真实气体的一种近似冲击波关系式

An Approximate Shock Wave Formula for Real Gases

以接近理想气体状态方程的取至第二维里系数的维里方程,作为考虑稠密效应的真实气体状态方程。利用冲击波基本关系式,依维里方程所包含的小参数,用摄动法求得冲击波后气体密度、压力及速度随冲击波速度及冲击波马赫数变化的显式表达式。结果显示,对相同的波前参数和冲击波马赫数,与理想气体相比,所得波后压力、速度及密度较低,尤其是密度,且二者的差异随冲击波马赫数增大而增大,随初始气体密度增大而增大,反映了气体分子自身体积和排斥作用的影响。理想气体的冲击波关系,可以视为本文所得冲击波关系的零级近似。这些关系适用于密度大约低于100 kg·m-3的气体,便于作冲击波性质和波后参数的分析。

On the basis of the expanded multi-dimensional Virial equation,the gas equation of state(EOS)is expanded the series to the second term,so that the density effect of real gas can be considered.Using the basic formula of the shock wave and small parameter contained in the Virial equation,the explicit expressions of the gas density,pressure and velocity behind the shock wave changing with the shock wave velocity and the shock wave Mach number are obtained by the perturbation method.The results show that for the same Mach number of the shock waves,compared with the results by the ideal gas model,the pressure,velocity and density behind the waves are all lower,especially the density.With the increase of the Mach number and the density of the gas,the difference in results will be even greater.These relations are the proper corrections to the ideal gas,which reflects the influence of the volume and repulsion effects of the gas molecule,and are fit for the gases whose density is lower than 100 kg·m-3.The formula of the shock wave for the ideal gas can be regarded as its zero-order approximation.It is very convenient to use these relations to analyze the properties of shock waves.