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

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

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

Gas isentropic expansion with external work

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:

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

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

Piston expander

Cryogenic turboexpander

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.

Isenthalpic – Joule-Thomson - expansion

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

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

Free expansion (exhaust)

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)

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)

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

Comparison of the processes for air

Cryogenic gas refrigerators

Heat exchangers RecuperativeRegenerative

Comparison of coolers

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

Examples of miniature Joule-Thomson refrigerator

Claude refrigerators

Stirling coolers

Stirling cooler

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

Stirling split cooler

Stirling cooler with linear motor

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

Stirling cooler configuration: Stirling cooler configuration:

Stirling cooler used for air liquefact -ion

Stirling cooler used for air liquefaction

Two stage Stirling refrigerator

Gifforda – McMahon cooler Gifforda – McMahon cooler

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

McMahon refrigerator

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

Pulse tube – free exhaust

Scheme of pulse tube cooler

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

Comparison of Stirling and orifice pulse tube cooler

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

Pulse tube

Two stage pulse tube

Pulse tube configuration

Paramagnetic salts

Magnetic coolers

Magnetic cooler

Magnetic cooler with moving paramagnetic

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.

Cooler efficiency at 80 K

„Family” of cryocoolers

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