The Shear-Driven Fluid Motion Using Oscillating Boundaries
The Shear-Driven Fluid Motion Using Oscillating Boundaries
复制标题
使用振荡边界的剪切驱动流体运动
DOI：
10.1115/1.4006362
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发表时间：
2012
影响因子：
2
通讯作者：
N. Daidzic
中科院分区：
文献类型：
--
作者：
M. Hossain;N. Daidzic
一个经典的Stokes第二问题已经知道了很长一段时间，并代表了非线性Navier-Stokes方程的少数精确解之一。然而，在简谐边界激励下的半无限区域内的牛顿流体的振荡流动仅导致流体在近壁附近来回风车。在这项研究中，我们提出的数学模型和数值模拟的牛顿流体和剪切稀化的非牛顿仿血液流体流动。正流量是由一个或两个无限边界平壁的周期性非谐振荡运动获得的。本文研究了半无限或有限二维几何中的振荡流动，边界条件为周期性或周期性的正正弦边界条件。使用的人血液流变学模型有：Power-Law、Sisko、Carreau和Herschel-Bulkley。采用有限体积离散的有限差分法求解一维含时非线性耦合守恒扩散型边界层质量、动量和能量方程。这是可能的测试的准确性，内部开发的计算程序与几个等温流动的分析解决方案，并与著名的经典斯托克斯的第一和第二个问题。在各种配置中以及在没有逆压梯度的情况下实现了正流速。身体的力量，如重力，被忽略了。利用同相正弦和整流正弦壁激励的计算产生了可观的净流量，该净流量从静止开始，在三到十个周期之后稳定并变得准稳定，这取决于流体流变学。假设壁面作动器的快速回程导致壁面总滑移，而在无滑移边界条件下存在前向壁面运动。剪切“驱动”和“驱动”流体区域被确定。剪切稀化流体流变学提供了许多有趣的结果，如塞状流。多平面扩散渗透层的相长干涉可以作为微尺度下实用的抽运机制。
A classical Stokes’ second problem has been known for a long time and represents one of the few exact solutions of nonlinear Navier-Stokes equations. However, oscillatory flow in a semi-infinite domain of Newtonian fluid under harmonic boundary excitation only leads to fluid wind-milling back and forth in close wall vicinity. In this study, we are presenting the mathematical model and the numerical simulations of the Newtonian fluid and the shear-thinning non-Newtonian blood-mimicking fluid flow. Positive flow rates were obtained by periodic yet nonharmonic oscillatory motion of one or two infinite boundary flat walls. The oscillatory flows in semi-infinite or finite 2D geometry with sawtooth or periodic rectified-sine boundary conditions are presented. Rheological human blood models used were: Power-Law, Sisko, Carreau, and Herschel-Bulkley. A one-dimensional time-dependent nonlinear coupled conservative diffusion-type boundary layer equations for mass, linear momentum, and energy were solved using the finite-differences method with finite-volume discretization. It was possible to test the accuracy of the in-house developed computational programs with the few isothermal flow analytical solutions and with the celebrated classical Stokes’ first and second problems. Positive flow rates were achieved in various configurations and in absence of the adverse pressure gradients. Body forces, such as gravity, were neglected. The calculations utilizing in-phase sawtooth and rectified-sine wall excitations resulted in respectable net flow which stabilizes and becomes quasi-steady, starting from rest, after three to ten periods depending on the fluid rheology. It was assumed that rapid return stroke of the wall actuator resulted in total wall slip while forward wall motion existed with no-slip boundary condition. Shear “driving” and “driven” fluid regions were identified. The shear-thinning fluid rheology delivered many interesting results, such as pluglike flow. Constructive interference of diffusive penetration layers from multiple flat surfaces could be used as practical pumping mechanism in micro-scales.