Xu X Y, Collins M W, Jones C J
Thermo-Fluids Engineering Research Centre, City University, London, U.K.
J Biomech Eng. 1992 Nov;114(4):504-11. doi: 10.1115/1.2894102.
Three-dimensional flows through canine femoral bifurcation models were predicted under physiological flow conditions by solving numerically the time-dependent three-dimensional Navier-stokes equations. In the calculations, two models were assumed for the blood, those of (a) a Newtonian fluid, and (b) a non-Newtonian fluid obeying the power law. The blood vessel wall was assumed to be rigid this being the only approximation to the prediction model. The numerical procedure utilized a finite volume approach on a finite element mesh to discretize the equations, and the code used (ASTEC) incorporated the SIMPLE velocity-pressure algorithm in performing the calculations. The predicted velocity profiles were in good qualitative agreement with the in vivo measurements recently obtained by Jones et al. The non-Newtonian effects on the bifurcation flow field were also investigated, and no great differences in velocity profiles were observed. This indicated that the non-Newtonian characteristics of the blood might not be an important factor in determining the general flow patterns for these bifurcations, but could have local significance. Current work involves modeling wall distensibility in an empirically valid manner. Predictions accommodating these will permit a true quantitative comparison with experiment.
通过对随时间变化的三维纳维-斯托克斯方程进行数值求解，预测了生理流动条件下犬股动脉分叉模型中的三维流动。在计算中，假定血液有两种模型，即（a）牛顿流体模型和（b）服从幂律的非牛顿流体模型。假定血管壁是刚性的，这是对预测模型的唯一近似。数值计算过程在有限元网格上采用有限体积法对方程进行离散，所使用的代码（ASTEC）在计算中采用了SIMPLE速度-压力算法。预测的速度剖面与琼斯等人最近获得的体内测量结果在定性上吻合良好。还研究了非牛顿特性对分叉流场的影响，未观察到速度剖面有很大差异。这表明血液的非牛顿特性可能不是决定这些分叉处总体流动模式的重要因素，但可能具有局部意义。目前的工作包括以经验有效的方式对血管壁的可扩张性进行建模。考虑到这些因素的预测将允许与实验进行真正的定量比较。
