Numerical Investigation on Mixing Efficiency and Exponential Fluid Stretching in Chaotic Mixing

The stretching and folding of fluid element during chaotic mixing field is studied using numerical method. The chaotic mixing process is caused by periodic secondary flow in a twisted curved pipe. Using the nonlinear discrete velocity field as the dynamical system, the present study connects the fluid particle's stretching along its trajectory in one period to a linearized time-varying variational equation. After numerical approximation of the variational equation, fluid stretching is calculated on the whole cross section. The stretching distribution shows an exponential fluid stretching and folding, which indicates an excellent mixing performance.

A Micromixer Using the Taylor-Dean Flow: Effects of Aspect Ratio and Inflow Condition on the Mixing

Chaotic mixing in three different types of curved-rectangular channels flow has been studied experimentally and numerically. Two walls of the channel (inner and top walls) rotate around the center of curvature and a pressure gradient are imposed in the direction toward the exit of the channel. This flow is a kind of Taylor-Dean flow. There are two parameters dominating the flow, the Dean number De (∝ the pressure gradient or the Reynolds number) and the Taylor number Tr (∝ the angular velocity of the wall rotation). In this paper, we analyze the physical mechanism of chaotic mixing in the Taylor-Dean flow by comparing experimental results and numerical ones. We produced three micromixer models of the curved channel, several centimeters long, with rectangular cross-section of a few millimeters side. The secondary flow is measured using laser induced fluorescence (LIF) method to examine secondary flow characteristics. Also we performed three-dimensional numerical simulations with the open source CFD solver, OpenFOAM, for the same configuration as the experimental system to study the mechanism of chaotic mixing. It is found that good mixing performance is obtained in the case of De ≤ 0.1 Tr, and it becomes more remarkable when the aspect ratio tends to large. And it is found that the mixing efficiency changes according to the aspect ratio and inflow condition.

A Micromixer Using the Taylor-Dean Flow: Effect of Inflow Conditions on the Mixing

Chaotic mixing in a curved-square channel flow is studied experimentally and numerically. Two walls of the channel (inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction toward the exit of the channel. This flow is a kind of Taylor-Dean flows. There are two parameters dominating the flow, the Dean number De (∝ the pressure gradient or the Reynolds number) and the Taylor number Tr (∝ the angular velocity of the wall rotation). In the present paper, we analyze the physical mechanism of chaotic mixing in the Taylor-Dean flow by comparing experimental and numerical results. We produced a micromixer model of the curved channel several centimeters long with square cross section of a few millimeters side. The secondary flow was measured using laser induced fluorescence (LIF) method to examine secondary flow characteristics. We also performed three-dimensional numerical simulations for the exactly same configuration as the experimental system to study the mechanism of chaotic mixing. It is found that good mixing performance is achieved for the case of De ≤ 0.1Tr, and that mixing efficiency changes according to the difference in inflow conditions. The flow is studied both experimentally and numerically, and both results agree with each other very well.

Numerical Simulation of Jet Issuing Diagonally Upward into Density-Stratified Fluid in Cylindrical Tank

This study simulates the behavior of a jet issuing into a two-layer density-stratified fluid in a cylindrical tank and the resulting mixing phenomena. The upper and lower fluids are water and an aqueous solution of sodium chloride (NaCl), respectively, with the lower fluid issuing diagonally upward from a nozzle on the bottom of the tank. The angle between the centerline of the jet and the tank bottom is 60°. The phenomena when the Reynolds number Re of the jet is 475, 1426, and 2614 are simulated. The mass concentration of the aqueous solution of NaCl is 0.02. The simulation successfully grasps the jet behavior and the resulting mixing, which agree with the authors’ experimental results at the corresponding Re value. The secondary flows that appear in the horizontal cross-sections consist of a pair of vortices and flows along the tank wall. The secondary flow at the density interface represents the intrusion of an internal density current, which gives rise to mixing along the interface.

Behavior of a Jet Issuing Diagonally Upward into Two-Layer Density-Stratified Fluid in a Cylindrical Tank

This study is concerned with the experimental investigation of a jet issuing diagonally upward into a two-layer density-stratified fluid in a cylindrical tank and the resulting mixing phenomena. The upper and lower fluids are water and an aqueous solution of sodium chloride (NaCl), respectively, and the lower fluid issues from a nozzle on the bottom of the tank. The angle between the centerline of the jet and the bottom of the tank is 60o, and the mass concentration of the NaCl solution is 0.02. The investigation reveals that secondary flow is caused by the jet in the horizontal cross-sections of the tank and that it is composed of a pair of vortices. It confirms that the secondary flow at the density interface corresponds to an internal density current. The investigation also clarifies the effect of the Reynolds number of the jet on mixing between the lower and upper fluids.

二次流实现流体混沌混合的数值研究

在加权残余法与谱方法相结合的基础上,分析了扭转弯管中的二次层流,并说明了在某些情况下将诱发混沌现象.根据二次流的动力学特性,建立了扭管不同截面之间的非线性映射关系,用数值方法研究了流体微团在该映射下的混合特性,并进行了实验研究.结果表明,利用不同的单元弯管的组合与连续扭转,可以实现流体在层流状态下的高效无切割混合.

流体混沌混合过程的可视化方法研究

为解决流体混沌混合的可视化问题 ,本文提出采用逆向庞加莱胞映射方法 ,来控制混沌系统数值模拟过程中的初始误差敏感 ,用插值胞映射的方法 ,来提高模拟效率。并用这一方法 ,成功地实现了扭转弯管中混沌混合过程的计算机动画模拟 ,研究表明 ,本文所提出的逆向庞加莱胞映射和插值胞映射相结合 ,可以大幅度提高模拟精度与速度 。