Cryogenics for superconducting devices
Philippe Lebrun Director, Joint Universities Accelerator School
JUAS 2019 Course 2 19 February 2019 Contents
• Introduction • Cryogenic fluids • Heat transfer & thermal insulation • Thermal screening with cold vapour • Refrigeration & liquefaction • Thermometry
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 2 • 훋훠훖훐훓, 훐훖훓 το 1 deep cold [Arist. Meteor.] 2 shiver of fear [Aeschyl. Eumenid.]
• cryogenics, that branch of physics which deals with the production of very low temperatures and their effects on matter Oxford English Dictionary 2nd edition, Oxford University Press (1989)
• cryogenics, the science and technology of temperatures below 120 K New International Dictionary of Refrigeration 4th edition, IIF-IIR Paris (2015)
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 3 Characteristic temperatures of cryogens
Normal boiling Critical point Cryogen Triple point [K] point [K] [K]
Methane 90.7 111.6 190.5
Oxygen 54.4 90.2 154.6
Argon 83.8 87.3 150.9
Nitrogen 63.1 77.3 126.2
Neon 24.6 27.1 44.4
Hydrogen 13.8 20.4 33.2
Helium 2.2 (*) 4.2 5.2
(*): l Point
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 4 Useful range of liquid cryogens & critical temperature of superconductors
Nb3Sn Nb-Ti Mg B2 YBCO Bi-2223
Helium Below Patm Above Patm Hydrogen
Neon
Nitrogen
Argon
Oxygen
0 20 40 60 80 100 120 140 160 180 T [K] Ph. Lebrun JUAS 2019 Cryogenics for SC devices 5 Cooling of superconducting devices
LHe 1.9 K LIN ~70 K SCHe 4.5 K LHe 4.2 K
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 6 Contents
• Introduction • Cryogenic fluids • Heat transfer & thermal insulation • Thermal screening with cold vapour • Refrigeration & liquefaction • Thermometry
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 7 Properties of cryogens compared to water
Property He N2 H2O
Normal boiling point [K] 4.2 77 373
Critical temperature [K] 5.2 126 647
Critical pressure [bar] 2.3 34 221
Liq./Vap. density (*) 7.4 175 1600
Heat of vaporization (*) [J.g-1] 20.4 199 2260
Liquid viscosity (*) [mPl] 3.3 152 278
(*) at normal boiling point
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 8 Specific heat of helium and materials
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 9 Specific heat of helium and materials
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 10 Vaporization of normal boiling cryogens under 1 W applied heat load
Let ℎ be the enthalpy of the fluid
At constant pressure 푄ሶ = 퐿푣푚ሶ with 퐿푣 = ℎ푣푎푝 − ℎ푙𝑖푞
[l.min-1] Cryogen [mg.s-1] [l.h-1] (liquid) (gas NTP)
Helium 48 1.38 16.4
Nitrogen 5 0.02 0.24
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 11 Amount of cryogens required to cool down 1 kg iron
Assuming perfect heat exchange between iron and the fluid
푇𝑖푛𝑖푡𝑖푎푙 푓𝑖푛푎푙 푠푎푡 න 푀퐹푒퐶퐹푒푑푇 = 푚 퐿푣 + ℎ푣푎푝 − ℎ푣푎푝 ≈ 푚 퐿푣 + 퐶푝 푇푓𝑖푛푎푙 − 푇푠푎푡 푇푓𝑖푛푎푙
Latent heat and Using Latent heat only enthalpy of gas
LHe from 290 to 4.2 K 29.5 litre 0.75 litre
LHe from 77 to 4.2 K 1.46 litre 0.12 litre
LN2 from 290 to 77 K 0.45 litre 0.29 litre
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 12 Phase diagram of helium
10000 SOLID
1000 SUPER- l LINE CRITICAL
He II He I CRITICAL 100 POINT PRESSURIZED He II SATURATED He I (Subcooled liquid)
Pressure[kPa]
10 VAPOUR
SATURATED He II 1 0 1 2 3 4 5 6 Temperature [K] Ph. Lebrun JUAS 2019 Cryogenics for SC devices 13 Helium as a cooling fluid
Phase domain Advantages Drawbacks
Fixed temperature Two-phase flow Saturated He I High heat transfer Boiling crisis
Supercritical Monophase Non-isothermal Negative J-T effect Density wave instability
Low temperature Second-law cost He II High conductivity Subatmospheric Low viscosity
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 14 Contents
• Introduction • Cryogenic fluids • Heat transfer & thermal insulation • Thermal screening with cold vapour • Refrigeration & liquefaction • Thermometry
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 15 Typical heat transfer coefficients at cryogenic temperatures
• Same basic processes as at temperatures above ambiant, but large variations in - absolute values - dependence on temperature
• These variations can be exploited for - cooling equipment - thermal insulation of cryostats
• Particular importance of two- phase heat transfer
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 16 Non-linear heat transfer to liquid cryogens Pool boiling nitrogen
~ 1.5 105 W/m2
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 17 Non-linear heat transfer to liquid cryogens Pool boiling helium
104 W/m2
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 18 Heat conduction in solids
푑푇 SA • Fourier’s law 푄ሶ = 푘 푇 퐴 T 2 푐표푛푑 푑푥
• Thermal conductivity 푘 푇 [W/m.K]
Q c o n dx 퐴 푇2 Integral form 푄ሶ푐표푛푑 = 푘 푇 푑푇 • dT 퐿 푇1
푇 [Thermal conductivity integral 2 푘 푇 푑푇 [W/m • 푇1
• Thermal conductivity integrals for standard construction materials are tabulated T 1
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 19 Thermal conductivity integrals of selected materials [W/m]
From vanishingly low temperature 20 K 80 K 290 K up to
OFHC copper 11000 60600 152000
DHP copper 395 5890 46100
1100 aluminium 2740 23300 72100
2024 aluminium alloy 160 2420 22900
AISI 304 stainless steel 16.3 349 3060
G-10 glass-epoxy composite 2 18 153
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 20 Non-metallic composite support post with heat intercepts
5 K cooling line (SC He)
Aluminium intercept plates glued to G-10 column
Aluminium strips to thermal shield at 50-75 K
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 21 Thermal radiation
• Wien’s law – Maximum of black-body power spectrum
휆푚푎푥 푇 = 2898 [μm. K]
• Stefan-Boltzmann’s law 4 – Black body 푄ሶ푟푎푑 = 𝜎 퐴 푇 with 𝜎 = 5.67 10−12 W/m2K4
4 – «Gray» body 푄ሶ푟푎푑 = 휀 𝜎 퐴 푇 with 휀 surface emissivity Qrad1 T T > T – Between «gray» surfaces at temperatures 푇1 and 푇2 1 2 1 ሶ 4 4 푄푟푎푑 = 퐸 𝜎 퐴 (푇2 − 푇1 ) 1 Qrad2 2 with 퐸 function of 휀1, 휀2 and geometry of facing surfaces
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 22 Emissivity of technical materials at low temperatures
Radiation from 290 K Radiation from 77 K Surface at 77 K Surface at 4.2 K Stainless steel, as found 0.34 0.12
Stainless steel, mech. polished 0.12 0.07
Stainless steel, electropolished 0.10 0.07
Stainless steel + Al foil 0.05 0.01
Aluminium, as found 0.12 0.07
Aluminium, mech. polished 0.10 0.06
Aluminium, electropolished 0.08 0.04
Copper, as found 0.12 0.06
Copper, mech. Polished 0.06 0.02
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 23 Residual gas conduction
• Two different regimes, depending upon the relative values of heat transfer distance 푑 and mean free path of gas molecules 휆푚표푙푒푐푢푙푒 • Viscous regime
– At higher pressure 휆푚표푙푒푐푢푙푒 ≪ 푑 푑푇 – Classical conduction 푄ሶ = 퐴 푘 푇 푟푒푠𝑖푑푢푎푙 푑푥 T1 T2 – Thermal conductivity 푘(푇) independant of pressure • Molecular regime d – At lower pressure 휆푚표푙푒푐푢푙푒 ≫ 푑 – Kennard’s law 푄ሶ푟푒푠𝑖푑푢푎푙 = 퐴 훼 푇 Ω 푃 (푇2 − 푇1) – Heat transfer proportional to pressure, independant of spacing between surfaces – Ω depends on gas species – Accommodation coefficient 훼 푇 depends on gas species, 푇1, 푇2 and geometry of facing surfaces
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 24 Multi-layer insulation (MLI)
• Complex system involving three heat transfer processes
– 푄ሶ푀퐿퐼 = 푄ሶ푟푎푑 + 푄ሶ푐표푛푡푎푐푡 + 푄ሶ푟푒푠𝑖푑푢푎푙
– With 푛 reflective layers of equal emissivity, 푄ሶ푟푎푑~ 1Τ(푛 + 1)
– Due to parasitic contacts between layers, 푄ሶ푐표푛푡푎푐푡 increases with layer density
– 푄ሶ푟푒푠𝑖푑푢푎푙 due to residual gas trapped between layers, scales as 1Τ푛 in molecular regime – Non-linear behaviour requires layer-to-layer modeling • In practice – Typical data available from (abundant) literature – Measure performance on test samples
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 25 Typical heat fluxes at vanishingly low temperature between flat plates [W/m2]
Black-body radiation from 290 K 401
Black-body radiation from 80 K 2.3
Gas conduction (100 mPa He) from 290 K 19
Gas conduction (1 mPa He) from 290 K 0.19
Gas conduction (100 mPa He) from 80 K 6.8
Gas conduction (1 mPa He) from 80 K 0.07
MLI (30 layers) from 290 K, pressure below 1 mPa 1-1.5
MLI (10 layers) from 80 K, pressure below 1 mPa 0.05
MLI (10 layers) from 80 K, pressure 100 mPa 1-2
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 26 Cross-section of LHC dipole cryostat
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 27 LHC cryostat heat inleaks at 1.9 K
Measured
푄ሶ = 푚ሶ ∆ℎ(푃, 푇)
He property tables
LHC sector (2.8 km) Total S7-8 @ 1.9 K
600
500
400 On full LHC cold sector (2.8 km) 300
[W] - Measured 560 W, i.e. 0.2 W/m 200
- Calculated 590 W, i.e 0.21 W/m 100
0 Calc. Meas.
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 28 Contents
• Introduction • Cryogenic fluids • Heat transfer & thermal insulation • Thermal screening with cold vapour • Refrigeration & liquefaction • Thermometry
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 29 Vapour cooling of cryostat necks and supports with perfect heat transfer
Cross-section A • Assuming perfect heat transfer between solid and vapour, i.e. 푇푠표푙𝑖푑(푥) = 푇푣푎푝표푟(푥) = 푇(푥) . m vapour flow Cp(T) 푄ሶ푐표푛푑 = 푄ሶ푏푎푡ℎ + 푚ሶ 퐶푝 푇 (푇 − 푇푏푎푡ℎ)
푑푇 퐴 푘 푇 = 푄ሶ + 푚ሶ 퐶 푇 (푇 − 푇 ) T T 푑푥 푏푎푡ℎ 푝 푏푎푡ℎ x Qcon • 퐶푝(푇) specific heat of vapour • 푘 푇 thermal conductivity of support
• 푄ሶ푏푎푡ℎ can be calculated by numerical integration for Tbath – different cryogens
Qbath LHe – different values of aspect ratio 퐿Τ퐴 – different values of vapour flow
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 30 He vapour screening of stainless steel neck between 300 K and 4 K
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 31 Vapour cooling of cryostat necks and supports in self-sustained mode
• A particular case of gas cooling is the self-sustained mode, i.e. the vapour flow is generated only by the residual heat 푄ሶ푏푎푡ℎ reaching the bath
• Then 푄ሶ푏푎푡ℎ = 퐿푣푚ሶ with 퐿푣 latent heat of vaporization
푑푇 • Given the general equation 퐴 푘 푇 = 푄ሶ + 푚ሶ 퐶 푇 (푇 − 푇 ) 푑푥 푏푎푡ℎ 푝 푏푎푡ℎ • The variables can be separated and integration yields
ሶ 퐴 푇 푘(푇) 푄푏푎푡ℎ = 퐶 (푇) 푑푇 퐿 푇푏푎푡ℎ 푝 1+ (푇−푇푏푎푡ℎ) 퐿푣 퐶푝(푇) • The denominator of the integrand 1 + (푇 − 푇푏푎푡ℎ) acts as an attenuation 퐿푣 factor of the thermal conductivity 푘(푇)
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 32 Reduction of heat conduction by self-sustained helium vapour cooling
Effective thermal Purely conductive Self-sustained conductivity integral from regime vapour-cooling 4 to 300 K [W.cm-1] [W.cm-1]
ETP copper 1620 128
OFHC copper 1520 110
Aluminium 1100 728 39.9
Nickel 99% pure 213 8.65
Constantan 51.6 1.94
AISI 300 stainless steel 30.6 0.92
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 33 Vapour cooling of cryostat necks and supports with imperfect heat transfer
Cross-section A • Introducing efficiency of heat transfer 푓 . between solid and vapour (0 ≤ 푓 ≤ 1) m vapour flow Cp(T) 푑푄 = 푓 푚ሶ 퐶푝(푇) 푑푇 Q+dQ x+dx T+dT • The steady-state heat balance equation dQ becomes x T
Q 푑 푑푇 푑푇 퐴 푘 푇 = 푓 푚ሶ 퐶 (푇) 푑푥 푑푥 푝 푑푥
Tbath • This non-linear equation needs to be solved by numerical integration Qbath LHe
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 34 Vapor-cooled current leads
Cross-section A • The (imperfect) heat transfer between solid Current I and vapour can be written 푑푄 = 푓 푚ሶ 퐶푝(푇) 푑푇 k(T) . m vapour flow • Introducing electrical resisitivity , the (T) 𝜌 푇 Cp(T) steady-state heat balance equation reads
Q+dQ 푑 푑푇 푑푇 𝜌 푇 퐼2 x+dx T+dT 퐴 푘 푇 − 푓 푚ሶ 퐶 푇 + = 0 dQ 푑푥 푑푥 푝 푑푥 퐴 x T • Assuming the material follows the Q Source: Wiedemann-Franz-Lorenz (WFL) law
푘 푇 𝜌 푇 = ℒ0 푇 −8 −2 with ℒ0 = 2.45 10 W. Ω. K T bath The aspect ratio 퐿Τ퐴 can be chosen for minimum Qbath LHe heat inleak 푄ሶ푏푎푡ℎ, and the minimum heat inleak does not depend on the material Ph. Lebrun JUAS 2019 Cryogenics for SC devices 35 Heat load of optimized current lead Uncooled 47 W/kA Material obeying the WFL law
Minimum residual heat load 1.04 W/kA
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 36 Beating the WFL law: HTS current leads
• The WFL law essentially states that good electrical conductors are also good thermal conductors • Efficient current leads need good electrical conductors with low thermal conductivity • Superconductors are bad thermal conductors Copper with zero resisitivity
Build current lead with superconductor up to temperature as high as possible, i.e. use HTS
HTS
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 37 HTS vs. normal conducting current leads
Resistive HTS (4 to 50 K) Type Resistive (above)
Heat into LHe [W/kA] 1.1 0.1
Total exergy [W/kA] 430 150 consumption
Electrical power [W/kA] 1430 500 from grid
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 38 Contents
• Introduction • Cryogenic fluids • Heat transfer & thermal insulation • Thermal screening with cold vapour • Refrigeration & liquefaction • Thermometry
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 39 Basic thermodynamics of refrigeration
T0= 300 K • First principle (Joule) 푄0 = 푄𝑖 + 푊
Q0 푄0 푄𝑖 W : mechanical • Second principle (Clausius) ≥ R 푇 푇 work 0 𝑖
Qi (= for reversible process)
Ti 푄𝑖 • Hence 푊 ≥ 푇0 − 푄𝑖 푇𝑖
• This equation can be written in three different ways
푄𝑖 푊 ≥ 푇0 ∆푆𝑖 − 푄𝑖 introducing entropy 푆 defined by ∆푆𝑖 = 푇𝑖
푇0 푇0 푊 ≥ 푄𝑖 − 1 where − 1 is called the Carnot factor 푇𝑖 푇𝑖
푇0 푊 ≥ ∆퐸𝑖 introducing exergy 퐸 defined by ∆퐸𝑖 = 푄𝑖 − 1 푇𝑖 Ph. Lebrun JUAS 2019 Cryogenics for SC devices 40 Minimum refrigeration work
• Consider the extraction of 1 W at liquid helium temperature 4.5 K, rejected at room temperature 300 K
• The minimum refrigeration work is
푇0 300 푊푚𝑖푛 = 푄𝑖 − 1 = 1 − 1 ≅ 65.7 W/W 푇𝑖 4.5
• In practice, the most efficient helium refrigerators have an efficiency 휂 of about 30% with respect to the Carnot limit
푊 65.7 푊 = 푚𝑖푛 = ≅ 220 W/W 푟푒푎푙 휂 0.3
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 41 Refrigeration cycles
T B • Introducing the temperature-entropy diagram – Consider the thermodynamic transform from A to B, involving heat transfer ∆푄 A 퐵 If it is reversible ∆푄 = 푇 푑푆 – Q 퐴 – ∆푄 is proportional to the area under the curve in S, entropy the temperature-entropy diagram • To make a refrigeration cycle, one needs a substance, the entropy of which depends on T D some other physical variable than temperature, T2 C e.g.
Q2 – Pressure of gas or vapor (compression/expansion) – Magnetization of solid (magnetic refrigeration) T1 A B • Refrigeration cycle ABCD Q 1 – ∆푄1 heat absorbed at 푇1 S – ∆푄2 heat rejected at 푇2
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 42 T-S diagram for helium
25 24 140 23 22 130 21 20 120 19 18 110 17 100 16 10 5 2 1 0.5 0.2 P= 0.1 MPa Red : liquid-vapour dome 15 90 14 Blue : isobars 13 80 12
Temperature [K] Black : isochores 11 70 10 100 50 20 10 5 = 2 kg/m³ Green: isenthalps 9 60 8
7 50 6
5 40 4
3 H= 30 J/g 2 0 5000 10000 15000 20000 25000 Entropy [J/kg.K]
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 43 A Carnot cycle is not feasible for helium liquefaction 82 kbar T 613 kbar 300 K • It would need a HP of 613 kbar! • There exists no true isothermal compressor • There exists no true isentropic compressor or expander
1.3 bar
4.5 K S
3.89 J/g.K 8.07 J/g.K
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 44 A real cycle needs internal heat exchange and para-isothermal compression
Practical compressors are adiabatic, need T aftercooling and if multistage, intercooling 300 K
Heat exchanger between HP and LP streams
20 bar
1.3 bar
4.5 K S 3.89 J/g.K 8.07 J/g.K
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 45 Refrigerator Liquefier
Compressor Compressor
HP LP HP LP
T0= 300 K T0= 300 K
Cold Box Cold Box R
T = 4.5 K T1= 4.5 K 1 LOAD LOAD LHe
Q1 Q1 T T 300 K isobar (1.3 bar)
-1 18.8 J.g-1 18.8 J.g 1543 J.g-1
R 4.5 K 4.5 K Q Q1 1 S S 4.2 23.1 -1 -1 4.2 J.g .K J.g-1.K-1 J.g-1.K-1
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 46 Thermodynamic equivalence between refrigeration and liquefaction
• What is the equivalent to 1 g helium liquefaction in terms of isothermal refrigeration at liquid helium temperature 푇1 = 4.5 K ? 푊푙𝑖푞 = 푚푙𝑖푞(푇0 ∆푆 − 푄1 − 푅)
with 푇0 = 300 K ∆푆 = 27.3 J/g. K
푄1 = 18.8 J/g 푅 = 1543 J/g
hence 푊푙𝑖푞 = 6628 J • Write that the same work is used to produce isothermal refrigeration at 4.5 K
푇0 푊푟푒푓 = 푄1 − 1 = 6628 J 푇1 hence 푄1 ≅ 100 J • For refrigerators and liquefiers of the same efficiency 1 g/s liquefaction 100 W refrigeration at 4.5 K
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 47 Measured refrigeration/liquefaction equivalence 12 kW @ 4.5 K helium refrigerators for LEP 2
Thermodynamic equivalence
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 48 Elementary cooling processes on T-S diagram T P1
A P2 (< P1)
B3 B1 H isenthalpic (Joule-Thomson valve) B'2 isobar B (heat exchanger) 2 adiabatic (expansion engine)
isentropic S
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 49 Brazed aluminium plate heat exchanger
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 50 Elementary cooling processes on T-S diagram T P1
A P2 (< P1)
B3 B1 H isenthalpic (Joule-Thomson valve) B'2 isobar B (heat exchanger) 2 adiabatic (expansion engine)
isentropic S
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 51 Cryogenic turbo-expander
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 52 Elementary cooling processes on T-S diagram T P1
A P2 (< P1)
B3 B1 H isenthalpic (Joule-Thomson valve) B'2 isobar B (heat exchanger) 2 adiabatic (expansion engine)
isentropic S
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 53 Joule-Thomson inversion temperatures
Isenthalps in T-S diagram can Maximum inversion have positive or negative slope, Cryogen i.e. isenthalpic expansion can temperature [K] produce warming or cooling inversion temperature Helium 43
Hydrogen 202
Neon 260
Air 603
Nitrogen 623
Oxygen 761
While air can be cooled down and liquefied by JT expansion from room temperature, helium and hydrogen need precooling down to below inversion temperature by heat exchange or work-extracting expansion (e.g. in turbines)
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 54 Two-stage Claude cycle
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 55 Claude-cycle helium refrigerators/liquefiers Air Liquide & Linde
HELIAL SL HELIAL ML HELIAL LL Max. Liquefaction capacity without LN2 25 L/h 70 L/h 145 L/h Max. Liquefaction capacity with LN2 50 L/h 150 L/h 330 L/h Compressor electrical motor 55 kW 132 kW 250 kW Specific consumption for liquefaction w/o LN2 645 W/W 552 W/W 505 W/W % Carnot 10% 12% 13%
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 56 E1
T1 Process cycle & T-S diagram of LHC E3 18 kW @ 4.5 K cryoplant
E4 T2 20 K - 280 K loads (LHC current leads)
MPa MPa MPa 1.9 0.4 0.1 LN2 Precooler 201 K T1 from LHC loads 50 K - 75 K loads E6 T3 (LHC shields) T2 E7 75 K T3
E8 T4 49 K LHC shields
Adsorber 32 K E9a T4
20 K E9b 13 K T5 T7 from LHC loads 10 K E10 T5 T7 4.5 K - 20 K loads 9 K T8 (magnets + leads + cavities) T6 E11 4.4 K MPa 0.3 E12 To LHC loads T6
E13 T8
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 57 LHC 18 kW @ 4.5 K helium cryoplants
33 kW @ 50 K to 75 K 23 kW @ 4.6 K to 20 K 41 g/s liquefaction 4 MW compressor power C.O.P. 220-230 W/W @ 4.5 K
Air Liquide
Linde
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 58 ITER 25 kW @ 4.5 K helium refrigerator
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 59 Oil-injected screw compressor
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 60 Compressor station of LHC 18 kW@ 4.5 K helium refrigerator
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 61 Contents
• Introduction • Cryogenic fluids • Heat transfer & thermal insulation • Thermal screening with cold vapour • Refrigeration & liquefaction • Thermometry
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 62 Definition of ITS90 in cryogenic range
Triple points H2 Ne O2 Ar Hg H2O
Primary thermometers
Pt resistance thermometer
He 4 gas thermometer
He 3 gas thermometer
He vapour pressure
0,1 1 10 100 1000 Temperature [K] Ph. Lebrun JUAS 2019 Cryogenics for SC devices 63 Primary fixed points of ITS90 in cryogenic range
Fixed point Temperature [K]
H2 triple point 13.8033
Ne triple point 24.5561
O2 triple point 54.3584
Ar triple point 83.8058
Hg triple point 234.3156
H2O triple point 273.16 (*) (*) exact by definition
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 64 Practical temperature range covered by cryogenic thermometers
Chromel-constantan thermocouple
Au-Fe thermocouple
Pt resistance
Rh-Fe resistance
CLTS
Allen-Bradley carbon resistance
Cernox
Ge resistance
1 10 100 1000 Temperature [K]
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 65 From temperature sensor to practical thermometer
Ge
RhFe wire
RhFe thin film
Cernox
Carbon A-B
Carbon TVO
CBT
1cm
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 66 Some references Books
• K. Mendelssohn, The quest for absolute zero, McGraw Hill (1966) • R.B. Scott, Cryogenic engineering, Van Nostrand, Princeton (1959) • G.G. Haselden, Cryogenic fundamentals, Academic Press, London (1971) • R.A. Barron, Cryogenic systems, Oxford University Press, New York (1985) • B.A. Hands, Cryogenic engineering, Academic Press, London (1986) • S.W. van Sciver, Helium cryogenics, Plenum Press, New York (1986, 2nd edition 2012) • K.D. Timmerhaus & T.M. Flynn, Cryogenic process engineering, Plenum Press, New York (1989) • J.G. Weisend (ed.), The handbook of cryogenic engineering, Taylor & Francis, Philadelphia (1998) • J.G. Weisend (ed.), Cryostat design: case studies, principles and engineering, Springer, Switzerland (2016)
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 67 Some references Reports & Proceedings
• Ph. Lebrun, An introduction to cryogenics, CERN-AT-2007-01 (2007) http://cdsweb.cern.ch/record/1012032?ln=en • Proceedings of CAS School on Superconductivity and Cryogenics for Particle Accelerators and Detectors, Erice (2002) – U. Wagner, Refrigeration – G. Vandoni, Heat transfer – Ph. Lebrun, Design of a cryostat for superconducting accelerator magnet – Ph. Lebrun & L. Tavian, The technology of superfluid helium http://cdsweb.cern.ch/record/503603?ln=en • Proceedings of CAS School on Superconductivity for Accelerators, Erice (2013) – P. Duthil, Basic thermodynamics – P. Duthil, Material properties at low temperatures – A. Alekseev, Basics of low-temperature refrigeration – B. Baudouy, Heat transfer and cooling techniques at low temperature – V. Parma, Cryostat design – Ph. Lebrun & L. Tavian, Cooling with superfluid helium https://cds.cern.ch/record/1507630?ln=en • Proceedings of ICEC, CEC/ICMC and IIR Cryogenics conferences
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 68 Additional slides Cryocoolers Carnot, Stirling and Ericsson cycles
All «sloping» cycles need internal heat exchange
For small machines, this is done by regenerative, rather than recuperative heat exchangers
alternating rather than continuous operation
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 70 Operation of a Gifford- McMahon cryocooler (Ericsson cycle)
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 71 Two-stage Gifford-McMahon cryocooler
CRYOMECH PT407 & CP970 compressor ~ 0.7 W @ 4.2 K & 25 W @ 55 K
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 72 Stirling and pulse-tube cryocoolers
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 73 Mini pulse-tube cryocoolers
ESA MPTC development model – 1W @ 77K
CEA/SBT coaxial PTC– 6W @ 80K
Ph. Lebrun JUAS 2019 Cryogenics for SC devices 74