Reduced models of unidirectional flows in compliant rectangular ducts at finite Reynolds number
Reduced models of unidirectional flows in compliant rectangular ducts at finite Reynolds number
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DOI：
10.1063/5.0062252
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发表时间：
2021-09
影响因子：
4.6
通讯作者：
Xiaojia Wang;I. Christov
中科院分区：
文献类型：
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作者：
Xiaojia Wang;I. Christov
软水力学，解决内部流动和柔性管道之间的相互作用，是微流体的核心问题。本文对具有软顶壁的矩形管道中牛顿流体的稳态流动进行了分析。所得到的流固相互作用（FSI）是在流动惯性消失和有限的情况下形成的。在小展弦比的第一阶，润滑近似表明压力只在顺流方向上变化。同时，柔顺壁面的细长细比使其流固界面表现为温克勒基础，位移完全由局部压力决定。流动和变形的耦合以及横截面上的平均可以得到一维简化模型。在流动惯性消失的情况下，严格定义了有效变形通道高度，以消除变形的展向依赖性。结果表明，以前使用的平均高度概念是可以接受的近似。从一维模型出发，导出了摩擦系数和相应的泊索依数。与刚性风管不同，柔性风管的泊泽维尔数不是恒定的，而是沿流方向变化的。依从性可以使泊泽维尔数增加四倍。有限流动惯量的模型是通过假设沿流速度的垂直抛物线变化而得到的。为了满足沿河道边缘的位移约束，在顺流方向引入弱张力，对类winkler基础模型进行正则化。导出了正则化模型的匹配渐近解。
Soft hydraulics, which addresses the interaction between an internal flow and a compliant conduit, is a central problem in microfluidics. We analyze Newtonian fluid flow in a rectangular duct with a soft top wall at steady state. The resulting fluid–structure interaction (FSI) is formulated for both vanishing and finite flow inertia. At the leading-order in the small aspect ratio, the lubrication approximation implies that the pressure only varies in the streamwise direction. Meanwhile, the compliant wall’s slenderness makes the fluid–solid interface behave like a Winkler foundation, with the displacement fully determined by the local pressure. Coupling flow and deformation and averaging across the cross-section leads to a one-dimensional reduced model. In the case of vanishing flow inertia, an effective deformed channel height is defined rigorously to eliminate the spanwise dependence of the deformation. It is shown that a previously-used averaged height concept is an acceptable approximation. From the one-dimensional model, a friction factor and the corresponding Poiseuille number are derived. Unlike the rigid duct case, the Poiseuille number for a compliant duct is not constant but varies in the streamwise direction. Compliance can increase the Poiseuille number by a factor of up to four. The model for finite flow inertia is obtained by assuming a parabolic vertical variation of the streamwise velocity. To satisfy the displacement constraints along the edges of the channel, weak tension is introduced in the streamwise direction to regularize the Winkler-foundation-like model. Matched asymptotic solutions of the regularized model are derived.