臺灣博碩士論文加值系統

有關低馬赫數流方面，許多實驗與理論報告已經提出，但在理論計算方面仍然具有研究之價值。依照Rossow壓力更正概念，本文建立一數值求解步驟來探討低馬赫數流之行為。首先在流場區域建立非結構四面體/稜鏡型網格，然後利用上述數值法求解三維尤拉/拿維-史脫克方程式。此數值方法包含四步Runge-Kutta時間積分法、以馬赫數表示之 Roe’s通量差分法及求解 Rossow’s 壓力更正方程式之含/不含鬆弛因子之Jacobi、Gauss-Seidel、Modified Gauss-Seidel疊代法。在本計算中，分別進行單核心運算及雙核心與四核心之平行運算等。為評估此數值方法，首先探討球體與圓型截面之收斂-發散噴嘴之非黏滯流。在不同馬赫數下，將計算所得之球表面壓力係數及速度分佈與勢流理論解比較並研究其收斂行為。至於噴嘴流，沿噴嘴中心線之壓力和速度分佈與一維等熵數值解比較。其次進行圓管黏滯流計算，將結果與解析解比較以確定本數值方法在求解層流時之準確性。
關鍵字: 非結構四面體/稜鏡型網格、壓力更正方程式、低馬赫數流、
平行運算

For the low-mach-number flows, a lot of experimental and theoretical results have been presented, but the theoretical computation is still worthwhile to study. According to the Rossow’s pressure correction concept, a numerical solution proceduce is created to investigate the low-mach-number flow behavior in this paper. First the unstructured tetrahedral and prismatic meshes are generated in the flow domain. Then the above-mentioned numerical approach is used to solve the three-dimensional Euler/Navier-Stokes equations. This approach includes four-step Runge-kutta time-integration scheme, revised form of Roe’s flux-difference-splitting method in terms of Mach number and Jacobi / Gauss-Seidel / Modified Gauss-Seidel interation methods with/without relaxation factor for solving the Rossow’s pressure correction equation. In the present calculations, the operations by using one core and duo cores/quad cores with parallel computations are processed. To evaluate this numerical method, the inviscid flow around sphere and passing through the converging-diverging nozzle with circular cross-section are investigated first. For the different Mach numbers, the computed pressure coefficient and velocity distributions on the surface of sphere are compared with those from the potential flow theory. Also, the history of convergence and computing time are studied. About the nozzle flow, the pressure and velocity distributions along the nozzle axis are presented. Comparing with those from the one-dimensional isentropic flow the present method is evaluated. Secondly, the computation of viscous pipe flow is processed. From the comparison betwteen the resent results and the analytical solution, the accuracy of current numercail approach for solving the laminar flow is confirmed.

Keywords: unstructured tetrahedral/prismatic meshes, pressure correction equation, low-mach-number flow, parallel computation

中文摘要................................................I
英文摘要...............................................III
誌謝.....................................................V
目錄....................................................VI
圖目錄..................................................IX
符號說明................................................XII
第一章 緒論..............................................1
1-1 前言..............................................1
1-2 文獻回顧..........................................2
1-3 研究內容..........................................3
第二章 統御方程式與數值方法..............................5
2-1 統御方程式........................................5
2-2 有限體積上風法....................................8
2-2-1 無黏滯性通量.................................8
2-2-2 黏滯性通量..................................12
2-3 壓力修正方程式...................................13
2-3-1 計算 各種數值方法...........................15
2-4 時間積分法.......................................21
2-4-1 時間步階....................................21
2-4-2 隱式殘值平滑法..............................22
2-5 邊界條件.........................................23
2-5-1 經過球體之外流場............................23
2-5-2 收斂發散噴嘴之內流場........................24
2-5-3 圓管之內流場................................24
2-5-4 固體面之邊界條件............................24
2-6 平行運算..........................................25
第三章 網格的建立.......................................26
3-1 建立球體與噴嘴流場之非結構四面體網格...........27
3-2 建立圓管內流場之非結構四面體與稜鏡型網格.......27
第四章 結果與討論.......................................29
4-1 具馬赫數項形式與原始形式之Roe通量差分法的探討..30
4-2 隱式殘值平滑法之探討...........................30
4-3 各種數值法之探討...............................30
4-4 收歛發散噴嘴內部之低馬赫數無黏性流.............34
4-5 圓管內部之低馬赫數黏性流.......................35
第五章 結論與建議.......................................36
5-1結論............................................36
5-2 建議...........................................37
參考文獻................................................38
表......................................................41
圖......................................................44
自述........................................................82

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