1. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 1 NSTX Supported by NSTX Center Stack Upgrade 25 April, 2011 Structural Analysis of the PF1 Coils & Supports (draft) Leonard Myatt (Myatt Consulting, Inc.)

2. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Executive Summary A structural assessment of the NSTX CSU Inner PF coils (PF1a/1b/1c) is presented based on finite element simulations of the coils and their support structures. A parametric 2D ANSYS EM field model is used to calculate Lorentz forces for 96 equilibria based on five different plasma conditions:  No plasma  2MA Circular plasma  2MA Shaped plasma  Following the disruption of a 2MA Circular plasma  Following the disruption of a 2MA Shaped plasma This also serves as a benchmark for the PPPL force calculation, with spot- checked agreement to <1%. The 2D stress analyses indicates that:  The re-designed SS bobbin structure…  Cu and insulation… A 3D stress analysis is used to evaluate the non-axisymmetric structural elements of the support design. The model shows that: Differential thermal strains… 2

3. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Introduction While the Center Stack upgrade includes many changes, this presentation focuses on PF1 coils (a, b & c, Upper & Lower) and their associated support structure. The structure is defined by a series of simplified CAD models provided by L. Morris. The coil dimensions and their operating currents are defined by C. Neumeyer’s: –NSTX_CS_Upgrade_110317.xls Sequentially coupled electromagnetic and structural analyses of the PF coil system are performed using ANSYS. 3 Section showing PF1L and Lower support structure

4. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Simplified 3D Model Some of the mechanical complexities shown in the previous slide need not be carried into the magnetic field or stress analysis. The geometry is de-featured (simplified) by L. Morris and imported into ANSYS as shown here. Some manipulations of the imported volumes are required in the ANSYS preprocessor. 4

5. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Things to Keep In Mind The EMag and stress analyses presented here are in SI units: –Flux Density [T] –Displacement [m] –Stress [Pa], 0.145 ksi/MPa –Force [N], 0.2248 lb/N, 1 kip =1000 lb The Cu conductor used in the PF coils will have a hardness similar to that of the TF conductor –Sy=262 MPa, Sm=(2/3)Sy=174 MPa –Membrane + Bending (M+B) Stress Limit at RT: (1.5)174=262 MPa –Membrane + Bending (M+B) Stress Limit at 100C: (0.9)(1.5)174=236 MPa The center stack coil support structure is made from Inconel 625: –S y ~65 ksi, S ut ~130 ksi, S m ~43 ksi (300 MPa) –Membrane + Bending (M+B) Stress Limit at RT: (1.5)300=450 MPa The PF1 coils are insulated with Epoxy-Glass. R. P. Reed reports properties in “Estimated and Compiled Properties of Glass/101K Epoxy/Kapton Composite Properties at Room Temperature,” July 15, 2009. Allowable static stress levels are defined by: –S  =(1/2 ~accounts for Cu bond)(2/3 SF from Zatz’ NSTX SDC)65=22 MPa –S n =(1/2 ~accounts for Cu bond)(2/3 SF from Zatz’ NSTX SDC)420=180 MPa 5

6. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Axisymmetric ANSYS EMag Model 6 The EMag model includes options for shaped (parameters listed in title) or circular (  =0,  =1) plasma representations. Uniform current densities are either applied to the smeared winding packs (as in OH, PF2-5 WPs) or to the actual conductor cross-section (as in PF1a/b/c). The helically wound WPs are idealized as arrays of aligned turns.

7. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Sample Field Results 7 The plot on the left shows lines of constant vector potential (rA z ) superimposed on a flux density plot for the 1 st equilibrium current set (EQ1, with a 2 MA shaped plasma). On the right is a similar plot for PF1aU.

8. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 ANSYS Structural Model 8 Axisymmetric approximation of the PF1 coil support structure is shown here. Detailed WPs are imported from EMag model. Contact elements are added above and below each of the (6) PF1 WPs. The PF1a/b structure is supported at the bottom (lower support). The PF1c structure is supported by the vacuum vessel (VV) at flange OD. Loads are imported from the EMag results.

9. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 2D Scoping Study The design space is extensive: (96) equilibria operating points for (5) different plasma conditions (no plasma, and circular & shaped plasmas before and after a disruption). The 2D field/stress models are based on a smeared WP representation to reduce the analysis time for this scoping study. The max stress in each of the PF1 WPs plus the center stack and PF1c casings are written to an array for each of these operating conditions. Results are imported into Excel and plotted as bar charts in order to give a simple visual representation. These are included in the following slides. 9

10. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1a Smeared WP Stress 10 EQ51 produces the highest stress in PF1a smeared WP (particularly from a Shaped plasma)

11. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1b Smeared WP Stress 11 EQ3 (&18) produces the highest stress in PF1b smeared WP (particularly from a Shaped plasma)

12. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1c Smeared WP Stress 12 EQ1 (&16) produces the highest stress in PF1c smeared WP (particularly from a Post Shaped plasma disruption)

13. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1a/b Center Casing Stress 13 EQ1 (&16) produces the highest stress in the Center Casing (particularly from a Post Circular plasma disruption)

14. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1c Casing Stress 14 EQ1 (&16) produces the highest stress in PF1c Casing (particularly from the three no-plasma cases)

15. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Equilibria Cases Leading to Max Smeared Stress Coil or StructureImportant Equilibria PF1a WPEQ51 (shaped) PF1b WPEQ3 (shaped) PF1c WPEQ1 (all three I p =0 cases) Center CasingEQ1 (post circular PD) PF1c CasingEQ1 (all three I p =0 cases) Equilibria which produce the highest stresses in the smeared WP scoping study are tabulated. 15

16. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Equilibria Cases Leading to Max Forces The “OH_PF_Forces” sheet in Neumeyer’s NSTX_CS_Upgrade_110317.xls lists the max radial and vertical forces from all equilibria. Focusing on PF1 coils, the max values are highlighted in yellow, and their corresponding equilibria are traced back to the “Forces_Circ”, “Forces_Shaped” and “PF_Currents_Forces” sheets. 16

17. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Summations of Vertical Forces for Grouped Coils Important FZ force sums are also reviewed:  “ PF1aU+PF1bU”  “PF1aU-PF1bU”  “ PF1aL+PF1bL”  “ PF1aL-PF1bL”  “ (PF1aU+PF1bU)+(PF1aL+PF1bL)”  “ (PF1aU+PF1bU)-(PF1aL+PF1bL) ” Spreadsheet TabPlasmaEQ# PF_Current_Forces ANSYS TIME: 1-8 0 MA1,3,31,33,34,51,52,84 Forces_Shaped ANSYS TIME: 9-13 2 MA18,33,51,54 Post-Disruption3 Forces_Circ ANSYS TIME: 14 Post-Disruption1 17

18. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Review Process These two force-based screening tools lead to 14 equilibria of interest. The smeared WP results point to a five equilibria subset of those 14 cases. The 2D model with discrete 1a/b/c WP constituents is used to determine Cu and insulation stresses for the enveloping 14 cases. All results are scanned for the max stresses and critical locations, as portrayed in the following slides. The TIME parameter in the plot legend ties those results to the particular equilibria tabulated in the previous slide. 18

19. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Worst Center Casing Stress (2D) Both smeared WP stress and force summation screening tools have accurately lead to the highest stress equilibrium for the center casing: –EQ1, Post Circular Disruption (TIME=14) PF1aU pushes down (-96kip) and PF1bU pushes up (83kip), which puts a bending stress of 140 MPa in the PF1a mandrel. Stress level well within 450 MPa M+B static limit. 19

20. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Worst Center Casing Weld Stress (2D) The max stress in the welds is produced by EQ31 (TIME=3), which results in the max separating force:  Fz(1aU & 1bU)-Fz(1aL & 1bL)  Total vertical tension: 112 kip At 50 MPa, the stress level easily passes the 450 MPa static stress limit. Fatigue should also not be an issue (analysis TBD). 20

21. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Worst PF1c Case Stress (2D) EQ1 (TIME=1) produces the largest (60 kip) vertical load on the PF1c coils (pushed away from the mid-plane). The simple restraint at the flange OD and the idealized cover/flange bond here in the 2D model results in a cover plate bending stress of 200 MPa. While the stress is well within the 450 MPa limit, a 3D model will provide greater accuracy in this region. 21

22. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1a Cu Max Hoop & Tresca Stress EQ51 (TIME=11) produces the largest radial force in PF1aU (390 kip), which results in the largest PF1a hoop stress, 17 MPa. EQ54 (TIME=12) also produces a large radial force in PF1aU (355 kip), but results in the largest PF1a Tresca stress, 30 MPa (driven mostly by vertical stress amplified by the cooling channel). 22

23. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1a Insulation Max Compression & Shear Stress The post-disruption of a circular plasma from EQ1 (TIME=14) produces the max PF1aU downward load (-96 kip) and results in the largest compressive stress in the insulation, -14 MPa (<180 MPa). Coil deformations also produce a 1 MPa normal tensile stress, which is below the 0.02% strain (2.4 MPa) limit. The shear stress in the PF1a insulation is also a max at this time point, 2.6 MPa (<22 MPa). 23

24. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1b Cu Max Hoop & Tresca Stress EQ18 (TIME=9) produces the largest radial force in PF1b (177 kip), which results in the largest hoop stress, 29 MPa. This same EQ18 also produces the largest Tresca stress, 34 MPa (24 parts hoop tension and 10 parts vertical compression). 24

25. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1b Insulation Max Compression & Shear Stress The post-disruption of a circular plasma from EQ1 (TIME=14) produces the 2 nd largest PF1bU upward load (83 kip, 84 kip when I p =0) and results in the largest compressive stress in the insulation, -19 MPa (<180 MPa). Coil deformations also produce a 1.8 MPa normal tensile stress, which is below the 0.02% strain (2.4 MPa) limit. The shear stress in the PF1b insulation is also a max at this time point, 2.8 MPa (<22 MPa). 25

26. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1c Cu Max Hoop & Tresca Stress While EQ33 (0 MA plasma) produces the largest net radial force in PF1c (-71 kip), EQ1 (TIME=1) produces the largest and smallest hoop stresses, ranging from -24 to +14 MPa. This same EQ1 also produces the largest Tresca stress, 36 MPa, due predominantly to a local contact stress. 26

27. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1c Insulation Max Compression & Shear Stress EQ1 (TIME=1) produces the largest PF1c repulsive loads (~60 kip) whenever I p =0, and results in the largest compressive stress in the insulation, -40 MPa (<180 MPa). Coil deformations also produce a 2 MPa normal tensile stress, which is below the 0.02% strain (2.4 MPa) limit. The shear stress in the PF1c insulation is also a max at this time point, 8 MPa (<22 MPa). These results are considered to be conservative based on the PF1c case support approximation. 27

28. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Insulation, Cu & Structure Stress Summary (2D) 28 2D smeared WP stress analyses of the 96 version H equilibria for five different plasma conditions help determine the most likely limiting operating conditions. Two force screening tools are also used: –Net radial and vertical forces on each coil –Net vertical forces based on various coil groupings Fourteen equilibria emerge as worthy of detailed analysis. PF1a/b/c coils are modeled as discrete conductors with turn and ground wrap insulation. Results show that: –Structure stresses are within design limits. –Cu and insulation stresses are within design limits. –Only a few of the 96 equilibria define the structure’s design space.

29. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Commentary The 2D results expose a couple of noteable results:  Two of the 14 enveloping equilibria result in compressive hoop stresses (a rather uncommon condition for a solenoid).  Some equilibria also produce “rim-bending” modes which result in modest thru-thickness tensile stresses in the insulation. This combination of radial EM forces (leading to hoop compression) and bending modes (leading to interlaminar tension) could be problematic at some point in the life of the coil. This is just a heads-up, as I will try to evolve the simulation in 3D. I do not expect any problems with the structure or Cu conductor. Cu stress is 1/4 th that of the OH conductor, which is qualified in “OH Conductor Fatigue Analysis,” NSTXU- CALC-133-09-00, Rev 0, Nov 2010. 29

30. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 30

31. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 3D Effects Parts of the structure are not axisymmetric. Here is a model which is used to determine the 3D stresses in these non- axisymmetric parts. 31

32. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1aU Support Bracket 32

33. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Lower Support 33

34. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 PF1cL Support 34

35. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Fatigue Characteristics of INCOLOY 625LCF 35 Special Metals, Inc., the manufacturer of Incoloy 625, shows the fatigue performance of alloy 625LCF at RT (Fig. 1). Applying the requisite factor of 2 on stress yields a design-basis (red) fatigue curve shown below. The curve clearly shows that peak stresses in the Incoloy structure should be kept below ~380 MPa. Fewer stress cycles at higher levels can be tolerated, but the curve is relatively flat, and 380 MPa seems to be a good design goal. This is one more reason to augment the structural capacity of the PF1a gussets and PF1c case.

36. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Center Tube Buckling Stability Loads from E1 produce a compressive load in the ¼” thick central tube of 86 kip, which raises the concern over buckling. Roark’s equation for the critical stress (  ') in thin cylindrical tubes is: –  '= E(t/R)/{3 1/2 (1- 2 ) 1/2 } –  '= (29Msi)(0.25/11.64)/{3 1/2 (1-  2 ) 1/2 } = 380 ksi The average stress in the central tube: –  tube =(86 kip)/(2  11.64”x0.25”) = 4.7 ksi The ratio of critical stress to max stress is ~80 (>>5  ) 36

37. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Simplistic Thermal-Stress Analysis (out dated) 37 Titus’ dots indicate 100C Coolant Temps Simplistic Thermal BCs Detailed thermal analysis is done by others. Future thermal stress calculation will probably use those results. Here is a simple thermal stress calculation which looks at the stresses produced by a 100C lower case next to a RT upper case. Differential strains produce a bending stress in the PF1bU bobbin of 320 MPa.

38. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Analysis Approach Summary A parametric 2D ANSYS field model of the PF coil system is developed and used to calculate forces on coils for 96 reference equilibria. Coils can be modeled as smeared current sources, or as aligned NxM arrays of discrete conductors with cooling water holes, turn wrap and ground insulation. An approximate 2D coil support structure is developed from Morris’ CAD model. Discrete conductor WPs are imported along with their EMag forces, and interact with the structure through contact elements. More realistic stresses in non-axisymmetric structural elements are obtained with 3D sector models. Central tube buckling safety is evaluated by a hand calc. 38

39. NSTX NSTX Center Stack Upgrade, PF1a/b/c Stress Analysis (draft)25 April 2011 Results Summary 39