1. NSTX ARMOR PLATE 2/18/10 NEUTRAL BEAM ARMOR PRELIMINARY ANALYSIS

2. NSTX ARMOR PLATE 2/18/10 OBJECTIVES Develop the Finite Element Model for The Armor Eddy Current Analysis –Show Mesh Density and Boundary Conditions Apply Disruption Case of Magnetic Vector Potential from Opera Data Tables –Data tables (provided by others) are contoured as inputs to this analysis. –Magnetic Flux B Field is contoured on the FE model –The Magnetic Vector Potential is contoured on the FE model as an input to this analysis. Provide Magnetic Results for: –Current Density at five discrete locations as a function of time. Trend identifies the critical time step during the disruption event –Current Density as a Vector Plot. This result shows directional trends of current during the disruption Develop the Finite Element Model for Transient Structural Results –Show the mesh and Structural Boundary Conditions Provide Transient Structural results for: –Max Displacement at highest current and final load step –Contour results for von Mises stress –Preliminary Reaction Load Magnitudes Provide Conclusions and Planned Recommendations

3. NSTX ARMOR PLATE 2/18/10 ASSUMPTIONS Magnetic Vector Potential Data Tables: – 2-D Opera Results uniformly expanded into 3-D as provided by Ron Hatcher through Srinivas Avasarala e-mail dated 2-9-10. –Opera Data encompasses Max disruption load case All Components are Merged Integral Solids from Pro-Engineer –No gaps or other nonlinear material properties Note: This will effect how load distributes through the structure. –Welded Reaction Points are Rigid fixed in all DOF Note: This artificially adds strength to the structure that does not in reality exist. –All Support Structure Braces are Merged Solids Note: Reaction Loads and moments are only approximate – not for final design –Transient Dynamic Analysis assumes 0.5% structural damping Single Uniform Material Property : 625 Inconel

4. NSTX ARMOR PLATE 2/18/10 MAGNETIC VECTOR POTENTIAL ELEMENT MESH THE ELEMENT MESH DENSITY Element Type 186 20 node brick Limited Type 187 10 node tetrahedral

5. NSTX ARMOR PLATE 2/18/10 Opera Program Magnetic Vector Potential Sum THE SPECIFIED INPUT ASSUMPTIONS FOR VECTOR POTENTIAL AT MAX TIME STEP THE SPECIFIED INPUT ASSUMPTIONS FOR VECTOR POTENTIAL AT MAX TIME STEP

6. NSTX ARMOR PLATE 2/18/10 Voltage Contour VOLTAGE DISTRIBUTION AT MAX TIME STEP All welds set to zero voltage

7. NSTX ARMOR PLATE 2/18/10 CURRENT DENSITY Four Discrete Locations Vs TIME THE MAX CURRENT DENSITY OCCURS AT TIME = 10.006 Sec 4,788 E4 Amps/ M**2

8. NSTX ARMOR PLATE 2/18/10 CURRENT DENSITY VECTORS At Max TIME Step CURRENT DENSITY VECTOR AT MAX TIME STEP Currents move to ground voltage as specified in boundary conditions. Higher concentrated values at sharp corners adjacent to welds.

9. NSTX ARMOR PLATE 2/18/10 Opera Program Flux Field at Max Time Step THE SPECIFIED INPUT ASSUMPTIONS FOR FLUX FIELD AT MAX TIME STEP THE SPECIFIED INPUT ASSUMPTIONS FOR FLUX FIELD AT MAX TIME STEP

10. NSTX ARMOR PLATE 2/18/10 Opera Program Flux Field at Time = 0.007 Sec THE SPECIFIED INPUT ASSUMPTIONS FOR FLUX FIELD AT TIME STEP = 0.007 THE SPECIFIED INPUT ASSUMPTIONS FOR FLUX FIELD AT TIME STEP = 0.007

11. NSTX ARMOR PLATE 2/18/10 STRUCTURAL MODEL

12. NSTX ARMOR PLATE 2/18/10 Structural Transient Boundary Conditions The Structural Boundary Conditions Are Defined All welds are rigidly constrained Symmetric Boundary

13. NSTX ARMOR PLATE 2/18/10 Transient Max Displacement Max Transient Displacement Trends During Disruption Occurs at 0.007 Seconds after Initiation Max Transient Displacement Trends During Disruption Occurs at 0.007 Seconds after Initiation Time = 0.007 Sec

14. NSTX ARMOR PLATE 2/18/10 Structural Transient Boundary Conditions The Displacement Results at Max Current Time Step is defined Note: The assumed rigid structural deflections will be larger on actual model Units are Meters.

15. NSTX ARMOR PLATE 2/18/10 Transient Max Displacement Typical Transient Stress Trends During Disruption Time = 0.007 Sec

16. NSTX ARMOR PLATE 2/18/10 Von Mises Stress at Max Current The Transient Equivalent Stress at Max Current is Low Based on the assumptions of zero voltage at the Welds The Transient Equivalent Stress at Max Current is Low Based on the assumptions of zero voltage at the Welds Max Stress = 1.6e7 Pa = 2,320 psi

17. NSTX ARMOR PLATE 2/18/10 Von Mises Stress at Max Current The Transient Equivalent Stress at Max Current is Low Based on the assumptions of zero voltage at the Welds The Transient Equivalent Stress at Max Current is Low Based on the assumptions of zero voltage at the Welds Max Stress = 1.6e7 Pa = 2,320 psi Max Bounded Stress = 6.2e7 Pa = 9,065 psi FX = -5820.6 N FY = 5653.7 N FZ = 8554.8 N MX = -778.5 NM MY = -759.4 NM MZ = 28.54 NM

18. NSTX ARMOR PLATE 2/18/10 CONCLUSIONS The Preliminary Armor Electromagnetic and a Transient Dynamic Structural analysis is complete based on the best OPERA information available as of today. The Electromagnetic Analysis based on the disruption data from Ron Hatcher is complete, however, this data may not represent the actual max values. A revision for this region is pending completion before March 1, 2010. The max current density (4,788 E4 Amps /M^2) occurs 0.006 seconds into the disruption event The max stress (9,065 psi) and X displacement (2.96 Mils) occurs at 0.007 seconds into the disruption event. The max reaction load occurs at 0.006 seconds near the center port welds is a total of 11,790 N (2,651 lbs). The stresses from these loads are minimal and well within the material capacity of 625 Inconel. Inclusion of the Reactor Vessel is required to fully capture the current share in these structures since the assumption of ground voltage at the weld locations may not be adequate.

19. NSTX ARMOR PLATE 2/18/10 RECOMMENDATIONS Initiate addition of new solid models from design to include the NSTX reactor vessels. Continue to refine analysis technique to facilitate the analysis of these models. Rerun all of the analysis when the refined Opera data becomes available for the max disruption event adjacent to the Armor Structure. Expand the structure runs to include sub models on the weld attachment points and bolts. Evaluate reductions in the stiffness on this structure by extracting the supports from the assumed rigid boundary. Initiate the Transient thermal analysis models for the Armor Tiles