激波反射是超声速和高超声流动中的常见现象。由于激波反射存在正规反射和马赫反射两种形态，且在某些参数范围内两者可以同时出现和相互转捩，因此激波反射对飞行器流场结构、气动力和气动热等有重要影响。人们研究了单个入射激波反射（简称单激波反射）的激波结构、转捩条件、决定各结构尺寸的物理机制、非对称效应和粘性效应的影响等问题，但尚未关注多入射激波的反射问题。本文研究双入射激波反射问题（简称双激波反射问题），即两道同侧入射激波在反射面上同一点的反射问题。我们通过理论和数值模拟，研究了双激波反射形态、不同反射形态出现的临界条件以及决定马赫杆尺寸的影响因素等。研究指出：1）双激波反射存在正规反射、前马赫反射和后马赫反射三种基本反射形态。前后马赫反射分别指第一道和第二道入射激波产生马赫反射，另一道则分别与该马赫反射的反射激波和马赫杆发生干扰。不仅如此，在前马赫反射中，反射激波马赫反射的反射激波和马赫杆发生干扰。不仅如此，在前马赫反射中，反射激波和第二道入射激波的相交存在双解现象。这表明双激波反射至少有四种基本形态。2）对于前马赫反射情况，第二道入射激波会迫使从三叉点发出的滑移线向反射面偏转额外角度，从而改变马赫杆下游流道的收缩程度，抬高马赫杆高度。进一步分析表明，马赫杆高度随第二道入射激波的强度增加先增加后减小，即存在极值现象。3）对于后马赫反射情况，第一道入射激波与第二道入射激波的马赫杆之间的第 IV 类干扰形成的超声速射流将马赫杆下游流道分成上下两个流道。上部流道的喉部在下部流道的喉部的上游。4）在前马赫反射和后马赫反射问题中发现了逆马赫反射现象，即在不满足冯? 诺依曼马赫反射必要条件的情况下也产生了马赫反射。这一发现丰富了逆马赫反射出现的情形。针对双激波反射问题研究的这些发现，丰富了激波反射理论，为进一步开展具有更多入射激波的激波反射问题研究提供了理论基础。
Shock reflection is a common phenomenon in supersonic and hypersonic flows. Due to the existence of both regular reflection and Mach reflection, the existence of double solution regions and transition between them, shock reflection has important influences on the flow field, aerodynamic force and aerodynamic heating of flight vehicles. Past studies have focused on the configurations of single incident shock wave reflection, the transition between various configurations, the physical mechanism determining the size of each structure, and the effect of asymmetry and viscosity on reflection. However, no attention has been paid to the reflection of multiple incident shocks, which is also a common phenomenon in supersonic and hypersonic flows. This paper deals with the reflection of two incident shock waves, that is, the re-flection of two incident shock waves is from the same side and at the same point on the reflecting surface. We use numerical simulation, shock-polar analysis and other theories borrowed from single shock reflection analysis to study the reflection patterns of double shock waves, the critical conditions for different reflection patterns, and the factors that determine the Mach stem size. Below are the main findings. 1) There are three types of double shock reflection: regular reflection, pre-Mach reflection and post-Mach reflection. Pre-Mach reflection means the first incident shock wave has Mach reflection while post-Mach reflection means the second incident shock wave has Mach reflection,with the other incident shock wave interfering with the reflected shock wave and Mach stem, respectively. In the pre-Mach reflection case, double solution exists at the intersection point of the reflected shock wave and the second incident shock wave. This shows that there are at least four reflection patterns in the reflection of double shock waves. 2) For the case of pre-Mach reflection, both theory and numerical simulation show that the second incident shock wave forces the slipline to deflect towards the reflecting surface. The height of the Mach stem is thus elevated by the second incident shock wave. Further analysis shows that the height of the Mach stem increases first and then decreaseswith the increase of the intensity of the second incident shock wave.3) For the case of post-Mach reflection, the interaction of the first incident shock wave and the Mach stem of the second incident shock wave leads to type IV shock interference. The resulting supersonic jet flow divides the quasi-one-dimensional flow duct downstream of Mach stem into two flow ducts. The throats of the two flow ducts occurat different positions, and the throat of the upper flow duct appears earlier.4) For both pre-Mach reflection and post-Mach reflection, inverse Mach reflection, that is, Mach reflection below the von Neumann condition, is observed. This provides an additional occasions of inverse Mach reflection. The phenomenon of double shock reflection is considered for the first time in this work. The results enrich the theory of shock reflection and provide a theoretical basis for problems in which multiple incident shock reflection occurs.
