Introduction to Cryogenics

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1 Introduction to Cryogenics Ph. Lebrun Accelerator Technology department, CERN CAS & ALBA School on Vacuum in Accelerators Platja d Aro, Spain May 2006

2 Contents Introduction Cryogenic fluids Heat transfer & thermal insulation Cryogenic distribution & cooling schemes Refrigeration & liquefaction Cryogen storage & transport Thermometry

3 cryogenics, that branch of physics which deals with the production of very low temperatures and their effects on matter Oxford English Dictionary 2 nd edition, Oxford University Press (1989) cryogenics, the science and technology of temperatures below 120 K New International Dictionary of Refrigeration 3 rd edition, IIF-IIR Paris (1975)

4 Characteristic temperatures of cryogens Cryogen Triple point [K] Normal boiling point [K] Critical point [K] Methane Oxygen Argon Nitrogen Neon Hydrogen Helium 2.2 (*) (*): λ Point

5 Cryogenic transport of natural gas: : LNG m 3 LNG carrier with double hull Invar tanks hold LNG at ~110 K

6 Densification, liquefaction & separation of gases Ariane 5 25 t LH 2, 130 t LO 2 Space Shuttle 100 t LH 2, 600 t LO 2

7 What are low temperatures? Entropy and temperature the entropy of a thermodynamical system in a macrostate corresponding to a multiplicity Ω of microstates is S = k B ln Ω adding reversibly heat dq to the system results in a change of its entropy ds with a proportionality factor T T = dq/ds high temperature: heating produces small entropy change low temperature: heating produces large entropy change 1 K is equivalent to 10-4 ev or J thermal energy a temperature is «low» when k B T is small compared with the characteristic energy of the process considered cryogenic temperatures reveal phenomena with low characteristic energy and enable their application

8 Characteristic temperatures of low-energy phenomena Phenomenon Debye temperature of metals High-temperature superconductors Low-temperature superconductors Intrinsic transport properties of metals Cryopumping Cosmic microwave background Superfluid helium 4 Bolometers for cosmic radiation Low-density atomic Bose-Einstein condensates Temperature few 100 K ~ 100 K ~ 10 K < 10 K few K 2.7 K 2.2 K < 1 K ~ μk

9 Cooling of superconducting devices

10 Characteristic temperatures of low-energy phenomena Phenomenon Debye temperature of metals High-temperature superconductors Low-temperature superconductors Intrinsic transport properties of metals Cryopumping Cosmic microwave background Superfluid helium 4 Bolometers for cosmic radiation Low-density atomic Bose-Einstein condensates Temperature few 100 K ~ 100 K ~ 10 K < 10 K few K 2.7 K 2.2 K < 1 K ~ μk

11 Vapour pressure at cryogenic temperatures Psat [kpa] 1.E+04 1.E+03 1.E+02 1.E+01 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 1.E-11 1.E T [K] He H2 Ne N2 Ar O2 CH4 CO2 H2O

12 Characteristic temperatures of low-energy phenomena Phenomenon Debye temperature of metals High-temperature superconductors Low-temperature superconductors Intrinsic transport properties of metals Cryopumping Cosmic microwave background Superfluid helium 4 Bolometers for cosmic radiation Low-density atomic Bose-Einstein condensates Temperature few 100 K ~ 100 K ~ 10 K < 10 K few K 2.7 K 2.2 K < 1 K ~ μk

13 Contents Introduction Cryogenic fluids Heat transfer & thermal insulation Cryogenic distribution & cooling schemes Refrigeration & liquefaction Cryogen storage & transport Thermometry

14 Useful range of cryogens Helium Hydrogen Below Patm Above Patm Neon Nitrogen Argon Oxygen T [K]

15 Properties of cryogens compared to water Property He N 2 H 2 O Normal boiling point Critical temperature Critical pressure Liq./Vap. density (*) Heat of vaporization (*) [K] [K] [bar] [J.g -1 ] Liquid viscosity (*) [μpl] (*) at normal boiling point

16 Vaporization of normal boiling cryogens under 1 W applied heat load Cryogen [mg.s -1 ] [l.h -1 ] (liquid) [l.min -1 ] (gas NTP) Helium Nitrogen

17 Amount of cryogens required to cool down 1 kg iron Using Latent heat only Latent heat and enthalpy of gas LHe from 290 to 4.2 K 29.5 litre 0.75 liter 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

18 Phase diagram of helium SOLID 1000 λ LINE SUPER- CRITICAL Pressure [kpa] 100 He II PRESSURIZED He II (Subcooled liquid) He I CRITICAL POINT SATURATED He I 10 VAPOUR SATURATED He II Temperature [K]

19 Helium as a cooling fluid Phase domain Advantages Drawbacks Saturated He I Fixed temperature High heat transfer Two-phase flow Boiling crisis Supercritical Monophase Negative J-T effect Non-isothermal Density wave instability He II Low temperature High conductivity Low viscosity Second-law cost Subatmospheric

20 Contents Introduction Cryogenic fluids Heat transfer & thermal insulation Cryogenic distribution & cooling schemes Refrigeration & liquefaction Cryogen storage & transport Thermometry

21 Typical heat transfer coefficients at cryogenic temperatures

22 Heat conduction in solids T 2 S Fourier s law: Q con = k ( T) S dt dx k(t): thermal conductivity [W/m.K] Q con dx dt Integral form: k(t) dt Q con = S L T2 k(t) dt T1 : thermal conductivity integral [W/m] T 1 Thermal conductivity integrals for standard construction materials are tabulated

23 Thermal conductivity integrals of selected materials [W/m] From vanishingly low temperature up to 20 K 80 K 290 K OFHC copper DHP copper aluminium aluminium alloy AISI 304 stainless steel G-10 glass-epoxy composite

24 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 K

25 Thermal radiation Wien s law Maximum of black body power spectrum λ max.t = 2898 [μm.k] Stefan-Boltzmann s law Q rad1 T 1 T 2 > T 1 ε 1 ε 2 Q rad2 Black body Q rad = σ A T 4 σ = 5.67 x 10-8 W/m 2.K 4 (Stefan Boltzmann s constant) Gray body Q rad = εσa T 4 ε emissivity of surface Gray surfaces at T 1 and T 2 Q rad = E σ A (T 14 T 24 ) E function of ε 1, ε 2, geometry

26 Emissivity of technical materials at low temperatures Radiation from 290 K Surface at 77 K Radiation from 77 K Surface at 4.2 K Stainless steel, as found Stainless steel, mech. polished Stainless steel, electropolished Stainless steel + Al foil Aluminium, as found Aluminium, mech. polished Aluminium, electropolished Copper, as found Copper, mech. Polished

27 Residual gas conduction T 1 T 2 d λ molecule : mean free path of gas molecules Viscous regime At high gas pressure λ molecule << d Classical conduction Q res = k(t) A dt/dx Thermal conductivity k(t) independant of pressure Molecular regime At low gas pressure λ molecule >> d Kennard s law Q res = A α(t) Ω P (T 2 T 1 ) Conduction heat transfer proportional to pressure, independant of spacing between surfaces Ω depends on gas species Accommodation coefficient α(t) depends on gas species, T 1,T 2, and geometry of facing surfaces

Multi-layer layer insulation (MLI) Complex system involving three heat transfer processes Q MLI = Q rad + Q sol + Q res With n reflective layers of equal emissivity, Q rad ~ 1/(n+1) Due to parasitic

28 Multi-layer layer insulation (MLI) Complex system involving three heat transfer processes Q MLI = Q rad + Q sol + Q res With n reflective layers of equal emissivity, Q rad ~ 1/(n+1) Due to parasitic contacts between layers, Q sol increases with layer density Q res due to residual gas trapped between layers, scales as 1/n in molecular regime Non-linear behaviour requires layer-to-layer modeling In practice Typical data available from (abundant) literature Measure performance on test samples

29 Typical heat fluxes at vanishingly low temperature between flat plates [W/m 2 ] 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 MLI (10 layers) from 80 K, pressure below 1 mpa 0.05 MLI (10 layers) from 80 K, pressure 100 mpa 1-2

30 Cross-section section of LHC dipole cryostat

31 Vapour cooling of necks and supports with perfect heat exchange Cross-section A. m vapour flow Cp(T) Assuming perfect heat exchange between solid and gas, i.e. T sol (x)=t gas (x)=t(x): Q con = Q + m& Cp(T) bath ( T T ) bath x T Q con T k dt dx ( T) A = Q + m& Cp(T) ( T ) bath T bath Cp(T): Specific heat of vapour k(t) : Thermal conductivity of the support Q bath T bath LHe Q bath can then be calculated by numerical integration for : - different cryogens, - different values of aspect ratio L/A - different values of vapour flow

32 Heat reaching the cold end of a stainless steel neck Q bath [W] Vapour cooling flow: A: 1 g/s B: 0.1 g/s C: 10-2 g/s D: 10-3 g/s F: no flow

33 Vapour cooling of necks and supports with perfect heat exchange in self-sustained sustained mode A particular case of gas cooling is the self-sustained mode, i.e. He vapour flow is generated only by the residual heat Q bath reaching the bath. Then: Q bath = L v m& (Lv: latent heat of vaporization) Given the general equation k dt dx ( T) A = Q + m& Cp(T) ( T ) bath T bath And after integration, we finally have: Q bath A L T ambient = T bath 1+ K(T) ( T T ) bath Cp(T) Lv dt Attenuation factor w.r. to pure conduction

34 Reduction of heat conduction by self-sustained sustained helium vapour cooling Effective thermal conductivity integral from 4 to 300 K Purely conductive regime [W.cm -1 ] Self-sustained vapour-cooling [W.cm -1 ] ETP copper OFHC copper Aluminium Nickel 99% pure Constantan AISI 300 stainless steel

35 Vapour cooling of necks and supports with imperfect heat exchange Cross-section A. m vapour flow Cp(T) dq = f m& Cp(T) dt With f, the efficiency of the heat transfer x+dx x Q+dQ dq T+dT T In steady state, the heat balance equation becomes: Q d dx dt k(t) A dx = f m& Cp(T) dt dx Q bath T bath LHe Numerical integration for solving this equation

36 Vapor-cooled current leads x+dx x Source: 2 ρ(t) I dx A Cross-section A Current I Q+dQ Q bath k(t) ρ(t) Q dq. m vapour flow Cp(T) T+dT T T bath LHe ρ(t): electrical resistivity dq = f m& Cp(T) dt In steady-state, heat balance equation: d dx dt k(t) A f m& Cp(T) dx Solid Vapour conduction cooling dt dx ρ(t) I + A 2 Joule heating Assuming the material of the lead follows the Wiedemann-Franz-Lorenz (WFL) law: k(t) ρ(t) = L T L 0 : Lorenz number ( W.Ω.K -2 ) 0 Then numerical integration = 0

37 Uncooled 47 W/kA Heat load of optimized current lead Material obeying the WFL law Minimum residual heat load 1.04 W/kA

Beating the WFL law: : HTS current leads The WFL law essentially states that good electrical conductors are also good thermal conductors Current leads need good electrical conductors

38 Beating the WFL law: : HTS current leads The WFL law essentially states that good electrical conductors are also good thermal conductors Current leads need good electrical conductors with low thermal conductivity Superconductors are bad thermal conductors with zero resisitivity Build current lead with superconductor up to temperature as high as possible, i.e. HTS

39 HTS vs. normal conducting current leads Type Resistive HTS (4 to 50 K) Resistive (above) Heat into LHe [W/kA] Total exergy consumption [W/kA] Electrical power from grid [W/kA]

40 Contents Introduction Cryogenic fluids Heat transfer & thermal insulation Cryogenic distribution & cooling schemes Refrigeration & liquefaction Cryogen storage & transport Thermometry

41 Transport of refrigeration in large distributed cryogenic systems 0.5 Temperature difference [K] Tore Supra Tevatron HERA LEP2 Pressurised He II Saturated LHe II He I UNK TESLA SSC (HEB) SSC (main Ring) Distance [km] LHC

42 Cryogenic distribution scheme: design issues Monophase vs. two-phase temperature control hydrostatic head & flow instabilities Pumps vs. no pumps efficiency & cost reliability & safety LN 2 cooldown and/or normal operation capital & operating costs of additional fluid safety in underground areas (ODH) Lumped vs. distributed cryoplants Separate cryoline vs. integrated piping Number of active components (valves, actuators) Redundancy of configuration

43 Tevatron distribution scheme Central helium liquefier, separate ring cryoline and satellite refrigerators

44 HERA distribution scheme Central cryoplant and separate ring cryoline

45 RHIC distribution scheme Central cryoplant and piping integrated in magnet cryostat

46 LHC distribution scheme Pt 5 Typical LHC Cross-section Vacuum Vessel Pt 4 8 x K Pt 6 Beam Screen Superconducting Coil Heat Exchang 1.8 K Supply t 3 1'800 SC magnets 24 km and K 36' K Pt 7 Thermal Shield Radiative Insulation Header E Line C' Support Post 96 tons of He Header D Header B Main Dipole Cryostat Pt 2 Pt 8 Header C Cryogenic plant Pt 1 Cryogenic Distribution Line Header F Cryoplants at five points, separate ring cryoline

47 Contents Introduction Cryogenic fluids Heat transfer & thermal insulation Cryogenic distribution & cooling schemes Refrigeration & liquefaction Cryogen storage & transport Thermometry

48 Thermodynamics of cryogenic refrigeration T 0 = 300 K Q 0 First principle [Joule] Q0 = Qi + W R W : mechanical work Second principle [Clausius] Q0 T 0 Q T i i Q i T i Hence, W T Q i 0 Qi Ti (= for reversible process) which can be written in three different ways: Qi 1 W T0 ΔSi Q introducing entropy S as ΔS i = i Ti 2 T0 W Qi 1 Ti Carnot factor 3 T0 W ΔE i introducing exergy E as ΔEi = Qi 1 Ti

49 Minimum refrigeration work Consider the extraction of 1 W at 4.5 K, rejected at 300 K The minimum refrigeration work (equation 2) is: T0 300 Wmin = Qi 1 = 1 1 = Ti W In practice, the most efficient helium refrigerators have an efficiency of about 30% w.r. to the Carnot limit. W W η min real = = = 220 W

50 C.O.P. of large cryogenic helium refrigerators C.O.P. 4.5K] Carnot 0 TORE SUPRA RHIC TRISTAN CEBAF HERA LEP LHC

51 T A ΔQ Refrigeration cycles and duties Introduction to the T-S diagram B S, entropy Thermodynamic transformation from A to B, if reversible: ΔQ = B A T ds To make a refrigeration cycle, need a substance, the entropy of which depends on some other variable than temperature T 2 T D C Pressure of gas: Compression/expansion cycle Magnetization of solid: magnetic refr. cycle T 1 A ΔQ 2 ΔQ 1 : heat absorbed at T 1 B ΔQ 2 : heat rejected at T 2 ΔQ 1 S Refrigeration cycle A B C D

52 T-S S diagram for helium Temperature [K] P= 0.1 MPa ρ= 2 kg/m³ H= 30 J/g Entropy [J/kg.K]

53 Elementary cooling processes on T-S T S diagram T P1 A P2 (< P1) B 1 B 3 H isobar (heat exchanger) B 2 B' 2 isenthalpic (Joule-Thomson valve) adiabatic (expansion engine) isentropic S

54 Brazed aluminium plate heat exchanger

55 Cryogenic turbo-expander

56 Maximum Joule-Thomson inversion temperatures Cryogen Maximum inversion temperature [K] 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)

57 Two-stage Claude cycle

58 E1 E3 T1 Process cycle & T-S T diagram of LHC K cryoplant 20 K K loads E4 T2 (LHC current leads) 50 K - 75 K loads (LHC shields) E6 E7 T3 LN2 Precooler 75 K T3 201 K T1 T2 1.9 MPa 0.4 MPa 0.1 MPa from LHC loads E8 T4 49 K LHC shields 32 K Adsorber E9a 20 K T4 E9b 13 K 10 K T5 T7 from LHC loads 4.5 K - 20 K loads E10 T5 T7 T6 T8 9 K (magnets + leads + cavities) E MPa To LHC loads 4.4 K T6 E12 E13 T8

59 LHC K helium cryoplants K to 75 K K to 20 K 41 g/s liquefaction 4 MW compressor power C.O.P K Air Liquide Linde

60 Oil-injected injected screw compressor

61 Compressor station of LHC 4.5 K heliumh refrigerator

62 Carnot, Stirling and Ericsson cycles

63 Operation of a Gifford-McMahon cryocooler (Ericsson cycle)

64 Two-stage Gifford McMahon cryocooler CRYOMECH PT407 & CP970 compressor ~ K & K

65 Contents Introduction Cryogenic fluids Heat transfer & thermal insulation Cryogenic distribution & cooling schemes Refrigeration & liquefaction Cryogen storage & transport Thermometry

66 Specific cost of bulk He storage Type Pressure [MPa] Density [kg/m 3 ] Dead volume [%] Cost [CHF/kg He] Gas Bag (1) MP Vessel HP Vessel (2) Liquid (3) (1): Purity non preserved (2): Not including HP compressors (3): Not including reliquefier

67 Bulk helium storage solutions gallon liquid container 2 MPa gas tanks 20 MPa gas cylinders

68 Contents Introduction Cryogenic fluids Heat transfer & thermal insulation Cryogenic distribution & cooling schemes Refrigeration & liquefaction Cryogen storage & transport Thermometry

69 Definition of ITS90 in cryogenic range Triple points H 2 Ne O 2 Ar Hg H 2 O Pt resistance thermometer He 4 gas thermometer He 3 gas thermometer He vapour pressure 0, Temperature [K]

70 Primary fixed points of ITS90 in cryogenic range Fixed point Temperature [K] H 2 triple point Ne triple point O 2 triple point Ar triple point Hg triple point H 2 O triple point (*) (*) exact by definition

71 From temperature sensor to practical thermometer Ge RhFe wire RhFe thin film Cernox Carbon A-B Carbon TVO CBT 1cm

72 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 Temperature [K]

73 Some references 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) K.D. Timmerhaus & T.M. Flynn, Cryogenic process engineering, Plenum Press, New York (1989) 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 Proceedings of ICEC and CEC/ICMC conferences

74 Refrigerator Liquefier Compressor Compressor HP T 0 = 300 K LP HP T 0 = 300 K LP Cold Box Cold Box R T 1 = 4.5 K T 1 = 4.5 K T Q 1 LOAD T 300 K LHe isobar (1.3 bar) LOAD Q J.g J.g J.g K Q J.g -1.K -1 S 4.5 K Q 1 R J.g -1.K -1 J.g -1.K -1 S

75 Thermodynamic equivalence between refrigeration and liquefaction What is the isothermal 4.5 K (T 1 ) refrigeration equivalent to 1 g.s -1 liquefaction of helium? & = m& T ΔS Q R ( ) Wmin.lique lique m& lique = 1 g.s, T0 = 300 K, ΔS = 27.3 W& min.lique = 6628 W J.g -1.K -1, Q = 18.8 J.g, R = 1543 J.g Write that the same amount of work is used to produce isothermal refrigeration at 4.5 K: T0 W& min.refrig = Q& 1 1 T1 Q & 1 = 100 W W & = W & 6628 W min.refrig min.lique = For refrigerators/liquefiers with the same efficiency: 1 g.s 1 LHe K

76 Stirling and pulse-tube cryocoolers

77 Mini pulse-tube cryocoolers ESA MPTC development model 77K CEA/SBT coaxial PTC 80K

Cryogenics for particle accelerators

Cryogenics for particle accelerators Ph. Lebrun CAS Course in General Accelerator Physics Divonne-les-Bains, 23-27 February 2009 Contents Low temperatures and liquefied gases Cryogenics in accelerators