本研究以三級Beta型史特靈致冷機為研究對象，結合實驗、CFD模擬及多目標最佳化，探討再生器長度配置對致冷性能之影響。實驗結果顯示，第三級再生器採用40目不鏽鋼網時，因熱交換面積不足而產生熱穿透現象；改用400目不鏽鋼網後雖可降低致冷溫度，但於高填充壓力與高轉速下仍受流動阻力及壓力降限制。
基於上述結果，本研究以400目再生器配置作為基準組，建立二維軸對稱擬三維（Quasi-3D）暫態數值模型，並以各階再生器長度為設計變數，結合代理模型與NSGA-II進行多目標最佳化，以第三級致冷頭溫度及指示功率為目標。結果顯示，縮減再生器長度可降低死區體積與流動阻力，提升低溫性能。為提高最佳化可靠度，本研究使用加點更新策略，使代理模型誤差收斂至5%以內。
最後，針對最佳組（Configuration 3）製作並實驗驗證。在2 bar、800 rpm下，第三級致冷頭最低溫度由基準組的176.53 K降至144.05 K，改善幅度達18.4%，驗證最佳化設計可提升三級Beta型史特靈致冷機之低溫性能。此外，將條件提高至4 bar、800 rpm後，第三級致冷頭溫度可進一步降至118.94 K，顯示最佳化再生器長度配置具有更低的致冷溫度。

This study investigates a three-stage Beta-type Stirling cooler through experiments, CFD simulation, and multi-objective optimization, focusing on the effect of regenerator length on cooling performance. Experiments showed that a 40-mesh stainless steel screen in the third-stage regenerator caused heat penetration due to insufficient heat transfer area. A 400-mesh screen lowered the temperature, but flow resistance and pressure drop still limited performance at high charging pressure and speed.
Based on this, the 400-mesh configuration was used as the baseline for a two-dimensional axisymmetric quasi-three-dimensional transient CFD model. The regenerator lengths of each stage were selected as design variables, and a surrogate model with NSGA-II was used to optimize the third-stage cold head temperature and indicated power. The results showed that shorter regenerators reduced dead volume and flow resistance, improving low-temperature performance. Infill sampling was used to reduce the surrogate-model prediction error to within 5%.
Finally, the optimal design, Configuration 3, was fabricated and experimentally evaluated. At 2 bar and 800 rpm, the minimum third-stage cold-head temperature decreased from 176.53 K to 144.05 K, corresponding to a reduction of 32.48 K (18.4%). At 4 bar and 800 rpm, the third-stage cold-head temperature was further reduced to 118.94 K, demonstrating the improved low-temperature performance of the optimized regenerator-length configuration.

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