本文使用橢圓形式的 RANS 方程式來模擬平板混合紊流場從紊流狀態發展到自我保持區域的過程，並使用非線性渦流黏滯係數模式來取代 Boussinesq 假說計算其中的雷諾應力。
所以本文將根據李權庭(2004)以熱線測速儀量測平板混合紊流場所得到的實驗數據，使用(1) standard k-ε model、(2) Abe (2003) 的模式、(3) GS (1993) 及(4) Rahman (2006) 的顯式代數雷諾應力模式來模擬包括(1) r=0.62 以及(2) r=0.39 的流場，並將這些結果與實驗數據作比較。
模擬結果顯示使用非線性渦流黏滯係數模式可以得到比 Boussinesq 假說更為準確的雷諾應力，但所模擬到的雷諾應力及紊流動能其變化幅度仍不及實驗值。

An elliptic set of Reynolds-averaged governing equations are used for the simulation of flow from the developing to self-preserved regions of the turbulent planar mixing layer. Two cases with r=0.62 and 0.39 which were experimentally investigated by Li (2004) are numerically studied.
From RANS turbulence models, including the standard k-ε model which is under the Boussinesq hypothesis, the explicit algebraic stress model of GS (1993), the nonlinear eddy-viscosity model of Abe (2003), and the low- Reynolds-number explicit algebraic stress model of Rahman (2006), are tested and their predictions of flow properties are compared with the measurement data of Li (2004) made by the hot-wire anemometry.
The comparison results show that the models associated with nonlinear eddy-viscosity formulation perform better on the predictions of the Reynolds stresses than the model associated with the Boussinesq hypothesis (i.e., standard k-ε model). Nevertheless, there still exist remarkable underpredicti- ons of the Reynolds stresses and the turbulent kinetic energy for all tested turbulence models in comparison with the measured data of Li (2004).

誌謝 I
摘要 II
ABSTRACT III
目錄 IV
表目錄 VI
圖目錄 VII
符號說明 VIII
第一章�緒論 1
1.1前言 1
1.2文獻回顧 2
1.2.1 RANS 方程式 3
1.2.2 Boussinesq 假說 3
1.2.3代數模式 4
1.2.4單方程式模式 4
1.2.5雙方程式模式 4
1.2.6非線性模式 5
1.2.7顯式代數雷諾應力模式(ERASM) 5
1.2.8以 EARSM 為構成方程式的雙方程式模式 6
1.3研究目的 7
第二章�物理問題與數學模式 8
2.1物理問題簡介 8
2.2數學模式 9
2.2.1 standard k-ε model 10
2.2.2 GS EARSM 10
2.2.3 Abe 模式 13
2.2.4 Rahman EARSM 14
2.2.5消除低雷諾數效應 15
第三章 數值方法 17
3.1演算法 17
3.2計算區域及邊界條件 17
3.3入口條件測試 18
3.4網格系統和格點測試 19
第四章 結果與討論 20
4.1模式驗證 20
4.2入口條件 21
4.3雷諾應力及紊流動能 21
4.4流場速度 23
4.5混合長度 23
4.5三維效應的影響 24
第五章 結論與未來工作 25
5.1結論 25
5.2未來工作 25
參考文獻 26
附錄 FLUENT 外加紊流模式的步驟 28

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