Experimental and numerical study of shock wave interactions near axis of symmetry

1948年，Courant和Friedrics证明，在轴对称流动中，只有不规则反射(马赫反射)才可能成为激波反射模式。这引起了激波研究界的极大关注，因为在激波管实验中，规则和不规则的激波反射都是可能的。许多研究人员进行了广泛的调查，并报告了相当多的实验获得的图像，似乎呈现出规则的反射。在本研究项目下，发展了一种非结构解自适应网格激波捕捉数值格式，并将其应用于激波在轴对称流动中的反射问题。数值模拟是在很难在实验上实现的高空间分辨率下进行的。并且发现，即使在实验图像显示为规则反射的情况下，反射图案也确实是不规则的。这表明数值模拟对于这一研究课题是非常重要的。1992年，索科洛夫提出了一种气体动力学机制，即激波在接近对称轴时会增强，结果是其入射角总是超过过渡角。另一方面，由于粘性、热传导和其他非平衡现象，激波反射的非定常性质，即不规则的激波反射总是作为规则反射开始的，已有报道。现在有必要将这一研究课题扩展到包括这样的物理现象。

Courant and Friedrics has shown in 1948 that only the irregular reflection (Mach reflection) is possible as a shock wave reflection pattern in an axi-symmetric flow. This drew much attention in the shock wave research community since regular and irregular shock reflections are both possible in shock tube experiments. Extensive investigations were carried out by many researchers and quite a few experimentally obtained images that seem to present regular reflections were reported. However, it is claimed that those images are due to insufficient resolution of the experiments and the decisive conclusions on this subject is not yet made.Under this research project, a shock capturing numerical scheme with unstructured solution-adaptive grids was developed and applied to the subject of shock wave reflection on the axis of axi-symmetric flow. The numerical simulations were done with the high spatial resolution that is difficult to achieve experimentally. And it is found out that the reflection pattern is indeed irregular even when an experimental image showed it to be the regular reflection. This is one of the indications that the numerical simulations are quite important for this research subject.In 1992 Sokolov proposed a gasdynamic mechanism that a shock wave strengthens as it approaches to the axis of symmetry and, as a result, its incident angle always exceeds the transition angle. On the other hand, the non-stationary nature of shock reflections in that a irregular shock reflection always starts as a regular reflection due to viscosity, heat conduction and other non-equilibrium phenomena has been reported. It is now necessary to extend this research subject including such physical phenomena.