We present a numerical method for simulating the flow induced by bubbles rising at large Reynolds number. This method is useful to simulate configurations of large dimensions involving a great number of bubbles. The action that each bubble exerts on the liquid is modelled as a volume source of momentum distributed over a few mesh-grid elements. The flow in the vicinity of the bubbles is thus not finely resolved. The bubbles are treated as Lagrangian particles that move under the influence of the hydrodynamic force exerted by the liquid. The determination of this force on a given bubble requires knowledge of the liquid flow that is undisturbed by this bubble. A model is developed to accurately estimate this disturbance for large-Reynolds-number objects and get rid of any spurious self-induced effect. Thanks to that, a homogeneous swarm of rising bubbles is simulated. Comparisons with experiments show a good agreement with the flow scales larger than the bubbles, which turn out to be controlled by the interactions between bubble wakes and rather independent of unresolved smaller scales. This method can be used to study the coupling between bubble-induced agitation and large-scale motions, such as those produced in industrial bubble columns.

中文翻译：

---

以大雷诺数运动的粗粒气泡产生的搅动的数值模拟

我们提出了一种数值方法来模拟由大雷诺数上升的气泡引起的流动。这种方法对于模拟包含大量气泡的大尺寸配置很有用。每个气泡对液体的作用被建模为分布在几个网格单元上的动量体积源。气泡附近的流动因此没有被精细地分辨。气泡被视为在液体施加的流体动力的影响下移动的拉格朗日粒子。确定给定气泡上的这种力需要了解不受该气泡干扰的液体流动。开发了一个模型来准确估计大雷诺数物体的这种干扰，并消除任何虚假的自诱导效应。多亏了这一点，模拟了一组均匀的上升气泡。与实验的比较表明，与比气泡大的流动尺度有很好的一致性，结果证明这是由气泡尾流之间的相互作用控制的，而不是独立于未解决的小尺度。该方法可用于研究气泡引起的搅拌与大规模运动之间的耦合，例如在工业气泡柱中产生的运动。