Numerical simulation of unsteady flows in Czochralski crystal growth by lattice Boltzmann methods
Numerical simulation of unsteady flows in Czochralski crystal growth by lattice Boltzmann methods
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DOI：
10.1016/j.ijheatmasstransfer.2014.03.002
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发表时间：
2014-07
影响因子：
5.2
通讯作者：
Haibo Huang;Xi-yun Lu;M. Krafczyk
中科院分区：
文献类型：
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作者：
Haibo Huang;Xi-yun Lu;M. Krafczyk
本研究提出了一个格子玻尔兹曼（LB）方法的热轴对称流，包括旋流或旋转的模型扩展。采用不可压缩轴对称格子BoltzmannD 2 Q9模型，通过在二维格子Boltzmann方程中插入源项求解轴向和径向速度。控制方位（或旋转）速度和温度的方程也由LBM求解。结果表明，与已有的混合格式相比，该格式具有更好的稳定性和一致性。它提供了一个显着的优势，在高雷诺数和高格拉肖夫数的熔体流动模拟。通过比较直拉法晶体生长中熔体流动的LB结果与基准解，验证了本方案的有效性。对高Grashof数非定常流动进行了详细研究。振荡开始的临界Grashof数约为2.5× 106。当2.5 × 10 6< Gr< 6× 10 6时，振荡振幅λ max与（Gr-Gr c）0.5成正比。分析了非定常流动的频率和流型。在Grashof数高达6× 10 7时，温度的平均值和均方根值的分布与三维模拟结果相似。
This study presents model extensions for a lattice Boltzmann (LB) approach to thermal axisymmetric flow including swirl or rotation. An incompressible axisymmetric lattice Boltzmann D2Q9 model was applied to solve the axial and radial velocities through inserting source terms into the two-dimensional lattice Boltzmann equation. The equations governing azimuthal (or swirling) velocity and the temperature were also solved by the LBM. It is found that this scheme is much more stable and consistent compared to previous hybrid schemes. It provides a significant advantage in simulation of melt flows with high Reynolds number and high Grashof number. The present scheme was validated by comparing the LB results with benchmark solutions for melt flow in Czochralski crystal growth. Unsteady flows with high Grashof numbers were studied in detail. The critical Grashof number for the onset of the oscillation is found to be about 2.5× 10 6. The oscillation amplitude ψ max is proportional to (Gr-Gr c) 0.5 for 2.5× 10 6< Gr< 6× 10 6. The frequencies and flow patterns of the unsteady flows are also analyzed. The distributions of the mean quantities of the temperature and rms of temperature at Grashof number as high as 6× 10 7 is found to be similar to those obtained by 3D simulations.