1. NCSX Vacuum Vessel Stress Analysis FDR Fred Dahlgren 17 May 2004

2. NCSX Vacuum Vessel Stress Analysis - FDR Fred Dahlgren Art Brooks Peter Titus NCSX Final Design Review May 19-20, 2004 PPPL Fred Dahlgren Art Brooks Peter Titus NCSX Final Design Review May 19-20, 2004 PPPL

3. Purpose of analysis: To varify the adequacy of the vessel design and assure the design criteria are met. Method: Finite element analysis using MSC/Nastran, Static(sol 101), Buckling(sol 105),Thermal(sol 153). Assumptions: -Vessel & port configuration as of 2 April ‘04 Pro-E models (based on Se121-011 ver.94). -Material of shell & port nozzles and cover plates fabricated from Inconel 625 Annealed – Grade 1 sheet per ASTM B 443. -Material properties (Linear elastic, isotropic material properties) taken from the Huntington Alloys International Inconel 625 product bulletin. -Rigid vertical structural support to eliminate rigid body modes. -Preliminary static model runs assumed isothermal, 1-g gravity, 1 Atmosphere external pressure @14.7psi. Subsequent runs include nominal thermal distribution during bakeout conditions. -Disruption loads are derived from Spark ver.20b inductive solutions for a stationary center plasma and a plasma displaced 10 cm vertically up from its central equilbrium position.

4. Material Properties(@ 200 deg.C - 392 deg.F): -Youngs Modulus28.7e6 psi -Shear Modulus11.1e6 psi -Poissons’ Ratio0.286 -Density0.305 lbs/cu. in. -Coeff. of Thermal Exp.7.3e-6 in./in.-deg.F Material Properties (@ 400 deg.C – 750 deg.F): -Youngs Modulus27.1e6 psi -Shear Modulus10.5e6 psi -Poissons’ Ratio0.294 -Density0.305 lbs/cu. In. -Coeff. of Thermal Exp.7.6e-6 in./in.-deg.F (From Huntington Alloys/Specialty Metals publication for Inconel 625)

5. Values from Pro-E Model used Material Thicknesses & port diameters for VV model ( inches): PartThicknessdiameter Shell0.375 Port 20.125 Port 30.125 Port 40.500 Port 60.250 Port 70.125 Port 80.125 Port 90.125 Port 100.125 Port 110.125 Port 120.500 Port 150.125 RF-Turret 0.188* Port 170.125 Port 180.125 Main Flange Dimensions: 0.65 wide x 0.85 deep, 0.375 weld

6. Model Details: 38,906 DOF’s 7782 GRID POINTS 7,228 CQUAD4 1,018 CTRIA3 40 MPC’s 4 SPC’s Boundary Conditions: Cylic-Symmetry @ welded edge via MPC’s, vertically fixed @ top clevis, circumferentially top & bot. of NB port Normal Operating Loads: Uniform external 14.7 psi Gravity – 1g Temperature 200 deg.C (max.) Bakeout: 400 deg.C (max) Off-Normal (EM Disruption) Loads: 320kA Plasma @ 1.7T 210kA Plasma @ 2.0T (High Beta) 320kA Plasma @ 1.7T @dZ=10cm (Inductively coupled solutions) MPC’s (cyclic-symm.) NCSX VACUUM VESSEL NASTRAN 120 DEG. FEA MODEL

7. DISPLACEMENTS FOR 1 ATMOSPHERE LOADING Run 120bbe3: 1 Atmosphere External Pressure Only

8. Peak Shell Displacement.125” Run 120bbe3: 1 Atmosphere External Pressure Only

9. Peak Tresca Stress @ Vertical Restraint 18 ksi Run 120bbe3: 1 Atmosphere External Pressure Only

10. Peak Tresca Stress @Outer Surface Z2 15.2 ksi Run 120bbe3: 1 Atmosphere External Pressure Only

11. Run 120bbe3: Tresca Stresses in the flange and weld areas are 1 to 7 ksi

12. Attempts to stiffen the shell locally – not very effective Added 2 Ribs.5 x 1” high Added 3 rd Rib.5 x 1” high

13. Peak shell deflection 0.085 for 0.5” thk. Shell & 1 Atmosphere Load

14. Run 120bbe3g – 1 Atmosphere External Pressure + 1g Gravity Loading

15. Added internal reinforcing Tee ribs Max. displacements less than 0.088” Port-9 Port-2 Shell Reinforcement 1” typ. 0.375 Run 120bbe2a-tribsf

16. Tresca Stress From 1 Atmosphere + Gravity Loading Stress @ Support 18.3 ksi Peak Stress @ turret/shell 20.9 ksi Run 120bbe3g – 1 Atmosphere External Pressure + 1g Gravity Loading

17. A cantilevered load, at various port ends, was applied via a concentrated weight of 500lbs to simulate a 250lb load at the end of the port extension ( 2x length =2x load) * Actual port end deflection with the port extension will be higher (~4x for 2x length). Max. deflection* 1.26” Run 120bbe3gf Cantilevered Loading Of Ports

18. Outer Surface (Z2) Tresca Stress From 500lb Cantilevered Load on Port Ends 34.2ksi Tresca Stress Run 120bbe3gf – 1 Atmosphere External Pressure + 1g Gravity Loading + 500lbs cantilevered

19. Inner Surface Tresca Stress 46.8 ksi Due To 500lb Cantilevered Load @ port18/turret intersection Run 120bbe3gf – 1 Atmosphere External Pressure + 1g Gravity Loading + 500lbs cantilevered

20. Tresca Stress reduced below 22ksi In the turret and weld region Stress & deflection still high but below allowables in Port 18 nozzle root 27.3ksi - ~1” displacement @end Increase nozzle thickness to.188”? Run 120bbegf-2 with turret wall 0.375” thick

21. Nominal bakeout temperature distribution: 400 deg.C uniform shell, 150 deg.C @ Port Flanges Run 120bbe2a-Thermal4 – Steady State Bakeout

22. Total Displacements due to bakeout temperatures: 400 deg.C shell 150 deg.C at port flanges Run 120bbe2a-tstress4 – Thermal Displacements

23. X-dir. Displacements due to bakeout temperatures: 400 deg.C shell 150 deg.C at port flanges Run 120bbe2a-tstress4 – Thermal Displacements

24. Displacements for gravity, pressure, and bakeout temperatures: 400 deg.C shell 150 deg.C @ port flanges Run 120bbe2a-tstress4 – Thermal + Pressure + Gravity Displacements

25. Tresca Stress Z1 Inner Surface due to gravity, pressure, and bakeout temperatures, 400 deg.C shell 150 deg.C at port flanges Run 120bbe2a-tstress4 – Thermal + Pressure + Gravity

26. Tresca Stress Z2 Outer Surface due to gravity, pressure, and bakeout temperatures, 400 deg.C shell 150 deg.C at port flanges Run 120bbe2a-tstress4 – Thermal + Pressure + Gravity

27. Buckling Eigenvalue = 12.99 - for 1 Atmosphere loading Run 120bbe3-buckle – Pre-load: 1 Atmosphere, Eigenvalue extraction method: Lanczos

28. Buckling mode shape local displacement between ports 9 & 2 Run 120bbe3-buckle

29. Poor CTRIA3 element orientation Reoriented elements produced higher critical load factor ~ 15.7 Run 120bbe3-buckle Run 120bbe2a-buckle

30. VDE – 320kA plasma @ 1.7 Tesla displaced 10 cm upward Ohmic – 320kA plasma @ 1.7 Tesla High Beta – 210kA plasma @ 2 Tesla Disruption loading (Static Runs): Note: These disruptions are assumed to occur instantaneously and utilize the fully inductive SPARK solution

31. Force Distribution From VDE-UP(Self Forces) – 1.7 Tesla, 320kA Plasma Current Stationary @ 10cm

32. Force Distribution From VDE-UP(External Field Forces) – 1.7 Tesla, 320kA Plasma Current Stationary @ 10cm

33. Total Displacements Due to VDE-UP Eddy Currents + Atmospheric Pressure + Gravity Loads Run: 120bbe2a-VDE Peak Inner Wall Shell Displacement: 0.20” Peak Outer Wall Shell Displacement: 0.25”

34. Tresca Stresses-Z1 (outer) Shell Surface For VDE-UP Eddy Currents + Atmospheric Pressure + Gravity Run: 120bbe2a-VDE 22.2 ksi Peak Stress 17.6 ksi

35. Tresca Stresses-Z2 (inner) Shell Surface For VDE-UP Eddy Currents + Atmospheric Pressure + Gravity Run: 120bbe2a-VDE 17.1 ksi 18.2 ksi Peak

36. Peak Tresca Stresses-Z2 @ Flange For VDE-UP Eddy Currents + Atmospheric Pressure + Gravity Run: 120bbe2a-VDE Peak Stress 27.6ksi

37. Peak Tresca Stresses-Z1 @ Flange For VDE-UP Eddy Currents + Atmospheric Pressure + Gravity Run: 120bbe2a-VDE Peak Stress 22.2ksi

38. Force Distribution From OHMIC(Self Forces) – 1.7 Tesla, 320kA Plasma Current Stationary

39. Force Distribution From OHMIC (External Field Forces) – 1.7 Tesla, 320kA Plasma Current Stationary

40. Peak Displacements Inner Wall: 0.130” Displacements Due to Ohmic Disruption Run: 120bbe2a-OHMIC Peak Displacements Outer Wall: 0.185” Peak Port Displacement: 0.358”

41. Tresca Stresses-Z1 (Outer) Surface For Ohmic Eddy Currents + Atmospheric Pressure + Gravity Run: 120bbe2a-OHMIC Peak Stress 13.6 ksi

42. Tresca Stresses-Z2 (inner) Surface For Ohmic Eddy Currents + Atmospheric Pressure + Gravity Run: 120bbe2a-OHMIC Peak Stress 16.1 ksi

43. Force Distribution From HighBeta (Self Forces) – 2.0 Tesla, 320kA Plasma Current Stationary

44. Force Distribution From HighBeta (External Field) – 2.0 Tesla, 320kA Plasma Current Stationary

45. Displacements Due to High Beta Disruption Run: 120bbe2a-HighBeta Peak Displacements Inner Wall: 0.138” Peak Displacements Outer Wall: 0.166”

46. Tresca Stresses-Z2 (inner) Shell Surface For High Beta Eddy Currents + Atmospheric Pressure + Gravity Run: 120bbe2a-HighBeta Peak Stress 14.7 ksi

47. Tresca Stresses-Z1 (outer) Shell Surface For High Beta Eddy Currents + Atmospheric Pressure + Gravity Run: 120bbe2a-HighBeta Peak Stress 16.1 ksi

48. Lowest Frequency Rocking mode ( 0.8 Hz)

49. Dynamic loading effects due to disruptions: -Assume a worst case amplification of the most severe disruption loading: 2 x VDE Statically applied, this will be an upper bound on the structural response ( structural damping and off-resonance attenuation will produce a much less severe response). Peak Stress Z2- outer surf. 28.3 ksiPeak Stress Z1- inner surf. 29.1 ksi Run: 120bbe2a-VDE-2X

50. Peak Tresca Z2 Stress @ exterior Flange edge 49.1 ksi Peak Tresca Z1 Stress @ interior Flange edge 47.2 ksi Run: 120bbe2a-VDE-2X

51. Critical Buckling under disruption loading Use the three previous disruption load cases together with external atmospheric pressure and gravity applied as a pre-load to determine differential stiffness for deriving the critical buckling load factor. To account for any dynamic effects use a factor of 2 for the upper bound (worst case) dynamic loading component (ie. Twice the eddy current EM loads). Determine the critical buckling load factor derived from the lowest positive root of the eigenvalue analysis. ASME generally recommends a minimal load factor of 4 to 5

52. 1 X VDE Eddy Current Loads, Eigenvalue = 12.02 X VDE Eddy Current Loads, Eigenvalue = 8.5 For a 2X dynamic amplification of a VDE disruption load, the critical load factor still exceeds 8X

53. 1 X OHMIC Eddy Current Loads, Eigenvalue = 15.92 X OHMIC Eddy Current Loads, Eigenvalue = 10.5 For Ohmic disruptions the critical load factor is reduced to 10.5 using the 2X dynamic loading.

54. 1 X HighBeta Eddy Current Loads, Eigenvalue = 14.72 X HighBeta Eddy Current Loads, Eigenvalue = 12.9 For High Beta disruptions the critical load factor is reduced to 12.9 using the 2X dynamic loading.

55. TABLE II VACUUM VESSEL STRESS ANALYSIS RESULTS SUMMARY Peak Displacements (Inches)Peak Stresses (ksi) Loading/case# & fileTotalRadialToroidalVerticalMajor Pr. Z1 Z2 Minor Pr. Z1 Z2 Tresca Z1 Z2 Pressure Only (1 Atmosphere) S.C.#1 – model-120bbe3 0.250 (port-2) +0.075 -0.126 +0.150 -0.156 +0.231 -0.231 18.0 12.0-17.4 -21.516.1 13.5 Pressure + Gravity S.C.#1 – model-120bbe3g 0.255 (port-2) +0.073 -0.150 +0.127 -0.180 +0.240 -0.217 23.3 11.9-13.8 -20.915.7 14.6 Press. + Grav. + 250lb Port End Load S.C.#1 – model-120bbe3gf2 1.27 (rf-2) +0.318 -0.186 +0.276 -0.192 +0.164 -1.240 37.5 26.2-46.9 -29.831.8 34.3 Press. + Grav. + 250lb Port End Load S.C.#1 – model-120bbe3gfr (reinforced) 1.04 (rf-2) +0.247 -0.169 +0.263 -0.176 +0.158 -1.010 37.3 26.1-35.5 -23.128.0 26.5 Pressure Only (1 Bar) (revised model) S.C.#1- model-120bbe2a 0.234 (port-2) +0.054 -0.110 +0.227 -0.227 +0.157 -0.152 13.5 12.3 - 12.3 -16.013.6 14.1 Press. + Grav. + 320kA-1.7T S.C.#1- model-120bbe2a-Ohmic 0.358 (port-2) +0.061 -0.267 +0.289 -0.319 +0.151 -0.179 21.3 23.0 -20.1 -26.017.1 17.7 Press. + Grav. + 320kA – VDE S.C.#1- model-120bbe2a-VDE 0.456 (port-2L) +0.135 -0.347 +0.382 -0.211 +0.221 -0.206 21.9 26.1-20.5 -29.522.2 27.6 Press. + Grav. + 210kA- 2.0T S.C.#1- model-120bbe2a-HighBeta 0.303 (port-10) +0.045 -0.223 +0.246 -0.274 +0.114 -0.153 18.7 19.7-16.1 -22.116.1 14.7 Press. + Grav. + 320kA – 2 x VDE S.C.#1- model-120bbe2a-VDE-2Xa 0.722 (port-2L) +0.330 -0.613 +0.553 -0.193 +0.374 -0.369 43.0 32.7-33.0 -48.347.2 49.1 Press. + Grav. + 210kA- 2.0T – 2 x H.B. S.C.#1- model-120bbe2a-HighBeta-2X Press. + Grav. + 320kA-1.7T – 2 x Ohmic S.C.#1- model-120bbe2a-Ohmic-2X Press. + Grav. + Thermal Bakeout S.C.#1 –model-120bbe2a-tstress4 0.598 (port-2L) +0.492 -0.058 +0.390 -0.355 +0.201 -0.460 18.7 16.1-23.0 -37.031.0 27.0

56. Table 2B – Section II of the ASME BPVC indicates a design stress intensity (S m ) of 30.4 ksi at the maximum operating temperature of 750 deg.F (~400 deg.C). For normal operations the maximum operating shell or nozzle temperature will be 400 deg.F (~200 deg.C), for which S m is 33.4 ksi. Appendix 4, Section VIII – Division 2 the general stress criteria and categories for vessel design based on stress analysis: CategoryDescriptionNot to exceed P m Primary membrane Stress (Average across solid section,1.0k x S m produced only by body forces and mechanical loads). P L Local Primary membrane Stress (Average stress across solid 1.5k x S m * section, includes discontinuities but not Stress concentrations). P b Primary bending stress (Stresses proportional to the distance from1.5k x S m * the centroid of a solid section – excludes discontinuities & str.conc.). QSecondary Membrane + bending stresses, self equilibrating, due3.0k x S m ** to thermal or mechanical loads, or discontinuities (excludes local stress concentrations. FIncremental stress added by stress concentrations (notch), thermal stresses producing thermal fatigue. * P l or P l + P b < 1.5k x S m, ( k typically = 1.0),** P L + P b + Q < 3.0k x S m (stress intensity range)

57. For normal operating conditions at 200 deg.C the worst case disruption loading (including 2X dynamic load factor) will produce a stress intensity of 49.2ksi in the flange at the interior flange surface. Since this may be considered a primary bending stress P b the allowable (not to exceed) stress will be: S Peak Tresca = 49.2 < 1.5kS m = 50.1 ksi For Bakeout at 400 deg.C (max temp) under gravity and atmospheric pressures: S Peak Tresca = 31.0 < 1.5kS m = 45.6 ksi For 200 deg.C worst case Tresca stress at welded sections: The peak VDE-2X Stress @ the lower port-10/shell intersection is 33.4 ksi. With a weld efficiency of 0.50: S Peak Tresca = 33.4/.50 = 66.8 ksi < 3kS m = 100.2 ksi Since this stress intensity includes primary + secondary stresses the code permits a value of 3kS m for the total range of stress intensity. The rational for this is the assumption that some localized plastic deformation in ductile materials is permissible during shakedown as long as the subsequent stress range in the locally yielded regions will remain in the elastic range.

62. Status: -The static runs for normal operations are completed. -A run with the bakeout thermal distribution and one with the normal operating temperature distribution are complete. -Runs with disruption loads are completed. -Runs for static buckling with pressure, gravity and disruption loading complete. -Buckling runs with upper bound dynamic loading (2 x disruption loads) complete. -Static runs with 2X disruption load factor are complete. -A 360 degree model (prior vessel) was used to evaluate asymmetric loading conditions and evaluate any global buckling conditions. Conclusions: -Stresses from the normal operating load runs in the shell and ports are below the allowable stress with the exception of the Port-18 cantilevered loading requirement. Recommend either thickening the turret wall and port nozzle to reduce stress at the nozzle/port intersection and to reduce vertical deflections of the port, or implement a radially compliant vertical nozzle support off the cryostat. Port-15 also needs support. -Shell displacements are generally low with the exception of the area between port2 and port9 which indicate a displacement of 0.125” total. May be reduced by thickening or reinforcing the shell locally to reduce these deflections.