1. VG1 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Upgrade Stave Study Topics Current Analysis Tasks –Stave Stiffness, ability to resist gravity sag, critical at upper and lower Φ –Stave thermal/mechanical aspects Heat transfer to evaporative cooling tubes Thermal strains from thermal gradient from chips to tubes Thermal strains from cool-down, room temperature to initial state (minus 25ºC) –Coolant tube sizing within confines of stave structure Analysis guided by realistic constraints on radiation length –Attempt to make analytical model representative at all times Radiation length driven design as always, issues focus on: –Composite material properties High modulus, optimized fiber orientation for maximum axial stiffness High conductivity fiber system for heat transport Issue to be addressed is CTE mismatch in the assembly – Al cooling tube or possibly PEEK –Stave length, gravity sag, bounded between fixed end and simple supports Estimate range to be ~60μm fixed to ~320 μm simple for present composite sandwich geometry Desire limit of ~50-75microns

2. VG2 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Stave Stiffness Structural Model for Gravity Sag

3. VG3 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Full Length (96cm) Model w/o Pins Sandwich model composed of solid elements –NASTRAN solver, FEMAP mesh generator Model Properties –K13D2U with 4/1 fiber orientation for facings –Carbon foam core –Side ribs from same material as facing –Aluminum End Cap with receiver holes for pins Simple support conditions imposed in interior of holes –Silicon modules and hybrids coupled to facing without compliance of dielectric cable Cable mass included with facing mass Sag 69 μm, but pin deflection not included

4. VG4 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Sag with Pin End Supports End Cap Material: Aluminum Steel 0.125in pins Kinematical BC on pins Max central sag 92.6 μm

5. VG5 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Small Distortion Evident in Pins Steel Pin Deflection: 0.8microns 0.125in diameter

6. VG6 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Pin Deflection Increased Sag to 92.6µm End of Pin: 0.8microns 3.3microns in stave

7. VG7 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade End Cap Distortion Pin engagement: 0.236” Side support: 0.394” Stave Ledge: 0.12” Ledge Side support pin

8. VG8 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Model Variations Model without pins versus model with pins Al end cap, Facing K13D2U 4/1, no pins: 67microns Same configuration with 0.125in dia steel pins: 92.6microns End Cap Material −Aluminum versus Composite, radiation length penalty −Stave gravity sag with Al: 92.6microns −Stave gravity sag with K13D2U 4/1: 101.5microns (this was not expected) −Matches stave facing CTE −Stave gravity sag with K13D2U balanced −Sag essentially same as the 4/1 fiber orientation −Uncouple Silicon Wafer and BeO −By reducing tensile modulus to nearly zero −Al End Cap, steel pins, facing K13D2U 4/1 −Sag increase from 92.6 to 104microns

9. VG9 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Revised Stave Model Why new model? –Attempt to reduce sag back down from ~100 μm –Continued assessment of contribution to stiffness from silicon modules and BeO hybrid –Correct mesh of sandwich core (one foam piece did not mesh), improve contact with stave facing Modifications –Increased pin diameter from 0.125in dia. to 0.173in dia –Added mass of hybrid and silicon wafer to facing mass (total decoupling of stiffness from detectors) –Mass of cable added to composite facing as before First Solution –End Cap Al –Support pins solid steel Next –evaluate hollow pins –different end cap material

10. VG10 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Gravity Solution Central deflection 90.5microns (as compared to 104 μm ) 674122 solid elements Stiffness of modules and hybrid not included 96cm long by 6.4cm wide composite stave

11. VG11 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Results continued Pin deflection 0.36microns Stave support 1.8microns XYZ restraint Opposite pin Y and Z Pin deflection reduced by half

12. VG12 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Results continued X and Y Y only

13. VG13 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Stave Thermal Mechanical FEA of Thermal Strain

14. VG14 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Distortion from Cool-Down Geometry –96cm long stave, with kinematic support at two end caps (no pins) –End caps, Al material –Stave facings, K13D2U with 4 to fiber orientation, maximizes axial stiffness –Al cooling tubes –Alternating pattern of silicon modules and BeO hybrids on upper and lower stave surface Shift in pattern providing detector hermeticity Thermal solution –50ºC temperature change, RM Temp to -25ºC –Thermal strain, wave pattern with nominally 10.6micron variation

15. VG15 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Cooling Thermal Gradient FEA solution for both Al and Carbon-Fiber Filled PEEK tubes –6 chips for each hybrid, 0.5W each: heat zone shifts top to bottom –Film coefficient 3000W/m 2 K, typical of Pixel stave for C 3 F 8, two parallel tubes –Lower peak chip temperature favors Al cooling tube

16. VG16 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Stave Cooling Tube Size Two-Phase Flow

17. VG17 i T i March 9, 2006 W. O. Miller ATLAS Silicon Tracker Upgrade Coolant Considerations Coolant –C 3 F 8, evaporative coolant –Enters at -25ºC through throttling process, with a quality of 0.3 (30% vapor) –Exit, near all vapor (assume quality ~0.8 to 0.88 for calculating require mass flow) Tube –Hydraulic diameter, 8mm, elongated providing 2mm of flat contact with stave composite facings –Tube length (2-pass) ~192cm (entrance and exit at same stave end) Capacity –For dissipated chip power 108W, need 2.2gm/sec Pressure drop –<25mbar in two pass two, without elbow –[will calculate for elbow next, along with heat transfer coefficient]