The Stirling cycle is a thermodynamic cycle that describes the general class of Stirling devices. This includes the original Stirling engine that was invented, developed and patented in 1816 by Robert Stirling with help from his brother, an engineer. 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. Another cycle that features isothermal heat-addition and heat-rejection processes is the Stirling cycle, which is an altered version of the Carnot cycle in which the two isentropic processes featured in the Carnot cycle are replaced by two constant-volume regeneration processes. The cycle is reversible, meaning that if supplied with mechanical power, it can function as a heat pump for heating or cooling, and even for cryogenic cooling. The cycle is defined as a closed regenerative cycle with a gaseous working fluid. "Closed cycle" means the working fluid is permanently contained within the thermodynamic system. This also categorizes the engine device as an external heat engine. "Regenerative" refers to the use of an internal heat exchanger called a regenerator which increases the device's thermal efficiency. The cycle is the same as most other heat cycles in that there are four main processes: compression, heat addition, expansion, and heat removal. However, these processes are not discrete, but rather the transitions overlap. The Stirling cycle is a highly advanced subject that has defied analysis by many experts for over 190 years. Highly advanced thermodynamics is required to describe the cycle. Professor Israel Urieli writes: "...the various 'ideal' cycles (such as the Schmidt cycle) are neither physically realizable nor representative of the Stirling cycle". 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".
Idealized Stirling cycle thermodynamics
The idealized Stirling cycle consists of four thermodynamic processes acting on the working fluid (See diagram to right):
Piston motion variations
Most thermodynamics textbooks describe a highly simplified form of Stirling cycle consisting of four processes. This is known as an "ideal Stirling cycle", because it is an "idealized" model, and not necessarily an optimized cycle. Theoretically, the "ideal cycle" does have high net work output, but it is rarely used in practical applications, in part because other cycles are simpler or reduce peak stresses on bearings and other components. For convenience, the designer may elect to use piston motions dictated by system dynamics, such as mechanical linkage mechanisms. At any rate, the efficiency and cycle power are nearly as good as an actual implementation of the idealized case. A typical piston crank or linkage in a so named "kinematic" design often results in a near-sinusoidal piston motion. Some designs will cause the piston to "dwell" at either extreme of travel. Many kinematic linkages, such as the well known "Ross yoke", will exhibit near-sinusoidal motion. However, other linkages, such as the "rhombic drive", will exhibit more non-sinusoidal motion. To a lesser extent, the ideal cycle introduces complications, since it would require somewhat higher piston acceleration and higher viscous pumping losses of the working fluid. The material stresses and pumping losses in an optimized engine, however, would only be intolerable when approaching the "ideal cycle" and/or at high cycle rates. Other issues include the time required for heat transfer, particularly for the isothermal processes. In an engine with a cycle approaching the "ideal cycle", the cycle rate might have to be reduced to address these issues. In the most basic model of a free piston device, the kinematics will result in simple harmonic motion.
Volume variations In beta and gamma engines, generally the phase angle difference between the piston motions is not the same as the phase angle of the volume variations. However, in the alpha Stirling, they are the same. The rest of the article assumes sinusoidal volume variations, as in an alpha Stirling with co-linear pistons, so named an "opposed piston" alpha device. caveat: Among the many inaccuracies in this article, a co-linear alpha configuration is referenced, above. Such a configuration would be beta. Alternatively, it would be an alpha, that has an unacceptably inefficient linkage system.
Pressure-versus-volume graph This type of plot is used to characterize almost all thermodynamic cycles. The result of sinusoidal volume variations is the quasi-elliptical shaped cycle shown in Figure 1. Compared to the idealized cycle, this cycle is a more realistic representation of most real Stirling engines. The four points in the graph indicate the crank angle in degrees.
The adiabatic Stirling cycle is similar to the idealized Stirling cycle; however, the four thermodynamic processes are slightly different (see graph above):
180° to 270°, pseudo-isothermal expansion. The expansion space is heated externally, and the gas undergoes near-isothermal expansion. 270° to 0°, near-constant-volume (or near-isometric or isochoric) heat removal. The gas is passed through the regenerator, thus cooling the gas, and transferring heat to the regenerator for use in the next cycle. 0° to 90°, pseudo-isothermal compression. The compression space is intercooled, so the gas undergoes near-isothermal compression. 90° to 180°, near-constant-volume (near-isometric or isochoric) heat addition. The compressed air flows back through the regenerator and picks up heat on the way to the heated expansion space. With the exception of a Stirling thermoacoustic engine, none of the gas particles actually flow through the complete cycle. So this approach is not amenable to further analysis of the cycle. However, it provides an overview and indicates the cycle work.
… excerpt ends here. Continue reading the full article.
