSu and estimate a safe deltaT between the cold mass and inlet helium for cool down based on the thermal stresses produced due to the difference in the co-efficient of thermal expansion. Unit under Study: Worst case scenario with end unit where helium enters into the magnet, where deltaT will be maximum. 2

3. Types of Analysis Performed 3D model analysis assuming coil to be a monolithic block with average properties – N. Dhanaraj 2D axisymmetric model with discrete model of cable cross sections – E. Voirin Both analyses used same material properties for individual materials. 3

4. 3D Analysis Materials: 4 Cooling Tubes, Al 6063-T6 Housing, Al 5083-O Cooling Strips, High Purity Aluminum Coil Block, Multiple Materials Wedge, Al 5083-O Coil Block surrounded by insulation Ground insulation ranging from 4 mm – 12mm

5. Cable Cross Section 5 250 microns E-glass/Epoxy Conductor Cross Section Courtesy of M. Lopes docdb-4882

6. Average Coil Properties - Derived 1.Thermal Conductivity 2.Co-efficient of Thermal Expansion 3.Elastic Modulus and Poisson’s Ratio 4.Shear Modulus 5.Specific Heat and Density 6

7. FEA Model 7 0.26 Million Elements with 1.24 Million nodes

8. Thermal Contact Conductance Contact due to a interference fit between the coil assembly and bobbin of 100 microns gives a contact pressure of 0.103 MPa and TCC of 10 W/m^2-K 8

9. Thermal-Stress Analysis Final Condition @ 1800 seconds Initial Condition: Cold Mass @ 300 K and Cooling Tube @ 260 K (helium temperature) Transient Thermal Analysis: 9

10. Steady State Stress Analysis – Fixed Face Stress Analysis @ every 200 sec increment shows maximum stress at 1800 seconds Boundary Condition: Fixed Face or Free Radial Face Steady State Stress Analysis: 10 Housing Shell Face Fixed (bolted to support module)

11. Steady State Stress Analysis – Free Radial 11

12. Weld Stresses 12

13. Weld Stresses (contd.) Al6063-T6 yield strength = 78 MPa in welded condition, B31.3. Also, this is localized stress in the cooling tube would go down if analyzed using SCLs. 13

14. Result Summary TSU Coil Numbers Ground Plane thickness (mm) Thermal Contact Conductance (W/m^2-K) Boundary Condition DeltaT (K)Maximum Stresses in Coils (MPa) 24-251210Fixed4039.1 [5671 psi] 24-251210Free Radial Motion 4040.7 [5910 psi] 14 Thermal-Stress Analysis Results Thermal Analysis (only) Results TSU Coil Numbers Ground Plane thickness (mm) Thermal Contact Conductance (W/m^2-K) Boundary Condition DeltaT (K)Cool down Rate (K/hr) 24-25410Fixed301 24-25410Perfectly Bonded 306.35 24-251210Fixed401

15. Conclusions The 3D analysis showed von mises stresses in the coils that exceeded the yield strength of the cold worked aluminum stabilizer, which has a room temperature yield strength of 30 MPa. A conclusion was made that the deltaT of 40 K was not safe to use and thus a deltaT of about 23 K shall be used assuming the stresses would decrease linearly with the smaller deltaT. The 3D analysis also provided information on the initial cool down rates. With a TCC of 10 W/m^2-K and a ground plane of 4 mm the cool down rate for the first 30 K was 1 K/hr, similarly for the same TCC and 12 mm ground plane, the cool down rate for the first 40 K was 1 K/hr. The cool down rate increases when a perfectly bonded condition is assumed between the coil and bobbin to about 6.35 K/hr. 15

16. Cool Down Parameters Comparison Experiment/MagnetDeltaT (K)Cool Down Rate (K/hr) Notes ATLAS40 K2.5From ambient to ~ 100 K [1] CDF20 K2deltaT measured between inlet and outlet helium [2] CMS50 KN/AdeltaT used up to 100 K, flow rate 90 g/s [3] DZeroN/A2Notes from paper for cool down up to 90 K [4]: helium temperature at the inlet to the solenoid tubing is 100 K below the support cylinder temperature with a minimum helium temperature of 80 K 16

17. TS3 Cool Down (40K DT) Axis-Symmetric Model Model Included Coils and composite coil wrappings. Since result of interest is stress in the the coils, structural model is unconstrained which raises resulting stress in coils, lowers in mandrel part. Sensitivity analyses performed for both the convection coefficient, and the thermal contact of the coils. 17

18. Bottom Coil Stress 5 W/m 2 /K Thermal Contact Conductance of Coil to Mandrel Maximum Stress in Coils occurs at 2280 sec (6720.5 psi) 18

19. Top Coil Stress 5 W/m 2 /K Thermal Contact Conductance of Coil to Mandrel Maximum Stress in Coils occurs at 2520 sec (5747 psi) 19

20. Contact Conductance Sensitivity Nandhini’s research showed this should be > 10 W/m 2 /K. High Sensitivity with a plateau Stress if a function of Delta T 20

21. Convection Coefficient Sensitivity Based off Flow rate of Helium Gas (30-114 gm/sec) = (1500-3500 W/m 2 /K) Low Sensitivity 21

22. Reduce Delta T steps from 40K down to 23K Coil Stress Reduces to 3662 psi 22 Reduce Delta T to 23K

23. Detailed Look at Composite Wrappings Weakest in tension in the out-of-plane direction as that pulls on epoxy without parallel strengthening of glass fibers. Failure Criteria: http://www.nedform.com/magento/en/araldite-f-hy-905-dy-040-dy-061.html?___from_store=nl http://www.nedform.com/magento/en/araldite-f-hy-905-dy-040-dy-061.html?___from_store=nl  Up for discussion:  UTS: 5.5 Mpa (800 psi)  Flexural Strength: 130 Mpa (19 ksi) 23

24. Composite Wrapping Strain No Problems with in plane stress  Maximum principal strain of 0.3%.  Tensile Failure Strain is 1.75% (Warp)  Tensile Failure Strain is 1.55% (Fill)  http://www.bnl.gov/magnets/staff/gupta/scmag-cours. http://www.bnl.gov/magnets/staff/gupta/scmag-cours 24

25. Bottom Coil Out of Plane Stress (472 psi) 25

26. Top Coil Out of Plane Stress (873 psi) 26

27. Top Coil Out of Plane Stress (811 psi) ( with increased Thermal Conductance of 10W/m 2 /K) 27

28. Failure Criteria?? Max Out of plane Stress = 811 psi > Epoxy UTS of only 800 psi  Obtained from Tensile tests But Flexural Strength is 19000 psi  Obtained from bending tests, which impart maximum tensile stress on the outer surface of the specimen at one location. Both Tensile stresses!?! Why the large difference in strength?  Theoretically, and with perfect materials, they should be the same  Tensile test takes the entire volume to maximum stress  Bending Test applies maximum stress to only a small portion  Statistical and has to do with voids / imperfections / mixing ratios in epoxies 28

29. Above UTS concerning??? VERY small location of maximum stress above 800 psi.  Much smaller chance of void  Glass fibers in that area will strengthen voids.  If it cracks because of a void in that very small volume, well there was already an imperfection there to begin with!  Crack would be along plane, not through to adjacent coil.  Model Boundary Conditions are conservative (zero structural supports) Stress in coils/epoxy would go down with supports which lower deformation in the mandrel.  Overall, not concerned that stress is above the UTS 29

30. Temperature Distribution at maximum out of plane stress. Occurs at 2640 sec. Questions? 30 Temperature Distribution