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

利用混沌提高三维流动中流体的混合效率

• 批准号: 13650064
• 负责人: FUNAKOSHI Mitsuaki
• 金额: $ 2.11万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650064/
• 关键词: Mixing; Chaos; Three-dimensional flow

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

作为典型混合装置静态混合器的一个例子，考虑了一个分隔管混合器（PPM）模型，它是由一个无限长的旋转圆柱内的轴向周期性的平板对的一个确定的角度。通过检查流体元素的混沌运动和由于由无限长平板的速度场和瞬态速度场组成的近似速度场引起的混合效率，获得了以下结果：（一）混合的效率可以通过PPM模型的推广来提高，在PPM模型中，一对平板的长度之比a可以是从1改变，这些板之间的角度可以从90度改变。(2)Poincare截面在少数情况下不足以作为混合效率的指标。轴向周期分离线U（n），移动到其中一个前缘的流体颗粒的横截面初始位置的集合， ...更多信息 对于n个周期内的板块，可以作为n个周期内混合的指标。也就是说，如果U（n）密集分布的区域大，则可以期待有效的混合。其次，通过PPM中的精确速度场的数值计算，发现该速度场在轴向压力梯度小的情况下具有逆流区域，与近似速度场有很大的不同。从精确速度场的Poincare截面出发，得到如下结果：（1）与近似速度场的结果类似，通过适当改变α值，可以缩小规则区域。(2)甚至对于精确的速度场也可以引入U（n）。如果U（n）密集分布的区域大，则可以期望有效的混合。通过计算流体线元在轴向运动一定周期时在横截面方向上的最大拉伸率，发现从分离线附近开始的线元被强烈拉伸，这种强烈拉伸主要有助于PPM中的有效混合。少

项目成果

Yoshinori Mizuno: "Chaotic mixing caused by an axially periodic steady flow in a partitioned-pipe mixer"Fluid Dynamics Research. (印刷中). (2004)

Yoshinori Mizuno：“分区管混合器中轴向周期性稳定流引起的混沌混合”流体动力学研究（2004 年出版）。

Mitsuaki Funakoshi: "Lagrangian chaos and mixing of fluids"Japan Journal of Industrial and Applied Mathematics. 18・2. 613-626 (2001)

Mitsuaki Funakoshi：“拉格朗日混沌和流体混合”日本工业和应用数学杂志18・2（2001）。