1. Dump Heating temperature (Revision 2, part 2) Ang Lee April 7, 2010 1

2. Slide from March 16, 2010 For structural calculation: 1) Buckling calculation: to find critical collapsing pressure Pcr for a given structure (E and t) and compare it with CGA (SF=2)or ASME (SF=3) code for the safety factor (SF).  Done 2)Stress calculation : if the structure passes the buckling SF requirement, then the working stress needs to be checked under the operating load (p=15 psi).-  done 3)The thermal stress due to temperature rise.  today 4)The combine stress due to the thermal and structure load (vacuum).  today 5)The deformation if it is required/interested.  today 2

3. Slide from March 16, 2010 Temperature (K) Result after 30 days 9Hz@10usec@400Mev@35mA =1.26KW 15 Hz@4usec@400 MeV@35mA =0.84kw Contact area100%50%100%50% Beam area= 24 cmx4 cm x 1 inch 412 (K) (139 C or 282 F) 539 (K) (266 C or 510 F) 374 (K)459 (K) Beam area= 12 cmx4 cm x 1 inch 422 (K)554 (K)381 (K)469 ( K) 3

4. ASME SEC VIII, Div 2,& SEC II, part D requirement 1)Pm (primary membrane)< Sm 2)Pm + Pb (primary bending) < 1.5*Sm 3)Pm+Pb+Q(secondary stress)< 3*Sm Where the thermal stress is considered to be secondary stress_ Q(self limiting stress) Where Sm is code allowable stress for a given temperature. It is based on Sec II, part D 4

5. FEA Structure model 5

6. Stress resultant Mode 1 100% contact Tmax=412 K (139 C/282F) Thermal stress_ksi (due to temperature rise) Structure_ksi (due to 15 psi) Thermal + structure_ksi Beam section _24cmx4cmx1” (ksi) 270.0627 Top plate _1” thick 41.50.46346.6 Sided section (0.25”) 281.928 6

7. Stress resultant _ continues Mode 2 50% contact (very close to 0% contact) Tmax=539K (266C /510F) Thermal stress _ ksi (due to temperature rise) Structure (due to 15 psi)_ ksi Thermal +structure (ksi) Beam section (ksi) 500.0650 Top plate670.46367 Sided section391.939 7

8. Stress for the beam section due to the thermal loading 8

9. Stress for the top plate under the thermal loading 9

10. Stress for the sided area under thermal loading 10

11. Stress criteria (ASME) Seems we need a material with a Sy (min. yield strength= 21 ksi at T=~300F such that Sm (allowable)=2/3*Sy=14 ksi at T=300 F (since Q_secondary stress)<3*Sm=42 ksi By looking on the ASME II, part D table Y 11

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13. Code requirement 13

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15. Code stress 15

16. Working &Allowable stress Material 1: C 10200; SB-187 ; copper rod -line19 Sy=6.3 ksi(300F)&5.6 ksi (450F) Then, its allowable Sm=2/3 Sy Sm=4.2 ksi (300 F) & 3.73 ksi (450F) 1)The stress due to the structure load has to be below the Sm. –> OK. Since max stress due to 15 psi is 1.9 ksi < both 4.2 & 3.72 ksi for given temperature. 2)Secondary stress due to the thermal loading : Sth<3*Sm = 12.6 & 11.19 ksi Beam section, Sth=27 ksi > 12.6 ksi-  not ok. Top plate,Sth=41.5 ksi > 12.6 ksi -> not ok Sided sectionSth=36 ksi > 12.6 ksi -  not ok 3)If we take a look it more aggressively: Beam section, if we take the “B “ contour and really don’t care that corner section Sth~18 ksi > 12.6  not ok and top plate, if we take “A” contour line, then Sth~14 ksi > 12.6 -  not ok again. 16

17. Working & Allowable stress Material 2,C-61400 or C-63000, Table Y, line 21—27, The Yield stress does not change too much as the temperature rise and stays around ~29 to 31 ksi range. Let ‘s take line 25 as an example: Plate or sheet, SB-169, C-61400,temper 025/or 060 Sy=31.1K (300F) & 30.4 ksi (450F) Then its allowable=Sm=30.4*2/3=20.6 ksi (450 F) 1)The stress due to the structure load has to be below the Sm. –> Yes. Since max stress due to 15 psi is 1.9 ksi<< 20.6ksi for given temperature. 2)Secondary stress due to the thermal loading : Sth<3*Sm = 62 ksi Beam section, Sth=27 ksi < 62 ksi-  ok! Top plate,Sth=41.5 ksi ok! Sided sectionSth=36 ksi < 62 ksi -  ok! 3)So, Material from line 21—27 will work for 100% contact case (most likely case) And also works for 50% contact case where the contact occurs only both end and the beam hits in the center portion-  very close to ~0% contact case (most pessimistic case. 17

18. Conclusion Six sided section needs to be a copper with Sy (min) = ~30 ksi at T=450 F due to thermal stress. 18

19. Implication for upstream 8”beam Pipe Since the 8” beam pipe is fixed at the upstream side, the thermal expansion due to the sided section will create a compressive force on that beam pipe besides 15 psi external pressure. We need to take a look 19

20. Implication for upstream 8”beam Pipe First mode will be most unlikely and second mode SF=11 should be sufficient. The beam pipe will be fine. 20

21. Temperature vs time for a given power (100% contact) _ additional Thermal W_0-10KW with DW=0.2KW) 21

22. Additional Thermal calculation W=0-10 KW with DW=0.2 KW This temperature vs the beam power curve is the maximum temperature after the “ curve flat” __steady state. 22

23. Appendix A _ Thermal stress for the beam section _50% contact case 23

24. Appendix A _ Thermal stress for the Top plate_50% contact case 24

25. Appendix A _ Thermal stress for the sided section_50% contact case 25