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Refrigeration and cryogenics Zakład Kriogeniki i Technologii Gazowych Dr hab. inż. Maciej Chorowski, prof. PWr

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Methods of lowering the temperature Isentropic expansion Isentropic expansion Joule-Thomson expansion Joule-Thomson expansion Free expansion – gas exhaust Free expansion – gas exhaust

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Gas isentropic expansion with external work

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Drop of the gas temperature: Entropy is a function of pressure and temperature S= S(p, T) Total differential must be equal to zero: Differential effect of isentropic expansion s shows the change in temperature with respect to the change of pressure:

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Gas isentropic expansion with external work We know from thermodynamics We get where: is coefficient of cubical expansion

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Gas isentropic expansion with external work For the ideal gas: After integration

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Piston expander

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Cryogenic turboexpander

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Isenthalpic – Joule-Thomson - expansion When gas, vapour or liquid expands adiabatically in an open system without doing any external work, and there is no increment in velocity on the system reference surface, the process is referred to as throttle expansion. In practice, this process is implemented by installing in the gas stream some hydraulic resistance such as throttling valve, gate, calibrated orifice, capillary, and so on.

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Isenthalpic – Joule-Thomson - expansion

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Temperature drop in Isenthalpic – Joule-Thomson - expansion Enthalpy is a function of pressure and temperature: h= h(p, T) Total differential must be equal to zero: Differential throttling effect μ h : Isenthalpic – Joule-Thomson - expansion

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Gas Maximal inversion temperature, K eksperyment z równania van der Walsa Argon765----- Azot604837 Hel – 3 39----- Hel – 4 4634,3 Neon230----- Powietrze650895 Metan953----- Tlen7711090 Wodór204,6223

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Free expansion (exhaust)

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1. Adiabatic process 2. Non equilibrium process – gas pressure and external pressure are not the same 3. Constant external pressure (p f = const.) 4. External work against pressure p f Free expansion (exhaust)

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Final gas temperature: I Law of Thermodynamics where: u 0, u f – initial and final gas internal energy v 0, v f – initial and final gas volume Free expansion (exhaust)

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For ideal gas: We get: Free expansion (exhaust)

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Comparison of the processes for air

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Cryogenic gas refrigerators

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Heat exchangers RecuperativeRegenerative

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Comparison of coolers

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Refrigerators with recuperative heat exchangers Joule – Thomson refrigerators Joule – Thomson refrigerators

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Examples of miniature Joule-Thomson refrigerator

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Claude refrigerators

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Stirling coolers

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Stirling cooler

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Stirling cycle is realized in four steps : 1. Step 1-2: Isothermal gas compression in warm chamber 2. Step 2-3: Isochoric gas cooling in regenerator 3. Step 3-4:Isothermal gas expansion with external work 4. Step 4-1: Isochoric gas heating in regenerator In Stirling refrigerator a cycle consists of two isotherms and two isobars

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Stirling split cooler

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Stirling cooler with linear motor

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Efficiency of Stirling cooler filled with ideal gas Work of isothermal compression Work of isothermal expansion Heat of isothermal expansion

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Stirling cooler configuration: Stirling cooler configuration:

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Stirling cooler used for air liquefact -ion

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Stirling cooler used for air liquefaction

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Two stage Stirling refrigerator

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Gifforda – McMahon cooler Gifforda – McMahon cooler

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Four steps of McMahon cycle: 1. Filling. 2. Gas displacement 3. Free exhaust of the gas 4. Discharge of cold chamber Efficiency of McMahon cooler: Gifforda – McMahon cooler Gifforda – McMahon cooler

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McMahon refrigerator

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Combination of McMahon and J-T cooler, 250 mW at 2,5 K

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Pulse tube – free exhaust

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Scheme of pulse tube cooler

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Development of pulse tube coolers Gifford, 1963, rather curiosity that efficient cooler Kittel, Radebaugh, 1983 orifice pulse tube Dr. Zhu et. al., 1994, multiply by-pass pulse tube

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Comparison of Stirling and orifice pulse tube cooler

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Pulse tube cooler for 77 K applications Weight:2.4 kg Dimensions (l x w x h):11.4 x 11.4 x 22 cm Capacity:2.5W @ 65K Ultimate low temperature:35K Input power2kW

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Pulse tube

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Two stage pulse tube

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Pulse tube configuration

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Adiabatic demagnetization of paramagnetic

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Paramagnetic salts

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Magnetic coolers

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Magnetic cooler

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Magnetic cooler with moving paramagnetic

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Three stage magnetic cooler with magnetic regenerator Ceramic magnetic regenerator material Gd2O2S with an average diameter of 0.35 mm for G-M and pulse tube cryocoolers.

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Cooler efficiency at 80 K

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„Family” of cryocoolers

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