本論文主要的目的在於利用反算法中之拉凡格式法(Levenberg-Marquardt Method)，以提升風量為目標，對離心式風扇的幾何形狀做最佳化設計，並選用套裝數值模擬軟體CFD-RC做為計算及分析的工具。離心式風扇中幾何形狀相當複雜，為了有效率的提高風量，透過靈敏性分析，篩選出對風量影響較大的設計參數，並針對這些參數做最佳化的設計。從結果顯示，利用拉凡格式法反算得到之最佳化風扇，在NACA扇葉翼形、扇葉入風角度以及蝸殼入風口半徑都有明顯改變，為了檢驗反算結果的正確性，利用統計學的觀點，假設一獨立之常變異誤差(Constant-variance Errors)來發展出預測參數99%之可信度邊界(Confidence Bounds)，由統計分析的結果顯示，本研究所預測之參數，皆落在於此邊界中；除此之外，透過流場分析比較可以發現，最佳化後的風扇能夠有效改善扇葉及蝸殼出風口的逆流現象，以及提升蝸殼流道的出風速度，風量也較初始風扇提升了約13.6%。
最後，為了驗證數值模擬的正確性，分別將初始參考風扇與最佳化後的風扇利用CNC做出實體，選擇符合AMCA-210-85規範之入口式風洞進行性能量測，並在全無響室中觀察噪音表現。由實驗的結果可以發現，最佳化後的風扇除了風量提升外並可有效降低噪音。

The Objective of this thesis is to utilize the technique of the Levenberg-Marquardt Method (LMM) together with the commercial package CFD-ACE+ in an inverse design problem to estimate the optimal shape of a centrifugal fan based on the desired volume flow rate of air.
The geometry of a centrifugal fan shape is generated using numerous design variables, which enables the completed shape of the fan to be constructed completely. The sensitivity analysis for the design variables is then performed to select only a few effective parameters as our final design variables.
Results show that the shape of NACA airfoil, blade inlet angle (β) and radius of inlet flow (Ri) are sensitive to the design and therefore they are chosen as our design variables. Statistical analysis is also considered to obtain the 99 % confidence bounds for the estimated design variables. The comparisons of the flow patterns between fan blades in the impeller for original and optimal fans indicated that the reverse flow in original fan is indeed severer than that in optimal fan and therefore the airflow rate in optimal fan is thus increased. Besides, the airflow rate can be increased by 13.6 %.
Finally the prototypes of the original and optimized centrifugal fans are fabricated and the fan performance tests are conducted on the basis of the AMCA-210-85 standard to verify the validity of this work. Also, for the noise of fans, the experimental measurement has been carried out in a hemi-anechoic chamber. Experiment results show that by utilizing the fabricated optimal fan, not only the airflow rate can be increased but also the noise of fan can be reduced, as a result, the performance of optimal fan is greatly improved.

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