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

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

Figure 3 – ANSYS Multiphysics Analysis Block Diagram

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

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

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

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

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

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.

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

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

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

Arch Segment w/ Air Magnetostatic Model Results: Joule Heat

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

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

Arch Segment w/ Air Magnetostatic Model Results: Current Density

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

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

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

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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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.

Single Lamination Bolted Assembly - Magnetostatic Model: Mesh

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

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

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

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

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

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