This study proposes two different strategies to enforce accurate volume conservation in volume-of-fluid (VOF)-based simulations of turbulent bubble-laden flows on coarse grids. It is demonstrated that, without a correction, minimal volume errors on a time-step level, caused by the under-resolution of the interface, can accumulate to significant deviations from the intended flow conditions despite the comparably good volume conservation properties of the geometric VOF method. In particular, large volume errors are observed for challenging setups combining coarse grid resolutions and comparably high Reynolds and Eötvös numbers. The problem is reinforced for long-term simulations in periodic domains, which are often performed to collect flow statistics of bubbly flows. The first proposed volume conservation method simply corrects the volume error of a bubble by uniformly adding or removing the respective amount of gas volume in the interface cells. The second proposed method performs an additional reconstruction and advection step of the VOF field using a non-divergence-free velocity field, which can be interpreted as a slight dilatation or contraction of the bubble. A comparison between the global flow statistics as well as the individual bubble dynamics for both volume conservation methods reveals that the results are quasi-identical for a number of challenging test cases, while the gas volume is accurately conserved. The proposed methods allow to perform numerical simulations of freely deformable bubbles in turbulent flows for setups that have previously been out of reach for this numerical framework.

中文翻译：

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在基于 VOF 的粗网格上充满气泡的湍流长期模拟中执行精确的体积守恒

本研究提出了两种不同的策略，以在粗网格上基于流体体积 (VOF) 的湍流气泡流模拟中强制执行精确的体积守恒。结果表明，尽管几何 VOF 具有相对良好的体积守恒特性，但如果不进行校正，由界面分辨率不足引起的时间步长水平上的最小体积误差可能会累积到与预期流动条件的显着偏差。方法。特别是，对于具有挑战性的设置，结合粗网格分辨率和相对较高的雷诺数和埃特沃斯数，会观察到较大的体积误差。对于周期性域中的长期模拟，该问题得到了加强，这些模拟通常用于收集气泡流的流动统计数据。第一种提出的体积守恒方法通过均匀地添加或去除界面单元中各自的气体体积量来简单地校正气泡的体积误差。第二种方法使用非无散度速度场对 VOF 场执行额外的重建和平流步骤，这可以解释为气泡的轻微扩张或收缩。两种体积守恒方法的全局流量统计数据以及单个气泡动力学之间的比较表明，对于许多具有挑战性的测试用例，结果几乎相同，而气体体积是准确守恒的。所提出的方法允许对湍流中可自由变形的气泡进行数值模拟，以实现以前该数值框架无法实现的设置。