Non-orthogonal multiple-relaxation-time lattice Boltzmann method for numerical simulation of thermal coupling with porous square cavity flow containing internal heat source
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摘要:
针对含内热源的多孔方腔内自然对流现象问题，采用非正交多弛豫时间（MRT）格子Boltzmann方法进行了研究。分析了Rayleigh数（104 ≤
Ra ≤ 106）、内热源布局方式（水平、垂直及对角布局）、内热源几何尺寸大小（A =1/16，1/8，3/16，1/4）及两内热源间的间距（S =5/64，13/64，21/64）对流动传热的影响。结果表明：在Ra =104，105和S =5/64的情况下，任意内热源几何尺寸，内热源采用对角布局方式可获得更好的对流换热效果；在Ra =105，106和S =13/64，21/64的情况下，水平布局方式更优；在内热源采用水平布局，Ra =104的情况下，任意内热源几何尺寸，对流换热效果均随着内热源间距的增大而增强；而随着Ra 增大，内热源几何尺寸减小，对流换热效果随着内热源间距的增大先增大后减小，而后随着内热源间距增大其对流换热效果减弱；对角布局也有相似规律，在其他条件一致的情况下，随着内热源几何尺寸的增加，其对流换热效果增强。-
关键词:
- 多孔方腔 /
- 内热源 /
- 自然对流 /
- Nusselt数 /
- 多弛豫时间(MRT) /
- Boltzmann模型
Abstract:In this paper, in order to solve the problem of natural convection in a porous square cavity containing an internal heat source, the non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann method was used. The influence of the value of Rayleigh number(104 ≤
Ra ≤ 106), internal heat source layout (horizontal, vertical and diagonal layout), internal heat source size (A =1/16, 1/8, 3/16, 1/4), and spacing (S =5/64, 13/64, 21/64) between two internal heat sources on convective heat transfer was analyzed. The results indicate that in the case ofRa =104, 105 andS =5/64, and the internal heat source is of any size, it can obtain better heat transfer by adopting the layout of diagonal; whenRa =105, 106 andS =13/64, 21/64, horizontal is better. In horizontal layout of the internal heat source, atRa =104, the convection heat transfer effect in any internal heat source size is enhanced as the internal heat source spacing increases. However, asRa increases, and internal heat source size decreases, the convective heat transfer effect first increases and then decreases with the increase of internal heat source space; then its effect decreases as internal heat source space increases. The layout of diagonal is in a similar situation. When other conditions are the same, the convective heat transfer effect increases with the increase of internal heat source size. -
图 2 流线图与等温线图比较(Ra=105，Da=10-2，Pr=1.0，ε=0.4)
Figure 2. Comparison of streamlines and isotherms (Ra=105, Da=10-2, Pr=1.0, ε=0.4)
图 3 不同Raleigh数、内热源几何尺寸大小及间距下布局方式对热壁面平均努塞尔数的影响
Figure 3. Influence of layout mode on heated wall average Nusselt number with different Rayleigh numbers, heat source sizes and spacing
图 4 不同Raleigh数、内热源几何尺寸大小及间距下布局方式对冷壁面平均努塞尔数的影响
Figure 4. Influence of layout mode on cold wall average Nusselt number with different Rayleigh numbers, heat source sizes and spacing
图 5 Ra=104，A=3/16，S=21/64下3种布局方式的流线图与等温线图
Figure 5. Streamlines and isotherms for three layout modes at Ra=104, A=3/16, S=21/64
图 6 Ra=105，A=1/8，S=5/64下3种布局方式的流线图与等温线图
Figure 6. Streamlines and isotherms for three layout modes at Ra=105, A=1/8, S=5/64
图 7 Ra=106，A=1/16，S=21/64下3种布局方式的流线图与等温线图
Figure 7. Streamlines and isotherms for three layout modes at Ra=106, A=1/16, S=21/64
图 8 水平布局时，不同Raleigh数、内热源几何尺寸大小及间距对热壁面平均努塞尔数的影响
Figure 8. Influence of different Rayleigh numbers, heat source sizes and spacing on heated wall average Nusselt number in horizontal layout
图 9 水平布局时，不同Raleigh数、内热源几何尺寸大小及间距下冷壁面局部努塞尔数的分布
Figure 9. Distribution of local Nusselt number on cold wall with different Rayleigh numbers, heat source sizes and spacing in horizontal layout
图 10 水平布局时，Ra=104，A=1/4，S=5/64，13/64，21/64下的流线图与等温线图
Figure 10. Streamlines and isotherms for horizontal layout at Ra=104, A=1/4, S=5/64, S=13/64, S=21/64
图 11 水平布局时，Ra=106，A=1/8，S=5/64，13/64，21/64下的流线图与等温线图
Figure 11. Streamlines and isotherms for horizontal layout at Ra=106, A=1/8, S=5/64, S=13/64, S=21/64
图 12 对角布局时，不同Raleigh数、内热源几何尺寸大小及间距下对热壁面平均努塞尔数的影响
Figure 12. Influence of different Rayleigh numbers, heat source sizes and spacing on heated wall average Nusselt number in diagonal layout
图 13 对角布局时，不同Raleigh数、热源几何尺寸大小及间距下冷壁面局部努塞尔数的分布
Figure 13. Distribution of local Nusselt number on cold wall with different Rayleigh numbers, heat source sizes and spacing in diagonal layout
图 14 对角布局时，Ra=106，A=1/16，S=5/64，13/64，21/64下的流线图与等温线图
Figure 14. Streamlines and isotherms for diagonal layout at Ra=106, A=1/16, S=5/64, S=13/64, S=21/64
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