Karani Hamid, Huber Christian
School of Earth and Atmospheric Sciences, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, Georgia 30332, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Feb;91(2):023304. doi: 10.1103/PhysRevE.91.023304. Epub 2015 Feb 5.
In this paper, we propose an approach for studying conjugate heat transfer using the lattice Boltzmann method (LBM). The approach is based on reformulating the lattice Boltzmann equation for solving the conservative form of the energy equation. This leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components with different thermal properties. The proposed source term formulation conserves conductive and advective heat flux simultaneously, which makes it suitable for modeling conjugate heat transfer in general multiphase or multicomponent systems. The simple implementation of the source term approach avoids any correction of distribution functions neighboring the interface and provides an algorithm that is independent from the topology of the interface. Moreover, our approach is independent of the choice of lattice discretization and can be easily applied to different advection-diffusion LBM solvers. The model is tested against several benchmark problems including steady-state convection-diffusion within two fluid layers with parallel and normal interfaces with respect to the flow direction, unsteady conduction in a three-layer stratified domain, and steady conduction in a two-layer annulus. The LBM results are in excellent agreement with analytical solution. Error analysis shows that our model is first-order accurate in space, but an extension to a second-order scheme is straightforward. We apply our LBM model to heat transfer in a two-component heterogeneous medium with a random microstructure. This example highlights that the method we propose is independent of the topology of interfaces between the different phases and, as such, is ideally suited for complex natural heterogeneous media. We further validate the present LBM formulation with a study of natural convection in a porous enclosure. The results confirm the reliability of the model in simulating complex coupled fluid and thermal dynamics in complex geometries.
在本文中，我们提出了一种使用格子玻尔兹曼方法（LBM）研究共轭传热的方法。该方法基于对格子玻尔兹曼方程进行重新表述，以求解能量方程的守恒形式。这导致了一个源项的出现，该源项在具有不同热特性的两相或两组分之间的界面处引入了跳跃条件。所提出的源项公式同时守恒传导热通量和对流热通量，这使其适用于一般多相或多组分系统中共轭传热的建模。源项方法的简单实现避免了对界面附近分布函数的任何修正，并提供了一种独立于界面拓扑结构的算法。此外，我们的方法与格子离散化的选择无关，并且可以很容易地应用于不同的对流扩散LBM求解器。该模型针对几个基准问题进行了测试，包括在具有与流动方向平行和垂直界面的两个流体层内的稳态对流扩散、三层分层区域中的非稳态传导以及两层环形区域中的稳态传导。LBM结果与解析解非常吻合。误差分析表明，我们的模型在空间上是一阶精确的，但扩展到二阶格式很简单。我们将LBM模型应用于具有随机微观结构的双组分非均质介质中的传热。这个例子突出了我们提出的方法独立于不同相之间界面的拓扑结构，因此非常适合复杂的天然非均质介质。我们通过对多孔封闭腔内自然对流的研究进一步验证了当前的LBM公式。结果证实了该模型在模拟复杂几何形状中复杂的耦合流体和热动力学方面的可靠性。
