Research of laminar liquid flow in asymmetric narrow channels

摘要

Purpose - The purpose of this paper is to find a solution of laminar liquid flow in asymmetric narrow channels. In many cases, an intuitive solution is much more useful and necessary for engineering applications, although numerical solutions can be obtained. Design/methodology/approach - The Navier-Stokes equations of laminar liquid flow in asymmetric narrow channels are simplified based on geometric characteristics of narrow channels, physical characteristics of liquid and boundary conditions. The simplified Navier-Stokes equations are solved theoretically. Verification of the obtained results is carried out based on comparing with the Jeffery-Hamel flow, which is an exact solution of liquid flow in convergent or divergent channels proposed by Jeffery. Findings - This paper proposed an intuitive solution of laminar liquid flow in asymmetric narrow channels. Obtained results show that the solution can provide a fairly precise flowrate, when a ratio between the width of the channel and the curvature of the boundary of the asymmetry channel is smaller than 0.2936/Re. Furthermore, the obtained solution of pressure distribution along the channel shows high enough accuracy, even though the Reynolds number reaches to higher than 105. Research limitations/implications - Because the authors assumed the width of the channel is far smaller than the curvature of the boundary of the asymmetric channel, the obtained results could only fit finite cases. Because the Navier-Stocks equations were finally simplified into one-dimensional, it is impossible to forecast separation flows; so the obtained results will fail when the Re number is too big. However, experiments should be carried out further to verify these problems. Originality/value - This paper proposes an intuitive solution of laminar liquid flow in asymmetric narrow channels, including the pressure distribution along the channel.