Stability of Fluid Flow through a Channel with Flexible Walls
Stability of Fluid Flow through a Channel with Flexible Walls
复制标题
流体通过柔性壁通道的稳定性
DOI：
10.1155/2021/8825677
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发表时间：
2021
影响因子：
1.2
通讯作者：
Edwards, Madeline M.
中科院分区：
文献类型：
--
作者：
Shubov, Marianna A.;Edwards, Madeline M.
本文总结了流体在柔性壁通道中运动并与壁面相互作用的稳定性问题的研究结果。船壁受到行波的影响。实验数据表明，流动流体的能量可以被结构（壁）传递和消耗，从而诱发“行波颤振”。流体-结构相互作用的稳定性问题分为两个部分：（a）具有谐波运动壁的通道中的流体流动的稳定性和（B）参与与流动的能量交换的固体结构的稳定性。流体流动的稳定性是研究的主要内容，通过求解流函数的初边值问题得到。本文的主要研究结果如下：（i）流函数的初始边界问题的严格公式化，流函数的初始边界问题是由流体-结构相互作用模型引起的，该模型考虑了流动的轴对称模式和通道壁附近的“无滑移”条件;（二）二重积分变换的应用（傅里叶变换和拉普拉斯变换）对方程以及边界和初始条件，（3）推导了流函数的傅里叶变换的显式公式;（iv）求出了n（x，y，t）的傅里叶逆变换，并证明了n（x，y，t）的重构可以通过复k-平面上的极限过程来获得，这允许我们使用留数定理并以留数的无穷级数的形式表示解。这项研究的结果是一个分析的解决方案，描述血液流经一个通道，灵活的墙壁，正在扰动的形式，行波。
In the present paper, we summarize the results of the research devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls. The walls of the vessel are subject to traveling waves. Experimental data show that the energy of the flowing fluid can be transferred and consumed by the structure (the walls), inducing “traveling wave flutter.” The problem of stability of fluid‐structure interaction splits into two parts: (a) stability of fluid flow in the channel with harmonically moving walls and (b) stability of solid structure participating in the energy exchange with the flow. Stability of fluid flow, the main focus of the research, is obtained by solving the initial boundary value problem for thestream function. The main findings of the paper are the following: (i) rigorous formulation of the initial boundary problem for the stream function,ψ(x,y,t), induced by the fluid‐structure interaction model, which takes into account the axisymmetric pattern of the flow and “no‐slip” condition near the channel walls; (ii) application of a double integral transformation (the Fourier transformation and Laplace transformation) to both the equation and boundary and initial conditions, which reduces the original partial differential equation to a parameter‐dependent ordinary differential equation; (iii) derivation of theexplicitformula for the Fourier transform of the stream function, ψ˜k,y,t; (iv) evaluation of the inverse Fourier transform of ψ˜k,y,t and proving that reconstruction ofψ(x,y,t) can be obtained through a limiting process in the complexk‐plane, which allows us to use the Residue theorem and represent the solution in the form of an infinite series of residues. The result of this research is an analytical solution describing blood flowing through a channel with flexible walls that are being perturbed in the form of a traveling wave.
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