This paper investigates the importance of molecular viscosity and diffusivity for the prediction of transitional and shock-driven mixing flows featuring high and low Reynolds and Mach number regions. Two representative problems are computed with implicit large-eddy simulations using the inviscid Euler equations (EE) and viscous Navier-Stokes equations (NSE): the Taylor-Green vortex at Reynolds number $\mathrm{Re}=3000$ and initial Mach number $\mathrm{Ma}=0.28$, and an air-${\mathrm{SF}}_6$-air gas curtain subjected to two shock waves at $\mathrm{Ma}=1.2$. The primary focus is on differences between NSE and EE predictions due to viscous effects. The outcome of the paper illustrates the advantages of utilizing NSE. In contrast to the EE, where the effective viscosity decreases upon grid refinement, NSE predictions can be assessed for simulations of flows with transition to turbulence at prescribed constant $\mathrm{Re}$. The NSE can achieve better agreement between solutions and reference data, and the results converge upon grid refinement. On the other hand, the EE predictions do not converge with grid refinement, and can only exhibit similarities with the NSE results at coarse grid resolutions. We also investigate the effect of viscous effects on the dynamics of the coherent and turbulent fields, as well as on the mechanisms contributing to the production and diffusion of vorticity. The results show that nominally inviscid calculations can exhibit significantly varying flow dynamics driven by changing effective resolution-dependent Reynolds number, and highlight the role of viscous processes affecting the vorticity field. These tendencies become more pronounced upon grid refinement. The discussion of the results concludes with the assessment of the computational cost of inviscid and viscous computations.

中文翻译：

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过渡和冲击驱动的混合流中的分子粘度和扩散效应

本文研究了分子粘度和扩散率对于预测具有高和低雷诺数和马赫数区域的过渡和冲击驱动混合流的重要性。使用无粘性Euler方程（EE）和粘性Navier-Stokes方程（NSE），通过隐式大涡模拟计算了两个代表性问题：Reynolds数处的Taylor-Green涡$\mathrm{回覆}=3000$ 和初始马赫数 $嘛=0.28$和空气${\mathrm{SF}}_6$气帘受到两个冲击波的影响 $嘛=1.2$。主要关注因粘性效应而导致的NSE和EE预测之间的差异。本文的结果说明了利用NSE的优势。与EE相反，在网格细化后有效粘度降低的EE中，可以评估NSE预测以模拟在规定的常数下向湍流过渡的流动$\mathrm{回覆}$。NSE可以在解决方案和参考数据之间达成更好的一致性，并且结果可以收敛到网格细化上。另一方面，EE预测与网格细化不收敛，并且只能在粗网格分辨率下显示与NSE结果的相似性。我们还研究了粘性效应对相干和湍流场动力学的影响，以及对促进涡旋产生和扩散的机理的影响。结果表明，名义上无粘性的计算可以显示出通过改变有效分辨率相关的雷诺数而引起的明显变化的流动动力学，并突出了粘性过程影响旋涡场的作用。这些趋势在网格细化时变得更加明显。