Stability of the flow of a fluid through a flexible tube at intermediate Reynolds number
Stability of the flow of a fluid through a flexible tube at intermediate Reynolds number
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中间雷诺数下流体通过柔性管流动的稳定性
DOI：
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发表时间：
1998
影响因子：
3.7
通讯作者：
V. Kumaran
中科院分区：
文献类型：
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作者：
V. Kumaran
使用线性稳定性分析，分析了流体在挠性管中流动的稳定性在雷诺数为1和104的范围内。该系统由密度为ρ、黏度为η、最大速度为V的牛顿流体通过半径为R的圆管的哈根-泊松流动组成。在R<；R<；HR区域内，圆管被密度为ρ、剪切模数为G、黏度为η的不可压缩粘弹性固体包围。在中间雷诺数范围内，稳定性取决于雷诺数Re=ρVr/η，无因次参数[Sum]=ρGr2/η2，粘度比ηr=ηS/η，半径H与扰动波数k之比。对于ηr=0，当雷诺数超过临界值Rec时，流动变得不稳定，并且临界雷诺数随着[Sum]的增加而增加。在高雷诺数极限下，发现Rec和[∝]α，其中α在0.7~0.75之间变化，H在1.1~10.0之间变化。对流动结构的分析表明，对于Re[GT]1，粘性应力被限制在厚度为Re−1/3的边界层内，按ηV/R表示的剪应力按Re 1/3增加。然而，即使在103Re<；105时，法向应力也不存在简单的标度律，因此临界雷诺数也不符合简单的标度关系。分析了ηr的变化对稳定性的影响，发现ηr的变化可以定性地改变稳定性特性。在相对较低的[η]值(约102)下，体系在所有的[SUM]值都可能变得不稳定，但在相对较高的[SUM]值(大于约104)时，只有当粘度比低于最大值η*Rm时，才会观察到不稳定。
The stability of the flow of a fluid in a flexible tube is analysed over a range of Reynolds numbers 1<Re<104 using a linear stability analysis. The system consists of a Hagen–Poiseuille flow of a Newtonian fluid of density ρ, viscosity η and maximum velocity V through a tube of radius R which is surrounded by an incompressible viscoelastic solid of density ρ, shear modulus G and viscosity ηs in the region R<r<HR. In the intermediate Reynolds number regime, the stability depends on the Reynolds number Re=ρVR/η, a dimensionless parameter [sum ]=ρGR2/η2, the ratio of viscosities ηr= ηs/η, the ratio of radii H and the wavenumber of the perturbations k. The neutral stability curves are obtained by numerical continuation using the analytical solutions obtained in the zero Reynolds number limit as the starting guess. For ηr=0, the flow becomes unstable when the Reynolds number exceeds a critical value Rec, and the critical Reynolds number increases with an increase in [sum ]. In the limit of high Reynolds number, it is found that Rec∝[sum ]α, where α varies between 0.7 and 0.75 for H between 1.1 and 10.0. An analysis of the flow structure indicates that the viscous stresses are confined to a boundary layer of thickness Re−1/3 for Re[Gt ]1, and the shear stress, scaled by ηV/R, increases as Re1/3. However, no simple scaling law is observed for the normal stress even at 103<Re<105, and consequently the critical Reynolds number also does not follow a simple scaling relation. The effect of variation of ηr on the stability is analysed, and it is found that a variation in ηr could qualitatively alter the stability characteristics. At relatively low values of [sum ] (about 102), the system could become unstable at all values of ηr, but at relatively high values of [sum ] (greater than about 104), an instability is observed only when the viscosity ratio is below a maximum value η*rm.