本論文係延續盧(2008)論文工作，說明與討論應用三震波匯流場十次多項式方程式配合斜震波理論計算穩態馬赫反射 (SMR) 流場三震波理論多重解的方法。四個關於速度，密度與溫度的斜震波公式於本論文討論。 吾人應用三震波匯流場十次多項式方程計算所得馬赫莖上下游壓力比值配合斜震波公式與滑線兩側壓力與轉折角相容條件，輔以馬赫反射之機械平衡與前後分界判斷式可以得到 、 、 、 、 、 主要穩態馬赫反射流場(幾何)性質之多重解。具體言，我們由上述十次多項式方程計算得到馬赫莖壓力比值後代入斜震波波角與轉折角關係式可求得 與 。隨後應用SMR機械平衡條件多項式方程求解其 ，若該解大於給予SMR題目的 ，則所得到的 與 解需分別修改成180°- 及- 以成為Inverse MR 解; 否則所得到的 與 解就是正確的MR之 與 解。其次應用滑線的壓力相容條件配合上述斜震波波角與轉折角關係式及斜震波上/下游流場馬赫數關係式可求得 與 ，此時應用SMR前後分界條件多項式方程求解其 ，若該解大於給予SMR題目的 ，所得的 與 解就是後向反射震波MR正確的答案; 否則所得到該 與 解需分別修改成180°- 及- 以成為前向反射震波MR正確之 與 的解。

This thesis is an extension of Lu’s (2008) work。Predictions or calculations of multiply possible theoretical solutions of steady Mach reflections (MR) using the tenth degree polynomial equation of three-shock confluences combining with oblique shock calculations are discussed and analyzed. Four additional oblique shock reflections concerning velocity、density and temperate are reported in this work.

Multiply possible theoretical solutions of steady MR can be systematically analyzed by examining (pressure-deflection) shock polar solutions. In particularly, it is noteworthy that, as ’s systematically decrease from beyond forbidden ( < 1) to Wuest limit, forward/backward facing separating, then to incident Mach angle conditions, the intersected solutions (between incident and reflected shock polars) move from beneath to , forward-facing and then to backward-facing reflected shock solutions. They finally enter into the inverse MR regime before reaching the incident Mach angle condition. One first obtains the Mach stem pressure ratio from the SMR tenth degree polynomial equation, then wave and deflection oblique shock relations are used to calculate and , respectively. Theoretical SMR von Neumann condition polynomial equation is then applied to determine this . If the problem given < von Neumann’s , the obtained and are inverse MR solutions with being corrected to be 180°- and - , respectively. Otherwise, the obtained and are correct solutions of MR. The same wave and defection oblique shock relations, oblique shock relations of pressure ratio and up/down -stream flow Mach numbers relations together with slipstream pressure compatibility conditions are then used to calculate and . Finally, theoretical separating forward-/backward- facing reflected shock polynomial equation is applied to determine this critical . If the problem’s < separating forward-/backward-facing reflected shock solution’s , the obtained and are correct backward-facing reflected shock solutions. Otherwise, they are forward-facing reflected shock solutions with being 180°-calculated and being –calculated . may also be effectively obtained by using = - with being correctly calculated as described above.

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