Low Temperature Stirling Engines



Theory 8 - Various losses in real engines

Besides losses due limited mechanical efficiency and non-isothermal expansion/compression, real engines suffer from further losses. Among the processes that reduce the output power of real engines some are related to the environment (non-constant buffer pressure) and other ones to heat transfer (limited  heat transfer and internal heat leakage).

Variable buffer pressure

For engines enclosed in a buffer vessel, the evolution of pressure within the vessel is not constant, as supposed to be in our previous chapters. Usually the buffer pressure increases when internal volume is higher, resulting in a defavorable increase of the work W- to be given back to the working fluid by the buffer module.

Furthermore, the buffer gas could also run trough a thermodynamic cycle and therefore suffer from thermodynamic losses, to be deduced from the nominal thermodynamic work of the working fluid.

Limited heat transfer

The heat flow within the heater and the cooler depends on the temperature difference ΔT between the gas and the heater and cooler themselves. In our analysis, Th and Tc do not correspond to the temperature of the heater and the cooler, but to the maximal and minimal temperatures of the working fluid. Therefore Th is smaller than heater temperature and Tc is higher than cooler temperature.

For fixed heater and cooler temperatures, if ΔT is zero then there is no heat flow and the engine will not run. When  ΔT is increasing (higher speed of the engine) then heat flow allows the engine to run. The speed will increase up to a maximum. Then increasing ΔT will drive Th and Tc closer from each other and the nominal work of the thermodynamic cycle will decrease, up to a certain point where the engine will stop.

Internal heat leakage

Internal heat leakage are due to heat flowing from the hot side of the engine toward the cold side. This heat flow appears because of conduction through the metallic parts of the engine, or by the cyclic proximity with hot/cold pistons. This internal heat flow corresponds to some energy that is extracted from the heat source and passed directly to the cold bath without being involved in the process aiming to transform heat into mechanical work.

 

 





Theory index

Theory 1 - Generic schematic
Theory 2 - Buffer pressure
Theory 3 - Mechanism effectiveness
Theory 4 - Optimal buffer pressure of the ideal Stirling Cycle
Theory 5 - Output work of engines with ideal Stirling cycle
Theory 6 - Pressurization of ideal Stirling cycle engines
Theory 7 - Crossley cycles engines
Theory 8 - Various losses in real engines





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