Three-dimensional flow structures in laminar falling liquid films
Three-dimensional flow structures in laminar falling liquid films
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DOI：
10.1017/jfm.2013.679
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发表时间：
2014-03
影响因子：
3.7
通讯作者：
G. Dietze;W. Rohlfs;K. Nährich;R. Kneer;B. Scheid
中科院分区：
文献类型：
--
作者：
G. Dietze;W. Rohlfs;K. Nährich;R. Kneer;B. Scheid
本文对四种具有三维表面波的垂直下降液膜的Navier-Stokes方程进行了全数值模拟。流动条件基于以前的几个实验研究，其中施加了流向和跨距波长，我们通过模拟周期波段来利用这些波长。所考虑的流动是层流，但接近于在其他地方观察到的间歇性波诱导湍流的条件。工作液体的范围从水到硅油，覆盖卡皮扎指数的很大一段(Ka=18Mbox--3923$)，它将毛细管与粘性力联系在一起。模拟是在超级计算机上进行的，使用有限体积代码以及流体体积和连续面力方法来考虑流动的多相性质。结果表明，由马蹄形波峰和毛细波纹组成的表面波将流场分成两个区域：一个是以惯性为主的大驼峰区域，局部雷诺数比平均值大五倍；另一个是粘性毛细管区，毛细管力和/或粘性力占主导地位。在惯性区，出现了一种复杂的不同尺度的涡旋结构，比那里的膜厚变化更复杂。相反，大流体粘性毛细管区的流动完全受局部自由表面曲率的控制，毛细管力的作用决定了液膜内的压力分布。这导致在毛细管槽下方形成流动分离区，并在毛细管波干扰区域形成跨向蜂窝状流动模式。在某些情况下，毛细管波在横跨方向上连接了大的马蹄形凸起，耦合了上述两个区域，并导致流动在三维和二维波动模式之间振荡。正如我们用Scheid等人的低维模型进行的模拟所表明的那样，这种情况会持续很长时间。(J.Fluid Mech，Vol.562,2006，pp.183-222)与我们在短时间内进行的直接模拟进行了令人满意的比较。调节机制与桥接毛细波相连，桥接毛细波从马蹄形隆起中排出液体，降低其振幅和波速，并使其沿流向缩回。总体而言，可以观察到，跨向流动结构(在二维研究中没有考虑在内)由于在该方向上没有重力而特别复杂。
Abstract Full numerical simulations of the Navier–Stokes equations for four cases of vertically falling liquid films with three-dimensional surface waves have been performed. Flow conditions are based on several previous experimental studies where the streamwise and spanwise wavelengths were imposed, which we exploit by simulating periodic wave segments. The considered flows are laminar but approach conditions at which intermittent wave-induced turbulence has been observed elsewhere. Working liquids range from water to silicone oil and cover a large interval of the Kapitza number ( $\textit {Ka}=18\mbox{--}3923$ ), which relates capillary to viscous forces. Simulations were performed on a supercomputer, using a finite-volume code and the volume of fluid and continuum surface force methods to account for the multiphase nature of the flow. Our results show that surface waves, consisting of large horseshoe-shaped wave humps concentrating most of the liquid and preceded by capillary ripples on a thin residual film, segregate the flow field into two regions: an inertia-dominated one in the large humps, where the local Reynolds number is up to five times larger than its mean value, and a visco-capillary region, where capillary and/or viscous forces dominate. In the inertial region, an intricate structure of different-scale vortices arises, which is more complicated than film thickness variations there suggest. Conversely, the flow in the visco-capillary region of large- $\textit {Ka} $ fluids is entirely governed by the local free-surface curvature through the action of capillary forces, which impose the pressure distribution in the liquid film. This results in flow separation zones underneath the capillary troughs and a spanwise cellular flow pattern in the region of capillary wave interference. In some cases, capillary waves bridge the large horseshoe humps in the spanwise direction, coupling the two aforementioned regions and leading the flow to oscillate between three- and two-dimensional wave patterns. This persists over long times, as we show by simulations with the low-dimensional model of Scheid et al. (J. Fluid Mech., vol. 562, 2006, pp. 183–222) after satisfactory comparison with our direct simulations at short times. The governing mechanism is connected to the bridging capillary waves, which drain liquid from the horseshoe humps, decreasing their amplitude and wave speed and causing them to retract in the streamwise direction. Overall, it is observed that spanwise flow structures (not accounted for in two-dimensional investigations) are particularly complex due to the absence of gravity in this direction.