In the past several decades, remarkable increases in global population, economic size, and urbanization lead to the exponential depletion of fossil fuels. Wagner et al 1 predicted that the Proved and Ultimately Recoverable Reserves would become scarce in the second half of the 21st century. In addition, all countries over the world are currently seriously relying on fossil fuel so that they are facing the energy crisis inevitably. Renewable energy, such as solar energy, wind energy,

Thermal-lag engines are external combustion engines with a single moving piston. This feature leads to lower manufacturing and maintenance costs than traditional Stirling engines. Although the original concept of thermal-lag engines was invented roughly 35 years ago, the information on thermal-lag engines is still limited. Therefore, this study focuses on thermal-lag engine performance by developing a three-dimensional computational fluid dynamics (CFD) model. The grid independence check and the time step independence check are firstly performed to select the number of elements and size of the time step for simulation. The CFD model is then validated by the experimental data, which were collected by measuring an existing prototype engine. It has been found that the CFD predictions are well fitted to the experimental data over the range of engine speed from 200 to 1600 rpm at temperatures of 1173 or 1273 K. Furthermore, the CFD model predicts that the maximum engine power is 21.1 W while the prototype engine practically generates the highest power of 22.35 W at 1000 rpm and 1273 K. Finally, a further parametric study shows that crank radius, piston diameter, working gas mass, working gas species, and heating temperature significantly affect engine power.

This study focuses on optimizing a 100-W-class β-Type Stirling engine by combining the modified thermodynamic model and the variable-step simplified conjugate gradient (VSCGM) method. For the modified thermodynamic model, non-uniform pressure is directly introduced into the energy equation, so the indicated power and heat transfer rates can reach energy balance while the VSCGM is an updated version of the simplified conjugate gradient method (SCGM) with adaptive increments and step lengths to the optimization process; thus, it requires fewer iterations to reach the optimal solution than the SCGM. For the baseline case, the indicated power progressively raises from 88.2 to 210.2 W and the thermal efficiency increases from 34.8 to 46.4% before and after optimization, respectively. The study shows the VSCGM possesses robust property. All optimal results from the VSCGM are well-matched with those of the computational fluid dynamics (CFD) model. Heating temperature and rotation speed have positive effects on optimal engine performance. The optimal indicated power rises linearly with the charged pressure, whereas the optimal thermal efficiency tends to decrease. The study also points out that results of the modified thermodynamic model with fixed values of unknowns agree well with the CFD results at points far from the baseline case.