1. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Thermal and Mechanical Analysis of the PXIE RFQ Andrew Lambert Engineering Division Lawrence Berkeley National Laboratory April 12, 2012

2. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Outline Thin Slice Model RF, Thermal, Structural, RF Frequency Shift Cutback Model RF, Thermal, Structural Cooling Channel Heat Load Coolant Temperature Rise & Frequency Change Pi-mode Rods Thermal Stress and Deformation Slug Tuners Temperatures Jacket Plate Cooling Channel Pressure Drop RFQ Stiffness/Strength RFQ Cooling System RFQ Vacuum System

3. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Cooling Schematic Cooling water does not flow between modules 12 cooling channels per module Pi-mode rods are on a separate cooling circuit

4. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 RFQ Thin Slice Model Finite element model of the RFQ body developed using ANSYS Simulation considers two volumes: 3-D slice of one quadrant of the cavity vacuum & RFQ copper body Nodes at shared surfaces link RF elements with Structural-Thermal elements Allows for exchange of heat flux and displacements due to thermal expansion

5. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 RF Analysis Region near the vane tips is especially important for accurate frequency prediction Mesh density enhanced 3x in this region Mesh refinement transfers to thermal-structural elements to ensure accurate displacements Maintains accuracy while keeping solution time convenient

6. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 RF Analysis Must determine scaling factor for power dissipation -> use vane tip-to-tip voltage Extract vane tip-to-tip voltage and scale with design voltage 2D FE Results PXIE (ANSYS) PXIE (CST MWS, G. Romanov) Frequency (MHz) 164.38 164.39 Q-Factor16794 16747

7. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Thermal-Structural Analysis 3-D slice 1-mm thick with tetrahedral elements Refined mesh at vane tips and at cooling channels Nodes on slice surfaces constrained to be coplanar to allow axial thermal growth and correct calculation of longitudinal stresses 2-D plane strain elements would over-constrain the model longitudinally, yielding artificially high axial compressive stresses

8. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Thermal Analysis Thermal loads Heat flux on vanes and walls from RF solution Cooling channel convection RF body power ~61 kW G. Romanov -> 139 W/cm x 445 cm = 62 kW Solution provides temperature contours and element heat flow

9. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Structural Analysis Mechanical loads on the model Temperature distribution Cooling water and vacuum pressure Symmetry constraints Structural solution yields stresses and displacements Maximum stress is ~14 MPa but is located at sharp corner, not physical Real stresses less than 6 MPa, annealed copper yield strength can be as low as 25 MPa -> yielding not a concern

10. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Final RF Analysis Predict frequency during steady state operation Help to determine sensitivity to cooling water temperature Utilizes structural displacements at nodes to morph the mesh Solution conditions are identical to initial RF simulation 2D FE Results Steady State (ANSYS) Frequency (MHz) 164.285 Q-Factor16799

11. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Frequency Shift and Tuning 2D FE Results Ideal (ANSYS) Steady State (ANSYS) Frequency (MHz) 164.379164.285 Quality Factor 1679416799 Frequency Shift (2D) Average Overall (kHz/ o C) -2.80 Vane (kHz/ o C) -16.70 Wall (kHz/ o C) 13.90 Sum of Vane & Wall (kHz/ o C) -2.80 Theoretical (kHz/ o C) -2.91 % Error 3.8% RFQ cavity resonant frequency can be shifted by altering the cooling water temperature Dynamic tuning can be achieved by varying the vane temp only Displacement from structural analysis are utilized in an ANSYS RF simulation to predict tuning performance +/- 100 kHz tuning range possible

12. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Cutback Model Model one quadrant of the cutback region due to semi-symmetry Reduces number of nodes, manageable solution times Utilizes CAD geometry to maintain consistency with design changes Includes cooling channel geometry for subsequent thermal solution

13. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Cutback RF Analysis Create vacuum geometry that includes all features of the cutbacks Refined mesh at the cutbacks and vane tips for more accurate RF solution Measure vane tip-to-tip voltage to determine scaling factor for subsequent thermal simulation

14. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Cutback RF to Thermal To couple RF heating to thermal solution, the two volumes must share common faces Nodes on these faces belong to both high-frequency elements and structural-thermal elements Highlighted blue-green surfaces above show the shared faces of the model

15. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Cutback Heat Flux Imported heat flux generated by the RF simulation ANSYS applies heat flux to each shared node between vacuum and copper body volumes Maximum heat flux occurs at the cutback region Average 3-6 W/cm 2 Required refined mesh

16. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Cutback Temperatures Thermal loads on FEA model RF heating from ANSYS simulation Cooling channel convection Solution for steady state operation yields temperature distribution Max temp of ~41.8 o C at the cutback tips Average temperature in copper body is ~23-26 o C

17. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Cutback Stresses Mechanical loads on model Imposed temperature distribution Cooling water and vacuum pressure Symmetry constraints Structural solution provides stresses & displacements Stress under 10 MPa Max stress of ~23 MPa is located at sharp corner of cutback geometry -> will further investigate this stress concentration

18. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Cooling Channel Heat Load Must determine total heat load carried by cooling channels RF heating on walls, vanes, cutbacks, & slug tuners Pi-mode rods on separate circuit Cooling Channel Heat Load per Channel (kW) Heat Load per Module (kW) Total Heat Load (kW) Cooling Channel Water Temp Rise ( o C) Corner1.285.1220.481.18 Wall1.415.6422.561.30 Vane1.746.9627.841.61 Total for 4 modules 70.76

19. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Longitudinal Temperature Rise and Frequency Shift Temperature profiles do not dramatically change from inlet to exit, there is slight increase in overall temperature Linear temperature gradient along length of RFQ, but not severe enough to cause significant thermal stresses in the axial direction Frequency changes ~10 kHz from entrance to exit of one RFQ module 2D FE Results EntranceExit Frequency (MHz) 164.285164.275 Q-Factor16799

20. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Pi-mode Rods and Slug Tuners Pi-mode rods and slug tuners can be seen in figure at right Determine temperatures and thermal stresses Jacket plates used to connect RFQ modules

21. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Pi-mode Rod Stresses Half model of pi-mode rod with surface heat flux and convective cooling through water passage Convection coefficient equal to 18,000 W/m 2 -K Deformation is small due to effective thermal management Stresses are low, < 4MPa, with max stresses occurring at rod- to-ferrule braze Pi-mode Rods ANSYS CST MWS (G. Romanov) Heat Load (W) 200188

22. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Slug Tuner Heating Thermal Loads RF heat flux Cooling channel convection Slug tuners cooled by conduction to the RFQ body Maximum temperature is below 30 o C Conduction is sufficient for slug tuner cooling

23. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Jacket Plate Analysis RFQ jacket plate design changed in two distinct ways: Only 6 bolt locations instead of the original 8 Plate thickness increased to 32 mm; the bolt/nut pockets no longer penetrate through the entire plate Highest stresses found at pocket where loading is applied Stress does not exceed the tensile yield strength of the stainless steel (207 MPa) Applied load will not significantly deform the slug tuner port holes

24. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Cooling Channel Pressure Drop Fully developed turbulent flow Assumes relatively smooth channels Cooling Channel Head Loss (m) Pressure Drop (kPa) Corner1.1611.31 Vane1.1711.42 Wall1.1210.97

25. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 RFQ Stiffness/Strength When bolted together, the four modules form a single, stiff structure that can be analyzed as a beam The large cross section of the 162.5 MHz RFQ is heavy, but extremely stiff in bending. Calculated parameters are: Cross section area: ∼ 794 cm 2 Weight/length: ∼ 6930 N/m ( ∼ 785 kg/module – body only) Moment area of inertia: ∼ 1.59x10 5 cm 4 Maximum stress and deflection of the RFQ due to its own weight is dependent on the design of the support system Worst case analysis helps to determine the type of support needed

26. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 RFQ Stiffness/Strength For worst case, the results are: Maximum stress: 2.3 MPa Maximum deflection: 0.17 mm For likely support points: Maximum stress: 0.58 MPa Maximum deflection: <0.02 mm The yield stress of the fully annealed copper can be as low as 25 MPa, but the stress due to support and handling are very low The SNS RFQ was supported using a 6-strut system Worst case support configuration Likely support configuration

27. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 RFQ Cooling System Each module has 12 cooling channels (8 wall, 4 vane) 12 mm diameter channels flow 0.26 l/s at 2.29 m/s velocity Reynolds number is 25,900 (turbulent flow) Maximum flow to prevent Cu erosion is 4.57 m/s Lower flow rate used to reduce chiller size Total system flow: 8.3 l/s wall, 4.1 l/s vane Nominal water temperature rise is 1.9 o C Commercial closed-loop chillers that meet system requirements are readily available Two units needed (one for vanes, one for walls) Small flow in pi-mode rods (.04 l/s each) necessary to limit axial thermal stresses

28. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 RFQ Vacuum System Primary gas loads are: module joint and tuner O-rings, cavity wall out-gassing and gas from LEBT RFQ body has 8 vacuum ports (2 per module) Vacuum could be achieved by four 10” Turbo- or cryo- pumps (two per RFQ side) Additional 4 vacuum ports are blanked off Cavity walls only need to be detergent cleaned (no baking) Viton O-ring seals are to be pre-baked and ungreased More detailed analysis will be required – possible that 8” pumps can be used

29. A. Lambert: Thermal and Mechanical Analysis PXIE RFQ Design Review, Berkeley, CA April 12, 2012 Summary Currently: Thermal, RF and Structural finite element analysis of the RFQ body nearly complete Cutback thermal analysis, pi-mode rod thermal stress and slug tuner RF heating calculations are nearly complete Flow/pressure drop calculations for RFQ body cooling channels are complete Future Work: Finish stiffness/strength calculations, specify support system Final cooling system specification Detailed vacuum analysis