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August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 1
Analysis cases• Approach:
Start simple to get information— • with speed
• with confidence
• that is useful
Description Geometry Loading1 Comparison with rough estimate rectangular block Uniform heat generation2 Block of SS with beam heating same as case 1 Beam profile = circular3 Block of Cu with beam heating equiv volume and surf area Beam profile = square4 Block of Cu inside Macor equiv volume and surf area Beam profile = square5 Cu inside Macor inside SS equiv volume and surf area Beam profile = square6 Detailed geometry actual but defeatured Beam profile = circular7 Detailed geometry actual but defeatured Beam profile = truncated gaussian
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 2
Case 1: hand calc comparison model
4.55 cm
18.1 cm
18.1 cm
-Uniform heating of block using equiv volume heat generation (36.3W)-Same surface area (982 cm^2)-Radiation to “space” node at 298K (view factor=1)-Larger mass than hand calc-Emissivity = 0.1
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 3
Case 1: comparison results
• Steady state temperature same as hand calc– 520 K
• Transient results same as hand calc if we set hand calc mass equal to FEA model mass
520K
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 4
Case 2: SS block with circular heating
Steady state
temps
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0.002
-20 -15 -10 -5 0 5 10 15 20
Axisym m etric beam profile (m m )
Bea
m h
eat
load
(W
/mm
^2/m
m d
epth
)
-Power deposition = 0.798 W/mm-Absorbed thickness = 45.5 mm-Absorbed power = 36.3 W-Xsec area of heated volume = 491 mm^2-SS conductivity = 16.3 W/m-K-SS density = 8.0 g/cc-SS C = 0.5 J/g-degC-Emissivity = 0.1-Mass = 11.9 kg
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 5
Truncated gaussian beam profile
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
-15 -10 -5 0 5 10 15
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 6
Case 2: SS block with circular heating
• Transient results
295
345
395
445
495
545
0 10 20 30 40 50 60 70 80 90 100
Time (hr)
Tem
p (
K)
Center
Corner
whole block heating
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 7
Case 3: Copper block by itself
87 mm
79 mm15.3 mm
-Power deposition = 0.876 W/mm-Absorbed thickness = 15 mm-Absorbed power = 13.14 W-Xsec area of heated volume = 484 mm^2-Cu conductivity = 391 W/m-K-Cu density = 8.9 g/cc-Cu C = 0.385 J/g-degC-Emissivity = 0.4-Mass = 0.94 kg
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 8
Case 3: Copper block results
Steady state temps Transient temp at corner
295
315
335
355
375
395
415
435
455
0 2 4 6 8 10
Time (hr)
Tem
p a
t co
rner
(K
)
443K
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 9
Case 4: Copper block in Macor-Cu emissivity = 0.5
Macor features:-Power deposition = 0.46 W/mm-Absorbed thickness = 12 mm-Absorbed power = 5.52 W-Xsec area of heated volume = 484 mm^2-Macor conductivity = 1.46 W/m-K-Macor density = 2.52 g/cc-Macor C = 0.79 J/g-degC-Emissivity = 0.5-Mass = 0.32 kg
97.2 mm
86.2 mm33 mm
Macor
Cu
View with half ofMacor not shown
Isometric view
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 11
Case 4: Transient results
295
345
395
445
495
545
0 5 10 15
Time (hr)
Te
mp
(K
)
Cu center
Cu corner
M acor center
M acor corner
402K
477K
513K
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 12
Case 5: Simplified geometry Cu+Macor+SS
SS features:-Power deposition = 0.798 W/mm-Absorbed thickness = 64.08 mm-Absorbed power = 51.1 W-Xsec area of heated volume = 484 mm^2-SS conductivity = 16.3 W/m-K-SS density = 8 g/cc-SS C = 0.5 J/g-degC-Emissivity = 0.5-Mass = 11.5 kg
Front sectional view(plane normal to beam) Side sectional view
Overall width=95 mmCavity width=88 mm
Overall height=234 mmCavity height=183 mm
Overall depth=98 mmCavity depth=45 mm
SS
Macor
Cu
3D view
August 7, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 13
Case 5: Simplified geometry Cu+Macor+SS
Tin melts
295
345
395
445
495
545
595
0 2 4 6 8 10
Time (hour)
Te
mp
era
ture
(K
)
Cu centerCu cornerMacor centerMacor cornerSS centerSS corner
322 degC
272 degC
222 degC
172 degC
122 degC
72 degC
22 degC
SS center
SS corner
Macor corner
Macor center
Cu cornerand center
565K
555K
482K
438K
409K
August 15, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 14
Case 6: Simplified geometry Cu+Macor+SS
295
345
395
445
495
545
595
645
695
0 2 4 6 8 10
Time (hour)
Te
mp
era
ture
(K
)
Cu centerCu cornerMacor centerMacor cornerSS centerSS corner
Emissivities:Cu = 0.7Macor = 0.25SS = 0.25
644K
641K
567K
492K
463K
August 15, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 15
Case 7: Simplified geometry Cu+Macor+SS
Emissivities:Cu = 0.7Macor = 0.75SS = 0.7
295
345
395
445
495
545
0 2 4 6 8 10
Time (hour)
Te
mp
era
ture
(K
)
Cu centerCu cornerMacor centerMacor cornerSS centerSS corner
511K
510K
442K
415K
387K
August 15, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 16
Case 8: Simplified geometry Cu+Macor+SS, 4 foot aluminum bar attached
295
345
395
445
495
545
0 2 4 6 8 10
Time (hour)
Tem
per
atu
re (
K)
Cu centerCu cornerMacor centerMacor cornerSS centerSS cornerAl@SS endAl@opposite end
Emissivities:Cu = 0.7Macor = 0.75SS = 0.7Alum = 0.7
495K
415K
377K
323K
310K
August 15, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 17
295
345
395
445
495
545
0 2 4 6 8 10
Time (hour)
Tem
per
atu
re (
K)
Cu centerCu cornerMacor centerMacor cornerSS centerSS cornerAl@SS endAl@opposite end
Case 11: Simplified geometry Cu+Macor+SS, 4 foot aluminum bar attached,
with free convection
Emissivities:Cu = 0.7Macor = 0.75SS = 0.7Alum = 0.7
488K
407K
359K
312K
303K
August 15, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 18
295
345
395
445
495
545
595
645
0 2 4 6 8 10
Time (hour)
Tem
per
atu
re (
K)
Cu centerCu cornerMacor centerMacor cornerSS centerSS cornerAl@SS endAl@opposite end
Case 12: Simplified geometry Cu+Macor+SS, 4 foot aluminum bar attached,
with free convection
Emissivities:Cu = 0.7Macor = 0.25SS = 0.25Alum = 0.7
612K
517K
367K
315K
304K
August 15, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 19
295
345
395
445
495
545
595
645
0 2 4 6 8 10
Time (hour)
Tem
per
atu
re (
K)
Cu centerCu cornerMacor centerMacor cornerSS centerSS cornerAl@SS endAl@opposite end
Case 13: Same as 12, but with new beam loading values
Emissivities:Cu = 0.7Macor = 0.25SS = 0.25Alum = 0.7
620K
520K
372K
316K
304K
August 21, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 20
Comparison 1
Power deposition (W/mm):Cu = 0.876Macor = 0.460SS = 0.798
Steady State Temps for different emissivitiesCopper inside Macor inside Stainless housing
100
150
200
250
300
350
400
(#7) Cu emis=0.7, Macor emis=0.75, SSemis=0.7
(#5) Cu emis=0.5, Macor emis=0.5, SSemis=0.5
(#6) Cu emis=0.7, Macor emis=0.25, SSemis=0.25
Te
mp
era
ture
(d
eg
C)
copper
Macor center
Macor corner
Stainless center
Stainless corner
August 21, 2003 K. Chow, LHC Luminosity Detector Thermal Analysis 21
Comparison 2 EmissivitiesCu = 0.7Macor = 0.75SS = 0.7Al = 0.7
Power deposition (W/mm):Cu = 0.876Macor = 0.460SS = 0.798
Steady State Temperatures for different conditions
0
50
100
150
200
250
(#7) without aluminum bar,no convection
(#8) with aluminum bar, noconvection
(#11) with aluminum bar,free convection
Tem
per
atu
re (
deg
C)
copperMacor center
Macor corner
Stainless center
Stainless corner
Aluminum end
August 21, 2003 22
Comparison 3: Steady State Temps for Different Conditions
Power deposition (W/mm):Cu = 0.876Macor = 0.460SS = 0.798
Power deposition (W/mm):Cu = 0.983Macor = 0.326SS = 0.894
0
50
100
150
200
250
300
350
(#11) Cu emis=0.7, Macoremis=0.75, SS emis=0.7, Al
emis=0.7
(#12) Cu emis=0.7, Macoremis=0.25, SS emis=0.25, Al
emis=0.7
(#13) Cu emis=0.7, Macoremis=0.25, SS emis=0.25, Al
emis=0.7
Tem
per
atu
res
(deg
C)
copper
Macor center
Macor corner
Stainless center
Stainless cornerAluminum end