A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient
A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient
复制标题
DOI：
10.1017/jfm.2021.691
复制
发表时间：
2021-09
影响因子：
3.7
通讯作者：
S. Gasow;A. Kuznetsov;M. Avila;Yan Jin
中科院分区：
文献类型：
--
作者：
S. Gasow;A. Kuznetsov;M. Avila;Yan Jin
多孔介质中自然对流的建模由于其在环境和工程问题中的重要意义而受到越来越多的关注。最先进的模拟是基于经典的宏观Darcy - oberbeck - boussinesq （DOB）方程，该方程被广泛接受用于捕获多孔介质中对流的潜在物理，前提是Darcy数$Da$很小。在本文中，我们分析和扩展了Gasow等人（J. Fluid Mech, vol. 891, 2020, p. A25）最近的孔隙解析直接数值模拟（DNS），并表明在DOB中被忽略的宏观扩散与浮力和达西阻力（相对于Da）处于同一量级。因此，即使$Da$的值很小，也必须模拟宏观扩散。我们提出了一个“双长度尺度扩散”模型，其中孔隙尺度对动量输运的影响近似为宏观扩散项。这一项由宏观长度尺度和孔隙尺度共同决定。它包括一个仅取决于孔隙尺度几何形状的输运系数。与使用DOB方程的模拟相比，我们模型的模拟得到了更精确的舍伍德数、质量浓度的均方根和速度的均方根。特别地，我们发现Sherwood数$Sh$随着孔隙度的减小和Schmidt数$(Sc)$的增大而增大。此外，对于高Ra值和高孔隙率，Sh$呈非线性变化。这些趋势与DNS一致，但在DOB模拟中没有捕捉到。
Abstract The modelling of natural convection in porous media is receiving increased interest due to its significance in environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which are widely accepted to capture the underlying physics of convection in porous media provided the Darcy number, $Da$, is small. In this paper we analyse and extend the recent pore-resolved direct numerical simulations (DNS) of Gasow et al. (J. Fluid Mech, vol. 891, 2020, p. A25) and show that the macroscopic diffusion, which is neglected in DOB, is of the same order (with respect to $Da$) as the buoyancy force and the Darcy drag. Consequently, the macroscopic diffusion must be modelled even if the value of $Da$ is small. We propose a ‘two-length-scale diffusion’ model, in which the effect of the pore scale on the momentum transport is approximated with a macroscopic diffusion term. This term is determined by both the macroscopic length scale and the pore scale. It includes a transport coefficient that solely depends on the pore-scale geometry. Simulations of our model render a more accurate Sherwood number, root mean square (r.m.s.) of the mass concentration and r.m.s. of the velocity than simulations that employ the DOB equations. In particular, we find that the Sherwood number $Sh$ increases with decreasing porosity and with increasing Schmidt number $(Sc)$. In addition, for high values of $Ra$ and high porosities, $Sh$ scales nonlinearly. These trends agree with the DNS, but are not captured in the DOB simulations.