Non-orthogonal multiple-relaxation-time lattice Boltzmann simulation of natural convection in porous square cavity with internal heat source
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摘要:
为了增强多孔方腔内流体流动与传热效果，采用非正交多松弛格子Boltzmann方法（MRT-LBM）对含有内热源的多孔方腔自然对流传热现象进行了数值模拟。研究了不同冷源布置方案（Scheme A~Scheme F）、内热源结构形式（Case 1、Case 2、Case 3）、内热源位置（
a 、b ）、Darcy数、Rayleigh数等对多孔方腔内流体流动与传热的影响。计算结果表明：冷源布置方案对腔内流体流动与传热具有重要影响，当冷源左右对称布置时，腔内温度场及流场亦对称分布；在高Rayleigh数下采用Scheme A的双上部冷源布置方案能明显提高腔内的传热强度；内热源的形状对腔内对流传热影响很大，高Rayleigh数下，Case 3的布置方式更好。内热源的位置a 和b 对腔内的传热影响明显，提出了热壁面平均Nusselt数与位置a 的拟合关系式，存在最佳的位置a （a =0.25），使得腔内的对流传热最强；热壁面平均Nusselt数亦随b 值变化表现出特定的变化规律。随着b 值的增加，热壁面平均Nusselt数呈现先增后减再增的趋势。-
关键词:
- 多松弛(MRT)格子 /
- Boltzmann模型 /
- 内热源 /
- 自然对流 /
- 多孔方腔
Abstract:In order to enhance the effect of fluid flow and heat transfer in the porous square cavity, the non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) is used to simulate the natural convective heat transfer in the porous square cavity with internal heat source. The effects of different cold source arrangements (Scheme A-Scheme F), internal heat source structure (Case 1, Case 2, Case 3), internal heat source location (
a ,b ), Darcy number, and Rayleigh number on fluid flow and heat transfer in square cavity are studied. The calculation results show that the arrangement of the cold source has an important influence on the fluid flow and heat transfer. When the cold source is symmetrically distributed, the temperature field and the flow field in the cavity are also symmetrically distributed; under high Rayleigh number, the double upper cold source arrangement of Scheme A can significantly improve the heat transfer intensity in the cavity; the shape of the internal heat source has a great influence on the convective heat transfer in the cavity. Under the high Rayleigh number, case 3 is arranged better. The positionsa andb of the internal heat source have obvious influence on the heat transfer in the cavity. The fitting relationship between the average Nusselt number of the hot wall surface and the positiona is proposed, and there is an optimal positiona (a =0.25), which makes the convective heat transfer in the cavity strongest; the average Nusselt number of the hot wall surface also shows a specific variation law with the change ofb value. With the value ofb increases, the average Nusselt number of the hot wall surface increases first, then decreases and finally increases. -
图 2 六种不同等温冷源边界布置方案
Figure 2. Six different isothermal cold source boundary arrangements
图 3 不同方法流线及等温线图比较(Ra=106，Da=10-4，ε=0.4， Pr=1.0)
Figure 3. Comparison of streamlines and isotherms with different methods (Ra=106, Da=10-4, ε=0.4, Pr=1.0)
图 4 六种不同等温边界布置下的等温线图和流线图
Figure 4. Isotherms and streamlines for six different isothermal boundary arrangements
图 5 六种不同等温边界布置下的速度分布
Figure 5. Velocity profiles with six different isothermal boundary arrangements
图 6 六种不同等温边界布置下热壁面平均Nusselt数随Darcy数变化
Figure 6. Variation of average Nusselt number at hot wall surface with Darcy number under six different isothermal boundary arrangements
图 7 六种不同等温边界布置下热壁面平均Nusselt数随Rayleigh数变化
Figure 7. Variation of average Nusselt number at hot wall surface with Rayleigh number under six different isothermal boundary arrangements
图 8 六种不同等温边界布置下热壁面局部Nusselt数变化
Figure 8. Variation of local Nusselt number at hot wall surface with six different isothermal boundary arrangements
图 9 三种不同内热源结构形式下方腔内的流线图和等温线图
Figure 9. Streamlines and isotherms in square carity under three different internal heat source structures
图 10 三种不同内热源结构形式下热壁面平均Nusselt数随Rayleigh数变化
Figure 10. Variation of average Nusselt number at hot wall surface with Rayleigh number in cavity under three different heat source structures
图 11 三种不同内热源结构形式下的速度分布
Figure 11. Velocity profiles in cavity under three different internal heat source structures
图 12 不同a值下方腔内的等温线图和流线图
Figure 12. Isotherms and streamlines in square cavity at different values of a
图 13 不同a值下热壁面局部Nusselt数变化
Figure 13. Variation of local Nusselt number at hot wall surface under different a values
图 14 热壁面平均Nusselt数随a值变化
Figure 14. Average Nusselt number at hot wall under different surface versus a values
图 15 不同b值下方腔内的等温线图和流线图
Figure 15. Isotherms and streamlines in square cavity at different values of b
图 16 不同b值下方腔水平中平面的速度分布
Figure 16. Velocity profiles in the horizontal mid-plane of square cavity under different b values
图 17 热壁面平均Nusselt数随b值变化
Figure 17. Average Nusselt number at hot wall surface versus b values
图 18 不同b值下热壁面局部Nusselt数变化
Figure 18. Variation of local Nusselt number at hot wall surface under different b values
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