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Dump Heating Temperature(Revision 1 )

Ang LeeMarch 2, 2010

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Geometry and Loading

Fig 1 Dump Geometry

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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).

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Material Property

Kxx(W/mK) Cp(J/kgK) density (kg/m^3)

Copper 383 385 8900Steel 44 470 7800

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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”).

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FEA Model

Fig 2 FEA model

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Result and Discussion

1) The solution is running for 1 min=(15*60=900 pulses).

2) 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

3) The temperature history is shown in Fig 4

Fig 3a The temperature Profile after 1 min

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Result & Discussion

Fig 3b The details of temperature distribution

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Result and Discussion

Fig 4 The Temperature vs time (100% contact)

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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

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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

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Table 1 Summary of the ResultMaximum temperature (K) after 1 min (900 pulses)

(copper melting point ~1273 K)

Contact area (%)

100 % 50% (down stream)

<~1% at the very front

25% front and 25% back

50% At the center

10% at the center

5% at the center

1% at the center

0% no contact at all

T (K) for the beam spot of 24 cmx4 cm x 1 inch

374 396 414 414 375 376 386 403 414

T (K) For the beam spot of 12cmx4 cm x 1 inch

420 440 470 470 420 420 429 454 470

* Note: The bold phase temperature are probably most likely case if the proper care being taken to insure a contact around the beam spot.

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Case for the very tiny contact in the front

Fig 7 Case of the very tiny contact in the front3/2/2010, A. Lee

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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 center3/2/2010, A. Lee

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Fig 9 The Temperature as Function of the Contact Area

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0 10 20 30 40 50 60 70 80 90 100300

320

340

360

380

400

420

440

460

480

500

Hot spot temperature after 1 min vs contact area

Beam spot 24 cm x 1 inch x 4 cm Beam spot 12 cm x 1 inch x4 cm

Contact Area (%)

Tem

pera

ture

afte

r 1 m

in (9

00 p

ulse

s)

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Appendix A: Temperature plot

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Fig A-17 The temperature based on the “instantaneous heating” and “average heating “ approach