Geometric similarity ratio is one of the important factors that affects the disturbance amplitude of shock-wave front in viscosity measurement. In this paper, the Euler difference scheme of two-dimensional (2D) equations of viscous fluid mechanics is used to simulate the disturbance amplitude damping curves under different geometric similarity ratios, and the corresponding numerical solutions are shown. The samples of aluminum shocked to 80 GPa are taken as an example. The simulation results show that the initial conditions, material viscosity, wavelength, and sample geometric similarity ratio affect the evolution of the shock front sine wave disturbance. For flyer-impact flow field, the phase shift increases from 0 to a certain value with the viscosity coefficient for sample with wavelength λ = 6 mm and geometric similarity ratio h/λ = 0.05, 0.1. So, the geometric similarity method can be used to measure the viscosity of material. But it is found that the phase shift is sensitive to the geometric similarity ratio, which should be considered in Zaidel’s equation. So, some flyer-impact experiments will be carried out to determine the simulation results, and find the quantity relation of phase shift and viscosity of material in the future investigation.

中文翻译：

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粘度测量中几何相似比对冲击波阵面扰动幅值的影响

几何相似比是影响粘度测量中冲击波阵面扰动幅度的重要因素之一。本文利用粘性流体力学二维（2D）方程的欧拉差分格式模拟了不同几何相似比下的扰动幅值阻尼曲线，并给出了相应的数值解。以冲击到 80 GPa 的铝样品为例。仿真结果表明，初始条件、材料粘度、波长和样品几何相似比影响激波前缘正弦波扰动的演化。对于飞行器冲击流场，对于具有波长的样品，相移随粘度系数从 0 增加到某个值λ = 6mm与几何相似比H/λ = 0.05, 0.1。因此，几何相似法可以用来测量材料的粘度。但发现相移对几何相似比敏感，在Zaidel方程中应考虑这一点。因此，将进行一些飞行撞击实验以确定模拟结果，并在未来的研究中找到材料的相移和粘度的数量关系。