Small-scale two-dimensional turbulence shaped by bulk viscosity
Small-scale two-dimensional turbulence shaped by bulk viscosity
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DOI：
10.1017/jfm.2019.531
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发表时间：
2019-07
影响因子：
3.7
通讯作者：
E. Touber
中科院分区：
文献类型：
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作者：
E. Touber
体积剪切粘度比的三个数量级的二氧化碳中经常被报道，但总是被忽略时，预测aerodynamic负载在外部（火星探测）或内部（换热器，热交换器）湍流。最近（也是第一次）对这一问题的数值研究表明，尽管这种看似任意的简化，螺线管湍流动能实际上是可以很好地预测的。目前的工作认为，这样的结论可能反映了从配置的选择，而不是提供一个明确的声明上的鲁棒性的动能转移到使用斯托克斯假设的限制。两个不同的渐近制度（欧拉-朗道和斯托克斯-牛顿）的本征模式的Navier-Stokes方程被确定。在欧拉-朗道制度，早期的研究中捕获的，声波和熵波被阻尼的传输系数和耗散的动能，甚至更迅速地为高体积粘度的流体和/或强迫频率。如果动能最初或持续地通过螺线管运动注入，则对湍流动能的影响仍然很小。然而，在斯托克斯-牛顿制度，扩散体压缩和平流等温压缩被发现占上风，并通过涡度膨胀相关性促进小尺度拟能。在没有体积粘度的情况下，向斯托克斯-牛顿制度的转变发生在耗散尺度内，并且在实践中没有观察到。相反，在高体积粘度下，斯托克斯-牛顿制度可以与惯性范围重叠，并在小尺度上破坏拟能，然后通过摩擦消散。因此，具有相当大的惯性范围和大的体积剪切粘度比的流动应该经历增强的传递到小规模螺线管动能，因此更快的耗散率导致传热性能的修改。数值观测这种传输仍然是昂贵的，目前的模拟仅限于二维湍流。然而，这里奠定的理论提供了有用的指导方针，设计实验研究跟踪斯托克斯-牛顿制度和相关的修改的湍流动能，预计将持续在三维湍流。
Bulk-to-shear viscosity ratios of three orders of magnitude are often reported in carbon dioxide but are always neglected when predicting aerothermal loads in external (Mars exploration) or internal (turbomachinery, heat exchanger) turbulent flows. The recent (and first) numerical investigations of that matter suggest that the solenoidal turbulence kinetic energy is in fact well predicted despite this seemingly arbitrary simplification. The present work argues that such a conclusion may reflect limitations from the choice of configuration rather than provide a definite statement on the robustness of kinetic-energy transfers to the use of Stokes’ hypothesis. Two distinct asymptotic regimes (Euler–Landau and Stokes–Newton) in the eigenmodes of the Navier–Stokes equations are identified. In the Euler–Landau regime, the one captured by earlier studies, acoustic and entropy waves are damped by transport coefficients and the dilatational kinetic energy is dissipated, even more rapidly for high bulk-viscosity fluids and/or forcing frequencies. If the kinetic energy is initially or constantly injected through solenoidal motions, effects on the turbulence kinetic energy remain minor. However, in the Stokes–Newton regime, diffused bulk compressions and advected isothermal compressions are found to prevail and promote small-scale enstrophy via vorticity–dilatation correlations. In the absence of bulk viscosity, the transition to the Stokes–Newton regime occurs within the dissipative scales and is not observed in practice. In contrast, at high bulk viscosities, the Stokes–Newton regime can be made to overlap with the inertial range and disrupt the enstrophy at small scales, which is then dissipated by friction. Thus, flows with substantial inertial ranges and large bulk-to-shear viscosity ratios should experience enhanced transfers to small-scale solenoidal kinetic energy, and therefore faster dissipation rates leading to modifications of the heat-transfer properties. Observing numerically such transfers is still prohibitively expensive, and the present simulations are restricted to two-dimensional turbulence. However, the theory laid here offers useful guidelines to design experimental studies to track the Stokes–Newton regime and associated modifications of the turbulence kinetic energy, which are expected to persist in three-dimensional turbulence.