A new method to optimise finite dimensions thermodynamic models: application to an irreversible Stirling engine

Different economical configurations, due for instance to the relative cost of the fuel they consume, can push a heat engine into operating whether at maximum efficiency or at maximum power produced. Any relevant design of such a system hence needs to be based, at least partly, on the knowledge of its specific `power vs. efficiency' characteristic curve. However, even when a simple model is used to describe the engine, obtained, for example, thanks to finite dimensions thermodynamics, such a characteristic curve is often difficult to obtain and takes an explicit form only for the simplest of these models. When more realistic models are considered, including complex internal subsystems or processes, an explicit expression for this curve is practically impossible to obtain. In this paper, we propose to use Graham's scan algorithm in order to directly obtain the power vs. efficiency curve of a realistic Stirling engine model, which includes heat leakage, regenerator effectiveness, as well as internal and external irreversibilities. Coupled with an adapted optimisation routine, this approach allows to design and optimise simple or complex heat engine models. Such a method can then be useful during the practical design task of any thermal power converter, almost regardless of its own internal complexity.