Thermodynamic optimization of a Stirling engine

A Stirling engine configuration consisting of two cylinders, a regenerator and a sliding disc actuating mechanism (“swashplate”) is considered in this paper. A mathematical model, which combines fundamental and empirical correlations, and principles of classical thermodynamics, mass and heat transfer accounting for variable heat transfer coefficients, is developed. The proposed model is then utilized to simulate numerically the system transient and steady state response under different operating and design conditions. A system global optimization for maximum performance in the search for optimal parameters that lead to maximum cycle efficiency is performed with low computational time. Appropriate dimensionless groups are identified and the results presented in normalized charts for general application. The numerical results show that the two-way maximized system efficiency, ηmax,max, occurs when two system characteristic parameters, the ratio between the total swept volume during the expansion, and the total swept volume, φ, and the ratio between the heat transfer area of the hot side heat exchanger and the total heat exchange area, y, are optimally selected, i.e., (φ,y)opt≅(0.5,0.4). The two-way maximized cycle efficiency found with respect to the optimized parameters is sharp, in the sense that a 225% variation of the calculated efficiency values was observed within the range of tested configurations in this study, and “robust” (i.e., relatively insensitive) to the variation of several parameters, thus stressing the importance to be considered in actual design. It is also found that the twice-maximized cycle efficiency and the total engine work output increase monotonically with the temperature of the hot source, Th. As a result, the model is expected to be a useful tool for simulation, design, and optimization of Stirling engines.