论文标题
在欧拉气体的二元混合物的冲击结构中的次冲击的完整分类，具有不同的自由度
A Complete Classification of Sub-Shocks in the Shock Structure of a Binary Mixture of Eulerian Gases with Different Degrees of Freedom
论文作者
论文摘要
基于有理扩展热力学的多温模型，研究了多原子Eulerian气体具有不同程度的分子自由度的二元混合物中的休克结构。由于场方程系统是双曲线的，因此电击结构解决方案并非总是规律的，并且可以形成不连续的零件（子打击）。对于给定的质量比和成分的特定热量的值，我们将可能的子打击确定为电击波的马赫数$ m_0 $ $ m_0 $，而成分的浓度$ c $也会改变。在平面$（C，M_0）$中，我们确定了子打击形成的可能区域。获得了分析以验证冲击波的速度何时在未受干扰或扰动的平衡状态下达到特征速度，这为子震动形成提供了必要的条件。当冲击的速度大于未受干扰状态下的最大特征速度时，条件就变得有必要和足够。也就是说，没有子震动的区域，仅适用于一个成分的子震动或两个成分的子打击。最有趣的案例是，较轻的分子比沉重的分子具有更高的自由度。在这种情况下，各个区域的拓扑变得不同。我们还使用各个区域中的参数在数值上求解了字段方程的系统，并确认子震动是否出现。最后，明确得出了成分中的加速度波与其他成分中的子打击之间的关系。
The shock structure in a binary mixture of polyatomic Eulerian gases with different degrees of freedom of a molecule is studied based on the multi-temperature model of rational extended thermodynamics. Since the system of field equations is hyperbolic, the shock-structure solution is not always regular, and discontinuous parts (sub-shocks) can be formed. For given values of the mass ratio and the specific heats of the constituents, we identify the possible sub-shocks as the Mach number $M_0$ of the shock wave and the concentration $c$ of the constituents change. In the plane $(c,M_0)$, we identify the possible regions for the sub-shock formation. The analysis is obtained to verify when the velocity of the shock wave meets a characteristic velocity in the unperturbed or perturbed equilibrium states that gives a necessary condition for the sub-shock formation. The condition becomes necessary and sufficient when the velocity of the shock becomes greater than the maximum characteristic velocity in the unperturbed state. Namely, the regions with no sub-shocks, a sub-shock for only one constituent, or sub-shocks for both constituents are comprehensively classified. The most interesting case is that the lighter molecule has more degrees of freedom than that of the heavy one. In this situation, the topology of the various regions becomes different. We also solve the system of the field equations numerically using the parameters in the various regions and confirm whether the sub-shocks emerge or not. Finally, the relationship between an acceleration wave in a constituent and the sub-shock in the other constituent is explicitly derived.
