本研究主要是以數值模擬對震波通過背向式階梯之流場進行分析，探討在不同階梯高度，不同壁面溫度及不同震波馬赫數之下，震波對壁面熱傳效應之影響。統御方程式是使用納維爾-史脫克方程式(Navier-Stokes equation)，並於數值方法上，對黏滯項及對流項之空間差分分別採用四階精度的中央差分法及五階精度的Weighted Essentially Non-Oscillatory Scheme(WENO)，而在時間積分上採用顯式的四階Runge-Kutta scheme，進行二維平面流場之分析。 計算結果發現對於流場之結構方面，在背向式階梯的角落部份由於剪切層的效應會產生渦卷，當反射震波與渦卷產生交互做用會造成複雜的流場結構。於階梯底部壁面加入溫度變化雖然對震波結構影響較小，但影響底部壁面紐塞爾數。在相同馬赫數、階梯高度下，壁面絕熱與壁面加至熱 時，其流場結構並無太大之改變。但對於階梯高度之改變，會對紐塞爾數造成影響，當階梯高度越高，其紐塞爾數會隨之增加。對瑞理數的影響參數是震波與階梯底部壁面之間的溫度差。

Numerical simulations of shock wave passing through a two-dimensional backward-facing step channel are performed to investigate the effects of shock wave Mach number, channel step height, and channel bottom wall temperature variation on the flowfield structure and heat transfer. The compressible Navier-Stokes equations governing the flowfield in planar coordinates are discretized using the fifth order accuracy Weighted Essentially Non-Oscillatory (WENO) and the fourth order accuracy central difference schemes for the convective and diffusive terms, respectively. The governing equations are integrated with the fourth order accuracy Runge-Kutta scheme. Computed results show that the interactions of the step corner induced vortex with the reflected shock waves from the walls form complicated flow structures. The effects of shock wave Mach number, channel step height, and channel bottom wall temperature variation on the heat transfer are characterized by the nondimensional parameter, Nusselt number. The variation of wall temperature is represented by Rayleigh number. For the fixed shock wave Mach number condition, the calculated local Nusselt number increases with increasing the step height and Rayleigh number. For the fixed Rayleigh number condition, the calculated Nusselt number decreases with increasing Mach number but increases with increasing step height.

中文摘要………………………………………………………………………i英文摘要………………………………………………………………………ii誌 謝………………………………………………………………………iii 目 錄………………………………………………………………………iv 圖 目 錄………………………………………………………………………vi 表 目 錄………………………………………………………………………vii 符號說明………………………………………………………………………viii 第一章 緒論………………………………………………………………………1 1-1 前言………………………………………………………………………1 1-2 研究動機…………………………………………………………………2 1-3 文獻回顧…………………………………………………………………2 第二章 物理問題…………………………………………………………………7 2-1 物理模式…………………………………………………………………7 2-2 基本假設…………………………………………………………………7 第三章 數值方法…………………………………………………………………9 3-1 統御方程式 …………………………………………………………9 3-2 時間積分…………………………………………………………………12 3-3 空間差分…………………………………………………………………12 3-4 起始條件與邊界條件……………………………………………………18 3-4.1 起始條件…………………………………………………………………18 3-4.2 邊界條件…………………………………………………………………18 3-5 局部平均紐賽爾數及紐賽爾數……………………………………………20 3-6 瑞理數………………………………………………………………………20 第四章 結果與討論 ……………………………………………………………21 4-1 程式驗證……………………………………………………………………21 4-2 格點測試……………………………………………………………………22 4-3 流場結構分析………………………………………………………………23 4-4 階梯高度對紐塞爾數(Nusselt number)之影響………………………25 4-5 馬赫數對紐塞爾數之影響…………………………………………………28 第五章 結論與未來展望……………………………………………………………30 5-1 結論……………………………………………………………………30 5-2 未來展望…………………………………………………………………31 參考文獻…………………………………………………………………………………32

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