Newtonian Fluid Flow in a Long Vertical Converging Tube

長垂直漸縮管內牛頓流體流動

翁輝竹(Huei-Chu Weng) ； 高源鍇(Yuan-Kai Kao)

《中國機械工程學刊》 37卷1期 (2016/02) Pp. 61-67

摘要

探討漸縮幾何在不同驅動機制下對流體元件內流體流動的影響實為有趣之研究。本論文結合壓力及重力驅動機制，發展牛頓流體於長垂直漸縮管內流動之數學模式。該流動可簡化為完全發展流，其流場及其特性解可由圓柱座標系統下Navier-Stokes方程式經簡化後以數值方法獲得。考慮水於長垂直漸縮玻璃管內流動，透過給予不同體積流率來量測壓降以進行比較，該數學模式可獲得驗證。研究結果發現，漸縮幾何效應可導致壓力延著管長呈現非線性分布，並促成橫向及縱向速度的增加。若流體流動所需壓降(或體積流率)增加，此幾何效應將可進一步被放大。

並列摘要

It is desirable to understand the role of converging geometry in influencing the flow in fluidic devices with different driving mechanisms. In this study, a mathematical model is developed of the combined pressure- and gravity-driven flow of Newtonian fluids through a long vertical converging tube. The fully developed solutions of the flow field distributions as well as the corresponding characteristics are solved using a numerical method based on a reduced form of Navier-Stokes equations in a cylindrical coordinates system. The numerical results are validated experimentally by pressure drop measurements of water flow in a glass tube for differential volume flow rates pumped from different levels within a reservoir. It is found that the effect of converging geometry is to raise the nonlinearity of pressure distribution along the tube and the magnitudes of longitudinal and transversal velocities. This effect can be further enhanced by increasing the pressure drop, which linearly increased with the increasing volume flow rate.

並列關鍵字

converging/diverging tube ； sudden contraction/expansion ； nozzle/diffuser ； convergent/divergentflow