1. THERMAL ANALYSIS SUMMARY FOR LBNE-BLIP IRRADIATION TESTS P. Hurh 2/19/2010

2. Irradiation Temperature is Important  Material Property changes are dependent upon irradiation temperature  Annealing while being irradiated Changes in thermal conductivity with neutron dose (dpa) at different irradiation temperatures (Bonal et al 2009). Effects of neutron irradiation on the Young’s modulus of pitch coke graphite (Bonal et al 2009)..

3. What irradiation temperature range is desired for LBNE-BLIP testing?  NOvA 700 KW graphite target temperature range is predicted to be 700-900 ºC (1000-1200 ºK).  IHEP 2 MW graphite max target temperature range is predicted to be 380-430 ºC (650-700 ºK).  To see larger changes in material properties, lower irradiation temperatures desired.  Goal temperature range: 300-800 ºC ?? (600-1100 ºK)

4. Sample Capsule Layout  33 gpm per “box”  Flow areas matched to balance flow  Thermal analysis on capsules only

5. Capsule Schematic (NTS) Sample Volume 0.005” Gap0.01” SS Window Graphite Filler SS Capsule

6. Capsule under pressure Contact Area, r0 Gap Volume  With gas in gap volume, contact area and gap volumes change as pressure differential changes (and vice versa)  Under vacuum, conduction only in contact area with radiative heat transfer in gap volume

7. ANSYS model Z. Tang Model with input from 1 st MARS analysis (sigma=4.23 mm)

8. 1 st Pass MARS analysis

9. Vacuum, no contact Z. Tang Model with input from 1 st MARS analysis (  x =  y =4.23 mm, 90 µA)

10. Contact Conductance  Many variables (pressure, interstitial fluid, elasticity, plasticity, surface roughness, maximum asperity, temperature, thermal conductance…)  Many different measured values (most studies focus on relative differences rather than absolute values)  For higher contact pressures and/or for vacuum environment, no reliable predictive method unless all variables are controlled (and known)  Perhaps a more reliable predictive method for low contact pressure with gas environment (more later)

11. Vacuum Contact Conductance Values In air environmentIn vacuum environment  Varying values in both vacuum and air (curves 1 and 3 in left graph, curves 4 and 6 in right graph)  100 kN/m 2 is pressure range of interest  This survey indicates a range of 200 to 1000 W/m 2 /K for vacuum  G. P. Peterson, Texas A&M

12. Vacuum Contact Conductance Values  Above indicates range of 400-1600 (W/m 2 /K) for SS surfaces  Incropera & DeWitt, Fundamentals of heat transfer

13. Vacuum Contact Conductance Values  Above indicates 241 and 452 (W/m 2 /K) for SS surfaces in vacuum  Song et al, Thermal Gap Conductance of Conforming Surfaces in Contact, Journal of Heat Transfer, Vol. 115, pg 538.

14. Vacuum, contact everywhere Conductance = 200 W/m 2 /K

15. Vacuum, contact everywhere Conductance = 1000 W/m 2 /K  Note reduction in temperature is only ~200 K  Gaps between samples impeding heat flow  This was actually done to mimic contact in air which varies from 1000 to 3000 W/m 2 /K

16. Thermal/Contact Model (Simos)  Window deformation modeled  Contact conductance only in contact areas  Samples modeled as full width plates

17. Thermal/Contact Model (Simos)  Roughly matches Tang analysis  Almost uniform temperature profile  Conductance = 200 W/m 2 /K  Beam spot used?  400 W/g

18. Thermal/Contact Model (Simos)  Does not match Tang analysis  Almost uniform temperature profile  Conductance = 1000 W/m 2 /K  Beam spot used?  400 W/g

19. Gas Environment  Provides larger contact conductance values  Provides GTE gap conductance values (compared to radiation)  Provides interstitial conductive fluid in areas where contact is questionable (uneven sample/window surfaces)  Adds the variable of capsule internal pressure to the thermal problem (as temperature varies, internal pressure varies, changing contact area)

20. Helium gas filled, no contact

22. Helium, no contact, sensitivity  So, Tang’s sensitivity analysis showed some sensitivity to thermal conductivity of sample material (spreading of heat transversely)  For factor of 5 reduction in k, less than a factor of 2 increase in temperature delta across gap  Contact may decrease temperatures further  Helium may keep samples too cold?

23. Simplistic Model  In order to better understand the effects of gas in the sample capsule, a spreadsheet model was created  1-dimensional heat transfer model (no transverse heat transfer)  Treated as 1 mm wide annular rings  Each ring has a gap conductance value calculated  Contact area determined by deflection and volume/pressure calculations (manual iteration)

24. Simplistic Model  For rings within contact area, contact conductance calculated with Song & Yovanovich method for low pressure contact:

25. Simplistic Model Good Agreement with measurements in our regime!

26. Simplistic Model  For gap distances GTE 25 µm, conductance modeled as simple conduction through gas (thermal conductivity, k g )

27. Simplistic Model  Model assumes atmospheric pressure inside capsule when welding complete (cool)  Model uses an average beam sigma based on latest BLIP phosphor image (7.855 mm)  Model uses peak energy deposition scaled from first MARS analysis and adjusted for higher current (136 W/g)  Model accounts for changes in volume due to window deflection and sample expansion

28. Simplistic Model  Calculates new window to fluid heat transfer coefficient using expected flows and hydraulic diameter correlations (6170 W/m 2 /K)  Does not account for temperature rise through SS window foil or through sample thickness (predicts only sample surface temperature next to window)  Assumes 30 feet of water head (13 psi) when installed at BLIP

29. Simplistic Model: Helium Results

30. Simplistic Model: Argon Results

31. Simplistic Model: Summary  Helium is least sensitive to contact issues (35 K range)  Argon is not bad (240 K range)  Temperature range for Argon is good match for desired range (500K – 800 K)  Actual temperatures may be lower due to transverse heat flow (especially for Argon) and boiling

32. Compare with vacuum  Vacuum contact scaled from Simos best case model  Vacuum gap from Tang worst case model (not scaled yet)  Vacuum has largest range and sensitivity to contact (>1000 K) and can get very hot

33. Future Work  Z. Tang’s model can be used with the simplistic model’s contact area prediction to more accurately model the Argon gas case (and use new energy deposition results)  Recommend using Argon environment  Temperature Range matches desired  OK range in extremes  Relatively easy to weld in argon purged glove-box  Temperature Monitoring via annealing threshold  Need to work with Simos to see evidence of threshold in past runs