轴对称波纹管中振荡流动与壁面剪切应力的闭式解

中文摘要 AI 辅助

波纹管中的脉动流动出现在血流动力学和微流体领域，其中振荡驱动力和几何收缩共同决定输运和壁面载荷。我们将Womersley关于刚性圆管中振荡流动的经典解推广到半径缓慢变化的刚性轴对称管。在润滑近似下，我们推导了任意Womersley数下轴向速度剖面、体积流量、相位滞后和壁面剪切应力的闭式表达式。使用三维格子玻尔兹曼模拟来评估该理论的有效性范围。分析表明，局部速度剖面沿管变化强烈，从宽段的类活塞形到瓶颈附近的更抛物线形。循环最大流量随波纹度增加而减小，但这种减小随脉动性增强而减弱，反映了从准稳态标度$\langle R^{-4}\rangle^{-1}$到高频标度$\langle R^{-2}\rangle^{-1}$的交叉。壁面剪切应力在瓶颈处最大，并随Womersley数增加而减小。对于正弦波纹，由于局部剪切放大和全局水力阻力之间的竞争，瓶颈壁面剪切应力对波纹度的依赖是非单调的。时间平均壁面剪切应力和振荡剪切指数的闭式表达式进一步将理论与标准血流动力学指标联系起来。

英文摘要

Pulsatile flow in corrugated tubes arises in hemodynamics and microfluidics, where oscillatory forcing and geometric constrictions jointly determine transport and wall loading. We extend Womersley's classical solution for oscillatory flow in a rigid circular tube to rigid axisymmetric tubes of slowly varying radius. Within the lubrication approximation, we derive closed-form expressions for the axial velocity profile, volumetric flow rate, phase lag, and wall shear stress at an arbitrary Womersley number. Three-dimensional lattice Boltzmann simulations are used to assess the regime of validity of the theory. The analysis shows that the local velocity profile varies strongly along the tube, ranging from plug-like in wide sections to more parabolic near bottlenecks. The cycle-maximum flow rate decreases with increasing corrugation, but this reduction weakens as pulsatility increases, reflecting a crossover from the quasi-steady scaling $\langle R^{-4}\rangle^{-1}$ to the high-frequency scaling $\langle R^{-2}\rangle^{-1}$. The wall shear stress is maximal at the bottleneck and decreases with Womersley number. For sinusoidal corrugations, the bottleneck wall shear stress depends non-monotonically on the corrugation because of the competition between local shear amplification and global hydraulic resistance. Closed-form expressions for the time-averaged wall shear stress and oscillatory shear index further connect the theory to standard hemodynamic metrics.

发表机构

• Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IET-2), Forschungszentrum Jülich（亥姆霍兹尤利希埃尔朗根-纽伦堡可再生能源研究所）
• Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）

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