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首页> 外文期刊>Applied Mathematical Modelling >Dynamic Responses Of Shear Flows Over A Deformable Porous Surface Layer In A Cylindrical Tube
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Dynamic Responses Of Shear Flows Over A Deformable Porous Surface Layer In A Cylindrical Tube

机译：圆柱管中可变形多孔表面层上剪切流的动力响应

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摘要

This paper investigates dynamic responses of a viscous fluid flow introduced under a time dependent pressure gradient in a rigid cylindrical tube that is lined with a deformable porous surface layer. With the Darcy's law and a linear elasticity assumption, we have solved the coupling effect of the fluid movement and the deformation of the porous medium in the Laplace transform space. Governing equations are deduced for the solid displacement and the fluid velocity in the porous layer. Analytical solutions in the transformed domain are derived and the time dependent variables are inverted numerically using Durbin's algorithm. Interaction between the solid and the fluid phases in the porous layer and its effects on fluid flow in tube are investigated under steady and unsteady flow conditions when the solid phase is either rigid or deformable. Examples are presented for flows driven by a Heaviside or a sinusoid pressure gradient. Significant effects of the porous surface layer on the flow in the tube are observed. The analytical solutions can be used to test more complicated numerical schemes.
机译：本文研究了在随时间变化的压力梯度下，内衬有可变形多孔表面层的刚性圆柱管中引入的粘性流体流动的动力响应。利用达西定律和线性弹性假设，我们解决了拉普拉斯变换空间中流体运动与多孔介质变形的耦合效应。推导了多孔层中的固体位移和流体速度的控制方程。推导了变换域中的解析解，并使用Durbin算法对时间相关变量进行了数值反演。当固相为刚性或可变形时，在稳定和非稳定流动条件下，研究了多孔层中固相与液相之间的相互作用及其对管内流体流动的影响。给出了由Heaviside或正弦压力梯度驱动的流的示例。观察到多孔表面层对管中流动的显着影响。解析解可用于测试更复杂的数值方案。

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