August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis1 Analysis cases Approach: Start simple to get information— with speed with confidence that is useful

August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis2 Case 1: hand calc comparison model 4.55 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, 2003K. Chow, LHC Luminosity Detector Thermal Analysis3 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, 2003K. Chow, LHC Luminosity Detector Thermal Analysis4 Case 2: SS block with circular heating Steady state temps -Power deposition = 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, 2003K. Chow, LHC Luminosity Detector Thermal Analysis5 Truncated gaussian beam profile

August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis6 Case 2: SS block with circular heating Transient results

August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis7 Case 3: Copper block by itself 87 mm 79 mm 15.3 mm -Power deposition = W/mm -Absorbed thickness = 15 mm -Absorbed power = W -Xsec area of heated volume = 484 mm^2 -Cu conductivity = 391 W/m-K -Cu density = 8.9 g/cc -Cu C = J/g-degC -Emissivity = 0.4 -Mass = 0.94 kg

August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis8 Case 3: Copper block results Steady state temps Transient temp at corner 443K

August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis9 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 mm 33 mm Macor Cu View with half of Macor not shown Isometric view

August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis10 Case 4 Steady state temps

August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis11 Case 4: Transient results 402K 477K 513K

August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis12 Case 5: Simplified geometry Cu+Macor+SS SS features: -Power deposition = W/mm -Absorbed thickness = 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 mm Cavity width=88 mm Overall height=234 mm Cavity height=183 mm Overall depth=98 mm Cavity depth=45 mm SS Macor Cu 3D view

August 7, 2003K. Chow, LHC Luminosity Detector Thermal Analysis13 Case 5: Simplified geometry Cu+Macor+SS Tin melts 322 degC 272 degC 222 degC 172 degC 122 degC 72 degC 22 degC SS center SS corner Macor corner Macor center Cu corner and center 565K 555K 482K 438K 409K

August 15, 2003K. Chow, LHC Luminosity Detector Thermal Analysis14 Case 6: Simplified geometry Cu+Macor+SS Emissivities: Cu = 0.7 Macor = 0.25 SS = K 641K 567K 492K 463K

August 15, 2003K. Chow, LHC Luminosity Detector Thermal Analysis15 Case 7: Simplified geometry Cu+Macor+SS Emissivities: Cu = 0.7 Macor = 0.75 SS = K 510K 442K 415K 387K

August 15, 2003K. Chow, LHC Luminosity Detector Thermal Analysis16 Case 8: Simplified geometry Cu+Macor+SS, 4 foot aluminum bar attached Emissivities: Cu = 0.7 Macor = 0.75 SS = 0.7 Alum = K 415K 377K 323K 310K

August 15, 2003K. Chow, LHC Luminosity Detector Thermal Analysis17 Case 11: Simplified geometry Cu+Macor+SS, 4 foot aluminum bar attached, with free convection Emissivities: Cu = 0.7 Macor = 0.75 SS = 0.7 Alum = K 407K 359K 312K 303K

August 15, 2003K. Chow, LHC Luminosity Detector Thermal Analysis18 Case 12: Simplified geometry Cu+Macor+SS, 4 foot aluminum bar attached, with free convection Emissivities: Cu = 0.7 Macor = 0.25 SS = 0.25 Alum = K 517K 367K 315K 304K

August 15, 2003K. Chow, LHC Luminosity Detector Thermal Analysis19 Case 13: Same as 12, but with new beam loading values Emissivities: Cu = 0.7 Macor = 0.25 SS = 0.25 Alum = K 520K 372K 316K 304K

August 21, 2003K. Chow, LHC Luminosity Detector Thermal Analysis20 Comparison 1 Power deposition (W/mm): Cu = Macor = SS = 0.798

August 21, 2003K. Chow, LHC Luminosity Detector Thermal Analysis21 Comparison 2 Emissivities Cu = 0.7 Macor = 0.75 SS = 0.7 Al = 0.7 Power deposition (W/mm): Cu = Macor = SS = 0.798

August 21, Comparison 3: Steady State Temps for Different Conditions Power deposition (W/mm): Cu = Macor = SS = Power deposition (W/mm): Cu = Macor = SS = 0.894