Cascaded lattice Boltzmann method based on central moments for axisymmetric thermal flows including swirling effects
Cascaded lattice Boltzmann method based on central moments for axisymmetric thermal flows including swirling effects
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DOI：
10.1016/j.ijheatmasstransfer.2018.09.059
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发表时间：
2018-06
影响因子：
5.2
通讯作者：
Farzaneh Hajabdollahi;K. Premnath;S. Welch
中科院分区：
文献类型：
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作者：
Farzaneh Hajabdollahi;K. Premnath;S. Welch
提出了一种基于中心矩和多重松弛时间的级联格子Boltzmann方法，用于模拟轴对称圆柱坐标系中由浮力和/或旋流效应驱动的热对流。在这方面，轴向动量分量和径向动量分量随压强的动力学由含有伪笛卡尔形式的几何质量和动量源项的二维Navier-Stokes方程来表示，而方位向动量和温度场的演化都由带有适当的局部源项的平流-扩散型方程来模拟。在此基础上，采用D2Q9格子求解子午面内的流体运动，采用D2Q5格子求解方位向动量场和温度场，建立了包含三个分布函数的级联LB型格式。利用一种新的对称算符分裂技术，在每个分布函数的级联碰撞步骤周围，通过碰撞前和碰撞后的源步骤，包括了流场的几何质量和动量源项以及温度场的能量源项。这些结果导致了一个特别简单和紧凑的公式，以根据适当的零阶矩和一阶矩的变化来一致地直接表示各种几何源项的影响。对几种复杂的浮力驱动的热流进行了数值模拟，并考虑了圆柱几何结构中的旋转效应，结果表明，在速度场和热场结构以及以Nusselt数给出的换热速率方面，新的轴对称级联LB格式与以前的基准结果符合得很好。此外，与用于轴对称流动模拟的其他碰撞模型相比，该方法具有二阶精度，并且与其他碰撞模型相比，在数值稳定性方面有了显著的改善。
A cascaded lattice Boltzmann (LB) approach based on central moments and multiple relaxation times to simulate thermal convective flows, which are driven by buoyancy forces and/or swirling effects, in the cylindrical coordinate system with axial symmetry is presented. In this regard, the dynamics of the axial and radial momentum components along with the pressure are represented by means of the 2D Navier-Stokes equations with geometric mass and momentum source terms in the pseudo Cartesian form, while the evolutions of the azimuthal momentum and the temperature field are each modeled by an advection-diffusion type equation with appropriate local source terms. Based on these, cascaded LB schemes involving three distribution functions are formulated to solve for the fluid motion in the meridian plane using a D2Q9 lattice, and to solve for the azimuthal momentum and the temperature field each using a D2Q5 lattice. The geometric mass and momentum source terms for the flow fields and the energy source term for the temperature field are included using a new symmetric operator splitting technique, via pre-collision and post-collision source steps around the cascaded collision step for each distribution function. These result in a particularly simple and compact formulation to directly represent the effect of various geometric source terms consistently in terms of changes in the appropriate zeroth and first order moments. Simulations of several complex buoyancy-driven thermal flows and including rotational effects in cylindrical geometries using the new axisymmetric cascaded LB schemes show good agreement with prior benchmark results for the structures of the velocity and thermal fields as well as the heat transfer rates given in terms of the Nusselt numbers. Furthermore, the method is shown to be second order accurate and significant improvements in numerical stability with the use of the cascaded LB formulation when compared to other collision models for axisymmetric flow simulations are demonstrated.