基于随机位移方法的植被水流纵向离散研究
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摘要
在天然河道中,离散主要是由纵向流速在横断面分布的不均匀所引起,当河道中存在部分挺水植被时,流速分布的不均匀性更加明显。为了研究部分挺水植被水流中的纵向离散,假设各变量在垂向是不变的,模拟一个由流向和横向组成的二维域,引入了基于拉格朗日观点的随机位移模型,该方法直接使用独立运动的离散颗粒来描绘物质的输移,不再需要求解随流扩散方程。随机位移模型主要根据水深平均流速和横向紊动扩散系数的横向分布来确定污染物的分布。其中,流速横向分布公式采用了基于剪切涡的简化经验公式,该公式的优点在于不用对二次流系数进行率定,且物理意义明确;另外,利用量纲关系及遗传算法给出了剪切涡外层宽度的显性经验公式,分析可得剪切涡外层宽度主要由水深和河床阻力决定,植被的直径和密度对于涡旋外层结构影响较小;根据以往实测资料,提出了横向紊动扩散系数的横向分布模型,揭示了横向紊动扩散系数在交界处远大于稳定区的动力特性。为了验证随机位移模型预测的准确性,在长直部分植被水槽进行了室内试验,流场中不同点的浓度过程线的实测值与模拟值吻合良好,表明随机位移模型可以有效地模拟部分挺水植被水流纵向离散,为生态河道污染物混合输移的评估提供了新的方法。
In natural rivers, the dispersion is mainly caused by the non-uniform distribution of longitudinal flow velocity in the cross-section. The inhomogeneity of the velocity distribution is more obvious when there is partial emergent vegetation in the river. In order to study the longitudinal dispersion in the flow with partially emergent vegetation, assuming that the variables are constant in the vertical direction, a two-dimensional domain consisting of flow direction and lateral direction was simulated, and the Random Displacement Model(RDM) based on Lagrangian method was introduced. This model directly uses discrete particles with independent motion to describe the transport of matter, and it is no longer necessary to solve the advection-diffusion equation. The RDM simulates the distribution of pollutants mainly based on the transverse distribution of the vertically average flow velocity and transverse turbulence diffusion coefficient. Among them, the lateral velocity distribution formula adopts a simplified empirical formula based on shear vortex. The advantage of this formula is that it does not require rating the secondary flow coefficient,and the physical meaning is clear; with the dimensional relationship and the genetic algorithm, the explicit empirical formula of the outer layer width of the shear vortex was proposed, which is mainly determined by the water depth and the bottom friction. The diameter and density of the vegetation have little effect on the outer structure of the vortex. Besides, the model of the lateral distribution of the turbulent diffusion coefficient was given based on previous measured data, revealing the dynamic characteristics that the lateral turbulence diffusion at the junction is much greater than that of the stable zone. In order to verify the accuracy of the random displacement model, an indoor experiment was conducted in a long and straight partial vegetated water tank. The measured values of the concentration process lines at different points in the flow field agree well with the simulated values, indicating that the RDM can effectively simulate longitudinal dispersion of flow with partial vegetation, and provide a new method for the assessment of the mixing and transport of pollutants in ecological rivers.
In natural rivers, the dispersion is mainly caused by the non-uniform distribution of longitudinal flow velocity in the cross-section. The inhomogeneity of the velocity distribution is more obvious when there is partial emergent vegetation in the river. In order to study the longitudinal dispersion in the flow with partially emergent vegetation, assuming that the variables are constant in the vertical direction, a two-dimensional domain consisting of flow direction and lateral direction was simulated, and the Random Displacement Model(RDM) based on Lagrangian method was introduced. This model directly uses discrete particles with independent motion to describe the transport of matter, and it is no longer necessary to solve the advection-diffusion equation. The RDM simulates the distribution of pollutants mainly based on the transverse distribution of the vertically average flow velocity and transverse turbulence diffusion coefficient. Among them, the lateral velocity distribution formula adopts a simplified empirical formula based on shear vortex. The advantage of this formula is that it does not require rating the secondary flow coefficient,and the physical meaning is clear; with the dimensional relationship and the genetic algorithm, the explicit empirical formula of the outer layer width of the shear vortex was proposed, which is mainly determined by the water depth and the bottom friction. The diameter and density of the vegetation have little effect on the outer structure of the vortex. Besides, the model of the lateral distribution of the turbulent diffusion coefficient was given based on previous measured data, revealing the dynamic characteristics that the lateral turbulence diffusion at the junction is much greater than that of the stable zone. In order to verify the accuracy of the random displacement model, an indoor experiment was conducted in a long and straight partial vegetated water tank. The measured values of the concentration process lines at different points in the flow field agree well with the simulated values, indicating that the RDM can effectively simulate longitudinal dispersion of flow with partial vegetation, and provide a new method for the assessment of the mixing and transport of pollutants in ecological rivers.
引文
[1]槐文信.环境水力学基础[M].武汉:武汉大学出版社,2014.
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[3]Huai W,Shi H,Song S,et al.A simplified method for estimating the longitudinal dispersion coefficient in ecological channels with vegetation[J].Ecological Indicators,2017,92(5):91-98.
[4]Perucca E,Camporeale C,Ridolfi L.Estimation of the dispersion coefficient in rivers with riparian vegetation[J].Advances in Water Resources,2009,32(1):78-87.
[5]Follett E,Chamecki M,Nepf H.Evaluation of a random displacement model for predicting particle escape from canopies using a simple eddy diffusivity model[J].Agricultural&Forest Meteorology,2016,224:40-48.
[6]Guillon V,Bauer D,Fleury M,et al.Computing the longtime behaviour of NMR propagators in porous media using apore network random walk model[J].Transport in Porous Media,2014,101(2):251-267.
[7]Gardiner C W.Handbook of Stochastic Methods[M].Berlin:Springer,1985.
[8]Hoteit H,Mose R,Younes A,et al.Three dimensional modeling of mass transfer in porous media using the mixed hybrid finite elements and the random walk methods[J].Mathematical Geology,2002,34(4):435-456.
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[10]Wilson J D,Yee E.A critical examination of the random displacement model of turbulent dispersion[J].Bound-Layer Meterorol,2007,125(3):399-416.
[11]Liang Dongfang,Wu Xuefei.A random walk simulation of scalar mixing in flows through submerged vegeta-tions[J].Journal of Hydrodynamics,2014,26(3):343-350.
[12]White B,Nepf H M.A vortex-based model of velocity and shear stress in a partially vegetated shallow channel[J].Water Resources Research,2008,44(1):W01412.
[13]White B L,Nepf H M.Shear instability and coherent structures in shallow flow adjacent to a porous layer[J].Journal of Fluid Mechanics,2007,593:1-32.
[14]Chen G,Huai W,Han J.Flow structure in partially vegetated rectangular channels[J].Journal of Hydrodynamics,2010,22(4):590-597.
[15]Nepf H M,Sullivan J A,ZAvistoski R A.A model for diffusion within emergent vegetation[J].Limnology and Oceanography,1997,42(8):1735-1745.
[16]Fisher H,List E,Koh R,et al.Mixing in inland and coastal waters[M].New York:Academic,1979.
[2]Camporeale C,Ridolfi L.Riparian vegetation distribution induced by river flow variability:A stochastic approach[J].Water Resources Research,2006,42(10):W010415.
[3]Huai W,Shi H,Song S,et al.A simplified method for estimating the longitudinal dispersion coefficient in ecological channels with vegetation[J].Ecological Indicators,2017,92(5):91-98.
[4]Perucca E,Camporeale C,Ridolfi L.Estimation of the dispersion coefficient in rivers with riparian vegetation[J].Advances in Water Resources,2009,32(1):78-87.
[5]Follett E,Chamecki M,Nepf H.Evaluation of a random displacement model for predicting particle escape from canopies using a simple eddy diffusivity model[J].Agricultural&Forest Meteorology,2016,224:40-48.
[6]Guillon V,Bauer D,Fleury M,et al.Computing the longtime behaviour of NMR propagators in porous media using apore network random walk model[J].Transport in Porous Media,2014,101(2):251-267.
[7]Gardiner C W.Handbook of Stochastic Methods[M].Berlin:Springer,1985.
[8]Hoteit H,Mose R,Younes A,et al.Three dimensional modeling of mass transfer in porous media using the mixed hybrid finite elements and the random walk methods[J].Mathematical Geology,2002,34(4):435-456.
[9]Israelsson P H,Kim Y D,Adams E E.A comparison of three lagrangian approaches for extending near field mixing calculations[J].Environ Model Softw,2006,21(12):1631-1649.
[10]Wilson J D,Yee E.A critical examination of the random displacement model of turbulent dispersion[J].Bound-Layer Meterorol,2007,125(3):399-416.
[11]Liang Dongfang,Wu Xuefei.A random walk simulation of scalar mixing in flows through submerged vegeta-tions[J].Journal of Hydrodynamics,2014,26(3):343-350.
[12]White B,Nepf H M.A vortex-based model of velocity and shear stress in a partially vegetated shallow channel[J].Water Resources Research,2008,44(1):W01412.
[13]White B L,Nepf H M.Shear instability and coherent structures in shallow flow adjacent to a porous layer[J].Journal of Fluid Mechanics,2007,593:1-32.
[14]Chen G,Huai W,Han J.Flow structure in partially vegetated rectangular channels[J].Journal of Hydrodynamics,2010,22(4):590-597.
[15]Nepf H M,Sullivan J A,ZAvistoski R A.A model for diffusion within emergent vegetation[J].Limnology and Oceanography,1997,42(8):1735-1745.
[16]Fisher H,List E,Koh R,et al.Mixing in inland and coastal waters[M].New York:Academic,1979.