Exchanging data between computational fluid dynamic and thermodynamic models for improving numerical analysis of Stirling engines

Abstract

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,

Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method

“…In this study, the performance of the compact 100-W-class β type Stirling engine in Ref. [18] is optimized by the VSCGM, proposed by Cheng and Lin [28], where the modified thermodynamic model, proposed by Cheng and Phung [17], plays the role of a direct solver, which generates the indicated power and the thermal efficiency necessary for estimating the objective function. The optimization method exploits both the highly convergent speed of the VSCGM and the advantages of the modified thermodynamic model such as computational time, memory resource, and the cyclic balance between heat transfer and indicated power.…”

“…In the modified thermodynamic model, proposed by Cheng and Phung [17], pressure losses are directly introduced into the energy equation, so heat transfer rates and indicated…”

“…In the modified thermodynamic model, proposed by Cheng and Phung [17], pressure losses are directly introduced into the energy equation, so heat transfer rates and indicated power meet the energy balance at the final cycle. This builds a solid foundation for multigoal optimization based on these two parameters, as mentioned in Section 3.1.…”

“…The CFD model serves two purposes: (1) completing our proposed modified thermodynamic model, as mentioned in detail in Ref. [17], and (2) verifying optimal solutions, which are obtained from the combination of VSCGM and the modified thermodynamic model. The matching process between the CFD model and the modified thermodynamic model for the baseline case generates values of unknowns listed in Table 3.…”

“…The modified non-ideal adiabatic model, proposed by Yang and Cheng [7], overcomes several shortcomings of the non-ideal adiabatic thermodynamic model by adding a temporal variation of temperature and pressure loss in the heater, cooler, and regenerator and introducing mechanical loss to obtain shaft power. Recently, Cheng and Phung [17] proposed a modified thermodynamic model by completely removing the adiabatic condition on expansion and compression chambers and simultaneously introducing non-uniform pressure to the energy equation so cyclic heat transfer rates and cyclic indicated power can balance at the final cycle. This energy balance lays a firm foundation for optimization in this study.…”