Cryogenic Fluids. European Advanced Cryogenics School. Henri Godfrin. European Advanced Cryogenics School Chichilianne
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1 Cryogenic Fluids European Advanced Cryogenics School Henri Godfrin European Advanced Cryogenics School Chichilianne
2 Fluids : basic concepts 3 states of matter: solid / liquid / gas Influence of temperature and pressure Example: water At (constant) atmospheric pressure: - if T : Solidification -if T : Evaporation At constant temperature (20 C) : - if P : Evaporation -if P : Solidification Liquid state : saturated vapour pressure P Liquid boiling at temperature T : in equilibrium with the gas at pressure P. It is a dynamical equilibrium (exchange of atoms) A well defined pressure corresponds to each temperature : saturated vapour pressure T European Advanced Cryogenics School 2
3 Phase diagram of Water Triple point: solid-liquid-gas coexistence (thermometry!) Solids have a saturated vapour pressure too! Critical point vapour and fluid phases are indistinguishable European Advanced Cryogenics School 3
4 Cryogenic fluids (nitrogen, hydrogen, helium, etc ) Nitrogen Pc=33 bars P (mbar) Solid Liquid Critical point Vapour Triple point Tc = 126 K T (K) The dependence P = f (T) is a characteristic of the fluid. It is tabulated and can be used for thermometer calibration. European Advanced Cryogenics School 4
5 One exception : helium No solidification at low Pressure! solid increase P at low temperatures (T<1K; P>25bar) European Advanced Cryogenics School 5
6 Boiling cryogenic fluids A cryogenic fluid at atmospheric pressure is always boiling And therefore, on the P(T) curve P (mbar) Critical point Liquid 1000 Vapour T ( K) European Advanced Cryogenics School 6
7 1 st transformation Vapour (P) Heating in a closed vessel P et T will increase following the curve till the critical point. For each value of P, one value of T Liquid (T) Heater Not recommended! Except in special cases, one never closes the output of a cryogenic reservoir (vent) European Advanced Cryogenics School 7
8 2 d transformation Heating an open vessel At atmospheric pressure, for instance Vapour (P) T = Constant (77K for Nitrogen) Liquid (T) The helium level drops, with production of vapour. Heater European Advanced Cryogenics School 8
9 3 d transformation P Closed vessel, with external supply of gas under pressure (bottle or compressor) Vapour (P) Liquid (T) T increases in principle following the P(T) curve In practice, the equilibrium P(T) is not reached instantaneously = stratification within the liquid. Poor thermal conduction Hotter in the upper part European Advanced Cryogenics School 9
10 4 th transformation Closed vessel under depression (vacuum pump) Pump T diminishes following P(T) Vapour (P) At each value of P corresponds a value of T till the triple point. Liquid (T) In this case : better equilibrium Cold on the top : convection flow European Advanced Cryogenics School 10
11 Latent heat of vaporisation An important property related to vaporisation L vap : Amount of heat needed in order to evaporate a given amount of liquid Heating : expressed in watts Energy supplied = Watts x sec. = Joules L vap characterises the volatility Expressed in : joules / gram or joules / litre More practically : in litres of liquid evaporated per hour for 1 Watt. Liquid Nitrogen 1 watt evaporates 0,022 litre / hour Liquid Helium : more «volatile» 1 watt evaporates 1,4 litre / hour For the same applied power, helium evaporates at a rate 1400/22 = 70 times faster than Nitrogen. Z Z litres evaporated Chauffage time power L vap European Advanced Cryogenics School 11
12 Ideal Gases T >> Liquefaction temperature Standard Volume = 1 Mole V = 22,4 litres (22400 cm 3 ) T = 0 C (273,15 K) P = 1 Bar (10 5 Pa) For all gases same number of molecules Na = 6, (Avogadro s number) The masses depend on the gas considered M = molar masse (in grams) He : 1 atom / molecule M = 4 g H 2 : 2 atoms / molecule M = 2 g N 2 : 2 atoms / molecule M = 28 g The density at a given T and P is given by M (grams) P (Pascal ) 273,15 (in g / cm 3 ) 10 5 T (Kelvin) European Advanced Cryogenics School 12
13 Properties of Cryogenic Fluids Boiling temperatures at atmospheric pressure «permanent gases» Butane : 263 K Propane : 230 K Freon : de 140 à 240 K CO 2 : 195 K Xenon : 165 K Krypton : 121 K Methane : 111 K Argon : 87 K Interest of liquefying gases : storage and transportation Oxygen : 90 K (O 2, N 2, He, H 2, Ar, CH 4, ). CO : 82 K Fluor : 85 K Nitrogen : 77,3 K Neon : 27,2 K Deuterium : 23,6 K Hydrogen : 20,3 K Helium 4 : 4,21 K Helium 3 : 3,2 K European Advanced Cryogenics School 13
14 Properties of Cryogenic Fluids 1 litre of evaporated liquid gives ca litres of gas at room temperature and atmospheric pressure, i.e. 1 m 3 (more precisely; from 700 to 800 litres). Example : the gas contained in a bottle (O 2, N 2, He) (50 litres at 150 bars) 7,5 m 3 NPT This corresponds to about 10 litres of liquid 10 litres of liquid ~ Ø30 cm / h = 40 cm weight : a few kg Bottle 50 L Ø 25 cm / h = 1,50 m weight : ~ 60 kg European Advanced Cryogenics School 14
15 Nitrogen in air : 80 % Liquid Nitrogen 1 st liquefaction in 1877 (Cailletet) Boiling T at atmospheric pressure : 77,4 K Range of temperatures accessible by varying the pressure : from 62 K / 128 mbar to 126 K / 33 bars Density : slightly less than water : 800 g/litre at 77 K Heat of evaporation : 1 watt evaporates 22,6 cm 3 /hour liquid (L vap = 199 j/g) European Advanced Cryogenics School 15
16 Liquid Nitrogen Thermal conductivity : similar to that of an insulator Comparable to Teflon at 300 K, 1000 times less than Copper k = 1,38 mw/cm.k Viscosity : small = 1500 micropoises 7 times less than water Correspondence liquid / gas : 1 L liquid 700 L gas NTP Other applications : Food cooling and conservation Inert : microelectronics, metallurgy, cleaning, Car industry European Advanced Cryogenics School 16
17 Oxygen in air : 20 % Liquid Oxygen Boiling T at atmospheric pressure : 90,2 K Range of temperatures accessible by varying the pressure : From 54,4 K / 1,2 mbar to 154 K / 50 bars Density : somewhat larger than water : 1140 g/litre at 90 K Heat of evaporation : 1 watt evaporates 15 cm 3 /hour liquid European Advanced Cryogenics School 17
18 Liquid Oxygen Seldom used in Cryogenics (only calibrations) Danger : avoid contact with oil, grease Correspondence liquid / gas : 1 L liquid 800 L gas NPT Other applications : Steel, cutting, combustion (furnaces) Medical, space, European Advanced Cryogenics School 18
19 Liquid Hydrogen The lightest gas (balloons) Danger = flammable Boiling T at atmospheric pressure : 20,2 K (Dewar 1898) Range of temperatures accessible by varying the pressure : from 13,8 K / 70 mbar to 33 K / 12,7 bars Density : the lightest liquid : (rockets) 70 g/litre at 20 K Heat of evaporation : L vap = 445 J/g 1 watt evaporates 115 cm 3 /hour liquid (5 times more than nitrogen) European Advanced Cryogenics School 19
20 Liquid Hydrogen Thermal conductivity : similar to that of an insulator like LN2 k = 1,18 mw/cm/k Viscosity : 70 times smaller than water 140 micropoises Correspondence liquid / gas : 1 L liquid 780 L gas NPT Other applications : Rocket fuel (Ariane 4 and 5) Industry of micro components (inert atmosphere), chemistry, European Advanced Cryogenics School 20
21 Liquid Hydrogen 2 isotopes : Deuterium and Tritium In H 2 : 2 spin orientations are possible Ortho Para In equilibrium : 300 K 75% of ortho and 25% of para 20 K 0,2% of ortho and 99,8% of para Transformation ortho para exothermal and slow Catalyser to accelerate the transformation Releases 450 J/g Liquefaction without catalyser = large % of ortho large evaporation in the storage dewar. European Advanced Cryogenics School 21
22 Liquid Neon Noble gas: 10 times more expensive than Helium Boiling T at atmospheric pressure : 27 K Range of temperatures accessible by varying the pressure : Density : from 24,5 K / 425 mbar to 44,5 K / 27,8 bars 1210 g/litre at 27 K Heat of evaporation : 1 watt evaporates 35 cm 3 /hour liquid European Advanced Cryogenics School 22
23 Liquid Neon Thermal conductivity : similar to that of an insulator Viscosity : small, 8 times less than water Correspondence liquid / gas : 1 L liquid 1350 L gas NTP Other applications : Light tubes European Advanced Cryogenics School 23
24 Liquid Argon Boiling T at atmospheric pressure : 87,3 K Range of temperatures accessible by varying the pressure : Density : from 83,8 K / 690 mbar to 150,9 K / 50 bars 1400 g/litre at 87 K Gas NPT = 1,78 g/litre heavier than air! Heat of evaporation : 1 watt evaporates 16 cm 3 /hour liquid European Advanced Cryogenics School 24
25 Liquid Argon Thermal conductivity : similar to that of an insulator Like nitrogen Viscosity : rather low, 4 times less than water Correspondence liquid / gas : 1 L liquid 784 L gas NTP Other applications : Inert atmosphere, welding Industry of micro components (inert atmosphere) European Advanced Cryogenics School 25
26 Physical constants for the GAS state Molar Mass M (grams) Densiy NTP (g/cm 3 ) Viscosity (micropoises) Thermal Conductivity k (mw/cm.k) Heat capacity of gaz Cp (j/g.k) 69 to 100 K to 300 K 0,09 to 100 K 0,26 to 300 K 1,04 from 100 K to 300 K Oxygen (O 2 ) 32 1, to 20 K 2 90 to 300 K 0,15 to 20 K 1,8 to 300 K 10,4 to 20 K 10,8 to 80 K 14,5 to 300 K Helium 4 ( 4 He) 4 1, to 80 K 14 to 5 K 200 to 300 K 0,1 to 4,2 K 1,5 to 300 K 5,2 European Advanced Cryogenics School 26
27 Helium 2 stable isotopes : 4 He = abundant 3 He = rare and expensive Helium 4 ( 4 He): Discovered in : 1868 = astronomical observation (chromosphere) 1895 = on earth (in air: 1/ ) (Ramsay) 1905 = in natural gas, in the USA The hardest gas to liquefy! (1908 in Leyden, Kamerlingh Onnes) European Advanced Cryogenics School 27
28 Helium 4 gas World consumption = 35 millions of m 3 / year Rare gas - Price ~ 8 Euros /m 3 NTP In natural gas wells : 0,1 à 0,5 % USA, Poland, Russia, Algeria Other applications : Balloons, diving Inert atmosphere, welding Pressurisation (rockets), spatial and nuclear engineering Leak detection European Advanced Cryogenics School 28
29 Liquid 4 He Boiling T at atmospheric pressure : 4,2 K Range of temperatures accessible by varying the pressure : Density : from 1 K / 0,1 mbar to 5,2 K / 2,26 bars 125 g/litre at 4,2 K Heat of evaporation : L vap = 20,9 J/g very low 1 watt evaporates 1400 cm 3 /hour liquid (65 times more than nitrogen) Correspondence liquid / gas : 1 L liquid 750 L gas NTPtriple) European Advanced Cryogenics School 29
30 Helium 3 Available since the 60 s : produced by nuclear reaction 6 Li + n 4 He + Tritium Tritium 3 He + Half-life of Tritium = 12 years Strategic (military industries) Very expensive : Price ~ 3000 Euros (2011) /litre of gas NTP! Applications : Low temperatures < 1 K 3 He liquid at 10-3 mbar T = 0,3 K Mixtures 3 He/ 4 He : a few mk Medical imaging (polarised gas) Neutron detectors European Advanced Cryogenics School 30
31 Helium 3 Boiling T at atmospheric pressure : 3,2 K Range of temperatures accessible by varying the pressure : from 0,3 K / 10-3 mbar to 3,33 K / 1,16 bars Density : 59 g/litre at 300 K Heat of evaporation : 1 watt evaporates ~ 3 litres/hour liquid (2 times more than 4 He) Correspondence liquid / gas : 1 L liquid 460 L gas NTP European Advanced Cryogenics School 31
32 4 He = a special liquid Properties are not classical Quantum mechanics Seen already in early studies : Discontinuity of physical constants at T = 2,17 K density (kg/cm3) 0,15 0,14 0,13 0,12 0,11 T (K) 1,50 2,50 3,50 4,50 European Advanced Cryogenics School 32
33 4 He : Heat capacity (C) C is the amount of heat needed to increase the temperature by 1 K for a given amount of matter. heat of evaporation For helium : Units : J / g.k or cal / g.k T < T boiling At 4,2 K : like water Heater C = 4,18 J / g / K Cooling : discontinuity at 2,17 K C (J/g) 10 C : and then 8 Lambda Point 6 Liquide I Liquide II 2,17 K 4 Pressure : 50 mbar 2 2 phases ( helium I and II) 2,17 T ( K) European Advanced Cryogenics School 33
34 Liquid 4 He : Heat capacity (C) C hélium. is very large from 4 to 8 J/g.K As a comparison : Copper at 4,2 K : C copper = 10-4 J/g.K C helium. / C copper = ! Copper at 300 K : C copper = 0,4 J/g.K C hélium / C copper = 10! Large thermal inertia of helium with respect to metals Also true for other cryogenic fluids European Advanced Cryogenics School 34
35 Viscosity ( ) Above de T : liquid I Small viscosity 4 He : Viscosity ( ) 60 times less than N 2 et 400 times less than H 2 O About 30 micropoises Below T : liquid II (T < 2,17 K) Superfluid Helium : superflow Unusual properties (micropoises) 30 T a b T (K) 1,50 2,50 3,50 European Advanced Cryogenics School 35
36 4 He : Viscosity ( ) Below T, depends on the kind of measurement a) damping of disk oscillations in the liquid Viscosity remains above 5 micropoises b) Flow in narrow slits (10-3 à 10-4 mm) (Kapitza) Large flow even with small P Difficult to measure Flow independent on P lower than 10-3 micropoises SUPERFLUID Liquid (micropoises) 30 T a b T (K) 1,50 2,50 3,50 European Advanced Cryogenics School 36
37 4 He : Viscosity ( ) Explanation = 2 fluids (TISZA) Helium II mixture of normal n and superfluid s component. Superfluid: Entropy = 0 Viscosity = 0 Only the normal component carries entropy. Oscillating Disc Slits Measures viscosity of normal fluid Measures of superfluid component n s n 1 at T s 1 at 0 K European Advanced Cryogenics School 37
38 4 He : Thermal conductivity (k) Liquid helium I Liquid 4 He - I is an insulator (better than Teflon) k = 4 times smaller than LN2 k = 0,27 mw/cm.k Liquid helium II (superfluid) k becomes very large (8000 W/cm.K at 1,9K!!) About 1000 times better than copper By far the best thermal conductor near T Consequence : in a superfluid helium bath No gradient between top and bottom of Dewar (no stratification). No bubbles (associated to T) Large conductivity and heat capacity : application for magnets. European Advanced Cryogenics School 38
39 4 He : Thermal conductivity (k) 2-fluids model Gradient of temperature? Displacement of x superfluid atoms From cold to hot parts Larger concentration in cold places No accumulation displacement in opposite direction of the normal atoms Entropy transport Heat is transported by dynamical flow transfer of energy Limits : Large apparent conductivity If heat flux is large Interactions in the normal fluid Flux max. ~ W/cm 2 for T ~ a few 0,1 K ds L W Hélium II Hélium I W k ds L T European Advanced Cryogenics School 39
40 2 experiments Figure 1 : reservoir fills Figure 2 : reservoir empties In both cases a film has formed giving rise to a flow of liquid ROLLIN FILM Properties of the film Flows from cold to hot places Evaporates at the hot point (T Consequences : 4 He : superfluid film Climbs along the cryostat s neck Climbs along pumping lines Heat leaks and reduced performance of refrigerators Need of film-burners or diaphragms at T ~ 1 K European Advanced Cryogenics School 40
41 4 He : superfluid film Flow rate Proportionnal to the smallest perimeter seen Thin film = 30 nm Displacement velocity 25 cm/sec (~ 1 km/h) Flow rate Perimeter , Flow rate i.e. Périmètre 0,27 cm 3 / hour!! cm 3 / sec.cm For bad surfaces (metals) *10 times! Independent on the level difference Flow rate vs. T 1 1,2 1,4 1,6 1,8 2 2,2 temperature (K) European Advanced Cryogenics School 41
42 4 He : fountain effect Fine powder = superleak (alumina) Only superfluid component flows Liquid helium fountain can reach one meter! Explanation : Heat input Superfluid normal conversion Flow of superfluid towards the hot point (osmotic pressure) Normal Fluid «pushed» towards the top of the capillary fountain effect Direct conversion of thermal energy in kinetic energy 1 meter Hear European Advanced Cryogenics School 42
43 Mixtures 3 He/ 4 He At T > 0,8 K : the liquids are miscible (like water and alcohol) At T < 0,8 K : separation in 2 phases (like water and oil) concentrated phase diluted phase 3He only 4He + a little of 3He In the lower phase : 3 He diluted in 4 He = diluted phase The concentration of 3 He depends on temperature 0,5 K ~ 20 % 3 He T ~ 0 K ~ 6,4 % 3 He Even at low temperatures, there is a finite solubility of 3 He in 4 He In the upper phase : concentrated 3 He (no 4 He) 4 He is superfluid in the diluted phase European Advanced Cryogenics School 43
44 Mixtures 4 He/ 3 He : dilution Equivalent to the evaporation of a liquid in the presence of another gas : ether in air cooling But upside-down! AIR 3He 3 He atoms ETHER 4He Continuous refrigeration circulation of 3 He from concentrated to diluted phases With a careful design, refrigeration down to mk temperatures ( 2 to 4 mk in the best dilution refrigerators ) European Advanced Cryogenics School 44
45 Schematic view of a dilution refrigerator European Advanced Cryogenics School 45
46 4 He = a special liquid Very dense vapour Liquid at 4,2 K 125 g/litre Vapour at 4,2K 17 g/litre factor 7,5 (180 for Nitrogen) Consequence on the amount of matter in an empty devwar at 4,2 K : 100 litres of vapour at 4,2 K = 10 m 3 of gas NTP Large enthalpy of the vapour Heating vapour from 4 K to 300 K recovering frigories!. Example : 1 kg of copper from 300 to 4,2 K Without recovering the gas enthalpy : 30 litres of helium recovering the gas enthalpy : only 0,4 litres needed Precooling with Liquid Nitrogen, this is not so critical : 0,5 litres without / 0,2 litres with gas enthalpy recovery. European Advanced Cryogenics School 46
47 Amount evaporated for cooling: Without using the gas enthalpy To cool down 1 kg of copper starting at 300 K 30 litres of liquid helium Pre-cooling with liquid Nitrogen From 77 to 4,2 K 2,5 litres of liquid He Using the gas enthalpy Ex : transferring from below To cool down 1 kg of copper from 300 to 4,2 K 0,5 litres of liquid He maximum use of gas enthalpy! Between these two approaches = litres / kg Important that transfer is slow and from below LN2 pre-cooling is important Metal (copper ) Vapour Metal (copper ) He European Advanced Cryogenics School 47
48 Storage of cryogenic fluids Usually called cryostats or «Dewar» Heat reaches the fluid by different ways: : - conduction by the neck Qc - radiation Q1 + Q2 These sources of heating can be calculated, expressed in watts, and thus the evaporated amount (losses) : Losses in litres / hour = N watt x 1,4 for helium = N watt x 0,022 for Nitrogen Typical losses : 1 storage 100 litres helium : 0,030 watt i.e. 1 litre / day 1 helium laboratory cryostat : 0,1 to 1 watt i.e. ~ 10 litres / day 1 LN2 cryostat : ~ a few 10 watt i.e. 5 litres / day 300K Qc Q2 Q1 4K ou 77K Vacuum European Advanced Cryogenics School 48
49 TACONIS EFFECT 300 K Thermo-acoustic oscillations. tube closed at the top immersed in liquid helium. Self-maintained phenomenon Evaporation ~ 0,1 l/h to more than 10 l/h!! 4 K Gazo Solution : Avoid this geometry Or, if unavoidable : Foresee a connection to recovery Anti-oscillantion damp volume (100 litres) Diaphragms European Advanced Cryogenics School 49
50 Thanks! European Advanced Cryogenics School 50
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