刚性圆管中血液周期振荡流的切应力分布

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的压力梯度与切应力之间的关系式。在此基础上，详细讲座了圆管中轴向流速和切变率谐波的变化规律，指出流速谐波和切变率谐波的幅值都将随着谐波次数的增大而逐渐减小。为了使所得结果便于应用。文章通过管轴向中心线流速与压力梯度之间的关系式，进一步给出一种利用管轴向中心线流速计算管内切应力分布的简便方法。该方法用于检测活体血管内血液振荡流的切应力分布，具有操作简单，精度较高的优点。最后，以人体颈动脉为例，讨论血液周期振荡流的切应力的分布特性。发现在任意时刻，除了邻近管壁处切应力急剧增大到一定数值之外，沿管截面切应力分布相当均匀且接近于零，呈现出与定常流不同的切应力分布特征。

Fluid Shear Stress Distribution of Periodic Oscillatory Blood Flow in Rigid Circular Tube

In this paper, by solving equations of periodic oscillatory blood flow in the circular tube, the relationship between shear stress and pressure gradient in the tube was obtained. Based on it, the behavior of harmonic components of axial velocity and shear rates in the circular tube was discussed in detail. The results show that the amplitudes of harmonic components of axial velocity and shear rates will decrease with the increase of harmonic numbers. For clinic application, a convenient method was proposed through the relationship between centerline velocity and pressure gradient that the distribution of blood flow shear stress could be obtained by measuring the centerline velocity in the tube. The method is simple in application and can get higher precision when it is used to determine the shear stress of periodic oscillatory blood flow in the tube in vivo. Finally, as an example, the properties of the shear stress distribution in periodic oscillatory flow of human carotid were discussed. The results show that the shear stress distribution at any given instant is almost uniform and close to zero within the cross-section, except very near the arterial wall where the shear stress increases rapidly to a certain value. There is obvious difference of shear stress distribution between oscillatory and steady blood flow in the tube.