An unsteady mathematical model to study the characteristics of blood flowing through an arterial segment in the presence of a couple of stenoses with surface irregularities is developed. The flow is treated to be axisymmetric, with an outline of the stenoses obtained from a three dimensional casting of a mildly stenosed artery [1], so that the flow effectively becomes two-dimensional. The governing equations of motion accompanied by appropriate choice of boundary and initial conditions are solved numerically by MAC (Marker and Cell) method in cylindrical polar coordinate system in staggered grids and checked numerical stability with desired degree of accuracy. The pressure-Poisson equation has been solved by successive-over-relaxation (SOR) method and the pressure-velocity correction formulae have been derived. The flexibility of the arterial wall has also been accounted for in the present investigation. Further, in-depth study in the flow pattern reveals that the separation Reynolds number for the multi-irregular stenoses is lower than those for cosine-shaped stenoses and a long single irregular stenosis. The present results predict the excess pressure drop across the cosine stenoses than the irregular ones and show quite consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.
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机译:建立了一个不稳定的数学模型,用于研究在具有一对表面不规则的狭窄的情况下流经动脉段的血液的特征。该流被视为轴对称的,具有从三维狭窄的狭窄动脉[1]的三维铸造获得的狭窄的轮廓[1],因此该流有效地变为二维。通过MAC(Marker and Cell)方法在交错网格的圆柱极坐标系中用数值方法求解伴随边界和初始条件适当选择的运动控制方程,并以所需的精度检查数值稳定性。通过逐次松弛法(SOR)求解了压力泊松方程,推导了压力速度修正公式。在本研究中也考虑了动脉壁的柔性。此外,对流型的深入研究表明,多不规则狭窄的分离雷诺数低于余弦形狭窄和较长的单个不规则狭窄的雷诺数。目前的结果预示了余弦狭窄处的压力下降将比不规则狭窄发生过多,并且与文献中已有的一些结果非常一致,这些证据足以证实所考虑的模型的适用性。
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