Abstract

In this paper, analytical and numerical studies of species separation in vertical and horizontal porous, cylindrical annular cells were presented. The binary fluid, saturating the porous medium, is a water–ethanol mixture. The thickness e of the horizontal and vertical columns is equal to \(R_o-R_i\), where \(R_i\) and \(R_o\) are, respectively, the internal and the external radii. H is the height of the vertical cell, and the length of the horizontal cell. Constant temperatures, \(T_{\mathrm{hot}}\) and \(T_{\mathrm{cold}}\), were imposed on the inner and outer cylinders. Since an important species separation, in thermogravitational column (TGC), is obtained for \(e<<H\), the same assumption was made for the two configurations. The analytical solution was obtained using the parallel flow approximation for both configurations. The governing equations were solved numerically for 2D and 3D configurations using two different software (Comsol Multiphysics and a spectral collocation method with Gauss–Lobatto–Chebyshev points). Velocity, temperature, mass fraction fields and time to reach steady state were compared for the two configurations. The amount of species separated at the top or the bottom of each cell was also compared for each configuration.

Graphical abstract

中文翻译：

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由二元混合物饱和的多孔垂直和水平圆柱形环形细胞中的热重力分离

摘要

本文介绍了垂直和水平多孔圆柱形环形细胞中物种分离的分析和数值研究。饱和多孔介质的二元流体是水-乙醇混合物。水平和垂直列的厚度e等于\(R_o-R_i\)，其中\(R_i\)和\(R_o\)分别是内部和外部半径。H是垂直单元格的高度和水平单元格的长度。恒温，\(T_{\mathrm{hot}}\)和\(T_{\mathrm{cold}}\), 被施加在内缸和外缸上。由于在热引力柱 (TGC) 中对于\(e<<H\)获得了重要的物种分离，因此对两种配置进行了相同的假设。使用两种配置的平行流近似获得解析解。使用两种不同的软件（Comsol Multiphysics 和具有 Gauss-Lobatto-Chebyshev 点的光谱配置方法）对 2D 和 3D 配置的控制方程进行数值求解。比较了两种配置的速度、温度、质量分数场和达到稳态的时间。还比较了每种配置在每个单元的顶部或底部分离的物种数量。

图形概要