Random walk simulation of organic particle sedimentation process in the open channels
CHEN Xiao1, LIU Zhao-wei1, CHEN Yong-can1,2
1. State Key Laboratory Hydroscience and Engineering, Tsinghua University, Beijing 100084, China;
2. College of Environment and Resources, Southwest University of Science and Technology, Mianyang 621010, China
Based on the main characteristics of open channel flows, this research built a random walk model for fine particles within the inhomogeneous open channel turbulence, with modifications concerning influences of the vertical inhomogeneity of turbulence intensity and loitering effect. Using the established model, the sedimentation loss of fine particles in the open channels was simulated. Simulation results showed that, when influence of the loitering effect was not considered, particle sedimentation loss rate could be calculated by the ratio of particle settling velocity to the water depth; when influence of the loitering effect was considered, particle sedimentation loss rate would have a 18%~27% reduction compared to quiescent environments. The reduction percentage was basically consistent with the asymptotic value of declining percentage of particle settling velocity (19%~25%) in the homogeneous turbulent fields. The conclusion of this article was mainly based on two premises that the resuspension of particle was not considered, and the loitering effect was the dominant mechanism of turbulence on particle settling. Proposed method and results can be applied to calculate the sedimentation process of particles to the channel bottom more accurately.
陈啸, 刘昭伟, 陈永灿. 明渠中有机质微粒沉降过程的随机游走模拟[J]. 中国环境科学, 2020, 40(11): 4813-4820.
CHEN Xiao, LIU Zhao-wei, CHEN Yong-can. Random walk simulation of organic particle sedimentation process in the open channels. CHINA ENVIRONMENTAL SCIENCECE, 2020, 40(11): 4813-4820.
Huang Y, Chen X, He S, et al. Sinking loss should be taken into account while studying the dynamics of Microcystis under light-availability control[J]. Journal of Hazardous Materials, 2016,314(aug.15):270-276.
[2]
McNair J N, Newbold J D, Hart D D. Turbulent transport of suspended particles and dispersing benthic organisms:how long to hit bottom?[J]. Journal of Theoretical Biology, 1997,188(1):29-52.
[3]
刘广州,胡嘉镗,李适宇.珠江口夏季海陆源有机碳的模拟研究——分布特征、贡献比重及其迁移转化过程[J]. 中国环境科学, 2020, 40(1):162-173. Liu G Z, Hu J T, Li S Y. Simulation of marine and terrestrial organic carbon in the Pearl River Estuary in summer——distribution characteristics, contribution rate and migration and transformation processes[J]. China Environmental Science, 2020,40(1):162-173.
[4]
McNair J N, Newbold J D. Turbulent particle transport in streams:Can exponential settling be reconciled with fluid mechanics?[J]. Journal of Theoretical Biology, 2012,300:62-80.
[5]
Reynolds C S, Wiseman S W. Sinking losses of phytoplankton in closed limnetic systems[J]. Journal of Plankton Research, 1982,4(3):489-522.
[6]
Reynolds C S, White M L, Clarke R T, et al. Suspension and settlement of particles in flowing water:comparison of the effects of varying water depth and velocity in circulating channels[J]. Freshwater Biology, 1990,24(1):23-34.
[7]
Everbecq E, Gosselain V, Viroux L, et al. Potamon:a dynamic model for predicting phytoplankton composition and biomass in lowland rivers[J]. Water Research, 2001,35(4):901-912.
[8]
Descy J P, Leitao M, Everbecq E, et al. Phytoplankton of the River Loire, France:a biodiversity and modelling study[J]. Journal of Plankton Research, 2011,34(2):120-135.
[9]
Jäger C G, Borchardt D. Longitudinal patterns and response lengths of algae in riverine ecosystems:A model analysis emphasising benthic-pelagic interactions[J]. Journal of Theoretical Biology, 2018,442:66-78.
[10]
Good G H, Ireland P J, Bewley G P, et al. Settling regimes of inertial particles in isotropic turbulence[J]. Journal of Fluid Mechanics, 2014,759.
[11]
Nielsen P. Turbulence effects on the settling of suspended particles[J]. Journal of Sedimentary Research, 1993,63(5):835-838.
[12]
Pasquero C, Provenzale A, Spiegel E A. Suspension and Fall of Heavy Particles in Random Two-Dimensional Flow[J]. Physical Review Letters, 2003,91(5):054502.
[13]
Fornari W, Picano F, Sardina G, et al. Reduced particle settling speed in turbulence[J]. Journal of Fluid Mechanics, 2016,808:153-167.
[14]
Rosa B, Parishani H, Ayala O, et al. Settling velocity of small inertial particles in homogeneous isotropic turbulence from high-resolution DNS[J]. International Journal of Multiphase Flow, 2016,83:217-231.
[15]
Miller J, Georgian T. Estimation of fine particulate transport in streams using pollen as a seston analog[J]. Journal of the North American Benthological Society, 1992,11(2):172-180.
[16]
Fornari W, Picano F, Brandt L, et al. Sedimentation of finite-size spheres in quiescent and turbulent environments[J]. Journal of Fluid Mechanics, 2016:640-669.
[17]
Dehbi A. Turbulent particle dispersion in arbitrary wall-bounded geometries:A coupled CFD-Langevin-equation based approach[J]. International Journal of Multiphase Flow, 2008,34(9):819-828.
[18]
Bocksell T L, Loth E. Random walk models for particle diffusion in free-shear flows[J]. AIAA journal, 2001,39(6):1086-1096.
[19]
Thomson D J. Random walk modelling of diffusion in inhomogeneous turbulence[J]. Quarterly Journal of the Royal Meteorological Society, 1984,110(466):1107-1120.
[20]
Legg B J, Raupach M R. Markov-chain simulation of particle dispersion in inhomogeneous flows:the mean drift velocity induced by a gradient in Eulerian velocity variance[J]. Boundary-Layer Meteorology, 1982,24(1):3-13.
[21]
邓安军,陈立,林鹏,等.紊动强度沿垂线分布规律的分析[J]. 泥沙研究, 2001,(5):33-36. Den A J, Chen L, Lin P, et al. Analyses on distribution rule of turbulence intensity along depth[J]. Journal of Sediment Research, 2001,(5):33-36.
[22]
Nezu I, Nakagawa H. Turbulence in open-channel flows[M]. Rotterdam:A.A.Balkeman Publishers, 1993:12-28.
[23]
Dreeben T D, Pope S B. Probability density function and Reynolds-stress modeling of near-wall turbulent flows[J]. Physics of Fluids, 1997,9(1):154-163.
[24]
Eggenhuisen J T, Cartigny M J B, de Leeuw J. Physical theory for near-bed turbulent particle suspension capacity[J]. Earth Surface Dynamics, 2017,5(2):269-281.
[25]
Bocksell T L, Loth E. Stochastic modeling of particle diffusion in a turbulent boundary layer[J]. International Journal of Multiphase Flow, 2006,32(10/11):1234-1253.
[26]
Wanner S C, Pusch M. Use of fluorescently labeled Lycopodium spores as a tracer for suspended particles in a lowland river[J]. Journal of the North American Benthological Society, 2000,19(4):648-658.
[27]
Reynolds C S. The long, the short and the stalled:on the attributes of phytoplankton selected by physical mixing in lakes and rivers[J]. Hydrobiologia, 1994,289(1-3):9-21.
[28]
Chen X, Liu Z, Chen Y, et al. Analytical expression for predicting the reduced settling velocity of small particles in turbulence[J]. Environmental Fluid Mechanics, 2020,20(4):905-922.
[29]
Murray S P. Settling velocities and vertical diffusion of particles in turbulent water[J]. Journal of Geophysical Research, 1970,75(9):1647-1654.
[30]
Zhou Q, Cheng N S. Experimental investigation of single particle settling in turbulence generated by oscillating grid[J]. Chemical Engineering Journal, 2009,149(1-3):289-300.
[31]
Roche K R, Drummond J D, Boano F, et al. Benthic biofilm controls on fine particle dynamics in streams[J]. Water Resources Research, 2017,53(1):222-236.
[32]
刘世昌,田小方,赵以军,等.搅拌方式对絮凝除藻效果的影响[J]. 中国环境科学, 2012,32(9):1688-1692. Liu S C, Tian X F L, Zhao Y J, et al. Effect of mixing process on flocculation and removal of algae[J]. China Environmental Science, 2012,32(9):1688-1692.