Wave Structure And Transition Of Mach Reflection In Two-dimensional Steady Supersonic Flows

Shock wave reflection is an important phenomenon in supersonic and hypersonic flow field, since it significantly impacts the aerodynamic performance. There are two basic types of shock reflection, regular reflection (RR) and Mach reflection (MR), the conditions and the basic flow structures of which have been studied thoroughly. However, there is little research about the detailed structure and the time history during RR-MR transition. In this thesis, wave structure and transition of shock wave reflection in two-dimensional steady supersonic flows are studied theoretically and numerically.Firstly, we outline the fundamental theory of shock wave reflections, including the two-shock-theory, three-shock-theory, shock polar, and several critical curves. We also give and test the CFD method used for computation of shock reflection in the rest of this thesis.Secondly, through elaborate numerical calculations and analysis for Mach reflection, we find that a series of expansion and compression waves exist over the slip line, even in the region immediately behind the leading part of the reflected shock wave, previously regarded as a uniform flow. These waves make the leading part of the slip line, previously regarded as straight, deviate nonlinearly towards the reflecting surface. When the transmitted expansion waves from the upper corner first intersect the slip line, an inflexion point is produced. Downstream of this inflexion point, compression waves are produced over the slip line. Taking into account the interaction between the various expansion and compression waves, we propose an analytical model, which can be used to determine the shape and position of the slip line and reflected shock wave, as well as the height of the Mach stem. Due to the consideration of more detailed structure, we predict a more accurate value of the height of the Mach stem than previous. We also briefly study the case with a subsonic portion behind the reflected shock wave. The global flow pattern is obtained through CFD and the starting point of the sonic line is identified through a simple analysis. The sonic line appears to coincide with the first Mach wave from the up corner expansion fan after transmitting from the reflected shock wave.At last, the flow evolution near the reflection point is studied for the time history during the transition from any steady RR to the steady MR when a finite perturbation is introduced into the reflection point. In order to study the time history, we build a transition model which contains two distinct stages: a self-similar and mixed RR/MR structure, followed by a pure pseudo steady MR structure. It is shown that the triple point moves at a constant velocity in the first stage, followed by a sudden drop during the pure pseudo steady MR stage. The time scale of transition is several times the characteristic time, which is defined as the time the upstream sound wave takes to travel a distance of the inlet width. The initial stage lasts about 1/5 of the transition time.