1

Dump Heating temperature(Revision 2, part 2)

Ang LeeApril 7, 2010

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. today4) The combine stress due to the thermal and structure load (vacuum). today5) The deformation if it is required/interested .today

3

Slide from March 16, 2010Temperature (K) Result after 30 days

9Hz@10usec@400Mev@35mA=1.26KW

15 Hz@4usec@400 MeV@35mA=0.84kw

Contact area 100% 50% 100% 50%

Beam area= 24 cmx4 cm x

1 inch412 (K)

(139 C or 282 F)

539 (K)(266 C or

510 F)

374 (K) 459 (K)

Beam area=12 cmx4 cm x 1

inch422 (K) 554 (K) 381 (K) 469 ( K)

4

ASME SEC VIII, Div 2 ,& SEC II, part D requirement

1) Pm (primary membrane)< Sm2) Pm + Pb (primary bending) < 1.5*Sm3) Pm+Pb+Q(secondary stress)< 3*SmWhere 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

5

FEA Structure model

6

Stress resultant

Mode 1100% 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)

27 0.06 27

Top plate_1” thick

41.5 0.463 46.6

Sided section (0.25”)

28 1.9 28

7

Stress resultant _ continues

Mode 250% 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)

50 0.06 50

Top plate 67 0.463 67

Sided section 39 1.9 39

8

Stress for the beam section due to the thermal loading

9

Stress for the top plate under the thermal loading

10

Stress for the sided area under thermal loading

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

12

13

Code requirement

14

15

Code stress

16

Working &Allowable stress

Material 1: C 10200; SB-187 ; copper rod -line19Sy=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 okSided section Sth=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 sectionSth~18 ksi > 12.6 not ok

and top plate, if we take “A” contour line, thenSth~14 ksi > 12.6 - not ok again.

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 060Sy=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 <62 ksi -> ok!Sided section Sth=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.

18

Conclusion

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

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

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.

21

Temperature vs time for a given power (100% contact) _

additional Thermal W_0-10KW with DW=0.2KW)

0 5 10 15 20 25 30 350

200

400

600

800

1000

1200

1400Temperature vs time for a given power

0.2KW1 kw2KW4KW6 KW8 KW10KW

time (days)

Tem

pera

ture

(K)

22

Additional Thermal calculationW=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.

0 2 4 6 8 10 120

500

1000

1500

2000

2500

Max Temperature as function of the beam power

100% contact, 24 cm beam area 50% contac 24 cm beam area

power (KW)

Max

imum

Tem

pera

ture

(K)

23

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

24

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

25

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