基于格子Boltzmann法的树木流场数值模拟
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摘要
通过多松弛时间格式的格子Boltzmann法(lattice Boltzmann method,LBM)对树木流场进行数值研究,树木简化为表征元尺度下的多孔介质,为了研究雷诺数Re=10 000下的流场,将大涡模拟结合LBM得到树木周围的流速和风压,并在模型前设置格栅,以此制造扰动并模拟B类场地下的流场。结果表明,树木下游不同位置的平均风速剖面与试验吻合良好;风压从迎风面到背风面显示出明显的变化梯度,而且其最大绝对值主要分布在迎风面和背风面附近; B类地貌下的树木遮蔽区下游风速有所减小,湍流度极大值在树冠顶部附近。
The flow field of a tree was numerically studied by Lattice Boltzmann method( LBM) in the format of multiple relaxation times. The tree was simplified to porous medias at scale of representative elementary volume. In order to study the tree flow field under Re = 10 000,large eddy simulation was introduced into LBM to obtain the wind velocities and wind pressures around the canopy. Then the grids were set in front of the model to produce turbulence and simulateflows under the B type site. The results show that the mean velocity profiles at different downstream locations behind the tree are in good agreement with the experiment results. The wind pressures exhibit a markedly changing gradient from the windward side to the leeward side. Moreover,the maximum absolute value is mainly distributed near the windward or leeward side. Additionally,when the terrain is B type,the downstream velocities behind the sheltered area decrease and the maximum turbulence intensity emerges near the top of the canopy.
The flow field of a tree was numerically studied by Lattice Boltzmann method( LBM) in the format of multiple relaxation times. The tree was simplified to porous medias at scale of representative elementary volume. In order to study the tree flow field under Re = 10 000,large eddy simulation was introduced into LBM to obtain the wind velocities and wind pressures around the canopy. Then the grids were set in front of the model to produce turbulence and simulateflows under the B type site. The results show that the mean velocity profiles at different downstream locations behind the tree are in good agreement with the experiment results. The wind pressures exhibit a markedly changing gradient from the windward side to the leeward side. Moreover,the maximum absolute value is mainly distributed near the windward or leeward side. Additionally,when the terrain is B type,the downstream velocities behind the sheltered area decrease and the maximum turbulence intensity emerges near the top of the canopy.
引文
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[21]中华人民共和国住房和城乡建设部,中华人民共和国国家质量监督检验检疫总局.建筑结构荷载规范:GB50009—2012[S]. 2012版.北京:中国建筑工业出版社,2012:220-228.
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[2] ROSENFELD M,MAROM G,BITAN A. Numerical simulation of theairflow across trees in a windbreak[J]. Boundary-Layer Meteorology,2010,135(1):89-107.
[3]解明镜,石磊.湖南农村住宅周边植被对自然通风影响的研究[J].湖南大学学报(自然科学版),2012,39(7):20-24.
[4]杨会,汤达明,朱辉,等.树冠对建筑流场影响的数值模拟及评价[J].桂林航天工业学院学报,2016(2):168-173.
[5] QIAN Y H,D'HUMIRES D,LALLEMAND P. Lattice BGK models for Navier-Stokes equation[J]. Europhysics Letters,1992,17:479-484.
[6] LALLEMAND P,LUO L S. Theory of the lattice Boltzmann method:dispersion,isotropy,Galileaninvariance,andstability[J]. Physical Review E,2000,61:6546-6562.
[7] HOU S,STERLING J,CHEN S,et al. A lattice Boltzmann subgrid model forhigh Reynolds number flows[J]. Field Institute Communication,1994,6(13):8-11.
[8] NITHIARASU P,SEETHARAMU K,SUNDARARAJAN T. Natural convective heattransfer in a fluid saturated variable porosity medium[J]. International Journal of Heat and Mass,1997,40(160):3955-3967.
[9] Guo Z L,Zhao T S. Lattice Boltzmann model for incompressible flowsthrough porous media[J]. Physical Review E,2002,66:162-173.
[10] D'HUMIRES D,GINZBERG I,KRAFCZYK M,et al Multiple-relaxation-time lattice Boltzmann models in threedimensions[J]. Philosophical Transactions,2002,360(1792):437-451.
[11] XIA Z,SHI Y,CHEN Y,et al. Comparisons of different implementations of turbulence modeling in lattice Boltzmann method[J]. Journal of Turbulent,2015,16(1):67-80.
[12]祝志文,陈魏,向泽,等.大跨度斜拉桥主梁气动力特性的大涡模拟[J].湖南大学学报(自然科学版),2013,40(11):26-33.
[13] TAKLE E S,HAO W,SHEN J. Shelterbelts and windbreaks:mathematical modeling and computers simulationsof turbulent flows[J]. Advances in Mechanics,2001,33(1):549-586.
[14] FANG F M,LIANG T C,CHUNG C Y,et al. On the simulation of flowaround discrete coniferoustrees[J]. Journal Chinese Institute of Engineers,2015,38(5):1-10.
[15] MOCHIDA A,TABATA Y,IWATA T,et al,Examining tree canopy models for CFD prediction of wind environment at pedestrian level. Journal of Wind Engineering and Industrial Aerodynamics,2008(97):1667-1677.
[16] GUO Z L,ZHENG C G,SHI B C. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method[J]. Chinese Physics,2002,11(4):366-374.
[17] GRANT F,NICKING W G. Direct field measurement of wind drag onvegetation for application to windbreak design and modeling[J]. Land Degradation&Development,1998,9(1):57-66.
[18] BABU V,NARASIMHAN A. Investigation of vortex shedding behind a porous square cylinder using lattice Boltzmann method[J]. Physics of Fluids,2010,22,053605.
[19] MARY I,SAGAUT P,DEVILE M. An algorithm for unsteady viscous flows at all speeds[J]. International Journal for Numerical Methods in Fluids,2015,34(5):371-401.
[20] YANG Y,XIE Z,TKT T,etal. Verification of a tree canopy model and an example of its application in wind environment optimization[J]. Wind&Structures An International Journal,2012,15(5):409-421.
[21]中华人民共和国住房和城乡建设部,中华人民共和国国家质量监督检验检疫总局.建筑结构荷载规范:GB50009—2012[S]. 2012版.北京:中国建筑工业出版社,2012:220-228.
[22] LIU J,CHEN JM,BLACK TA,et al. E-εmodeling of turbulent air flow downwind of a model forest edge[J]. BoundaryLayer Meteorology,1996,77(1):21-44.