基于第二粘性的Navier-Stokes方程组求解正激波结构

Investigation of Normal Shock Structure by Using Navier-Stokes Equations with the Second Viscosity

为考察气体第二粘性(体积粘性)对正激波内部流动的影响机制,数值求解含第二粘性的一维Navier-Stokes方程组.结果表明:第二粘性对激波内部的密度、热流和能量分布等物理量具有抹平效应,导致热流和熵流的峰值减小、激波厚度增加,体积粘性耗散的增加使得一部分机械能转化为内能;考虑第二粘性所计算的密度分布和激波厚度大为改善,与实验数据吻合较好;当马赫数为1.2≤Ma≤10,激波内部的Knudsen数满足0.12≤Kn≤0.4,对于马赫数Ma≤4.0的激波内部流动,考虑第二粘性的连续流Navier-Stokes方程组能够准确地模拟正激波结构.

To investigate influence mechanism of the second viscosity on internal flow of a normal shock wave,one-dimensional Navier-Stokes equations are numerically solved.It indicates that the second viscosity has a smoothing effect on density,heat flow and energy distribution in the shock wave,which results in a decrease of peak value of heat and entropy flows,and an increase of shock thickness.Due to the production of normal viscous dissipation,some lost mechanical energy is converted into internal energy.As considering the second viscosity,density distribution and shock thickness are greatly improved.They are in good agreement with experimental data.In addition,Knudsen number is obtained 0.12≤Kn≤0.4 within Mach number range from 1.2 to 10.It indicates that Navier-Stokes equations with the second viscosity simulate normal shock structure more accurately.