不稳定性对爆轰波楔面马赫反射的影响规律研究

The effect of the stability on the Mach reflection of detonations on a wedge

采用一种两步化学反应模型对胞格爆轰波的楔面马赫反射过程进行了数值研究,从而澄清和解释胞格不稳定性对马赫反射发展模式和自相似性的影响。考虑到反应欧拉方程源项的刚性问题,本文采用附加RungeKutta方法耦合非刚性对流项和刚性反应源项,对流项的离散采用五阶精度的WENO格式。计算结果表明,对于稳定胞格爆轰波而言,其马赫反射过程本质上与ZND爆轰波的马赫反射是一致的,整体上不存在自相似性,胞格不稳定性只是造成了三波点轨迹线局部小振幅的波动。在楔面顶点附近,由于马赫杆是强过驱的,爆轰波的马赫反射过程是自相似的。在远场,爆轰波马赫反射的三波点轨迹线渐近的趋向于一条直线,说明重新获得了自相似性。对于不稳定的爆轰波,由于自身的不稳定性可以与马赫反射的强度相匹配,定义其三波点的轨迹是困难的,进行自相似性分析没有意义。

The Mach reflection process of cellular detonations on a wedge is numerically studied with a two-step chemical reaction model in an attempt to elucidate the effect of the stability on the development and self-similarity on the Mach reflection. Considering the stiffness of the reactive source term,an addi- tive Runge-Kutta method is also used to couple the stiff reactive source term and the non-stiff convection which is discretised with a fifth-order WENO scheme. The numerical results suggest that the Mach reflection of a regular cellular detonation is in accordance with that of a ZND detonation. The self-simi- larity is lost due to the presence of the characteristic length and the cellular structures only result in the local fluctuations of the triple-point trajectory. In the near field, the Mach reflection process is self- similar due to the high overdrive. In the far field, the Mach reflection can lead to self-similarity asymptotically. For unstable detonations, the stability of the detonation front is comparable with the Mach stem. Thus locating the boundary of the Mach reflection becomes difficult and it may not be meaningful to carry out a self-similar analysis.