A MODEL OF PULSATILE FLOW IN A UNIFORM DEFORMABLE VESSEL
A MODEL OF PULSATILE FLOW IN A UNIFORM DEFORMABLE VESSEL
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DOI：
10.1016/0021-9290(92)90248-y
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发表时间：
1992-01-01
影响因子：
2.4
通讯作者：
ANDERSON, JL
中科院分区：
文献类型：
--
作者：
JOHNSON, GA;BOROVETZ, HS;ANDERSON, JL
模拟天然和人工管道中的血液流动通常需要大型计算机来数值求解Navier-Stokes方程。通常情况下，当解决方案是纯粹的数值时，对流体动力学的物理洞察力就会丢失。这里描述了求解最一般形式的Navier-Stokes方程的替代方案，其中假设解的函数形式以简化所需的计算。选择轴向压力梯度和速度分布的假设形式，以满足直的可变形血管中完全建立的脉动流的质量守恒。由此产生的方程被铸造在有限差分形式和明确解决。刚性壁和零施加压力的极限情况下的结果被发现是在良好的协议与解析解。与Klanchar等人[Circ. Res. 66，1624-1635（1990）]也显示出良好的一致性。应用该模型的现实生理参数值提供了洞察的脉动性质的流场的壁剪切发展的影响，在存在一个移动的壁边界。具体而言，该模型示出了流速和剪切速率对血管壁运动的幅度以及所施加的压力差与血管半径的振荡之间的相位差的依赖性。本模型可以作为一个有用的工具，有兴趣在量化的大小和性质的速度分布和剪切力的天然和人工生物管道的实验。
Simulations of blood flow in natural and artificial conduits usually require large computers for numerical solution of the Navier-Stokes equations. Often, physical insight into the fluid dynamics is lost when the solution is purely numerical. An alternative to solving the most general form of the Navier-Stokes equations is described here, wherein a functional form of the solution is assumed in order to simplify the required computations. The assumed forms for the axial pressure gradient and velocity profile are chosen such that conservation of mass is satisfied for fully established pulsatile flow in a straight, deformable vessel. The resulting equations are cast in finite-difference form and solved explicitly. Results for the limiting cases of rigid wall and zero applied pressure are found to be in good agreement with analytical solutions. Comparison with the experimental results of Klanchar et al. [Circ. Res. 66, 1624-1635 (1990)] also shows good agreement. Application of the model to realistic physiological parameter values provides insight as to the influence of the pulsatile nature of the flow field on wall shear development in the presence of a moving wall boundary. Specifically, the model illustrates the dependence of flow rate and shear rate on the amplitude of the vessel wall motion and the phase difference between the applied pressure difference and the oscillations of the vessel radius. The present model can serve as a useful tool for experimentalists interested in quantifying the magnitude and character of velocity profiles and shearing forces in natural and artificial biologic conduits.