Hall D Target System Review

J. Fochtman September 28,2011

Preliminary Desig

n Work

Purpose of Concept Review

• Review current concept and calculations• Discuss design challenges and concerns with

current concept• Address these concerns in the final design

Hall D Target Refrigerator

Magnetic Field Limitations:

Remote Motor <500 Gauss

Cold Head <1T

Remote motor option reduces 2nd stage power by 15%.

Reduces cold head vibration to ~1µm

PR Completed- Current ETA is Mid January 2011

Preliminary P&I Diagram

Can these lines be combined if CV1 is

removed?

Conceptual SystemTarget Cold Head

2nd stage thermal link

to condenser

1st stage driven

radiation shield

Condenser Cold Head Compressor

Conceptual Target & Condenser

OFHC Copper pipe conducts thermal energy from 2nd stage

Single target gas line, relief is central from target and condenser

Thin OFHC Copper disks, soldered to inner condenser surface with narrow spacing

3 radially positioned tubes allow thermal siphon between

target and condenser

Kapton film strip heater on this surface

Cold Head Power & Cool Down Times

• Second stage cooling power output is a function of the set* temperature (* this will be accomplished by using a Kapton ribbon heater)– Based on my understanding, the second stage power will be linear

between 4.2K (1.35 W)and 45K (36 W)– Above 45K, the power output is considered to be 36 W.

• 7 kg (~15 lbs) is the current estimate for mass of OFHC Copper thermally connected to second stage (condenser and cold tubing)

• Based on the above assumptions, cool down and condensing the gas in the current targets (He, H2, D2) will take ~14 hours

Hydrogen Target DetailsBased on estimated piping

volumes and known pressures, we need ~1000

liter accumulator.

Estimated mass of liquid H2 is 0.03 Kg

Based on estimated target volumes and surface

areas, the boiloff rates for a loss of vacuum (Q= 20

kW/m2) is ~5 g/s

Hydrogen SystemKnownsTemperature Gas 300 KTemperature Liquid 16 K 20.35K BP w 14.15K FPSystem P warm system 22.04 psia Vaccumulator Msystem Variable R

151.9604 kPa eqn 1 0.08949 -1 Vaccumulator -0.03337

System P cold system 16.07 psia eqn 2 0.122702 -1 Msystem -0.00153110.7987 kPa

Volume, piping 0.01206915 m3 Vaccumulator 0.9585 m3

Volume, condensor 2.540E-04 m3 Msystem 0.1191 kg

Volume, target tube 6.540E-05 m3

Volume, target 1.100E-04 m3

Volume, condenser/tube/target 4.294E-04 m3 (liquid volume) mass of liquid 0.032 kg

Density, gas- cold system 0.08949 kg/m3 Gaspak- Add-in

Density, gas- warm system 0.12270 kg/m3 Gaspak- Add-in

Density, liquid 75.19853 kg/m3 Gaspak- Add-in

Two equations based on "Conservation of Mass" in a closed volume system in two different states "Cold" and "Warm"

Vacuum Loss Relief Liquid- Hydrogen Target (H2)

Volume of liquid Vliq 4.29E-04 m3 from System Accum & Mass Tab

Conduction area, total Atotal 1.02E-01 m2 CAD

Temperature T 16.0 K from System Accum & Mass Tab

Pressure P 110799 Pa from System Accum & Mass Tab

Density LN2, normal operating condition ρ 75.20 kg/m3 Gaspac

Mass of Liquid H2 m 0.032 kg =ρ·Vliq

Heat Input q 20000 W/m2 maximum boiling heat input

Latent Heat l 454300 J/kg Airliquid Website

Mass Flow mdot 0.0045 kg/s =A·q/l

16.134 kg/hr

Duration of boil off t 7 s =m/mdot

H2 Pressure Loss Summary, Relief EventPexit Pressure at exit of each segment

Total ΔP -3341 Pa -or- -0.5 psi ω mass flow rate (constant)

P @ entering relief valve 172369 Pa g 25.0 psi T Temperature (constant)

P @ Target 175710 Pa g 25.5 psi L Length of segment.

Pressure Loss -1.9% d ID of section

Pressure Loss 0.981 A Area of section

Δz Height of outlet - height of inletSTD atmospheric pressure 101325 Pa 14.7 psi νe Specific Volume of fluid exiting section. Calculated with Hepac Add-in

Pressure at vent EXIT 172369 Pa g (Relief Valve Setting) 25.0 psi Vel Velocity, νe·ω/A

acceleration, gravity 9.807 m/s2 M Speed Sound Vel/√(k·R·T)

Mass Flow, ω 5.0 g/s Visc Viscosity Calculated with Hepac Add-inTemp, T 300 K Re Reynolds Number, Vel·d/(Visc·νe)

Pipe Roughness, ε 1.50E-06 m Crane TP-410M, page A-24 f friction factor. Swamee-Jain approximation of the Colebrook equation

K Resistance coeffi cient. For elbows, K=13.48f, for pipe, K=fL/D, for reducer, K = (1-(din/dout)^2)^2

cryo piping ID 18.03 ΔP Delta pressure. Based on Bernoulli ΔP = ρ·g·[Δz+f·L·V2/(D·2·g)]external piping ID 24 Pi Pressure at inlet of section (Pe + ΔP)

νi Specific Volume of fluid entering section. Calculated with Hepac Add-in

Gas Details e Pipe Roughness

Ratio of Specific Heat, k 1.409 Fundamentals of Thermodynamics, Wylen-Sontag, Table A-8 Cell Uses GasPAK Add-In

Gas Constant, R 4124.18 J/kg·K Fundamentals of Thermodynamics, Wylen-Sontag, Table A-8

Section Pexit Pexit ω T L d A Δz νe Vel Mach No. Visc Re f K ΔP Pi Pi νi ΔP/Pi

Pa g Pa abs kg/hr K m mm m2 m m3/kg m/s - Pa*s - - - Pa Pa g ps ig m3/kg -

12 3" pipe 172369 273694 18.00 300 0.076 24.0 0.000452 -0.076 4.528278 50.05 0.04 8.963E-06 29595 0.02364 0.075 20.6 172390 25.0030 4.528278 0.0%

11 .75 elbow 172390 273715 18.00 300 0.000 24.0 0.000452 -0.038 4.527938 50.04 0.04 8.963E-06 29595 0.02364 0.319 -0.1 172389 25.0030 4.527938 0.0%

10 3" pipe 172389 273714 18.00 300 0.076 24.0 0.000452 0.000 4.527940 50.04 0.04 8.963E-06 29595 0.02364 0.075 20.8 172410 25.0060 4.527940 0.0%

9 .75 elbow 172410 273735 18.00 300 0.000 24.0 0.000452 -0.038 4.527597 50.04 0.04 8.963E-06 29595 0.02364 0.319 -0.1 172410 25.0060 4.527597 0.0%

8 6" pipe 172410 273735 18.00 300 0.152 24.0 0.000452 -0.152 4.527598 50.04 0.04 8.963E-06 29595 0.02364 0.150 41.2 172451 25.0119 4.527598 0.0%

7 .75 elbow 172451 273776 18.00 300 0.000 24.0 0.000452 -0.038 4.526918 50.03 0.04 8.963E-06 29595 0.02364 0.319 -0.1 172451 25.0119 4.526918 0.0%

6 96" pipe 172451 273776 18.00 300 2.438 24.0 0.000452 0.000 4.526920 50.03 0.04 8.963E-06 29595 0.02364 2.402 664.1 173115 25.1083 4.526920 0.4%

5 .75 elbow 173115 274440 18.00 300 0.000 24.0 0.000452 -0.038 4.515983 49.91 0.04 8.963E-06 29595 0.02364 0.319 -0.1 173115 25.1082 4.515983 0.0%

4 36" pipe 173115 274440 18.00 300 0.914 18.0 0.000255 -0.914 4.515984 88.44 0.07 8.963E-06 39394 0.02222 1.127 973.8 174089 25.2495 4.515984 0.6%

3 .75 elbow 174089 275414 18.00 300 0.000 18.0 0.000255 -0.038 4.500042 88.13 0.07 8.9631E-06 39394 0.02222 0.300 -0.1 174089 25.2495 4.500042 0.0%

2 60" pipe 174089 275414 18.00 300 1.524 18.0 0.000255 0.000 4.500044 88.13 0.07 8.9631E-06 39394 0.02222 1.878 1620.6 175710 25.4845 4.500044 0.9%

1 .75 elbow 175710 277035 18.00 300 0.000 18.0 0.000255 -0.038 4.473763 87.61 0.07 8.9631E-06 39394 0.02222 0.300 -0.1 175710 25.4845 4.473763 0.0%

Hydrogen Target LOV Pressure Relief

Maximum pressure estimate inside the target is <26 psia

Deuterium Target DetailsBased on estimated piping

volumes and known pressures, we need ~1100

liter accumulator.

Estimated mass of liquid D2 is 0.07 Kg

Based on estimated target volumes and surface

areas, the boiloff rates for a loss of vacuum (Q= 20

kW/m2) is ~7 g/s

Deuterium SystemKnownsTemperature Gas 300 KTemperature Liquid 19.5 K 23.55K BP w 18.55K FPSystem P warm system 22.04 psia Vaccumulator Msystem Variable R

151.9604 kPa eqn 1 0.178819 -1 Vaccumulator -0.07651

System P cold system 16.07 psia eqn 2 0.245192 -1 Msystem -0.00306110.7987 kPa

Volume, piping 0.01206915 m3 Vaccumulator 1.1066 m3

Volume, condensor 2.540E-04 m3 Msystem 0.2744 kg

Volume, target tube 6.540E-05 m3

Volume, target 1.100E-04 m3

Volume, condenser/tube/target 4.294E-04 m3 (liquid volume) mass of liquid 0.074 kg

Density, gas- cold system 0.17882 kg/m3 Gaspak- Add-in

Density, gas- warm system 0.24519 kg/m3 Gaspak- Add-in

Density, liquid 173.16213 kg/m3 Gaspak- Add-in

Two equations based on "Conservation of Mass" in a closed volume system in two different states "Cold" and "Warm"

Vacuum Loss Relief Liquid- Deuterium Target (D2)

Volume of liquid Vliq 4.29E-04 m3 from System Accum & Mass Tab

Conduction area, total Atotal 1.02E-01 m2 CAD

Temperature T 19.5 K from System Accum & Mass Tab

Pressure P 110799 Pa from System Accum & Mass Tab

Density LN2, normal operating condition ρ 173.16 kg/m3 Gaspac

Mass of Liquid H2 m 0.074 kg =ρ·Vliq

Heat Input q 20000 W/m2 maximum boiling heat input

Latent Heat l 304400 J/kg Airliquid Website

Mass Flow mdot 0.0067 kg/s =A·q/l

24.079 kg/hr

Duration of boil off t 11 s =m/mdot

Deuterium Target LOV Pressure ReliefD2 Pressure Loss Summary, Relief Event

Pexit Pressure at exit of each segment

Total ΔP -3043 Pa -or- -0.4 psi ω mass flow rate (constant)

P @ entering relief valve 172369 Pa g 25.0 psi T Temperature (constant)

P @ Target 175412 Pa g 25.4 psi L Length of segment.

Pressure Loss -1.7% d ID of section

Pressure Loss 0.983 A Area of section

Δz Height of outlet - height of inletSTD atmospheric pressure 101325 Pa 14.7 psi νe Specific Volume of fluid exiting section. Calculated with Hepac Add-in

Pressure at vent EXIT 172369 Pa g (Relief Valve Setting) 25.0 psi Vel Velocity, νe·ω/A

acceleration, gravity 9.807 m/s2 M Speed Sound Vel/√(k·R·T)

Mass Flow, ω 7.0 g/s Visc Viscosity Calculated with Hepac Add-inTemp, T 300 K Re Reynolds Number, Vel·d/(Visc·νe)

Pipe Roughness, ε 1.50E-06 m Crane TP-410M, page A-24 f friction factor. Swamee-Jain approximation of the Colebrook equation

K Resistance coeffi cient. For elbows, K=13.48f, for pipe, K=fL/D, for reducer, K = (1-(din/dout)^2)^2

cryo piping ID 18.03 ΔP Delta pressure. Based on Bernoulli ΔP = ρ·g·[Δz+f·L·V2/(D·2·g)]external piping ID 24 Pi Pressure at inlet of section (Pe + ΔP)

νi Specific Volume of fluid entering section. Calculated with Hepac Add-in

Gas Details e Pipe Roughness

Ratio of Specific Heat, k 1.400 Fundamentals of Thermodynamics, Wylen-Sontag, Table A-8 Cell Uses GasPAK Add-In

Gas Constant, R 2063.65 J/kg·K Universal Gas Constant/Molecular Weight

Hall D Cold Return LineSection Pexit Pexit ω T L d A Δz νe Vel Mach No. Visc Re f K ΔP Pi Pi νi ΔP/Pi

Pa g Pa abs kg/hr K m mm m2 m m3/kg m/s - Pa*s - - - Pa Pa g ps ig m3/kg -

12 3" 0.75" #10 pipe 172369 273694 25.20 300 0.076 24.0 0.000452 -0.076 2.266049 35.06 0.04 8.963E-06 41433 0.02190 0.070 18.5 172388 25.0027 2.266049 0.0%

11 .75 #10 elbow 172388 273713 25.20 300 0.000 24.0 0.000452 -0.038 2.265896 35.06 0.04 8.963E-06 41433 0.02190 0.295 -0.2 172387 25.0027 2.265896 0.0%

10 3" 0.75" #10 pipe 172387 273712 25.20 300 0.076 24.0 0.000452 0.000 2.265897 35.06 0.04 8.963E-06 41433 0.02190 0.070 18.9 172406 25.0054 2.265897 0.0%

9 .75 #10 elbow 172406 273731 25.20 300 0.000 24.0 0.000452 -0.038 2.265741 35.06 0.04 8.963E-06 41433 0.02190 0.295 -0.2 172406 25.0054 2.265741 0.0%

8 6" 0.75" #10 pipe 172406 273731 25.20 300 0.152 24.0 0.000452 -0.152 2.265743 35.06 0.04 8.963E-06 41433 0.02190 0.139 37.1 172443 25.0108 2.265743 0.0%

7 .75 #10 elbow 172443 273768 25.20 300 0.000 24.0 0.000452 -0.038 2.265436 35.05 0.04 8.963E-06 41433 0.02190 0.295 -0.2 172443 25.0107 2.265436 0.0%

6 96" 0.75" #10 pipe 172443 273768 25.20 300 2.438 24.0 0.000452 0.000 2.265438 35.05 0.04 8.963E-06 41433 0.02190 2.225 603.4 173046 25.0982 2.265438 0.3%

5 .75 #10 elbow 173046 274371 25.20 300 0.000 24.0 0.000452 -0.038 2.260464 34.98 0.04 8.963E-06 41433 0.02190 0.295 -0.2 173046 25.0982 2.260464 0.0%

4 36" 0.75" #10 pipe 173046 274371 25.20 300 0.914 18.0 0.000255 -0.914 2.260465 61.97 0.07 8.963E-06 55151 0.02067 1.048 886.5 173933 25.2268 2.260465 0.5%

3 .75 #10 elbow 173933 275258 25.20 300 0.000 18.0 0.000255 -0.038 2.253197 61.78 0.07 8.9631E-06 55151 0.02067 0.279 -0.2 173932 25.2268 2.253197 0.0%

2 60" 0.75" #10 pipe 173932 275257 25.20 300 1.524 18.0 0.000255 0.000 2.253198 61.78 0.07 8.9631E-06 55151 0.02067 1.747 1479.3 175412 25.4413 2.253198 0.8%

1 .75 #10 elbow 175412 276737 25.20 300 0.000 18.0 0.000255 -0.038 2.241173 61.45 0.07 8.9631E-06 55151 0.02067 0.279 -0.2 175412 25.4413 2.241173 0.0%

Maximum pressure estimate inside the target is <26 psia

Helium Target DetailsBased on estimated piping

volumes and known pressures, we need ~800

liter accumulator.

Estimated mass of liquid He is 0.06 Kg

Based on estimated target volumes and surface

areas, the boiloff rates for a loss of vacuum (Q= 20

kW/m2) is ~100 g/s

Helium SystemKnownsTemperature Gas 300 KTemperature Liquid 4.15 KSystem P warm system 22.04 psia Vaccumulator Msystem Variable R

151.9604 kPa eqn 1 0.17771 -1 Vaccumulator -0.05679

System P cold system 16.07 psia eqn 2 0.243683 -1 Msystem -0.00305110.7987 kPa

Volume, piping 0.01206915 m3 Vaccumulator 0.8146 m3

Volume, condensor 2.540E-04 m3 Msystem 0.2016 kg

Volume, target tube 6.540E-05 m3

Volume, target 1.100E-04 m3

Volume, condenser/tube/target 4.294E-04 m3 (liquid volume) mass of liquid 0.055 kg

Density, gas- cold system 0.17771 kg/m3 Gaspak- Add-in

Density, gas- warm system 0.24368 kg/m3 Gaspak- Add-in

Density, liquid 127.25679 kg/m3 Gaspak- Add-in

Two equations based on "Conservation of Mass" in a closed volume system in two different states "Cold" and "Warm"

Vacuum Loss Relief Liquid- Helium (He)

Volume of liquid Vliq 4.29E-04 m3 from System Accum & Mass Tab

Conduction area, total Atotal 1.02E-01 m2 CAD

Temperature T 4.15 K from System Accum & Mass Tab

Pressure P 110799 Pa from System Accum & Mass Tab

Density LN2, normal operating condition ρ 127.26 kg/m3 Hepac

Mass of Liquid H2 m 0.055 kg =ρ·Vliq

Heat Input q 20000 W/m2 maximum boiling heat input

Latent Heat l 20300 J/kg Airliquid Website

Mass Flow mdot 0.1003 kg/s =A·q/l

361.064 kg/hr

Duration of boil off t 1 s =m/mdot

Helium Target LOV Pressure Relief

Maximum pressure estimate inside the target is <26 psia

He Pressure Loss Summary, Relief EventPexit Pressure at exit of each segment

Total ΔP -46466 Pa -or- -6.7 psi ω mass flow rate (constant)

P @ entering relief valve 172369 Pa g 25.0 psi T Temperature, assumes given heat input

P @ Target 218835 Pa g 31.7 psi L Length of segment.

Pressure Loss -21.2% d ID of section

Pressure Loss 0.788 A Area of section

Δz Height of outlet - height of inletSTD atmospheric pressure 101325 Pa 14.7 psi νe Specific Volume of fluid exiting section. Calculated with Hepac Add-in

Pressure at vent EXIT 172369 Pa g (Relief Valve Setting) 25.0 psi Vel Velocity, νe·ω/A

acceleration, gravity 9.807 m/s2 M Speed Sound Vel/√(k·R·T)

Mass Flow, ω 100.3 g/s Visc Viscosity Calculated with Hepac Add-inPipe Roughness, ε 1.50E-06 m Crane TP-410M, page A-24 Re Reynolds Number, Vel·d/(Visc·νe)

Temperature, initial 50 K f friction factor. Swamee-Jain approximation of the Colebrook equation

Heat Input, Q 20000 W/m2 K Resistance coeffi cient. For elbows, K=13.48f, for pipe, K=fL/D, for reducer, K = (1-(din/dout)^2)^2

cryo piping ID 18.03 ΔP Delta pressure. Based on Bernoulli ΔP = ρ·g·[Δz+f·L·V2/(D·2·g)]external piping ID 24 Pi Pressure at inlet of section (Pe + ΔP)

νi Specific Volume of fluid entering section. Calculated with Hepac Add-in

Gas Details e Pipe Roughness

Ratio of Specific Heat, k 1.667 HeCalc Cell Uses GasPAK Add-In

Gas Constant, R 2077.23 J/kg·K HeCalc

Section Pexit Pexit ω T L d A Δz νe Vel Mach No. Visc Re f K ΔP Pi Pi νi ΔP/Pi

Pa g Pa abs kg/hr K m mm m2 m m3/kg m/s - Pa*s - - - Pa Pa g ps ig m3/kg -

12 3" pipe 172369 273694 361.08 150 0.076 24.0 0.000452 -0.076 1.141484 253.08 0.35 1.2518E-05 425064 0.01432 0.045 1274.6 173644 25.1849 1.141484 0.7%

11 .75 elbow 173644 274969 361.08 150 0.000 24.0 0.000452 -0.038 1.136207 251.91 0.35 1.2518E-05 425060 0.01432 0.193 -0.3 173643 25.1848 1.136207 0.0%

10 3" pipe 173643 274968 361.08 150 0.076 24.0 0.000452 0.000 1.136208 251.91 0.35 1.2518E-05 425060 0.01432 0.045 1269.3 174913 25.3689 1.136208 0.7%

9 .75 elbow 174913 276238 361.08 150 0.000 24.0 0.000452 -0.038 1.131001 250.76 0.35 1.2519E-05 425055 0.01432 0.193 -0.3 174912 25.3689 1.131001 0.0%

8 6" pipe 174912 276237 361.08 125 0.152 24.0 0.000452 -0.152 0.943024 209.08 0.32 1.1106E-05 479115 0.01408 0.089 2071.2 176983 25.6693 0.943024 1.2%

7 .75 elbow 176983 278308 361.08 100 0.000 24.0 0.000452 -0.038 0.749415 166.15 0.28 9.8007E-06 542930 0.01385 0.187 -0.5 176983 25.6692 0.749415 0.0%

6 96" pipe 176983 278308 361.08 75 2.438 24.0 0.000452 0.000 0.562715 124.76 0.24 8.196E-06 649231 0.01355 1.376 19035.9 196019 28.4301 0.562715 9.7%

5 .75 elbow 196019 297344 361.08 50 0.000 24.0 0.000452 -0.038 0.351848 78.01 0.19 6.398E-06 831675 0.01316 0.177 -1.1 196018 28.4300 0.351848 0.0%

4 36" pipe 196018 297343 361.08 25 0.914 18.0 0.000255 -0.914 0.175497 68.94 0.23 4.1947E-06 1688558 0.01271 0.645 8678.9 204697 29.6887 0.175497 4.2%

3 .75 elbow 204697 306022 361.08 25 0.000 18.0 0.000255 -0.038 0.170546 67.00 0.23 4.1975E-06 1687432 0.01271 0.171 -2.2 204694 29.6884 0.170546 0.0%

2 60" pipe 204694 306019 361.08 25 1.524 18.0 0.000255 0.000 0.170547 67.00 0.23 4.1975E-06 1687432 0.01271 1.074 14140.2 218835 31.7393 0.170547 6.5%

1 .75 elbow 218835 320160 361.08 25 0.000 18.0 0.000255 -0.038 0.163054 64.05 0.22 4.202E-06 1685602 0.01271 0.171 -2.3 218832 31.7389 0.163054 0.0%

Maximum pressure estimate inside the target is <32 psia

ASME Pressure Relief

• What is maximum design pressure of similar targets?

• If the large flow area relief valve (needed for He) is used for Hydrogen and Deuterium, the valve is oversized. Would it be best to switch the relief valve based on the target gas?

• Where will the vent exit the Hall?ASME relief valve sizing

Gas Temp., R Pressure, P1,psia

Relief valve pressure set point, psig

Flow rate, kg/s (vapor generation

rate)

Flow rate, lb/hr

Compressibility Factor (Z)

Ratio of Specific

Heats, cp/cv

(k)

Gas Constant, C (US UNITS)

ASME Coeffi cient

of Discharge (K)

Molecular Weight,

g/mol (M)

Capacity correction factor due

to back pressure,

(Kb)

Minimum Flow Area,

in2 (using Sonic flow formula)

Published Flow Area,

in2

Orifice ID, in

Loss of Vacuum, He Target He 540 26.1 10 0.100 796 1 1.66 377.1 0.878 4.003 1 1.0696 1.4150 1.167

Loss of Vacuum, D2 Target D2 540 26.1 10 0.007 53 1 1.4 356.1 0.878 4.029 1 0.0754 0.1213 0.310

Loss of Vacuum, H2 Target H2 540 26.1 10 0.005 36 1 1.4 356.1 0.878 2.016 1 0.0716 0.1213 0.302

Next Steps

• Complete P&I diagram• Layout piping and refrigerator positions on

into Hall D model• Finalize the design and calculations• Receive and test cold head• Build and test target