粘性流体在弯曲管道内在交变压力梯度下的振荡流动

THE OSCILLATORY MOTION OF VISCOUS FLUID IN A CURVED PIPE UNDER ALTERNATE PRESSURE GRADIENT

在血液动力学中 ,一般只有在微血管中才可把血液运动近似看作定常运动 ,而在大动脉或动脉中 ,血液的压力在同一位置上是随时间周期性变化的。考虑到血管具有一定的弯曲度 ,本文引入了一种新的坐标系统 ,解决了弯管中的振荡流问题。给出了流体在弯管中运动的速度及切应力公式 ,并对切应力加以讨论。发现微弯管中的切应力将在壁面上获得极值。本文还通过计算机计算 ,得知流体对弯管两侧的冲刷力也是振荡的。并且随着压力差的增大 ,流体对弯管两侧的冲刷力的差值也增大 ;随着曲率的减小 ,此差值也减小。此结果较好地解释了动脉硬化形成的主要原因 :切应力的影响。对于进一步深入了解血液在血管中的流动 ,特别是血液在弯曲大动脉内流动特性的研究提供了理论依据。

In blood dynamics,only in a capillary,we can consider the blood movement as a constant motion.However,in arteries or bigger ones,blood pressure at the same point changes periodically with time.Considering vessels have some curve,we solve the oscillatory fluid problems of a curved pipe with circular section by introducing a new coordinate system.We also gave out some velocity and stress equations of this problem,and then discussed it in this paper.We also find the stress in the curved pipe will obtain the extreme point on the pipe wall.By using computer to calculate,we find the fluid flush on the curved pipe wall is also oscillatory.And the flush difference between the two sides increases as the curvature increases.To sum up,this paper gave a good explanation to one of the important cause of arteriosclerosis's formation-stress influence,and provides a useful theoretical support for the further study on the blood motion,especially on curved arteries.