Huang Z J, Merkle C L, Abdallah S, Tarbell J M
Department of Chemical Engineering, Pennsylvania State University, University Park 16802.
J Biomech. 1994 Apr;27(4):391-402. doi: 10.1016/0021-9290(94)90015-9.
Heart valves induce flow disturbances which play a role in blood cell activation and damage, but questions of the magnitude and spatial distribution of fluid stresses (wall shear stress and turbulent stress) cannot be readily addressed with current experimental techniques. Therefore, a numerical simulation procedure for flow through artificial heart valves is presented. The algorithm employed is based on the Navier-Stokes equations in generalized curvilinear coordinates with artificial compressibility for coupling of velocity and pressure. The algorithm applies a finite-difference technique on a body-conforming composite grid around the heart valve disk on which the numerical simulations are performed. Steady laminar flow over a backward-facing step and unsteady laminar flow inside a square driven cavity are computed to validate the algorithm. Two-dimensional, time-accurate simulation of flow through a tilting disk valve with a steady upstream Reynolds number as high as 1000 reveals the complex behavior of 'vortex shedding'. By scaling the results at the Reynolds number of 1000 to peak systolic flow conditions, the maximum value of shear stress on the valve disk is estimated to be 770 dyn cm-2. The 'apparent' Reynolds stress associated with vortex shedding is estimated to be as high as 3900 dyn cm-2 with a vortex shedding frequency of about 26 Hz. The 'apparent' Reynolds stress value is of similar magnitude as reported in experiments but would not be expected to damage blood cells because the spatial scales associated with vortex shedding are much larger than blood cell dimensions.
心脏瓣膜会引发血流紊乱，这在血细胞激活和损伤过程中发挥作用，但目前的实验技术尚无法轻易解决流体应力（壁面剪应力和湍流应力）的大小及空间分布问题。因此，本文提出了一种用于模拟人工心脏瓣膜内血流的数值模拟程序。所采用的算法基于广义曲线坐标系下的纳维 - 斯托克斯方程，并采用人工可压缩性来耦合速度和压力。该算法在围绕心脏瓣膜盘的贴合物体的复合网格上应用有限差分技术，在此网格上进行数值模拟。通过计算后向台阶上的稳态层流以及方腔驱动流体内的非稳态层流来验证该算法。对上游稳定雷诺数高达1000的倾斜盘式瓣膜内的血流进行二维时间精确模拟，揭示了“涡旋脱落”的复杂行为。通过将雷诺数为1000时的结果按峰值收缩期血流条件进行缩放，估计瓣膜盘上剪应力的最大值为770达因/平方厘米。与涡旋脱落相关的“表观”雷诺应力估计高达3900达因/平方厘米，涡旋脱落频率约为26赫兹。“表观”雷诺应力值与实验报道的量级相似，但预计不会损伤血细胞，因为与涡旋脱落相关的空间尺度远大于血细胞尺寸。
