An approach to combine the second-order and third-order analysis methods for optimization of a Stirling engine

Second-order and third-order models are the two main methods for Stirling cycle analysis. A second-order one has relatively reliable accuracy without detailed cyclic information, while a third-order one provides relatively comprehensive operational information with uncertainty. In this work, a third-order model, Sage, is tried to be improved by a second-order model, Improved Simple Analytical Model, and 100 W beta-type Stirling engine is used as a modelling prototype engine. As suggested by Improved Simple Analytical Model, the gap of the piston seal and the empirical multiplier for heat transfer of cooler in Sage should be adjusted. This is accomplished by combining these two models so that the effects of seal leakage loss, gas spring hysteresis loss, and piston friction loss could be considered in an improved Sage. The improved Sage indicates that the overall relative errors for the indicated power output and the thermal efficiency are reduced by over 30 percentage points and 20 percentage points, respectively. Pressure-volume diagrams provided by the improved Sage are much closer to the experimental ones, and the pattern similarities of pressure-volume diagrams increase from 78.6-81.4% to 80.8-85.0%. Performance simulation of the Stirling engine is carried out by the improved Sage and the results show that regenerator takes a major role in improving the performance of the 100 W beta-type Stirling engine. Lengths of regenerator, heater and cooler are optimized for the maximum indicated power output and the maximum thermal efficiency respectively, and the optimized values are increased by 15.9% and 25.2%, respectively.