Theoretical investigation of the performance of an Alpha Stirling engine for low temperature applications

The purpose of this paper is to explore the applicability and peculiarities of Alpha engines at low heat source temperature levels of 100 to 200°C. A parameter study of an Alpha engine has been carried out using the commercial Stirling software Sage. The obtained results revealed some interesting insights into the peculiarities of low-temperature Alpha-SEs. A method for optimising the system design-parameters for a SE is described in this paper. The compact design of a double-acting Alpha engine helps to reduce not only engine size and complexity but also costs. At low temperature differences single-cylinder displacer-type (gamma) engines are well documented, while little is known about the performance of Alpha multi-cylinder engines. In order to achieve the highest possible power output not only the thermodynamic side but also the mechanical side of the engine has to be optimised. This is especially important at low temperature differentials, where the conversion efficiencies are inherently small and the driving force for heat absorption and rejection by the working gas is low. It is mandatory not only to convert as much heat as possible to indicated work but also to transfer as much of this hard gained work to usable power output by minimising internal friction, when trying to keep the engine size as small as possible. The indicated power output of an engine of a specific swept volume is dependent on the temperature and pressure levels, the frequency, the phase angle between the two pistons, the working fluid, and the design of the heat exchangers and the regenerator. A simple model of an Alpha engine was created using the commercial SE simulation tool Sage. In order to explore the relations between those parameters a model was developed, where the design parameters (temperature, mean pressure, frequency, and phase angle) were varied, and the heat exchangers and the regenerator were then optimised for each of the parameter combinations to reach the maximum power output. Temperature and mean pressure are shown to have the expected positive influence on the power output. For the frequency and the phase angle, optimum values can be found that differ significantly from those found for high temperature engines. Helium is used as the benchmark working gas. It can be shown that the use of Nitrogen instead cuts the power output in half, whereas Hydrogen doubles the achievable power output. The mechanical efficiency of a kinematic SE is largely dependent on the load that is transferred from the pistons to the crankshaft during expansion and vice versa during compression, as it increases frictional losses. In double-acting engines an identical pressure oscillation acts on the opposing faces of a piston, although it is out of phase. The resulting forces can balance each other to some extent depending on the phase, and thus the net force applied to the crankshaft can be reduced. For a four cylinder engine it is shown that the Siemens arrangement balances internal forces on the pistons to a larger extent than the Franchot arrangement, so that the mechanical losses are inherently smaller and thus the brake power is larger even though the indicated work is identical for both engine types. The contribution of this work is the provision of a modelling methodology, and the identification of a number of insights for system-design considerations for low-temperature applications.