Improrement of the efficiency of the mixing of fluids in three-dimensional flows by the use of chaos

以静态混合器为例，研究了在无限长旋转圆筒内由一定角度的轴向周期平面板对组成的分隔板混合器（PPM）模型。在由无限长平面板速度场和瞬态速度场组成的近似速度场下，对流体单元的混沌运动和混合效率进行了检验，得到如下结果：(1)通过推广PPM模型，可以提高混合效率，其中一对平面板的长度比a可以从1改变，板与板之间的角度可以从90度改变。(2)在少数情况下，庞加莱截面不足以作为混合效率的指标。轴向周期。分离线U(n)是流体颗粒在n个周期内移动到某一个前缘的截面初始位置的集合，可以作为n个周期内混合的指标。也就是说，如果U(n)密集分布的区域较大，则期望有效混合。其次，通过对PPM下精确速度场的数值计算，发现该速度场在较小的轴向压力梯度下存在逆流区，与近似速度场有较大差异。从基于精确速度场的庞加莱剖面中得到如下结果：(1)与近似速度场的结果类似，将a改变为合适的值可以缩小规则区域。(2)对于精确的速度场，也可以引入U(n)。如果U(n)密集分布的区域较大，则期望有效混合。通过计算一定周期内流体线元在轴向运动中横截面上的最大拉伸速率，发现从分离线附近开始的线元被强烈拉伸，这种强烈拉伸是PPM中有效混合的主要原因。少

As an example of the static mixers that are typical mixing devices, a model of partitioned-pipe mixer (PPM) was considered which is composed of axially periodic pairs of plane plates of a definite angle within an infinitely long rotating cylinder. The following results were obtained by the examination of the chaotic motion of fluid elements and the efficiency of the mixing due to an approximate velocity field that is composed of the velocity field for an infinitely long plane plate and a transient velocity field: (1) The efficiency of the mixing can be improved by the generalization of the PPM model in which the ratio a of the lengths of a pair of plane plates can be changed from one, and the angle between these plates can be changed from 90 degree. (2) Poincare sections are not sufficient as the index of the efficiency of the mixing in a few. axial periods. Lines of separation U(n), the set of cross-sectional initial locations of fluid particles that move to one of the leading edges o … More f the plates within n periods, can be used as the index of the mixing in n periods. That is, if the region where U(n) is distributed densely is large, the efficient mixing is expected.Next, from the numerical computation of the exact velocity field in PPM, it was found that this velocity field has the reverse-flow region for a small axial pressure gradient and is considerably different from the approximate velocity field. From the Poincare sections based on the exact velocity field, the following results were obtained: (1) The regular region can be reduced by changing a to appropriate values, similarly to the result for the approximate velocity field. (2) U(n) can be introduced even for the exact velocity field. Efficient mixing is expected if the region where U(n) is distributed densely is large.From the computation of the largest stretching rate of fluid line elements in the cross-sectional direction in their axial motion by a definite period, it was found that the line elements starting near the lines of separation are strongly stretched and that this strong stretching mainly contributes to the efficient mixing in PPM. Less