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首页> 外文期刊>Journal of Fluid Mechanics >Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations
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Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

机译：非标准Hele-Shaw配置中控制界面不稳态的数值研究

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Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been devoted to devising strategies for controlling such patterns and reducing the growth of the interfacial fingers. We continue this research by reporting on numerical simulations, based on the level set method, of a generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is altered. First, we investigate how imposing constant and time-dependent injection rates in a Hele-Shaw cell that is either standard, tapered or rotating can be used to reduce the development of viscous fingering when an inviscid fluid is injected into a viscous fluid over a finite time period. We perform a series of numerical experiments comparing the effectiveness of each strategy to determine how these non-standard Hele-Shaw configurations influence the morphological features of the inviscid-viscous fluid interface. Surprisingly, a converging or diverging taper of the plates leads to reduced metrics of viscous fingering at the final time when compared to the standard parallel configuration, especially with carefully chosen injection rates; for the rotating plate case, the effect is even more dramatic, with sufficiently large rotation rates completely stabilising the interface. Next, we illustrate how the number of non-splitting fingers can be controlled by injecting the inviscid fluid at a time-dependent rate while increasing the gap between the plates. Our simulations compare well with previous experimental results for various injection rates and geometric configurations. We demonstrate how the number of non-splitting fingers agrees with that predicted from linear stability theory up to some finger number; for larger values of our control parameter, the fully nonlinear dynamics of the problem leads to slightly fewer fingers than this linear prediction.
机译：Hele-Shaw细胞的粘性指法实验导致醒目的模式形成，这是物理学和应用数学群落中强烈关注的主题多年来。最近，致力于设计用于控制这种模式并降低界面手指的生长的策略。我们通过报告基于水平集法的数值模拟来继续进行这项研究，该方法的级别模拟是改变了Hele-Shaw电池的几何形状的广义的Hele-Shaw模型。首先，我们研究了标准，锥形或旋转的高毛细胞中恒定和时间依赖的注射率如何用于减少粘性手术的发育，当粘性流体在有限内注入粘性流体时时间段。我们执行一系列数值实验，比较各种策略的有效性，以确定这些非标准的Hele-Shaw配置如何影响活性粘性流体接口的形态学特征。令人惊讶的是，与标准平行配置相比，平板的聚变锥度导致最终时间在最终时间降低粘性指法的度量，特别是仔细选择的注射率;对于旋转板壳体，效果甚至更戏剧，具有足够大的旋转速率，完全稳定界面。接下来，我们示出了如何通过以时间依赖的速率注入缺陷流体来控制非分裂手指的数量，同时增加板之间的间隙。我们的仿真对比较的各种注射率和几何配置的实验结果很好。我们展示了非分裂手指的数量如何同意，从线性稳定理论到某些手指编号预测的那样;对于我们的控制参数的更大值，问题的完全非线性动态导致手指稍微略小，而不是该线性预测。

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