高精度多差数有限差分法在二维渐扩管流态改变中的探索研究

发布时间：2019-05-17 18:49

【摘要】：渐扩管在抽水蓄能电站、给排水管道等水利工程领域及其他多种工程领域中均有十分广泛的应用。在工程应用中发现,渐扩管内的流场形态改变比较复杂,会出现波动、回流、漩涡及偏流等现象,至今不能得到很好的解释。这种流动形态的改变,对于渐扩管的应用十分不利。因此,对其中流场形态改变的研究是十分必要的。本文选择二维的渐扩槽道作为研究对象,参考参数多项式方法建立了二维渐扩流动问题的数值模型。并对其进行数值离散、方程线性化、以及误差控制等处理,使得模型能够可靠模拟二维渐扩流场。借鉴了相关数学理论与方法,以线性方程组系数矩阵的条件数作为参考,模拟计算流场在拟稳态时小流量逐步加载至大流量时流场形态的发展过程。研究发现,流场形态发生显著变化的点往往是系数矩阵的条件数发生跳跃的点,说明渐扩管内的流场形态改变与相关的数学机理有关系。其次,渐扩管的扩张角对流场形态改变的影响十分显著。大扩张角的渐扩管,流场形态的变化出现更快且变化后流场形态更加复杂。变化之后的流态主要表现为回流、漩涡和偏流等,与工程实际中的观察十分类似。同时,粘性对流场形态的改变点亦有影响。较大粘性下,需要将流量加至很大水平才会出现流态的突变。但各种粘性下流态改变时的雷诺数是相近的。表明雷诺数是层流时控制流态变化的主要因素之一。
[Abstract]:Gradually expanding pipe has been widely used in pumped storage power station, water supply and drainage pipeline and other engineering fields. In engineering application, it is found that the change of flow field in the gradually expanding tube is more complex, and there will be fluctuations, reflux, whirlpool and bias flow, which can not be well explained so far. The change of flow pattern is very disadvantageous to the application of gradually expanding tube. Therefore, it is very necessary to study the change of flow field morphology. In this paper, the two-dimensional gradually expanding channel is selected as the research object, and the numerical model of the two-dimensional gradually expanding flow problem is established by referring to the parameter polynomial method. The numerical discretization, equation linearization and error control are carried out, so that the model can reliably simulate the two-dimensional asymptotic flow field. Based on the relevant mathematical theories and methods, and taking the condition number of coefficient matrix of linear equations as a reference, the development process of flow field pattern when small flow rate is gradually loaded to large flow rate in quasi-steady state is simulated and calculated. It is found that the point where the flow field morphology changes significantly is often the jump point of the condition number of the coefficient matrix, which indicates that the change of flow field morphology in the gradually expanding tube is related to the related mathematical mechanism. Secondly, the influence of the expansion angle of the gradually expanding tube on the morphological change of the flow field is very significant. With the gradual expansion of the tube with large expansion angle, the flow field morphology changes faster and the flow field morphology is more complex after the change. After the change, the flow pattern is mainly reflux, vortex and bias flow, which is very similar to the observation in engineering practice. At the same time, viscosity also has an effect on the change point of flow field morphology. Under the condition of large viscosity, it is necessary to add the flow rate to a large level before there will be a sudden change of flow pattern. However, the Reynolds number is similar when the flow pattern of various viscous downflows is changed. It is shown that Reynolds number is one of the main factors controlling the change of flow pattern in laminar flow.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TV134

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