A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip
A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip
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DOI：
10.1002/fld.2549
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发表时间：
2012-05-10
影响因子：
1.8
通讯作者：
Dellar, Paul J.
中科院分区：
文献类型：
--
作者：
Bennett, Sam;Asinari, Pietro;Dellar, Paul J.
本文描述了二元气体混合物的晶格玻尔兹曼（LB）模型的发展，以及在壁面发生扩散滑移的密度梯度驱动下的通道流动的应用。单组分气体的LB方法通常使用非物理状态方程，其中压力和密度之间的关系根据所使用的标度而变化。这根本不适合扩展到含有不同分子质量气体的多组分系统。即使在低马赫数下，物种密度和压力也可能存在显著变化；因此，对于小波动，通常的线性化状态方程是不合适的。此外，现有的实现边界条件的方法不容易扩展到新的边界条件，如扩散滑移。针对多组分气体开发的新模型避免了一些其他LB模型的缺陷。所有物种共享一个计算网格，并且扩散率与粘度无关。模型恢复了混合物的NavierStokes方程和StefanMaxwell扩散方程。扩散滑移，气体混合物在平行于浓度梯度的壁面处的非零速度，成功地模拟并验证了一个简单的一维通道流动模型。为了提高格式的精度，需要进行二阶数值实现。这可以使用不增加计算时间的变量变换方法来实现。在不同的总压和浓度梯度条件下，对窄通道中氢气和水的扩散进行了模拟。版权所有：John Wiley & Sons， Ltd。
This paper describes the development of a lattice Boltzmann (LB) model for a binary gas mixture, and applications to channel flow driven by a density gradient with diffusion slip occurring at the wall. LB methods for single component gases typically use a non-physical equation of state in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multi-component systems containing gases of differing molecular masses. Substantial variations in the species densities and pressures may exist even at low Mach numbers; hence, the usual linearized equation of state for small fluctuations is unsuitable. Also, existing methods for implementing boundary conditions do not extend easily to novel boundary conditions, such as diffusion slip. The new model developed for multi-component gases avoids the pitfalls of some other LB models. A single computational grid is shared by all the species, and the diffusivity is independent of the viscosity. The NavierStokes equation for the mixture and the StefanMaxwell diffusion equation are both recovered by the model. Diffusion slip, the non-zero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple one-dimensional model for channel flow. To increase the accuracy of the scheme, a second-order numerical implementation is needed. This may be achieved using a variable transformation method that does not increase the computational time. Simulations were carried out on hydrogen and water diffusion through a narrow channel for varying total pressure and concentration gradients. Copyright (c) 2011 John Wiley & Sons, Ltd.