【摘要】：漸擴管在抽水蓄能電站、給排水管道等水利工程領(lǐng)域及其他多種工程領(lǐng)域中均有十分廣泛的應(yīng)用。在工程應(yīng)用中發(fā)現(xiàn),漸擴管內(nèi)的流場形態(tài)改變比較復(fù)雜,會出現(xiàn)波動、回流、漩渦及偏流等現(xiàn)象,至今不能得到很好的解釋。這種流動形態(tài)的改變,對于漸擴管的應(yīng)用十分不利。因此,對其中流場形態(tài)改變的研究是十分必要的。 本文選擇二維的漸擴槽道作為研究對象,參考參數(shù)多項式方法建立了二維漸擴流動問題的數(shù)值模型。并對其進行數(shù)值離散、方程線性化、以及誤差控制等處理,使得模型能夠可靠模擬二維漸擴流場。借鑒了相關(guān)數(shù)學(xué)理論與方法,以線性方程組系數(shù)矩陣的條件數(shù)作為參考,模擬計算流場在擬穩(wěn)態(tài)時小流量逐步加載至大流量時流場形態(tài)的發(fā)展過程。 研究發(fā)現(xiàn),流場形態(tài)發(fā)生顯著變化的點往往是系數(shù)矩陣的條件數(shù)發(fā)生跳躍的點,說明漸擴管內(nèi)的流場形態(tài)改變與相關(guān)的數(shù)學(xué)機理有關(guān)系。其次,漸擴管的擴張角對流場形態(tài)改變的影響十分顯著。大擴張角的漸擴管,流場形態(tài)的變化出現(xiàn)更快且變化后流場形態(tài)更加復(fù)雜。變化之后的流態(tài)主要表現(xiàn)為回流、漩渦和偏流等,與工程實際中的觀察十分類似。同時,粘性對流場形態(tài)的改變點亦有影響。較大粘性下,需要將流量加至很大水平才會出現(xiàn)流態(tài)的突變。但各種粘性下流態(tài)改變時的雷諾數(shù)是相近的。表明雷諾數(shù)是層流時控制流態(tài)變化的主要因素之一。
[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.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TV134

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