Baaijens J P, van Steenhoven A A, Janssen J D
Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands.
Biorheology. 1993 Jan-Feb;30(1):63-74.
The stationary flow of blood in a two-dimensional model of the bifurcation of the human carotid artery is simulated numerically using a finite element method. The Reynolds number is taken as equal to 300, corresponding to the value during the end-diastolic phase of the heart cycle. As constitutive equations, the Newtonian model and the non-Newtonian power-law and Casson models are used. The chosen model parameters corresponded with blood. The flow in this geometry is determined by the branching of the artery and the existence of a reversed flow area in the internal carotid artery. From the results of this problem, we conclude that the general flow structure is not influenced by the generalized (non-)Newtonian models. However, there are differences that cannot be neglected. First, the generalized Newtonian models result in axial and secondary velocity profiles that have 5-10% lower maximum values compared to the Newtonian model. Second, the pressure has higher values in the case of the generalized Newtonian models, especially in the internal carotid artery where these models give maximal 25% higher pressure values. Third, along the divider wall, the wall shear stresses are lower for the generalized Newtonian models; near the apex, this difference is maximal 40% in case of the power-law model. The generalized Newtonian models give higher wall shear stresses along the non-divider wall than the Newtonian model, the maximum difference being 5%. And fourth, in the internal carotid artery the reversed flow area is 10% reduced by the generalized Newtonian models. In general, the differences are more pronounced in the case of the power-law model.
采用有限元方法对二维人体颈动脉分叉模型中的血液稳态流动进行了数值模拟。雷诺数取为300，对应于心周期舒张期末期的值。作为本构方程，使用了牛顿模型、非牛顿幂律模型和卡森模型。所选模型参数与血液相对应。这种几何结构中的流动由动脉分支和颈内动脉中逆流区域的存在决定。从该问题的结果可以得出，一般流动结构不受广义（非）牛顿模型的影响。然而，存在一些不可忽视的差异。首先，广义牛顿模型导致轴向和二次速度剖面的最大值比牛顿模型低5%-10%。其次，在广义牛顿模型的情况下，压力值更高，特别是在颈内动脉中，这些模型给出的压力值最高可高出25%。第三，沿着分隔壁，广义牛顿模型的壁面剪应力较低；在顶点附近，幂律模型的这种差异最大可达40%。广义牛顿模型沿非分隔壁给出的壁面剪应力比牛顿模型高，最大差异为5%。第四，在颈内动脉中，广义牛顿模型使逆流区域减少了10%。一般来说，幂律模型情况下的差异更为明显。
