基于直接模拟蒙特卡罗方法计算单一气体及二元混合气体的平均自由程

Calculation of Mean Free Path of Pure Gas and Binary Gas Mixture Based on Direct Simulation Monte Carlo Method

运用直接模拟蒙特卡罗方法研究了单一及二元混合气体在平衡态时气体内部分子间的相互碰撞过程。采用可变硬球模型及可变软球模型两种分子间碰撞处理模型对单一及二元混合气体分子平均自由程、单位时间单位体积内碰撞次数在模拟温度为300~20000 K之间进行了模拟计算。为了检验这两种模型模拟计算的精确性,将其结果与对应模型下的理论计算结果进行比较,表明单一气体的模拟结果与理论计算结果相对偏差不超过0.7%,混合气体相对偏差不超过1.5%。同时将上述两种模型的模拟结果与传统硬球模型的计算结果进行比较,发现在硬球模型下,气体分子平均自由程在宽温度区间与其他两种模型相比有较大的误差,而单位时间单位体积内气体分子的碰撞次数与模拟温度的二分之一次方成正比,当模拟温度高于300 K时,其结果大于另外两种模型下的结果。

The direct simulation Monte Carlo method was used to study the collision process between the molecules when the pure and binary gas mixtures are in equilibrium.The mean free path and the number of collisions per unit time and unit volume are calculated by using variable hard sphere model and variable soft sphere model between 300 K and 20000 K.In order to check the accuracy of the simulation of the two models,the results are compared with the numerical calculation results under the corresponding models.The results show that the relative deviation of the simulation results of the pure gas and the calculation results does not exceed 0.7%,and the relative deviation of the mixed gas does not exceed 1.5%.The simulation results under the above two models are compared with the calculation results under the hard sphere model.It is found that under the hard sphere model,the mean free path of gas molecule has a larger error than the other two models at a wide range of temperatures,and the number of collisions gas molecule in unit time and volume is proportional to the square root of the simulated temperature.When the simulated temperature is higher than 300 K,the results are bigger than those of the other two models.