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Chaos Structure of the Flows in a Curved Duct of Rectangular Cross-section

矩形截面弯曲管道内流动的混沌结构

基本信息

批准号：
04650167
负责人：
YAMAMOTO Masaaki
金额：
$ 1.34万
依托单位：
Osaka institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1992
资助国家：
日本
起止时间：
1992 至 1993
项目状态：
已结题

项目摘要

We studied flows in a curved duct of a rectangular cross-section having an aspect ratio of 2nd curvature ratio of 8. In particular, periodic and quasi-periodic flow occurring above the Hopf bifurcation were calculated numerically. The symbolic dynamics was applied to the multi periodic flows which include a series of flow patterns. Results were as follows ; no flow patterns have stable equilibrium state, but a flow pattern consisting of each the pattern was stable. There existed the Dean number where asymmetric flow occurred intermittently. The corresponding attractor showed that fracial demension of the attractor was nearly two dimensional. A stretching and folding of the attractors was found along orbits, from which shaos seems to be strange attractor. the results were published in the Transaction of the Japan society of mechanical engineers. Furthermore, we simulated numerically the same flows by the method of the simultaneous displacement instead of the successive displacement. It was expected that the latter method decreased asymmetric distubance as possible. The results were as follws ; symmetric flows were obtained which were structurally unstable. Bifurcation of steady into steady into steady flow was observed below the Hopf bifurcation. Above the Hopf bifurcation, a few times of the double periodic behavior were observed. The geometry of the attractor was found to be simple, which resembled the Rossler band model. Consequently the attractor preliminary study, the model equation for the flow in a straight channel was obtained, and the theoretical procedure was preliminary study, the model equation for the flow in a straight channel was obtained, and the theoretical procedure was expected to be applicable to a curved duct flow.

我们研究了长径比为2曲率比为8的矩形截面弯曲管道中的流动。特别对Hopf分岔以上的周期流和拟周期流进行了数值计算。将符号动力学应用于包含一系列流型的多周期流。结果如下：没有一种流型具有稳定的平衡状态，但由每种流型组成的流型是稳定的。存在间歇性发生不对称流动的迪安数。相应的吸引子表明，吸引子的分形维数接近二维。在轨道上发现了吸引子的拉伸和折叠，从这个角度来看，shaos似乎是一个奇怪的吸引子。研究结果发表在《日本机械工程师学会学报》上。此外，我们用同时位移法代替连续位移法模拟了相同的流动。期望后一种方法尽可能地减少不对称距离。实验结果如下：得到了结构不稳定的对称流。在Hopf分岔下观察到定常流到定常流的分岔。在Hopf分岔之上，观察到几次双周期行为。发现吸引子的几何形状很简单，类似于罗斯勒带模型。通过对吸引子的初步研究，得到了直线通道内流动的模型方程，并对理论步骤进行了初步研究，得到了直线通道内流动的模型方程，并期望理论步骤适用于弯曲管道流动。