arXiv 2101.093232021-01-22physics.flu-dyn

压力波动对稀化液幕形状的影响

The effect of pressure fluctuations on the shapes of thinning liquid curtains

Bridget M. Torsey, Steven J. Weinstein, David S. Ross, Nathaniel S. Barlow

发表信息：: Journal of Fluid Mechanics, 910, A38 (2021)
DOI：: 10.1017/jfm.2020.1038

摘要：

本文研究了在正弦环境压力扰动作用下，一个在重力作用下变薄的无粘液膜（一个涂层幕）在垂直狭缝中的时间响应。理论研究采用了由\cite{weinp1}提出的双曲型偏微分方程。帘的响应由槽韦伯数$W_{e_0} = ρq V/2σ$表征，其中$V$是帘在槽处的速度，$q$是每单位宽度的体积流速，$σ$是表面张力，并且$ρ$是流体密度。流动扰动沿着具有相对于$\pm \sqrt{uV/W_{e_0}}$的帘的速度的特性行进，其中$u = \sqrt{V^2 + 2gx}$是在距槽下游距离$x$处的帘速度。当流动为亚临界（$W_{e_0} < 1$）时，狭缝附近的上游行进扰动影响幕帘中心线，并且狭缝处的幕帘中心线的斜率以作为$W_{e_0}$的函数的振幅振荡。相反，所有的扰动在超临界帘幕（$W_{e_0} > 1$）中向下游行进，并且帘幕在槽处的斜率是垂直的。在这里，我们专门检查下的超临界和亚临界流条件下的响应$W_{e_0} = 1$附近的窗帘推断是否有一个实质性的变化，在整体形状和幅度的窗帘响应。尽管缝附近的窗帘解决方案的局部差异，我们发现，亚临界和超临界窗帘有类似的响应，所有施加的正弦频率。

英文摘要：

We consider the time-dependent response of a gravitationally-thinning inviscid liquid sheet (a coating curtain) leaving a vertical slot to sinusoidal ambient pressure disturbances. The theoretical investigation employs the hyperbolic partial differential equation developed by \cite{weinp1}. The response of the curtain is characterized by the slot Weber number, $W_{e_0} = ρq V/2σ$, where $V$ is the speed of the curtain at the slot, $q$ is the volumetric flow rate per unit width, $σ$ is the surface tension, and $ρ$ is the fluid density. Flow disturbances travel along characteristics with speeds relative to the curtain of $\pm \sqrt{uV/W_{e_0}}$, where $u = \sqrt{V^2 + 2gx}$ is the curtain speed at a distance $x$ downstream from the slot. When the flow is subcritical ($W_{e_0} < 1$), upstream traveling disturbances near the slot affect the curtain centerline, and the slope of the curtain centerline at the slot oscillates with an amplitude that is a function of $W_{e_0}$. In contrast, all disturbances travel downstream in supercritical curtains ($W_{e_0} > 1$) and the slope of the curtain at the slot is vertical. Here, we specifically examine the curtain response under supercritical and subcritical flow conditions near $W_{e_0} = 1$ to deduce whether there is a substantial change in the overall shape and magnitude of the curtain responses. Despite the local differences in the curtain solution near the slot, we find that subcritical and supercritical curtains have similar responses for all imposed sinusoidal frequencies.

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英文摘要：

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