激波反射是超音速或高超音速流场中重要的流动结构，对飞行器的气动性能有着重要影响，是受到长期关注的前沿性课题。激波反射的两种基本类型是正规反射（RR）和马赫反射（MR），其产生的条件和基本流动结构已经清楚，但详细结构和两者转捩的时间过程尚缺乏研究。本文主要针对二维定常超音速流中激波马赫反射的波系结构与转捩等问题进行理论及数值研究。 首先，回顾激波反射的基本分析理论，包括二激波理论、三激波理论、激波极曲线以及反射类型临界曲线等。并介绍和验证了用于激波反射研究的数值方法。 接着，通过详细数值计算和推理，我们发现滑移线上存在一系列的膨胀波和压缩波，并且反射激波后三叉点附近流动是非均匀的，这在以前的研究中没有被考虑过。之前的研究认为滑移线的初始段为直线，而我们的研究发现其向对称面非线性倾斜。当滑移线与楔尾膨胀波的首道马赫波穿过反射激波的透射马赫波相交时，其形状产生拐点，开始逐渐向反方向倾斜。同时，透射膨胀波在滑移线上反射会产生反射压缩波。充分考虑各种膨胀波（马赫波）、激波（压缩波）以及滑移线之间的相互干扰，我们构造了理论模型，可用于分析滑移线和反射激波的位置与形状，以及马赫杆的高度。由于考虑了更为精细的波系结构，所以我们预测的马赫杆高度比以前的理论更加准确。另外，我们也讨论了反射激波后存在亚音速区的情况，分析了音速线与滑移线和反射激波的交点的位置，整体流动结构则由CFD给出。结果显示，音速线基本上与首道透射马赫波重合。 最后，针对双解区内定常RR向定常MR的转捩过程（转捩由反射点附近的扰动引起），我们构造了转捩预测模型。模型包含两个阶段：转捩初始时间存在一个自相似结构（RR/MR混合阶段），然后该结构逐渐演化为准定常MR结构。研究表明，三叉点的移动速度在第一阶段为常数，在第二阶段开始逐渐减小直至零。转捩完成时间为特征时间的几倍量级，其中特征时间定义为声波传播相当于入口高度的距离所需要的时间，RR/MR混合阶段的时间占总转捩时间的1/5左右。
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.
