封闭腔体中由扑动诱导的流动
Fluttering-induced flow in a closed chamber
AI总结：
本文研究封闭腔体内弹性薄板变形驱动的流体流动，建立双向流固耦合解析模型，揭示系统由四个无量纲参数控制，并给出线性稳定性增长率、频率及能量释放时间尺度。
摘要：
我们研究在封闭腔体中由弹性薄板的动态变形驱动的流体流动的产生。该薄板被压缩在腔体的侧壁之间，并将腔体分隔成两个独立部分，每个部分初始充满无粘流体。当允许腔体的两个隔室之间进行流体交换时，薄板变得不稳定，其运动使流体从静止状态发生位移。我们推导了一个解析模型，该模型考虑了流体与薄板之间双向耦合的相互作用。我们表明该系统依赖于四个无量纲参数：薄板相对于腔体横向尺寸的归一化超额长度 $Δ$；腔体的归一化垂直尺寸；腔体两部分之间的归一化初始体积差 $v_{\text{du}}(0)$；以及结构-流体质量比 $λ$。我们研究了系统演化早期时刻以及中等时刻的动力学。我们分别获得了围绕第二屈曲模态和第一屈曲模态振动的增长率和频率。在小振幅近似极限内，为这些线性稳定性特征推导了解析解。在中等时刻，我们研究了薄板如何从第二模态逃逸。给定腔体的尺寸，我们表明，如果 $λ\ll 1$，薄板的初始能量主要转化为流体的流体动力学能量；如果 $λ\gg 1$，则主要转化为薄板的动能。在这两种情况下，大部分初始能量在时间 $ t_{\text{p}}\simeq \ln[c Δ^{1/2}/v_{\text{du}}(0)]/σ$ 释放，其中 $σ$ 是增长率，$c$ 是常数。
英文摘要：
We study the emergence of fluid flow in a closed chamber that is driven by dynamical deformations of an elastic sheet. The sheet is compressed between the sidewalls of the chamber and partitions it into two separate parts, each of which is initially filled with an inviscid fluid. When fluid exchange is allowed between the two compartments of the chamber, the sheet becomes unstable, and its motion displaces the fluid from rest. We derive an analytical model that accounts for the coupled, two-way, fluid-sheet interaction. We show that the system depends on four dimensionless parameters: the normalized excess length of the sheet compared to the lateral dimension of the chamber, $Δ$; the normalized vertical dimension of the chamber; the normalized initial volume difference between the two parts of the chamber, $v_{\text{du}}(0)$; and the structure-to-fluid mass ratio, $λ$. We investigate the dynamics at the early times of the system's evolution and then at moderate times. We obtain the growth rates and the frequency of vibrations around the second and the first buckling modes, respectively. Analytical solutions are derived for these linear stability characteristics within the limit of the small-amplitude approximation. At moderate times, we investigate how the sheet escapes from the second mode. Given the chamber's dimensions, we show that the initial energy of the sheet is mostly converted into hydrodynamic energy of the fluid if $λ\ll 1$, and into kinetic energy of the sheet if $λ\gg 1$. In both cases most of the initial energy is released at time $ t_{\text{p}}\simeq \ln[c Δ^{1/2}/v_{\text{du}}(0)]/σ$, where $σ$ is the growth rate and $c$ is a constant.
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