Stirling cycle

[1] The ideal Otto and Diesel cycles are not totally reversible because they involve heat transfer through a finite temperature difference during the irreversible isochoric/isobaric heat-addition and heat-rejection processes.

The irreversibility renders the thermal efficiency of these cycles less than that of a Carnot engine operating within the same limits of temperature.

"Closed cycle" means the working fluid is permanently contained within the thermodynamic system.

"Regenerative" refers to the use of an internal heat exchanger called a regenerator which increases the device's thermal efficiency.

[2] The analytical problem of the regenerator (the central heat exchanger in the Stirling cycle) is judged by Jakob to rank "among the most difficult and involved that are encountered in engineering".

At any rate, the efficiency and cycle power are nearly as good as an actual implementation of the idealized case.

In the most basic model of a free piston device, the kinematics will result in simple harmonic motion.

The result of sinusoidal volume variations is the quasi-elliptical shaped cycle shown in Figure 1.

Also referred to as "pumping losses", the pressure drops shown in Figure 3 are caused by viscous flow through the heat exchangers.

[6] The flow losses shown here are relatively low, and they are barely visible in the following image, which will show the overall pressure variations in the cycle.

However, the heat exchangers still work well enough to allow the real cycle to be effective, even if the actual thermal efficiency of the overall system is only about half of the theoretical limit.

During the expansion process of the cycle, some work is actually done on the compression piston, as reflected by the upward movement of the trace.

At the end of the cycle, this value is negative, indicating that compression piston requires a net input of work.

A pressure/volume graph of the idealized Stirling cycle. In real applications of the Stirling cycles (e.g. Stirling engines) this cycle is quasi-elliptical.
A model of a four-phase Stirling cycle
Alpha type Stirling. Animated version.