Analysis of coupled problem between collapsible tube and pulsatile flow by means of computational mechanics

用计算力学方法解决了可折叠管与管内流动的耦合问题，研究了动脉硬化等血液疾病的流体动力学成因。可折叠管是一种血管模型。当采用管律时，耦合问题被表述为管轴向的一维问题。利用管律将血管内的脉动流动建模为在可折叠管中传播的孤立压力波。计算得到的压力波与实验结果吻合较好。提出了一种二维计算方法，以获得高精度的管律，并对大变形管进行了三维有限元计算，以校核管的三维效应。以主动脉弓为模型，采用有限元方法对锥形u型弯道内的三维脉动流进行了计算。由于主动脉弓具有高刚性，因此壁被认为是刚性的。将所得截面内的速度分布与实验结果进行了比较，并给出了截面内的二次流。提出了一种可折叠管轴向压力分布的计算方法，该可折叠管主要是由于管内低压引起的屈曲变形。对大变形管内的三维流动进行了数值模拟。将计算得到的截面轴向速度分布与实验结果进行了比较，两者吻合较好。计算了截面内二次流分布、管内剪切速率分布和管壁剪应力分布。结果表明，高壁剪应力区出现在8字形屈曲截面中心附近。

The coupled problem between collapsible tube and flow in it was solved by means of computational mechanics to researeh fluid-dynamic cause of blood disease such as arteriosclerosis. The collapsible tube is a model of blood vessels. When the tube law is used, the coupled problem is formulated as one-dimensional problem in the axial-direction of the tube. The pulsatile flow in a blood vessel is modeled as an isolated pressure wave propagating in the collapsible tube by using the tube law. The calculated pressure waves agreed well with experimental results. A two-dimensional calculation method is proposed to obtain the tube law with high accuracy and a three-dinensional FEM calculation of largely deformed tube by buckhng was performed to check three-dimensional effects of the tube on the tube law. A three-dimensional pulsatile flow calculation in a tapered U-bend as a model of an aortic arch was performed by means of FEM. The wall was asswned to be rigid due to the fact that the aortic arch has high rigidity. The obtained velocity profiles in the cross-sections are compared to experinental results, and secondary flow in the cross-section is shown. A method for calculating pressure distribution in the axial-direction pf the collapsible tube which is deformed largely by buckling due to low pressure in the tube was proposed. The three-dimensional flow in the largely deformed tube was numerically simulated. The axial velocity profiles in cross-sections obtained in the calculation were compared with experinental results, and reasonable agreement between them was obtained. The secondary flow distribution in the cross-sections, shear rate distribution in the tube and wall shear stress distribution are calculated. It is shown that high wall shear stress region occurs around the center of the cross'section which is buckled in figure-8 shaped.