Hydraulic Analysis of Water Flow in a Closed Conduit with Suction

Abstract

加蓋水流一般研究渠道流場，主要為研究水平流(主流方向)之速度剖面。在求解解析解時，由於水平速度遠大於垂直速度，往往採用完全發展流之假設，將垂直速度予以忽略，來簡化方程式。然而實際上，垂直速度是確實存在之物理量，尤其在水、土交界處，不僅具有水平速度，垂直速度更是不可忽略。本研究討論一耦合之二維流場，包含水層與等向且均質性之孔隙層，水層之控制方程式使用Navier-Stokes方程式，孔隙層之控制方程式則使用孔彈性介質理論。藉由引入流線函數，配合邊界條件，能夠求解出水層與孔隙層之速度剖面。最後將結果與前人比較、驗證，發現使用孔彈性介質理論，能夠簡化計算流程，且得到令人滿意的結果。

Generally, studies on channel flow mainly focus on the velocity profiles of the flow in the longitudinal (or streamwise) direction.Since the horizontal velocity is much greater than the vertical one, we usually take the assumption of fully developed flow when generating the analytical solutions.The vertical velocity is then ignored to simplify the governing equations. However, the vertical velocity is actually not negligible, especially at the interface of soil and water, as well as the horizontal velocity. In this study, we discuss a coupled two-dimensional flow field which includes a water layer and homogeneous porous medium layer with suction. In the water layer, Navier-Stokes’ equation is employed to describe the flow, whereas in the porous medium layer, instead of Brinkman-extended Darcy equation, poroelastic theory is addressed. Intro ducing the stream function with boundary conditions, we successfully find the solutions and draw the velocity profiles both in the water and the porous medium layer.Finally, by comparing the results with previous study, it shows that the present approach is able to simplify the algorithm process and the results are in a good agreement.