9.3 Stirling and Ericsson cycles

Gas power cycles are essential in thermodynamics, converting heat into work. Stirling and Ericsson cycles stand out for their unique features, using closed systems and regenerators to improve efficiency. They offer interesting alternatives to traditional internal combustion engines.

These cycles use isothermal and isochoric/isobaric processes to maximize work output. While they have high theoretical efficiencies, practical limitations affect their real-world performance. Understanding these cycles deepens our knowledge of thermodynamic principles and their applications.

Stirling and Ericsson Cycles

Principles and Components

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• Operate using a working fluid (air, helium, or hydrogen) that remains within the system
• Consist of four thermodynamic processes: isothermal compression, isochoric heat addition, isothermal expansion, and isochoric heat rejection (Stirling cycle)
• Comprise two isothermal processes (compression and expansion) and two isobaric processes (heat addition and rejection) (Ericsson cycle)
• Utilize a regenerator to store and transfer heat between the hot and cold sides of the engine, improving thermal efficiency

Engine Components

• Include a cylinder, two pistons (a power piston and a displacer piston), a regenerator, and heat exchangers for heat addition and rejection (Stirling engine)
• Contain a cylinder, a piston, a displacer, a regenerator, and heat exchangers for heat addition and rejection (Ericsson engine)

Thermodynamic Processes in Cycles

Stirling Cycle Processes

• Isothermal compression occurs at a constant low temperature, with heat being rejected to the external sink
• Isochoric heat addition involves the transfer of heat from the regenerator to the working fluid at a constant volume
• Isothermal expansion occurs at a constant high temperature, with heat being added to the working fluid from an external source
• Isochoric heat rejection involves the transfer of heat from the working fluid to the regenerator at a constant volume

Ericsson Cycle Processes

• Isothermal compression occurs at a constant low temperature, with heat being rejected to the external sink
• Isobaric heat addition involves the transfer of heat from an external source to the working fluid at a constant pressure
• Isothermal expansion occurs at a constant high temperature, with heat being added to the working fluid from an external source
• Isobaric heat rejection involves the transfer of heat from the working fluid to the external sink at a constant pressure

Stirling vs Other Gas Cycles

Advantages of Stirling and Ericsson Cycles

• Have higher theoretical thermal efficiencies compared to other gas power cycles (Otto and Diesel cycles) due to their regenerative nature and the use of isothermal processes
• Allow for the use of various heat sources (solar energy, geothermal energy, and waste heat) due to their closed-cycle nature, making them more versatile than open-cycle engines
• Produce lower noise and vibration levels compared to internal combustion engines, as they do not involve explosive combustion processes
• Result in lower emissions compared to internal combustion engines, as the combustion process is separated from the working fluid

Disadvantages of Stirling and Ericsson Cycles

• Have lower power-to-weight ratios compared to internal combustion engines, making them less suitable for mobile applications (automobiles, aircraft)
• Increase complexity and cost compared to other gas power cycles due to the presence of a regenerator
• Can result in slower response times to load changes compared to internal combustion engines due to heat transfer limitations

Efficiency and Work Output of Cycles

Thermal Efficiency Calculation

• Given by the ratio of the net work output to the heat input: $\eta = W_{net} / Q_{in}$
• Equal to the Carnot efficiency for an ideal Stirling or Ericsson cycle: $\eta = 1 - (T_c / T_h)$, where $T_c$ is the low temperature and $T_h$ is the high temperature
• Lower than the ideal values due to various irreversibilities (heat transfer limitations, friction, and pressure drops)

Work Output Calculation

• Determined by multiplying the net work output per cycle ($W_{net}$) by the number of cycles per unit time ($N$): $Power = W_{net} \times N$
• Net work output ($W_{net}$) is the difference between the work done by the engine during expansion ($W_{exp}$) and the work done on the engine during compression ($W_{comp}$): $W_{net} = W_{exp} - W_{comp}$
• Calculated by determining the work done during each process using the appropriate thermodynamic equations for isothermal, isochoric, or isobaric processes, and then summing the work values
• Lower than the ideal values due to various irreversibilities (heat transfer limitations, friction, and pressure drops)