本文首先討論Olim & Dewey (1992)與Sandeman (2000)提出弱擬似穩態馬赫反射流場三震波理論的修正理論，吾人於許多Olim & Dewey (1992)實驗條件下，應用其修正理論計算得到Sin(phi2)值(phi2 意指反射震波之波角)都是大於1，所以phi2值不存在，亦即其論文中許多之Wir 與qw+X 曲線圖中數據是錯誤的；Sandeman (2000)提出圖解法求取三震波點路徑角(X)，吾人分別應用Olim & Dewey (1992)實驗數據X角及Liu (1996)擬似穩態馬赫反射流場入射震波下游流場聲波公式計算X 角，三者比較發現當楔型斜平面角較小時，Sandeman方法得到X角比上述聲波理論得到之X角更遠離實驗量測之 角，當楔型斜平面角較大時，Sandeman方法得到 角與實驗量測X角差異很大。之後應用牛頓數值方法求解局部及整體擬似穩態馬赫反射流場三震波理論十四個變數之非線性十四聯立方程式，文中說明牛頓數值方法如何解此聯立方程組，並對各種不同類型之局部擬似穩態馬赫反射震波極圖解(全部共六種類型)有系統地每2度變化phi2及phi3猜值(包含全部後向反射震波解(自phi2後向馬赫波角至phi2=90度)與全部前向反射震波解(自phi2=90度 至phi2前向馬赫波角))，配合擬似穩態馬赫反射十階多項式理論，分析所得到之牛頓數值解，初步成功地得到 phi2及phi3猜值於馬赫反射(pressure-deflection)震波極圖解平面上的切線法，來描述 及 猜值對牛頓數值方法求解局部擬似穩態馬赫反射三震波理論解之影響。此切線法之結論為：於phi2與phi3猜值位置描繪出此二切線，其相交點位置將會鄰近於上述十階多項式理論所得到震波極圖解上交點解，而後將該phi2及phi3猜值代入牛頓數值方法計算所得到之結果，半數以上亦為相當接近上述該鄰近交點之近似解(須排除不適當phi2及phi3猜值所得到無解之狀況)，一般而言，若phi2及phi3猜值鄰近phi2及phi3理論解，則牛頓數值方法都能準確地得到該擬似穩態馬赫反射流場理論震波解。吾人之後改變分離流邊界收斂條件，觀察其對局部擬似穩態馬赫反射流場多重解之影響(共七種類型，三十二個實驗例子)。我們發現入射震波極與反射震波極非常接近且增大分離流收斂條件得到之解，多數是鄰近所選擇 及 猜值而偏離十階多項式理論所得到之解，也就是所選 猜值於何處則所得到之 值答案亦將出現在所猜之 猜值附近。實驗方面，應用陰影法及紋影法兩種型態之拍攝方法，進行流場可視化實驗，同時依據可視化流場之對比度公式可以了解影響甚鉅之刀片遮光高度，隨後作一系列之變化遮光比例實驗，觀察遮光條件是否會影響對比度。吾人發現當遮光比較低時，擬似穩態馬赫反射流場之反射波於照片中較不清楚，且反射波為白色，當遮光比較高時，照片中之反射波較為清楚，且反射波為黑色。最後將所作之 及 系列遮光比之實驗照片繪其馬赫反射流場入射震波下游流場之聲波圖與量測此流場波型結構，並將實驗結果分別應用局部三震波理論、整體三震波理論及上述之聲波理論分析與討論實驗結果。

Works of Olim & Dewey (1992) and Sandeman (2000), which proposing revised three-shock theories of weak pseudo-steady Mach reflections (MR), are first discussed. Using Olim & Dewey (1992) experiments and their revised theory for calculating reflected shock wave angles (phi2), we obtain, in many cases, values of larger than 1! Therefore, many datum in their graphs (Olim & Dewey (1992)) of Wir vs. qw+X are incorrect; Sandeman (2000) proposed a graphical method for calculating the triple-point trajectory angle (X). We again use experiments along with Liu (1996) for calculating X angles. It is found that, when reflecting angles of pseudo-steady MR are small, predictions obtained from Sandeman (2000) deviate more from Olim & Dewey’s (1992) experiments than those obtained from Liu’s (1996) sound structure theory downstream of pseudo-steady MR. On the other hand , when reflecting angles of pseudo-steady MR are not small, predictions obtained from Sandeman (2000) compare badly with the experiments. The focus of this thesis is to study numerical solutions of 14 nonlinear algebraic conservation equations, describe 14 flow valuables downstream of incident, reflected, and Mach shocks of perfect-gas pseudo-steady MR using the Newton method. Rationality about algorithms used in successfully computing correct solutions of pseudo-steady MR is explained. In general, with phi2 and phi3 values properly chosen, numerical solutions of pseudo-steady MR using the Newton method agree well with corresponding theoretical solutions obtained from the tenth degree polynomial equation of three-shock confluences Henderson (1964) and Liu (2003). Effects of varying guessed phi2 (reflected shock wave angle) and phi3 (Mach stem wave angle) on computed Newton numerical solutions of local and global three-shock theoretical solutions of pseudo-steady MR are systematically analyzed, with respect to six different types of (pressure-deflection) theoretical solutions of them. The range of guessed phi2 of these Newton numerical works (for each of these six different types) start from backward (forward)-facing Mach angle of phi2 to phi2=90 degree for all reflected backward (forward)-facing reflected shock solutions. They are then carried out for every two degrees of guessed phi2 for a given guessed phi3. It is found that a useful graphical “tangent” method on the (pressure-deflection) plane can successfully describe the effects of varying guessed phi2 and phi3 on these computed Newton numerical solutions. The results are that intersection points between phi2 and phi3 tangents are close to computed Newton numerical solutions of pseudo-steady MR using these guessed values of phi2 and phi3 for more than half of these obtained solutions. The effect of varying converging conditions of slipstream compatibility (pressure and deflection) conditions is subsequently studied for seven different theoretical pseudo-steady MR solution patterns using 32 (existing) experimental cases. It is found that, when portions of computed incident and reflected shock polars are indistinguishable, pseudo-steady MR phi2 (for fixed phi3 conditions) solutions obtained from the Newton’s method are almost always close to guessed phi2 values as values of converging conditions of slipstream compatibility requirements become large. Experimentally, shadowgraph and schlieren methods are applied to obtain flow visualization photographs of pseudo-steady MR experiments. A series of light-shielding tests are performed to examine this effect of knife-edge shielding on image contrast of schlieren photographs. It is found that obtained images (lighter) of reflected waves are more sensitive to lowering knife-edge shielding percentage than those images (darker) of incident and Mach shock waves. Finally, sound wave structures downstream of incident shock of these flow visualization photographs of Ms=1.36 ,qw=8 degree are drawn along with their comparisons with computed local and global three-shock theoretical pseudo-steady MR solutions.

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