本文針對β型菱形驅動史特靈引擎發展相關的熱力及動力數值模擬，並藉由這些相關模式進行各部位零件與不同工作條件的模擬，目的在找出引擎的最佳的功輸出及熱效率。首先為熱力學模式的分析，將引擎分為三個控制容積包括環狀再生通道、壓縮室、以及膨脹室。接著由理想氣體定律和熱力學第二定律求得控制容積內的壓力、溫度、以及熱傳量的變化。進而算出引擎的輸出功及熱效率。在推導出熱力學模式之後，便可以對引擎的重要的幾何參數尺寸進行研究。此外，更進一步推導菱形機構運動的關係式，利用先前在熱力學模式所算出的膨脹室及壓縮室內氣體的壓力，如將其加以轉換成作用在活塞及移氣器上的力，便可以輸入菱形機構運動的關係式裡，得到作用在引擎的力矩。引擎力矩可分成摩擦力力矩、氣體作用力矩、慣性力矩、以及負載力矩。引擎的暫態運作情況便可知悉。再藉由一連串的參數分析，可以得到引擎在不同零件尺寸以及運轉條件下的運作狀況。

This paper aims at finding the optimum performance of the beta-type Stirling engine with rhombic-drive mechanism under different operational and geometrical constraints through the coupling of the thermodynamic and the dynamic model. First, a thermodynamic model has been proposed. By taking into account of the non-isothermal effects, the effectiveness of the regenerative channel, and the thermal resistance of the heating head, the energy equations for the control volumes in the expansion chamber, the compression chamber, and the regenerative channel can be derived and solved. Results are presented to show the essential information during the operation of the engine, including the periodic variation of the pressure, temperature, and heat transfer inside the chambers. Then the power output and thermal efficiency of the engine are calculated. Several key factors that affect the engine performance were discussed detail through an extensive parameter study based on the thermodynamic model. The detailed gas pressure profile inside the chambers was obtained during the thermodynamic model simulation. The gas pressure was then translated to the force that exerted on the piston and the displacer and was inputted to the derived dynamic model of the rhombic-drive mechanism. In this manner, the transient rotational speed of the engine is calculated through the equation of conservation of angular momentum before the steady-state regime is reached. The torque of the engine can be calculated as long as the gas force torque, the inertia torque, the friction torque, and the load torque are verified. The parameters that affect the transient state of the engine are studied. A conclusion was drawn for improving the performance of the engine under different geometrical and operating conditions.

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