A Three-Shock Theoretical Analysis of Steady Mach Reflections

• Main Authors: Chih-Hao Huang, 黃致豪
• Other Authors: Jong-Jian Liu
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/30077795144918675079

碩士 === 國立成功大學 === 工程科學系碩博士班 === 94 === ABSTRACT In this thesis, we apply the equations of motion of steady Mach reflections and the oblique shock theory to derive polynomial expressions of the forms of f(r,Mo,P1) of downstream sonic and strong/weak separating conditions of reflected shocks of perfect-gas steady Mach reflections. We then obtain polynomial expressions of the forms of f(r,M0) for the limiting Mach angle condition of the above two expressions. We then add boundaries delineated forward/backward facing reflected shock, Mechanical equilibrium, M2=1 and reflected shock strong/weak separating conditions on the (M0,q1) map of shih(2004). This is followed by systematically investigating multiply possible three shock theoretical solutions of steady Mach reflections in perfect triatomic gases. Pressure-deflection shock polar solutions are used to help illustrate different solution behaviors of these theoretical three-shock solutions. M0 is flow Mach no. upstream of incident shock, M1 is flow Mach no. downstream of incident shock, M2 is flow Mach no. downstream of reflected shock,q1 is flow deflection downstream of incident shock. We show that solution curves of M1=1 , WuestI, reflected shock forward-facing sonic, reflected shock forward-strong/weak separating, and reflected shock forward/backward facing conditions are not intersected. On the other formed, polynomial expressions of intersected point between solution curves of WuestII, reflected shock backward-facing sonic, reflected shock backward-strong/weak separating, Mechanical equilibrium are derived and computed results are marked on the (M0,q1) theoretical solution map of perfect triatomic gas steady Mach reflection.