||A study on turbulence models for accurate prediction in compressor flows
||Department of Aeronautics & Astronautics
現今科技的進步，使數值方法越趨成熟，讓數值方法儼然成為設計氣渦輪機的主流工具，因此如何選擇合適的數值方法便成為一門重要的學問。故本文主要探討三種紊流模型k-ω SST model、k-ε low-Re model與k-ε v2f model，在二維DCA、CD葉片與三維葉片NASA stage 37的預測準確性。藉此判斷適合用在此類流場之紊流模型。根據二維葉片之結果，在設計與非設計條件下，v2f model的預測皆相當精準，且分離氣泡、層紊流轉換與分離現象等許多複雜流動，都能夠完整地模擬到，而low-Re model是最不準確的。在stage 37的研究當中，SST model和v2f model具備較符合實驗的計算結果，但兩者結果十分相似，需仰賴更多結果方能決定兩者之優劣。值得注意的是，缺乏輪轂洩漏流對徑向分佈預測的影響，造成壓力與溫度預測不足。另外在壓縮比與絕熱效率性能圖中，目前SST model多能預測出相似的性能曲線，而最大的壓縮比誤差約為5.8%，因此準確度還是相當良好。
Nowadays, the numerical simulation is a mature technology due to the advancement of science and technology. Numerical analysis has also become the mainstream tool for designing gas turbines. However, how to choose an appropriate numerical method becomes a very important issue. In this thesis, the performance of three different turbulence models, namely SST, low-Re, and v2f models, in some 2D and 3D compressor-blade flows has been investigated. These compressor-blade flows are: 2D DCA and CD blades, and a 3D NASA stage 37. The results of DCA and CD blades indicate that v2f models can return more accurate prediction at both design and off-design conditions. In particular, many complicated flows, such as separation bubbles, transition and separation, can be captured. In 3D NASA stage 37, the prediction by the SST and v2f model is much better than low-Re model, and their results are very similar. However, without considering hub leakage flow, magnitudes of pressure and temperature are overestimated. Other comparisons like pressure ratio and adiabatic efficiency characteristic map, SST model can predict reasonably well, with maximum error being 5.8%.
Extended Abstract II
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 3
1.3 研究動機與目的 7
1.4 論文架構 8
第二章 數值方法與數學模型 9
2.1 數值方法 9
2.2 統御方程式 10
2.3 紊流模型 12
2.3.1 k-ω SST model 13
2.3.2 k-ε low-Re model17
2.3.3 k-ε v2f model 19
第三章 二維葉片分析 23
3.1 二維葉片 23
3.2 DCA葉片 24
3.2.1 網格與邊界條件 25
3.2.2 數據計算 27
3.3 CD葉片 28
3.3.1 網格與邊界條件 29
3.3.2 數據計算 32
3.4 結果與討論 32
3.4.1 DCA葉片 32
3.4.2 CD葉片 36
第四章 三維葉片分析 71
4.1 三維葉片 71
4.2 NASA stage 37 72
4.2.1 網格與邊界條件 73
4.2.2 數據計算 77
4.3 網格測試 80
4.4 結果與討論 84
4.4.1 徑向分佈 84
4.4.2 壓縮機性能 88
第五章 結論與未來展望 102
5.1 結論 102
5.2 未來展望 104
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