11.3 Gas refrigeration cycles

Gas refrigeration cycles

Principles and components

Unlike vapor-compression systems that rely on phase changes, gas refrigeration cycles use a single-phase gas (air, helium, or nitrogen) as the working fluid. The gas never condenses or evaporates; instead, cooling is produced entirely through compression and expansion of the gas. This makes gas cycles well suited for reaching extremely low temperatures where vapor-compression systems can't operate.

The basic components of a gas refrigeration cycle are:

1. Compressor — increases the pressure and temperature of the gas
2. Hot-side heat exchanger — rejects heat from the high-pressure, high-temperature gas to the surroundings
3. Expansion device (expander or turbine) — drops the pressure and temperature of the gas, producing the cooling effect
4. Cold-side heat exchanger — absorbs heat from the space or substance being cooled into the low-pressure, low-temperature gas

The efficiency of a gas refrigeration cycle depends on:

• Properties of the working fluid — monatomic gases like helium have a high specific heat ratio ($\gamma$), which affects the temperature swing during compression and expansion
• Pressure ratio across the compressor
• Heat exchanger effectiveness — how closely the heat exchangers approach ideal heat transfer

Thermodynamic processes

A standard gas refrigeration cycle involves four processes:

1. Compression (1→2): The gas is compressed, ideally isentropically, raising both its pressure and temperature.
2. Heat rejection (2→3): At constant pressure, the hot compressed gas rejects heat to the surroundings in the hot-side heat exchanger.
3. Expansion (3→4): The gas expands through a turbine or expander, ideally isentropically, dropping its pressure and temperature below the cold-space temperature.
4. Heat absorption (4→1): At constant pressure, the cold gas absorbs heat from the refrigerated space in the cold-side heat exchanger.

The ideal cycle therefore consists of two isentropic processes and two isobaric processes. You can visualize this on both P-v and T-s diagrams. On a T-s diagram, the isentropic steps are vertical lines, and the isobaric steps are curved lines that slope upward to the right. The enclosed area on the T-s diagram represents the net work input per unit mass.

One thing that trips students up: because the gas doesn't change phase, the temperature does change during heat addition and rejection. This means the average temperature difference between the gas and the reservoirs is larger than in a vapor-compression cycle, which is a major reason gas cycles have lower COPs for the same temperature limits.

Types of gas refrigeration cycles

Brayton (reversed) cycle

The reversed Brayton cycle is the most common gas refrigeration cycle. In its refrigeration form, it runs the gas-turbine power cycle in reverse: work is input to move heat from cold to hot.

• It's an open or closed steady-flow cycle using a continuous stream of gas through a compressor, heat exchanger, turbine, and cold-side heat exchanger.
• Typical working fluids are air, helium, or nitrogen.
• The turbine recovers some of the compression work, reducing the net work input.

Where it's used: Aircraft cabin cooling (air cycle machines), natural gas liquefaction, and industrial process cooling. Aircraft systems favor the Brayton cycle because the working fluid is simply cabin air, eliminating the need to carry a separate refrigerant.

Advantages: Simple construction, high reliability, and the working fluid is often free (ambient air). Disadvantages: Lower COP than vapor-compression systems for moderate-temperature applications. Performance drops as the pressure ratio deviates from its optimum.

Stirling cycle

The Stirling refrigeration cycle is a closed cycle that operates with a fixed mass of gas (often helium) and includes a regenerator, which is the key component distinguishing it from the Brayton cycle.

The four processes in an ideal Stirling cycle are:

1. Isothermal compression — heat is rejected at $T_h$
2. Constant-volume regenerative cooling — the gas passes through the regenerator, transferring heat to the regenerator matrix
3. Isothermal expansion — heat is absorbed at $T_c$
4. Constant-volume regenerative heating — the gas passes back through the regenerator, recovering the stored heat

Because both heat transfer processes are isothermal, the ideal Stirling cycle has the same COP as the Carnot cycle. In practice, the COP is lower due to imperfect regeneration, dead volume, and seal leakage.

Where it's used: Cryocoolers for infrared detectors, superconducting device cooling, and small-scale laboratory refrigeration.

Advantages: Highest theoretical efficiency among practical gas cycles, quiet operation, capable of reaching very low temperatures. Disadvantages: The regenerator is difficult to manufacture with high effectiveness, and precise piston/displacer motion control is required.

Other gas refrigeration cycles

• Ericsson cycle: Similar to the Stirling cycle but replaces the constant-volume processes with constant-pressure processes. It also achieves Carnot COP in the ideal case. The separate compression and expansion steps allow more design flexibility.
• Gifford-McMahon cycle: A closed regenerative cycle that separates the compressor from the cold head using valves and a displacer. Commonly used in cryogenic applications such as MRI scanner cooling and particle accelerator systems.
• Pulse tube refrigerator: Uses oscillating pressure waves to produce cooling with no moving parts at the cold end. This eliminates vibration and wear, making it highly reliable. Used in cooling infrared sensors and in space applications where mechanical simplicity is critical.

Performance of gas refrigeration cycles

Efficiency metrics

The coefficient of performance (COP) measures how effectively the cycle converts work input into cooling:

$COP = \frac{Q_c}{W_{net}}$

where $Q_c$ is the heat removed from the cold space (cooling capacity) and $W_{net}$ is the net work input to the cycle.

The Carnot COP sets the upper bound for any refrigeration cycle operating between temperatures $T_c$ and $T_h$:

$COP_{Carnot} = \frac{T_c}{T_h - T_c}$

Both temperatures must be in absolute units (Kelvin or Rankine). Notice that as $T_c$ drops toward zero, the Carnot COP also drops toward zero. This is why achieving very low temperatures requires disproportionately more work.

The actual COP of any real gas cycle is always less than the Carnot COP because of irreversibilities: friction in the compressor and turbine, pressure drops through piping and heat exchangers, and heat transfer across finite temperature differences.

Factors affecting performance

You can improve the COP of a gas refrigeration cycle by:

• Optimizing the pressure ratio — there's a sweet spot. Too low and the temperature swing is insufficient; too high and compressor work dominates.
• Minimizing pressure drops through well-designed ducting and heat exchangers.
• Increasing heat exchanger effectiveness — getting the gas temperatures closer to the reservoir temperatures reduces irreversibility.
• Choosing the right working fluid — helium is preferred for cryogenic applications because it remains gaseous at very low temperatures and has favorable transport properties.

Exergy analysis is a powerful tool for identifying where the losses occur in a gas refrigeration system. Exergy destruction (lost work potential) happens due to:

• Friction in the compressor and expander
• Heat transfer across finite temperature differences in heat exchangers
• Mixing of streams at different temperatures or pressures
• Pressure drops across system components

By quantifying exergy destruction in each component, you can target the biggest sources of inefficiency for design improvements.

Applications of gas refrigeration systems

Low-temperature and cryogenic applications

Gas refrigeration systems dominate in applications requiring temperatures far below what vapor-compression systems can reach (roughly below $-40°C$ to $-80°C$):

• Cryogenic cooling — producing liquid nitrogen ($77 \text{ K}$), liquid hydrogen ($20 \text{ K}$), or liquid helium ($4.2 \text{ K}$) for industrial, medical, and research use
• Gas liquefaction — natural gas is cooled to about $-162°C$ ($111 \text{ K}$) for LNG storage and transport
• Space and defense cooling — satellite-borne infrared detectors and space telescopes require stable cryogenic temperatures with minimal vibration, making pulse tube and Stirling coolers ideal

Industrial and commercial applications

• Brayton-cycle systems are used in aircraft environmental control systems (cabin air conditioning), natural gas processing plants, and industrial process cooling in chemical plants.
• Stirling-cycle systems serve as cryocoolers for infrared sensors, superconducting electronics, and small-scale medical/scientific refrigeration.
• A shared advantage across these applications is that gas cycles can use environmentally benign working fluids (air, helium, nitrogen) with zero ozone depletion potential and zero global warming potential.

Limitations and challenges

Gas refrigeration systems have real drawbacks you should be aware of:

• Lower COP than vapor-compression systems for moderate-temperature cooling, which makes them impractical for typical residential or commercial HVAC.
• Lower cooling capacity per unit size — the absence of latent heat exchange means more mass flow is needed for the same cooling load.
• High operating pressures and temperatures require specialized materials and seals, increasing cost.
• Efficiency drops sharply at very low temperatures because irreversibilities become proportionally larger relative to the shrinking Carnot COP.

Design challenges include minimizing gas leakage, developing materials that withstand extreme thermal cycling, and integrating gas refrigeration subsystems with broader energy systems to recover waste heat or share compression work.