A complete classification of sub-shocks in the shock structure of a binary mixture of Eulerian gases with different degrees of freedom
A complete classification of sub-shocks in the shock structure of a binary mixture of Eulerian gases with different degrees of freedom
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DOI：
10.1063/5.0094835
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发表时间：
2022-04
影响因子：
4.6
通讯作者：
T. Ruggeri;S. Taniguchi
中科院分区：
文献类型：
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作者：
T. Ruggeri;S. Taniguchi
基于有理扩展热力学多温度模型，研究了具有不同分子自由度的多原子欧拉气体二元混合物的激波结构。由于场方程组是双曲的，因此激波结构解并不总是规则的，并且可以形成不连续部分（子激波）。对于给定的成分质量比和比热值，我们根据冲击波的马赫数 M0 和成分的平衡浓度 c0 的变化确定可能的次激波。在平面（c0，M0）中，我们确定了亚激波形成的可能区域。分析验证了激波速度何时满足未扰动或扰动平衡状态下的特征速度，这为次激波形成提供了必要条件。当激波速度大于未扰动状态下的最大特征速度时，该条件成为充分必要条件，即对没有子激波的区域、仅一种成分的子激波或两种成分的子激波进行综合分类。最有趣的情况是，较轻的分子比重的分子具有更多的自由度。在这种情况下，各个区域的拓扑变得不同。我们还利用不同区域的参数对场方程组进行了数值求解，并确定了是否存在次激波。最后，明确推导了一个成分中的加速度波与另一成分中的次激波之间的关系。
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 heat of the constituents, we identify the possible sub-shocks as the Mach number M0 of the shock wave and the equilibrium concentration c0 of the constituents change. In the plane ( c0, M0), 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, which 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 various regions and confirm whether the sub-shocks emerge or not. Finally, the relationship between an acceleration wave in one constituent and the sub-shock in the other constituent is explicitly derived.