Conjugate heat and mass transfer in the lattice Boltzmann equation method.
Conjugate heat and mass transfer in the lattice Boltzmann equation method.
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DOI：
10.1103/physreve.89.043308
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发表时间：
2014-04
期刊：
影响因子：
--
通讯作者：
Like Li;Chen Chen-Chen;R. Mei;J. Klausner
中科院分区：
文献类型：
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作者：
Like Li;Chen Chen-Chen;R. Mei;J. Klausner
基于我们之前提出的二阶精确狄利克雷和诺伊曼边界格式，提出了格子玻尔兹曼方程方法中共轭传热传质的界面处理。本质上满足传热（质量）传递界面温度（浓度）及其通量的连续性，无需迭代计算，无需有限差分计算，由微观分布函数即可方便地获得界面温度（浓度）及其通量。本处理考虑了界面的局部几何形状，因此可以直接应用于弯曲界面问题，例如多孔介质中的共轭传热和传质。对于没有切向梯度的直界面或弯曲界面，消除了沿离散晶格速度方向的界面通量之间的耦合，因此可以大大简化所提出的界面方案。进行了多项数值测试来验证所提出的共轭界面处理的适用性和准确性，包括（i）包含两种不同流体的通道中的稳定对流扩散，（ii）通道中的不稳定对流扩散，（iii）具有两种不同固体材料的圆形域内的稳定热传导，以及（iv）拉伸蠕动流中球形液滴的不稳定传质。详细检验了模拟内部温度（浓度）场、界面温度（浓度）和热（质量）通量的精度和收敛顺序，并与文献中“半格子划分”处理得到的结果进行了比较。目前的分析和数值结果表明，仅当界面固定在晶格链接的中心时，半晶格划分方案才具有二阶精度，而当前的处理对于任意链接部分都保持二阶精度。对于弯曲界面，本处理产生二阶精确的内部和界面温度（浓度）以及一阶精确的界面热（质量）通量。与半格划分方案相比，这三个量中的每一个都获得了收敛阶数的增加。测试 (iv) 中计算的表面平均舍伍德数与已发表的结果非常吻合。
An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer in porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved interfaces, the present treatment yields second-order accurate interior and interfacial temperatures (concentrations) and first-order accurate interfacial heat (mass) flux. An increase of order of convergence by one degree is obtained for each of these three quantities compared with the half-lattice division scheme. The surface-averaged Sherwood numbers computed in test (iv) agree well with published results.