近幾年來低溫差和聚焦型太陽能史特靈引擎的研究正蓬勃發展著，其中熱交換器的性能對於引擎整體效率顯得更為重要。過去在其他有關於史特靈引 擎熱交換器的數值研究中，大多學者選擇以直管和對稱的溫度邊界條件做為其模擬的條件，但是在本研究裡為了符合實際應用的情況，取而代之的，我們以平行板推疊式的多層結構和非對稱的溫度邊界條件做為研究討論的對象。
本研究主要目的為分析不同的影響參數下貝它型史特靈引擎其平行板推疊式熱交換器之流動和熱傳特性。因此我們在變截面的模擬區域中進行了二維層流、不可壓縮流和振盪式流動的數值分析。所考量的影響參數分別為動力雷諾數 (即無因次震盪頻率) 、堵塞比和無因次的加熱板長 (即熱交換器的幾何條件)。此外，在分析變截面流道時我們使用流函數渦量法以較高效率獲得具有高品質的渦和二次流。
從研究結果中我們可以得知在速度波峰和溫度波谷之間的相位差隨著動力雷諾數越高而增加但是最終會達到一個定值，所以不會發生"溢位"的問題。受振盪式流動和變截面流道影響之下其殘餘熱和渦流效應將會影響熱交換器的性能。接著使用摩擦係數和紐森數去分析動力雷諾數、堵塞比和無因次的加熱板長對於史特靈引擎熱交換器的影響。增加動力雷諾數將會提升熱交換器的熱傳性能。從堵塞比分析中可以觀察到時空平均摩擦係數會在堵塞比小於0.3時大幅度增加且時空平均紐森數在堵塞比小於0.4時驟升。因此當堵塞比降低時，其摩擦造成的能量損失會上升但熱傳率會增加，所以在熱交換器的設計中選擇一個合適的堵塞比是非常重要的且其選擇的值必須視設計時所擁的條件和情況而定。對於無因次的加熱板長的分析中發現摩擦係數與其本身的關聯性是微乎其微的，但是紐森數隨著無因次加熱板長的減少而增加。因此減少無因次的加熱板長將會增加熱傳性能但並不會造成摩擦的能量損失。
最後我們得到了一個時空平均紐森數的修正方程式，其考慮了四個相關的參數Reω, BR, Lw 和 As。因此未來在發展利用平行板推疊式熱交換器於貝它型史特靈引擎之性能技術，其將對於熱交換器的設計有所參考和幫助。

In recent years, the study of low temperature difference and focus type solar Stirling engine are booming. The heat exchanger performance becomes more important to the engine overall efficiency. In previous numerical investigations of Stirling engine heat exchanger, the straight pipe and symmetric temperature boundary conditions are often chosen for simulation, but in this research we discuss the multi-layer structure of parallel plate stack and asymmetric temperature boundary conditions in order to obey the practical situation.
This research is mainly aimed at the analysis of the flow and heat transfer characteristics of parallel plate stack heat exchanger in beta type Stirling engine for different parameters. The numerical analysis is carried out for 2-D laminar incompressible oscillating flow in a variable cross-sectional simulation domain and three parameters, kinetic Reynolds number Reω, blockage ratio BR and dimensionless heated plate length Lw (i.e. geometry conditions of heat exchanger) are examined. In addition, a Stream-Function-Vorticity Formulation is used to efficiently obtain a high quality vortex and secondary flow in the variable cross-section analysis.
The results show that the phase difference between the wave crest of horizontal velocity and the wave trough of temperature increases with the increase of kinetic Reynolds number, but it will eventually reach a certain value. Therefore, the problem of overflow will not occur. The conditions of oscillating flow and variable cross-section cause the residual heat and vortex effect which will affect the heat transfer performance of heat exchanger. The friction coefficient and Nusselt number varied with three different parameters Reω, BR and Lw are presented to analyze their effects on Stirling engine heat exchanger. The increase of kinetic Reynolds number Reω will improve the thermal performance. For the parameter of blockage ratio, the friction coefficient and Nusselt number both apparently increase for BR<0.3 and BR<0.4 respectively. The decrease of blockage ratio will increase both the energy loss of friction and the heat transfer rate. Therefore, in the design of Stirling engine choosing an appropriate blockage ratio is very important and this should depend on the conditions and situations of the design. The dimensionless heated plate length Lw has very small effect on friction coefficient but the Nusselt number increases with the decrease of the Lw. Therefore, the decrease of the Lw will enhance the thermal performance and will not bring the energy loss of friction.
Finally, the correlation equation of the space-time averaged Nusselt number among four different parameters Reω, BR, Lw and As is obtained. It will be helpful to the design of the parallel plate stack heat exchanger in beta type Stirling engine.

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