We performed numerical simulations of a homogeneous swarm of bubbles rising at large Reynolds number, $Re=760$ , with volume fractions ranging from 1 % to 10 %. We consider a simplified model in which the interfaces are not resolved, but which allows us to simulate flows with a large number of bubbles and to emphasize the interactions between bubble wakes. The liquid phase is described by solving, on an Eulerian grid, the Navier–Stokes equations, including sources of momentum which model the effect of the bubbles. The dynamics of each bubble is determined within the Lagrangian framework by solving an equation of motion involving the hydrodynamic forces exerted by the fluid accounting for the correction of the fictitious self-interaction of a bubble with its own wake. The comparison with experiments shows that this coarse-grained simulations approach can reliably describe the dynamics of the resolved flow scales. We use conditional averaging to characterize the mean bubble wakes and obtain in particular the typical shear imposed by the rising bubbles. On the basis of the spectral decomposition of the energy budget, we observe that the flow is dominated by production at large scales and by dissipation at small scales and we rule out the presence of an intermediate range in which the production and dissipation are locally in balance. We propose that the $k^{-3}$ subrange of the energy spectra results from the mean shear rate imposed by the bubbles, which controls the rate of return to isotropy.

中文翻译：

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粗粒度模拟中大量上升气泡引起的湍流

我们对以大雷诺数上升的均匀气泡群进行了数值模拟， $回复=760$ ，体积分数范围为 1% 至 10%。我们考虑一个简化模型，其中界面未解析，但它允许我们模拟具有大量气泡的流动并强调气泡尾流之间的相互作用。通过在欧拉网格上求解纳维-斯托克斯方程来描述液相，包括模拟气泡效应的动量源。每个气泡的动力学是在拉格朗日框架内通过求解涉及流体施加的流体动力的运动方程来确定的，该方程考虑了气泡与其自身尾流的虚拟自相互作用的校正。与实验的比较表明，这种粗粒度模拟方法可以可靠地描述所解析的流动尺度的动力学。我们使用条件平均来表征平均气泡尾流，并特别获得上升气泡所施加的典型剪切力。在能量预算的谱分解的基础上，我们观察到流动主要由大尺度的生产和小尺度的耗散主导，并且我们排除了生产和耗散局部平衡的中间范围的存在。我们建议 $k^{-3}$ 能谱的子范围是由气泡施加的平均剪切速率产生的，它控制着各向同性的返回速率。