Thermal Analysis of the C200 Calorimeter Shai Ehrmann

California State University, Los Angeles

Tasks Accomplished July - August

• • • • • • • • • Prepared and repaired 250 PMTs for GRINCH Removed 50 PMTs for HCAL from Big HAND Measured flatness of HCAL scintillator sample Studied 100 light guides for ECAL by measuring flatness and perpendicularity Conducted experimental study of thermal conductance and cooling of light guides Calculated thermal properties of ECAL – Temperature gradients – Heating and cooling times Researched heat induced transparency loss Conducted thermal annealing experiments Began 3D thermal analysis of ECAL – Prepared input files – Assisted Silviu Covrig with ANSYS analysis 2

What is the C200 calorimeter?

• Designed to maintain permanent heat annealing to lead glass blocks.

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What is the C200 calorimeter?

• Designed to maintain permanent heat annealing to lead glass blocks.

• Calorimeter receives heat from several heaters to ideally maintain a 1-dimensional linear temperature gradient. The entire system is insulated on all sides.

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What is the C200 calorimeter?

• Designed to maintain permanent heat annealing to lead glass blocks.

• Calorimeter receives heat from several heaters to ideally maintain a 1-dimensional linear temperature gradient. The entire system is insulated on all sides.

• Calorimeter is comprised of lead glass blocks attached to light guides, which provide a cooling temperature gradient for proper PMT functioning.

*Q(A) and Q(B) denote the desired direction of heat flux

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What is the C200 calorimeter?

• Designed to maintain permanent heat annealing to lead glass blocks.

• Calorimeter receives heat from several heaters to ideally maintain a 1-dimensional linear temperature gradient. The entire system is insulated on all sides.

• Calorimeter is comprised of lead glass blocks attached to light guides, which provide a cooling temperature gradient for proper PMT functioning.

• Lead glass blocks are organized in a 20x20 array, while light guides are organized in a skewed 10x20 array.

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Primary Heat Analysis

• Thermal analysis is essential to ensure design feasibility and efficiency.

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Primary Heat Analysis

• Thermal analysis is essential to ensure design feasibility and efficiency.

• Heat is provided from a main heater to achieve Q(A) and from an auxiliary heater to achieve Q(B), which together administer an appropriate temperature gradient throughout the system.

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Primary Heat Analysis

• Thermal analysis is essential to ensure design feasibility and efficiency.

• Heat is provided from a main heater to achieve Q(A) and from an auxiliary heater to achieve Q(B), which together administer an appropriate temperature gradient throughout the system.

Desired Temperatures: Surface A → 225 °C Surface B → 175 °C Surface C → 50 °C

Corresponding Heat Required:

𝑄(𝐴) = 0.16 𝑊 𝑝𝑒𝑟 𝑏𝑙𝑜𝑐𝑘 𝑄(𝐵) = 0.46 𝑊 𝑝𝑒𝑟 𝑏𝑙𝑜𝑐𝑘 ∑𝑄 𝐴 = 64 𝑊 ∑𝑄 𝐵 = 92 𝑊 𝑄 𝑡𝑜𝑡𝑎𝑙 = ∑𝑄 𝐴 + ∑𝑄 𝐵 = 156 𝑊 •

Primary heat analysis shows that the regime requires a net power of 156 W.

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Light Guide Temperature Gradient Study

• Goal: to test cooling at PMT and to study heat transfer in the light guide.

*Light guide with approximately 2 cm of wool glass insulation 10

Light Guide Temperature Gradient Study

• Goal: to test cooling at PMT and to study heat transfer in the light guide.

• We attach a copper radiator to amplify cooling effect.

* The copper radiator acts as a heat exchanger to ensure and maintain appropriate temperature at cool end.

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Light Guide Temperature Gradient Study

• Goal: to test cooling at PMT and to study heat transfer in the light guide.

• We attach a copper radiator to amplify cooling effect.

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Results verify the efficacy of a copper radiator in cooling; as T1 approached 200 ᵒC, T3 remained below 40 ᵒC.

T1 T2 T3 12

Heat up and cool down

• For experiment logistics and safety we assess the amount of time necessary to heat up the C200 calorimeter and the effects of cool down.

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Heat up and cool down

• For experiment logistics and safety we assess the amount of time necessary to heat up the C200 calorimeter and the effects of cool down.

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Solving the heat equation for the specific thermal system, we find that the regime of lead glass heating will ideally achieve a thermal gradient within 1% of equilibrium in 75 hours, within 5% in 40 hours, and within 10% in 30 hours.

Time-Based Temperature Profile Initial Profile 10 hours, 50% Equilibrium 30 hours, 90% Equilibrium 40 hours, 95% Equilibrium 75 hours, 99% Equilibrium

225 ᵒC Lead Glass 175 ᵒC

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Heat up and cool down

• Cool down in the case of immediate shut off will primarily occur by convection and conduction through the light guides due to low thermal conductivity in foam glass insulation. 15 𝑾 𝒌 = 𝟎. 𝟎𝟓 𝒎 ∙ 𝑲 Foam Glass Insulation Lead Glass Light Guide 𝑾 𝒌 = 𝟏. 𝟎𝟓 𝒎 ∙ 𝑲

Heat up and cool down

• Cool down in the case of immediate shut off will primarily occur by convection and conduction through the light guides due to low thermal conductivity in foam glass insulation. •

Analysis shows that the temperature gradient in the calorimeter will reach approximately 10 ᵒC/cm at the onset of cooling and will relax until reaching room temperature.

225 ᵒC 175ᵒC 50ᵒC Lead Glass Light Guide 16

Expansion Cycles

• Steel bracing will expand more rapidly and with greater magnitude than lead glass during heat up. 17

Expansion Cycles

• Steel bracing will expand more rapidly and with greater magnitude than lead glass during heat up. • Expansion is relatively minimal, and should not compromise the mechanical integrity of the calorimeter.

∆L = 0.15 mm ∆L = 1 mm

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Expansion Cycles

• Steel bracing will expand more rapidly and with greater magnitude than lead glass during heat up. • Expansion is relatively minimal, and should not compromise the mechanical integrity of the calorimeter.

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The effective linear thermal expansion between the surfaces of lead glass and the surfaces of steel bracing will create a gap of 1.4 mm on the sides and 3 mm on the top .

These gaps will be mediated with spring bracing to maintain compression on the lead glass array.

∆L = 3 mm ∆L = 1.4 mm

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Expansion Cycles

• Steel bracing will expand more rapidly and with greater magnitude than lead glass during heat up. • Expansion is relatively minimal, and should not compromise the mechanical integrity of the calorimeter.

• The effective linear thermal expansion between the surfaces of lead glass and the surfaces of steel bracing will create a gap of 1.4 mm on the sides and 3 mm on the top. These gaps will be mediated with spring bracing to maintain compression on the lead glass array.

• During the cooling cycle, steel will contract more rapidly. The peripheral blocks of lead glass will contract more quickly than the inner blocks and leave small gaps due to shrinking.

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Lead Glass Annealing

• Goal: to study the relationship between annealing time, temperature and effectiveness in reducing radiation damage.

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Lead Glass Annealing

• Goal: to study the relationship between annealing time, temperature and effectiveness in reducing radiation damage.

• Data was taken for lead glass blocks at various durations and temperatures of heat soaking to measure the magnitude of damage reduction.

Results verify that annealing temperature and annealing duration are both important factors in eliminating radiation damage.

Block

A B C D E

Temperature [ ᵒC]

200 200 250 225 225

Duration [Hours]

4 2 4 2 8

Damage Reduction Factor

11.22

3.60

66.72

25.23

58.50

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Lead Glass Annealing

• Goal: to study the relationship between annealing time, temperature and effectiveness in reducing radiation damage.

• Data was taken for lead glass blocks at various durations and temperatures of heat soaking to measure the magnitude of damage reduction. Results verify that annealing temperature and annealing duration are both important factors in eliminating radiation damage.

• Several blocks were re-annealed in order to attain maximum transparency.

Results showed that blocks do not have the same base absorption.

Block

C D E

Temperature [ ᵒC]

225 250 250 225

Re-anneal Data Duration [Hours]

12 12 16 12

Base Absorption [µA]

~ 0.5

~ 0.7

~ 0.75

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Conclusion

• The study of thermal annealing of lead glass blocks allows us to quantify the radiation damage reduction.

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Conclusion

• The study of thermal annealing of lead glass blocks allows us to quantify the radiation damage reduction.

• During heating and cooling cycles, the C200 design maintains mechanical stability.

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Conclusion

• The study of thermal annealing of lead glass blocks allows us to quantify the radiation damage reduction.

• During heating and cooling cycles, the C200 design maintains mechanical stability.

• The net heat loss through insulation is approximated at 225 W; however the real heat loss will be much greater due to insulation gaps and bracing design. We can thus estimate that the heaters should generate at least 1 kW.

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Conclusion

• The study of thermal annealing of lead glass blocks allows us to quantify the radiation damage reduction.

• During heating and cooling cycles, the C200 design maintains mechanical stability.

• The net heat loss through insulation is approximated at 225 W; however the real heat loss will be much greater due to insulation gaps and bracing design. We can thus estimate that the heaters should generate at least 1 kW.

• The light guides measured for flatness and perpendicularity are of adequate quality to allow for proper attachment to lead glass and to PMTs.

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