Modelling finger propagation in elasto-rigid channels
Modelling finger propagation in elasto-rigid channels
复制标题
模拟弹性刚性通道中的手指传播
DOI：
10.1017/jfm.2021.219
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发表时间：
2021
影响因子：
3.7
通讯作者：
Fontana J
中科院分区：
文献类型：
--
作者：
Fontana J
我们对两相流固耦合问题进行了理论研究，在该问题中，空气以恒定的体积流量被驱动到上边界为弹性薄板的充满液体的Hele-Shaw通道中。采用推进气液界面参考系中的深度平均模型，通过数值模拟研究了定常和非定常界面传播模式。在轻微折叠的通道中，稳定传播的界面采用类似于刚性Hele-Shaw单元中的经典Saffman-Taylor手指的形状。随着初始坍塌程度的增加，沟道深度的诱导梯度改变了扩展手指的形态，并促进了从尖端分裂到弯曲界面上的小尺度指进的各种不稳定性，这与实验定性地一致。该模型具有复杂的解结构，具有广泛的稳定和不稳定、稳定和时间周期模式，其中许多模式具有相似的驱动压力。我们发现我们的模型与Ducloué等人的实验数据有很好的定量一致性。(J.Fluid Mech，Vol.819,2017，p.121)用于手指宽度、板材轮廓和手指压力，前提是模型中包括考虑通道上壁和下壁上存在液体膜的修正。
We conduct a theoretical study of a two-phase fluid–structure interaction problem in which air is driven at constant volume flux into a liquid-filled Hele-Shaw channel whose upper boundary is an elastic sheet. A depth-averaged model in the frame of reference of the advancing air–liquid interface is used to investigate the steady and unsteady interface propagation modes via numerical simulation. In slightly collapsed channels, the steadily propagating interface adopts a shape that is similar to the classic Saffman–Taylor finger in rigid Hele-Shaw cells. As the level of initial collapse increases, the induced gradients in channel depth alter the morphology of the propagating finger and promote a variety of instabilities from tip splitting to small-scale fingering on the curved interface, in qualitative agreement with experiments. The model has a complex solution structure with a wide range of stable and unstable, steady and time-periodic modes, many of which have similar driving pressures. We find good quantitative agreement between our model and the experimental data of Ducloué et al. (J. Fluid Mech., vol. 819, 2017, p. 121) for the finger width, sheet profile and finger pressure, provided that corrections to account for the presence of liquid films on the upper and lower walls of the channel are included in the model.
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