本研究使用套裝軟體 CFD-ACE+及應用拉凡格式法(Levenberg-Marquardt Method)搭配，探討二維反算問題於可壓縮流場情況下，進行渦輪機葉片冷卻通道形狀最佳化設計之研究。
然而為了節省整體模擬時間、降低往後相關研究之實驗成本，及在忽略冷卻通道中的冷卻液型態及冷卻液流速下，整體模型使用二維型態進行模擬。
本文主要探討二維原型NASA C3X葉片中的冷卻通道在不同配置下的溫度變化，在不增加葉片面積及固定冷卻通道之形狀參數的情況下做最佳化設計，分別探討了冷卻通道在不同的初始條件下最佳化後的溫度變化情形，分別以原始模型一及原始模型二表示更可細分成四個範例，然而吾人以設計參數10個與30個進行探討，設計參數為10個時，設定當其圓形冷卻通道位置不改變，對其孔洞大小作最佳化設計，但對其圓形冷卻通道之圓孔有做極大值與極小值之邊界限制，以避免葉片之破裂，而設計參數為30個時，設定當其圓形冷卻通道位置X軸及Y軸位置皆會改變，並對其孔洞大小作最佳化設計，並也對其圓形冷卻通道之圓孔做極大值與極小值之邊界限制，以避免葉片之破裂，其中範例一及範例二使用原始模型一進行最佳化之設計，範例一為進行設計參數10個之最佳化設計，而範例二為進行設計參數30個之最佳化設計，而範例三及範例四使用原始模型二進行最佳化之設計，其中範例三為進行設計參數10個之最佳化設計，而範例四為進行設計參數30個之最佳化設計。
其模擬結果顯示，最佳化之結果皆落在邊界限制中，除此之外在不破壞葉片結構之前提下，最佳化後的葉片平均溫度皆有明顯之下降。

A two-dimensional inverse design problem is examined in this thesis using a general purpose commercial code (CFD-ACE+) and the Levenberg-Marquardt Method (LMM) to estimate the optimal shape and position of cooling passage for turbine guide vane under severe environments. The aim is to achieve a design that minimizes the average temperature of vans and ensure the structure strength. Considering the massive computational cost of 3-D models, numerical optimization process is performed based on 2-D cross-sectional models.

Present study consists of four cases. Case 1 are optimized base on original design 1 while the shape of each cooling passage are considered as design variables. Case 2 are optimized base on original design 1 while the shape and position of each cooling passage are considered as design variables. Case 3 are optimized base on original design 2 while the shape of each cooling passages are considered as design variables. Case 4 are optimized base on original design 2 while the shape and position of each cooling passage are considered as design variables. Fixed vane area is considered as the constraint in each of the case. The result shows that the average temperature of vane has great decreasing by the present optimization algorithm.

參考文獻
[1] 西安交通大學渦輪機教研室編1975,燃氣輪機裝置
[2] Bingxu , W.,Weihong , Z.,Gongnan , X.,Yingjie, X,and Manyu X.,2015,“Multiconfiguration Shape Optimization of Internal Cooling Systems of a Turbine Guide Vane Based on Thermomechanical and Conjugate Heat Transfer Analysis,”Journal of Heat Transfer, NO. 061004-7
[3] Tetsuya ,Y., Daisuke ,S., Kazuhiro ,N.,2011,“Conjugate Heat Transfer Simulation of Cooled Turbine Blades Using Unstructured-Mesh CFD Solver,”American Institute of Aeronautics and Astronautics ,NO. 980-8579.
[4] Hylton, L. D., Milhec, M. S., and Turner, E. R., 1983, “Analytical 　　　　 and Experimental Evaluation of the Heat Transfer Distribution Over the Surface of Turbine Vanes,” NASA Report No. CR-168015.
[5] Nowak, G., and Nowak, I., 2012, “Shape Design of Internal Cooling Passages Within a Turbine Blade,”.
[6] Chmielniak, T., Wroblewski, W., Nowak, G., and Wecel, D., 2003,
“Coupled Analysis of Cooled Gas Turbine Blades,” ASME Paper No. GT2003-38657.
[7] Takahashi, T., Watanabe, K., and Sakai, T., 2005, “Conjugate Heat Transfer Analysis of a Rotor Blade With Rib-Roughened Internal Cooling Passages,”ASME Paper No. GT2005-68227.
[8] Bunker, R. S., 2006, “Axial Turbine Blade Tips: Function, Design, and Durability,”.
[9] Facchini, B., Magi, A., and Greco, A. S. D., 2004, “Conjugate Heat Transfer Simulation of a Radially Cooled Gas Turbine Vane,” ASME Paper No.GT2004-54213.
[10] Nowak, G., and Wroblewski, W., 2011, “Optimization of Blade Cooling System With Use of Conjugate Heat Transfer Approach” .
[11] Mangani, L., Cerutti, M., Maritano, M., and Spel, M., 2010, “Conjugate Heat Transfer Analysis of NASA C3X Film Cooled Vane With an Object-Oriented CFD Code,” ASME Paper No. GT2010-23458.
[12] Kim, K. Y., and Lee, Y. M., 2007, “Design Optimization of Internal Cooling Passage With V-Shaped Ribs” .
[13] Dennis, B., Egorov, I., Dulicravich, G., and Yoshimura, S., 2003, “Optimization of a Large Number Coolant Passages Located Close to the Surface of a Turbine Blade,” ASME Paper No. GT2003-38051.
[14] Nowak, G., and Wroblewski, W., 2007, “Thermo-Mechanical Optimization of Cooled Turbine Vane,” ASME Paper No. GT2007-28196.
[15] B. E. Launder, and D. B. Spalding, 1974, “The numerical computation of turbulent flows”, Computer Methods in Applied Mechanics and Engineering.
[16] D. B. Spalding, B. E. Launder, A. P. Morse and G. Maples, 1974 ,“Combustion of hydrogen-air jets in local chemical equilibrium(a guide to the CHARNAL computer program)”, NASA Contractor Reports.
[17] D. W. Marquardt, 1963,”An Algorithm for Least-Squares Estimation of Nonlinear Parameters”, Journal of the Society for Industrial and Applied Mathematics.