In this paper, we study the blood flow through blood vessels of various radii (including the case of variable cross section as well as modeling the blood flow through venae and arteries). Two approaches are discussed in order to mimic the dependence of blood viscosity on red blood cells aggregation, which changes with the shear rate and position inside the vessel: Two microstructural parameters together with empirical constitutive equations as a characteristic of aggregation are proposed, namely the microinertia as well as the volume fraction of blood particles (erythrocytes, platelets and leukocytes). Consequently, the Navier–Stokes system of equations for an incompressible fluid is supplemented by a constitutive equation for the moment of inertia in one case and for the volume fraction in another. The problems are solved numerically by the finite volume method for vessels of various geometries in spatial description. A comparison with experimental data for a narrow capillary shows the efficiency of the proposed constitutive equations for describing blood flow. Also, velocity profiles are obtained on the basis of compiled empirical formula for various sections of a blood vessel of variable radius. In addition, the flow through vessels of the human circulatory system, such as the inferior vena cava and the carotid artery, are studied.

在本文中，我们研究了通过各种半径的血管的血流（包括可变横截面的情况以及对通过静脉和动脉的血流进行建模）。为了模拟血液粘度对红细胞聚集的依赖关系，讨论了两种方法，红细胞聚集随着剪切速率和血管内位置的变化而变化：提出了两个微观结构参数以及作为聚集特征的经验本构方程，即微惯性以及血液颗粒（红细胞、血小板和白细胞）的体积分数。因此，不可压缩流体的纳维-斯托克斯方程组在一种情况下由惯性矩和另一种情况下体积分数的本构方程补充。该问题通过空间描述中各种几何形状的容器的有限体积法进行数值求解。与狭窄毛细管的实验数据的比较显示了所提出的描述血流的本构方程的效率。此外，根据针对不同半径的血管的各个部分编制的经验公式获得速度分布。此外，流经人体循环系统血管的流量，如下肢血管研究了腔静脉和颈动脉。