Dump Heating Temperature (Revision 1 )

1. Dump Heating Temperature(Revision 1 ) Ang Lee March 2, 2010

2. Geometry and Loading Fig 1 Dump Geometry

3. Geometry and Loading • Given by Fernanda G/Larry A./Rob R as shown Fig 1. • Pulse Frequency=15 Hertz (15 pulses/sec). • Pulse width=20e-6 second. • Energy/per pulse=6.24 KJ/15=0.416 KJ/pulse. • Beam spot (revised on Feb, 2010)=24 cmx4 cmx1” as well as 12 cmx4 cm x 1” (* Provided by L. Allen & F. Garcia) • Top plate is 1 inch thick copper. • The copper tube is 0.25” thick. • Surrounding Steel is ~36” in diameter & 108” in length. • Only “mass cooling” available (cool down by the mass).

4. Material Property Kxx(W/mK) Cp(J/kgK) density (kg/m^3) Copper 383 385 8900 Steel 44 470 7800

5. FEA Model • Model with a thermal element (solid 90). • Only half structure is modeled due to its symmetry. • The contact between the copper insert and steel surrounding only occurs on the top. • Several different contact scenarios have been studied extensively to understand a worst case. • Both “ instantaneous” heating and “average heating approach have been used and the difference is relative small for this particular case. Therefore, we’ll use “average” heating approach to save both “real clock”&“CPU” time, as well as the disk usage. • Note: The instantaneous heating  pulse on for 20e-6 sec and “off” for 1/15”. The “average” heating  by average one pulse energy over 1/15 second period, the energy input will be continuously on ( instead of the “On” and “Off”).

6. FEA Model Fig 2 FEA model

7. Result and Discussion The solution is running for 1 min=(15*60=900 pulses). The maximum temperature is Tmax=375 K. The initial temperature is 300 K (room temperature). So, delta T due the heating is only 74 K after 1 min pulses. It is assuming 100% contact and the beam spot is 24 cmx 1 inch x 4 cm The temperature history is shown in Fig 4 Fig 3a The temperature Profile after 1 min

8. Result & Discussion Fig 3b The details of temperature distribution

9. Result and Discussion Fig 4 The Temperature vs time (100% contact)

10. Contact Area and Beam Spot Effect • The temperature rise is about Delta T= ~74K for the case of beam area= 24 cm x 4 cm x 1 inch with a 100% contact area on the top. • Two studies need to be done to understand how much temperature effect will be in respect to these two important parameters (uncertainty) : beam spot and contact area • Fig 5 shows the Tmax=414 K or delT=114 K after 1 min if the contact area is “0%” and Beam area is 24 cm x 4 cm x 1 inch x 24 cm • Fig 6 shows the Tmax =470 K or delT=170 K after 1 min if the contact area is “0%”and the beam area =12 cm x 4 cm x 1 inch. • Both cases are well below to the Copper melting temperature =1000 C =1273 K

11. Temperature For the case of “0% “ contact area Fig 5 Temperature for the beam area =4 cm x 1 inch x24 cm at 0% contact area; Tmax=414 K and DelT=114 K after 1 min. Fig 6 Temperature for the beam area =4 cm x 1 inch x12 cm at 0% contact area; Tmax=470 K and DelT=170 K after 1 min. Copper melting =1000 C =1273 K

12. Table 1 Summary of the ResultMaximum temperature (K) after 1 min (900 pulses)(copper melting point ~1273 K) * Note: The bold phase temperature are probably most likely case if the proper care being taken to insure a contact around the beam spot.

13. Case for the very tiny contact in the front Fig 7 Case of the very tiny contact in the front

14. Sample of the temperature plot for the case of 5% contact area in the center Fig 8 The case for the 5% contact at the center

15. Fig 9 The Temperature as Function of the Contact Area

16. Impression • The temperature curve seems relatively flat: a)between the range of 376 K~414 K for the beam spot of 24 cm x 1 inch x 4 cm, b) and range of 420 K ~470 K for the beam spot of 12 cm x 1 inch x 4cm. • There is not much difference in terms of temperature as long as the contact area > 10%, occurring around the beam area. • The current design seem to be adequate since the copper melting point ~1200 K.

17. Appendix A: Temperature plot Fig A-1 Temperature for the case of contact area 100% & beam spot=4 cm x 1 inch x 24 cm Fig A-2 Temperature for the case of contact area 50 % at the front & beam spot=4 cm x 1 inch x 24 cm

18. Appendix A: Temperature plot Fig A-3 Temperature for the case of contact area < ~1% at the front & beam spot=4 cm x 1 inch x 24 cm Fig A-4 Temperature for the case of contact area 25% at the front and 25% at the back & beam spot=4 cm x 1 inch x 24 cm

19. Appendix A: Temperature plot Fig A-5 Temperature for the case of contact area = ~50% at the center & beam spot=4 cm x 1 inch x 24 cm Fig A-6 Temperature for the case of contact area = ~10% at the center & beam spot=4 cm x 1 inch x 24 cm

20. Appendix A: Temperature plot Fig A-7 Temperature for the case of contact area < ~5% at the center & the beam spot=4 cm x 1 inch x 24 cm Fig A-8 Temperature for the case of contact area 1 % at the the center & the beam spot=4 cm x 1 inch x 24 cm

21. Appendix A: Temperature plot Fig A-9 Temperature for the case of contact area =0 % & the beam spot=4 cm x 1 inch x 24 cm Fig A-10 Temperature for the case of contact area= 100 % & the beam spot=4 cm x 1 inch x 12 cm

22. Appendix A: Temperature plot Fig A-11Temperature for the case of contact area =50 % at the front& the beam spot=4 cm x 1 inch x 12 cm Fig A-12 Temperature for the case of contact area<~1 % at the front & the beam spot=4 cm x 1 inch x 12 cm

23. Appendix A: Temperature plot Fig A-13Temperature for the case of contact area =25 % at the front and 25% at the back & the beam spot=4 cm x 1 inch x 12 cm Fig A-14 Temperature for the case of contact area=~50% at the center & the beam spot=4 cm x 1 inch x 12 cm

24. Appendix A: Temperature plot Fig A-15Temperature for the case of contact area =10 % at the front and 25% at the back & the beam spot=4 cm x 1 inch x 12 cm Fig A-14 Temperature for the case of contact area=~5% at the center & the beam spot=4 cm x 1 inch x 12 cm

25. Appendix A: Temperature plot Fig A-15Temperature for the case of contact area =1% at the front and 25% at the back & the beam spot=4 cm x 1 inch x 12 cm Fig A-16 Temperature for the case of contact area=0% & the beam spot=4 cm x 1 inch x 12 cm

26. Appendix A: Temperature plot Fig A-17 The temperature based on the “instantaneous heating” and “average heating “ approach