Poumaëre Nelson, Pier Benoît, Raynal Florence
Laboratoire de Mécanique des Fluides et d'Acoustique, Université de Lyon, École centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon 1, CNRS, F-69134 Écully, France.
Phys Rev E. 2022 Jul;106(1-2):015107. doi: 10.1103/PhysRevE.106.015107.
We investigate the distributions of residence time for in-line chaotic mixers; in particular, we consider the Kenics, the F-mixer, and the multilevel laminating mixer and also a synthetic model that mimics their behavior and allows exact mathematical calculations. We show that whatever the number of elements of mixer involved, the distribution possesses a t^{-3} tail, so that its shape is always far from Gaussian. This t^{-3} tail also invalidates the use of second-order moment and variance. As a measure for the width of the distribution, we consider the mean absolute deviation and show that, unlike the standard deviation, it converges in the limit of large sample size. Finally, we analyze the performances of the different in-line mixers from the residence-time point of view when varying the number of elements and the shape of the cross section.
我们研究了在线式混沌混合器的停留时间分布；具体而言，我们考虑了肯尼克混合器、F型混合器和多级层压混合器，以及一个模拟它们行为并允许进行精确数学计算的合成模型。我们表明，无论所涉及的混合器元件数量如何，该分布都具有(t^{-3})尾部，因此其形状总是远离高斯分布。这种(t^{-3})尾部也使得二阶矩和方差的使用无效。作为分布宽度的一种度量，我们考虑平均绝对偏差，并表明与标准差不同，它在大样本量的极限情况下收敛。最后，我们从停留时间的角度分析了不同在线式混合器在改变元件数量和横截面形状时的性能。
