This paper investigates the structure of normal shock waves for a planar steady flow of non-ideal dilute gases under variable viscosity and thermal conductivity using the Navier–Stokes–Fourier approach to the continuum model. The gas is assumed to follow the simplified van der Waals equation of state along with the power-law temperature-dependent coefficients of shear viscosity, bulk viscosity, and thermal conductivity. A closed system of nonlinear differential equations having a variable Prandtl number (\(\Pr \)) is formulated. Exact analytical solutions of the shock wave structure in non-ideal gases are derived for \(\Pr \rightarrow \infty \) and \(\Pr \rightarrow 0\) limits, and the corresponding profiles for velocity and temperature are obtained. For \(\Pr \rightarrow 0\), an isothermal shock is encountered for high Mach numbers. It appears sooner in non-ideal gases. The solution profiles for \(\Pr =2/3\) are obtained numerically and compared with the corresponding profiles for \(\Pr \rightarrow 0\), 3/4, and \(\infty \) under the same initial conditions. Qualitative agreement is obtained with the theoretical and experimental results for the shock wave structure. The inverse shock thickness is computed for different values of \(\Pr \), and it is found that the inverse shock thickness increases with an increase in the Prandtl number. The bulk viscosity, the non-idealness parameter, the specific heat ratio, the power-law index, and the pre-shock Mach number have a significant effect on the shock wave structure.

本文使用Navier–Stokes–Fourier方法对连续模型进行研究，研究了可变粘度和热导率下非理想稀薄气体的平面稳定流动的法向冲击波的结构。假定气体遵循简化的范德华状态方程，以及与幂律温度相关的剪切粘度，体积粘度和导热系数。拟定了一个具有可变Prandtl数（\（\ Pr \））的非线性微分方程的封闭系统。推导了非理想气体中冲击波结构的精确解析解，其极限为\（\ Pr \ rightarrow \ infty \）和\（\ Pr \ rightarrow 0 \），并获得了相应的速度和温度曲线。对于\（\ Pr \ rightarrow 0 \），对于高马赫数会遇到等温冲击。在不理想的气体中出现得更快。通过数值获得\（\ Pr = 2/3 \）的解轮廓，并将其与相同初始条件下\（\ Pr \ rightarrow 0 \），3/4和\（\ infty \）的对应轮廓进行比较。定性与冲击波结构的理论和实验结果吻合。针对不同的\（\ Pr \）值计算反冲击厚度，并且发现反冲击厚度随着普朗特数的增加而增加。体积粘度，非理想参数，比热比，幂律指数和预激马赫数对冲击波结构有重要影响。