Thin-film flow in helically wound shallow channels of arbitrary cross-sectional shape
Thin-film flow in helically wound shallow channels of arbitrary cross-sectional shape
复制标题
任意横截面形状的螺旋缠绕浅通道中的薄膜流动
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
J. Green
中科院分区：
文献类型：
--
作者：
D. Arnold;Y. Stokes;J. Green
本文研究粘性流体薄膜在重力作用下沿任意截面形状、任意扭转和曲率的螺旋缠绕浅槽的定常流动。这扩展了我们以前的工作[D. J. Arnold等人，“Thin-Film Flow in helically-wound rectangular channels of arbitrary torsion and curvature，”J. Fluid Mech.764，76-94（2015）]。Navier-Stokes方程表示在一个新的，非正交坐标系适合于通道底部。通过假设通道深度与其宽度相比较小，并且垂直方向上的流体深度与其典型的水平范围相比也较小，我们能够解析地求解速度分量和压力。利用这些结果，得到了自由表面形状的微分方程，该方程通常必须用数值方法求解。出于理解矿物加工中使用的静态螺旋颗粒分离器中的流动的目的，我们研究了螺旋颗粒分离器的流动。
We consider the steady, gravity-driven flow of a thin film of viscous fluid down a helically wound shallow channel of arbitrary cross-sectional shape with arbitrary torsion and curvature. This extends our previous work [D. J. Arnold et al., “Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature,” J. Fluid Mech. 764, 76–94 (2015)] on channels of rectangular cross section. The Navier-Stokes equations are expressed in a novel, non-orthogonal coordinate system fitted to the channel bottom. By assuming that the channel depth is small compared to its width and that the fluid depth in the vertical direction is also small compared to its typical horizontal extent, we are able to solve for the velocity components and pressure analytically. Using these results, a differential equation for the free surface shape is obtained, which must in general be solved numerically. Motivated by the aim of understanding flows in static spiral particle separators used in mineral processing, we i...