Figure 1 – NSTX Upper Umbrella Assembly Upgrade Design: Version 4

1. Figure 1 – NSTX Upper Umbrella Assembly Upgrade Design: Version 4

2. Figure 2 – Single Segment 3-Strap Assembly Solid Model: Version 4

3. Figure 3 – ANSYS Multiphysics Analysis Block Diagram

4. Figure 4 – Single Segment 3-Strap Assembly FEA Model: Mesh

5. Figure 5 – Single Segment 3-Strap Assembly Electric Model Results: Voltage

6. Fig. 6 – Single Segment 3-Strap Assembly Electric Model Results: Current Density

7. Figure 7 – Single Segment 3-Strap Assembly Electric Model Results: Joule Heat

8. Fig. 8 – Single Segment 3-Strap Assembly Thermal Model Results: Temperature

9. Study: Determine Current Best-Practice to Perform Magnetostatic Analysis in ANSYS 12.0 WorkBench • New SOLID236/237 magnetic analysis elements • Have both Magnetic Vector Potential (MVP) and Line Edge method capability. Replaces SOLID97 and SOLID117. • Compatible with WB generated Electric, Thermal, and Static Structural analyses meshes. • No 3D MVP or Line Edge contact elements • Requires conformal mesh with shared nodes across the joints, which makes modeling assemblies including frictional and pressure-dependent electric and thermal contact impossible, or • Non-conformal/ dissimilar mesh, with duplicate nodes across the joint. Magnetic coupling using CPINTF command requires nearly-matched meshing, which is difficult to achieve in a large assembly. • Above problems are greatly reduced if modeling the air enclosure, and modeling the magnetic coupling across the joints, are not necessary • May be valid for materials with a relative magnetic permeablity = 1. • Goal: Prove with a comparison study.

10. Air B = 1 T I = 4074 A Merged Volumes Outer-most Lamination Arch Segment with Air Enclosure: Solid Model

11. Conformal Mesh: Nodes shared at Interface (perfect magnetic coupling) Outer-most Lamination Arch Segment with Air Enclosure: Mesh

12. Arch Segment w/ Air Magnetostatic Model Results: Current Density (A/m^2)

13. Arch Segment w/ Air Magnetostatic Model Results: Joule Heat

14. SOLID236: LINE EDGE METHOD Arch Segment w/ Air Magnetostatic Model Results: Magnetic Flux (Metal +Air)

15. Arch Segment w/ Air Magnetostatic Model Results: Magnetic Flux (Metal Only)

16. Arch Segment w/ Air Magnetostatic Model Results: Current Density

17. Arch Segment w/ Air Magnetostatic Model Results: Lorentz Forces (N)

18. Arch Segment w/ Air Magnetostatic Model Results: Magnetic Flux (Metal Only)

19. Arch Segment w/ Air Magnetostatic Model Results: Lorentz Forces (N)

20. SOLID186 Stress and reaction force results closely agree with hand-calculated values. Arch Segment w/ Air Static Structural Model Results: von Mises Stress (Pa)

21. SOLID236 LINE EDGE METHOD Arch Segment _No Air - Magnetostatic Model Results: Magnetic Flux (Tesla)

22. Arch Segment _No Air - Magnetostatic Model Results: Current Density (A/m^2)

23. Arch Segment _No Air - Magnetostatic Model Results: Lorentz forces (N)

24. Arch Segment _No Air - Magnetostatic Model Results: Magnetic Flux (Tesla)

25. Arch Segment _No Air - Magnetostatic Model Results: Lorentz Forces (N)

26. SOLID186 Stress and reaction force results closely agree with hand-calculated values. Arch Segment _ No Air - Static Structural Model Results: von Mises Stress (Pa)

27. Total Reaction Force: ANSYS = 262.5 lbf MathCAD = 262.6 lbf Hoop Stress: ANSYS = 729.9 psi MathCAD = 729.3 psi Arch _ No Air - Static Structural WB Model Results: von Mises Stress (psi)

28. Arch _ No Air_Neg Az - Magnetostatic Model Results: Magnetic Flux (Tesla)

29. Arch _ No Air_Neg Az - Magnetostatic Model Results: Lorentz Forces (N)

30. Arch _ NoAir_NegAz - Static Structural WB Model Results: von Mises Stress (psi)

31. Arch _NoAir_.3Ty+(-1)Tz - Magnetostatic Model Results: Magnetic Flux (Tesla) IsoView

32. Arch _NoAir_.3Ty+(-1)Tz - Magnetostatic Model Results: Magnetic Flux (Tesla) Side View

33. Arch _NoAir_.3Ty+(-1)Tz - Magnetostatic Model Results: Lorentz Forces (N)

34. Arch _NoAir_.3Ty+(-1)Tz – Static Structural Model Results: von Mises Stress (psi) Iso View

35. Arch _NoAir_.3Ty+(-1)Tz – Static Structural Model Results: von Mises Stress (psi) Side View

36. Conclusions • SOLID236 results using line edge method closely agree with hand-calculated classic solution values. • SOLID117 results are not valid • No difference between results with air enclosure modeled and without. • Modeling without air enclosure is valid only for cases where all materials have a relative magnetic permeability = 1, and where magnetic coupling across the joint is not required (static analysis, no eddy current calculation). • Unlike MVP method, negative values of Az are allowed • Combined Fields: Az input as a vector with magnitude and direction • Use WPRO to rotate WP so that Z-direction is aligned with Az direction, then use CSWP to define coordinate system aligned with WP • Apply Az = resultant, magnitude of vector • Must change to metric units in WB prior to SOLVE so that the Lorentz forces in newtons from Magnetostatic analysis scale correctly. • Can switch back to english units after solution.

37. Single Lamination Bolted Assembly - Magnetostatic Model: Mesh

38. Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Magnetic Flux (Tesla)

39. Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Current Density (A/m^2)

40. Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Lorentz Forces (N)

41. Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Magnetic Flux (Tesla)

42. Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Current Density (A/m^2)

43. Single Lamination_.3Ty+(-1)Tz - Magnetostatic Results: Lorentz Forces (N)