The developed mathematical model was applied for study of fluid dynamics in a rotational bioreactor for bone tissue engineering by in vitro technology. The research goal is finding an optimal mode for rotation ensuring proper cyclic loading from fluid upon the cell-seeded biomaterial. The basis for developing a mathematical model of a bioreactor was a design of rotational type biological reactor used in medical research; the liquid flow is generated through viscosity mechanism due to surface rotation. Mathematical description of flow in a reactor cavity was performed with Navier—Stokes equations. It was assumed that flow regime in the boundary layer is laminar. Numerical algorithm was accomplished using a fluid flow solver “Fluent” in the code package ANSYS-12. Four variants of generating the rotational motion in the reactor cavity were considered. A series of parametric computations was performed for the rotation frequency f in the range 0.05 ≤ f ≤ 0.25 Hz. The paper offers visualization of velocity fields in the vertical plane. The distributions for shear stress and pressure in the working zone of reactor were calculated and analyzed. Simulations demonstrated that a method of fluid rotation by driving the outer cylinder with an offset axis is the best for arranging a cyclic pressure and cyclic shear stress on the biological material.

中文翻译：

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用于骨组织工程的旋转生物反应器封闭腔中的流体流动

所开发的数学模型被用于体外研究骨组织工程旋转生物反应器中的流体动力学。技术。研究目标是找到一种最佳的旋转模式，以确保从流体到播种生物材料上的适当循环载荷。建立生物反应器数学模型的基础是医学研究中使用的旋转式生物反应器的设计。由于表面旋转，液体通过粘性机制产生。使用Navier-Stokes方程对反应堆腔中的流动进行数学描述。假定边界层的流动状态是层流的。数值算法是使用代码包ANSYS-12中的流体流动求解器“ Fluent”完成的。考虑了在反应堆腔中产生旋转运动的四个变体。对旋转频率f在0.05≤范围内进行了一系列参数计算˚F ≤0.25赫兹。本文提供了垂直平面内速度场的可视化。计算并分析了反应器工作区的切应力和压力分布。模拟表明，通过用偏心轴驱动外圆柱体来进行流体旋转的方法最适合在生物材料上布置循环压力和循环剪切应力。