Central Moments-based Cascaded Lattice Boltzmann Method for Thermal Convective Flows in Three-Dimensions
Central Moments-based Cascaded Lattice Boltzmann Method for Thermal Convective Flows in Three-Dimensions
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DOI：
10.1016/j.ijheatmasstransfer.2017.12.085
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发表时间：
2017-10
期刊：
影响因子：
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通讯作者：
Farzaneh Hajabdollahi;K. Premnath
中科院分区：
文献类型：
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作者：
Farzaneh Hajabdollahi;K. Premnath
由热效应驱动的流体运动，例如由于差热三维(3D)封闭空间中的浮力而引起的运动，在一些自然环境和工程应用中会出现。它由Navier-Stokes方程(NSE)的解和热能输运方程(CDE)相结合来表示。在这项研究中，我们发展了新的基于中心矩的三维格子Boltzmann方法，并对三维十五速度(D3Q15)格子及其子集，即三维七速度(D3Q7)格子采用多重松弛时间，在双分布函数框架下求解三维温度场的CDE。它们的碰撞算子导致了包含更高阶项的级联结构，从而提高了稳定性。在这种方法中，流体的运动由另一个三维级联的LB模型来求解。由于表示流动动力学和温度场输运的碰撞不变量的数目不同，CDE和NSE的三维级联式的碰撞算符的结构明显不同。与已有的数值基准解相比，新的三维级联热对流模型在立方腔体封闭空间的两个垂直相对面上的自然对流换热得到了验证。结果表明，流场和热场的分布、峰值对流速度的大小以及以努谢尔数表示的换热速率都有很好的定量一致性。
Fluid motion driven by thermal effects, such as that due to buoyancy in differentially heated three-dimensional (3D) enclosures, arise in several natural settings and engineering applications. It is represented by the solutions of the Navier-Stokes equations (NSE) in conjunction with the thermal energy transport equation represented as a convection-diffusion equation (CDE) for the temperature field. In this study, we develop new 3D lattice Boltzmann (LB) methods based on central moments and using multiple relaxation times for the three-dimensional, fifteen velocity (D3Q15) lattice, as well as it subset, i.e. the three-dimensional, seven velocity (D3Q7) lattice to solve the 3D CDE for the temperature field in a double distribution function framework. Their collision operators lead to a cascaded structure involving higher order terms resulting in improved stability. In this approach, the fluid motion is solved by another 3D cascaded LB model from prior work. Owing to the differences in the number of collision invariants to represent the dynamics of flow and the transport of the temperature field, the structure of the collision operator for the 3D cascaded LB formulation for the CDE is found to be markedly different from that for the NSE. The new 3D cascaded (LB) models for thermal convective flows are validated for natural convection of air driven thermally on two vertically opposite faces in a cubic cavity enclosure at different Rayleigh numbers against prior numerical benchmark solutions. Results show good quantitative agreement of the profiles of the flow and thermal fields, and the magnitudes of the peak convection velocities as well as the heat transfer rates given in terms of the Nusselt number