In this dissertation, two novel numerical models, namely, the enhanced thermodynamic model and the CFD-dynamic (CFDD) model are proposed based on improving the pre-existing numerical models of Stirling engines. More specifically, the enhanced thermodynamic model removes some shortcomings of the pre-existing second-order thermodynamic models: (i) The direct introduction of the absolute pressure distribution into the energy equation; (ii) Complete elimination of the adiabatic assumption in the derivation of the model; (iii) Calculation of mass flow rates based directly on the mass balance equation, global mass conservation equation, and ideal-gas equation of state; and (iv) The effect of the high solution of the temperature and pressure distributions due to splitting not only regenerators but also heaters and coolers on the engine performance. The novel CFDD model details the effect of the 3D flow and thermal fields on the dynamics of the mechanical mechanisms. This removes the limitation of the thermodynamic-dynamic models in which the thermodynamic models only focus on the one-dimensional flow and thermal fields. These two novel models are applied to the following problems: (i) The convergence of the 3D CFD solution for the rhombic-drive β-type Stirling engine (RDβTSE) can be speeded up using the proposed exchanging data procedure in which the low computation time of the enhanced thermodynamic model and the detailed 3D flow and thermal fields of the CFD model are combined; (ii) The limited information on behaviors of friction hinders us from understanding, optimizing, and designing Stirling engine. From the detailed description of the interaction between working gas and mechanical mechanism of the CFDD model for RDβTSE and given the experimental dependence of loading torque on cyclic-averaged engine speed, the dependence between damping coefficients and instantaneous engine speed can be numerically recovered using the steepest descent method; (iii) Based on the advantages of the enhanced thermodynamic model, such as the low computation time, balance between indicated power and net rate of heat transfer, and high resolution of temperature and pressure distributions and the rapid convergence of the variable-step simplified gradient method (VSCGM), both indicated power and thermal efficiency of the RDβTSE and the crank-drive thermal-lag engine (CDTLE) are optimized; (iv) The detailed description of the interaction between working gas and mechanical mechanism of the CFDD model is exploited to understand the dynamics of the CDTLE. Several operating modes are numerically observed. And, the influence of several parameters on shaft power, brake efficiency, and instantaneous engine speed is investigated; and (v) Phase analyses of the CDTLE are performed using the CFDD model and discrete Fourier transform. The contribution of the phase differences between pressure and volume to the work generation is mathematically pointed out. The phase difference between pressure and volume is associated with the different shapes of the P-V diagram and their physics. In addition, the phase differences between piston displacement and temperatures are used to clarify the thermal-lag phenomenon. Finally, the effect of loading torque, friction coefficient, and heating temperature on the phase difference between pressure and volume, and between piston displacement and temperatures of the first sine waves are studied.

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