توصیف احتمالاتی انتقال بار بستر بعد از آستانه در یک بررسی آزمایشگاهی با استفاده از روش ردیابی سرعت ذره

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری سازه های آبی، گروه علوم و مهندسی آب، دانشگاه فردوسی مشهد

2 دانشیار گروه علوم و مهندسی آب ، دانشگاه فردوسی مشهد

3 استادیار/ دانشکده مهندسی عمران و محیط زیست، دانشگاه گلسگو، گلسگو، اسکاتلند

4 گروه مهندسی سازه‌های آبی، دانشکده آب و خاک، دانشگاه علوم کشاورزی و منابع طبیعی گرگان، گلستان، ایران

چکیده

حرکت رسوب با اهمیت فراوانی که در مهندسی و علم هیدرولیک دارد فیزیک کاملاً شناخته شده‌ای ندارد. نادیده گرفتن حرکت نوسانی و طبیعت ناپیوسته انتقال بار بستر، کاربرد روابطی که بر این اساس برای تخمین بار انتقال رسوب ارائه شده‌اند را دچار چالش کرده است. این پژوهش سعی دارد حرکت غیرمعلق (حرکت بار بستر) یک ذره با وزن‌های متفاوت را در شرایط مختلف جریان با استفاده از تکنیک‌های رهگیری ذره، مورد کاوش قرار دهد و آن را در قالب توابع توزیع احتمالاتی توصیف کند. با مشخص شدن رفتار آماری در رابطه با عامل یا عوامل مؤثر انتقال در رژیم‌های مختلف انتقال رسوب، می‌توان اظهار نظر دقیق‌تری داشت. در این راستا با استفاده از تکنیک رهگیری ذره (PTV)، موقعیت ذره در هر سری آزمایش مشخص شد. در نهایت با محاسبه سرعت لحظه‌ای ذره توابع توزیع احتمالاتی مختلف بر داده‌ها برازش داده شد تا بهترین تابع با توجه به معیار سنجش آماری کولموگروف-اسمیرنوف (در سطح اطمینان 5 درصد) انتخاب شود. نتایج نشان داد که انتقال ذره در اعداد رینولدز پایین جریان از تابع توزیع لوگ-نرمال و در اعداد رینولدز جریان بالا از تابع توزیع نرمال تبعیت می‌کند. همچنین به وسیله این مشاهدات در رابطه با عامل حرکت در شرایط مختلف رژیم انتقال رسوب بحث شد که با توجه به ویژگی‌های توابع توزیع احتمالاتی به دست آمده، انتقال رسوب در شرایط آستانه با عاملیت ارتباط ذره-بستر و در شرایط تعادلی تحت نیروهای سیال انجام می‌شود. در انتها با توجه به تفاوت رفتار حرکت رسوب در رژیم انتقال ضعیف و تعادلی می‌توان دو پارامتر آستانه معرفی کرد. با توجه به اهمیت کاربرد نتایج در مهندسی، به دلیل اینکه قالب پژوهش، قالب آماری و توصیف پدیده تصادفی بوده است می‌توان با در نظر گرفتن شرایط مختلف انتقال رسوب (با نمایندگی پارامتر عدد رینولدز ذره) احتمال وقوع سرعت ذرات را با استفاده از توابع توزیع ارائه شده، تخمین زد. همچنین نتایج این پژوهش در شرایط هیدرولیکی مشابه از جمله پژوهش‌های اکو-هیدرولیک و تونل باد قابل استفاده می‌باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Probabilistic description of coarse particle motion above threshold by particle tracking velocimetry method in an experimental study

نویسندگان [English]

  • Hamed Farhadi 1
  • kazem Esmaili 2
  • Manousos Valyrakis 3
  • Abdolreza Zahiri 4
1 Phd candidate for hydro structures, Water Science and Engineering Department, Ferdowsi University of Mashhad
2 Associate Professor Department of Water Science and Engineering , Ferdowsi University of Mashhad
3 Assistant professor/School of engineering, University of Glasgow, Glasgow, United Kingdom
4 Water and soil engineering faculty, Water engineering department, Gorgan university of agricultural sciences and natural resources, Gorgan, Iran
چکیده [English]

Sediment motion behavior plays an essential role in sediment and hydraulic engineering, though its physics is still not fully understood. Ignoring the stochastic nature of the sediment transport leads to various equations for bedload transport which are now being challenged due to their results. In this study, the non-suspended particle motion (bedload transport) in different hydraulic conditions was assessed by a particle tracking technique called Particle Tracking Velocimetry (PTV). The results of the PTV were applied to describe the particle behavior throughout the probability distribution functions. Knowing the particle motion behavior would guide learning more about the parameter/s governing the particle transport in different sediment transport regimes. The instantaneous particle velocity was measured after calibrating and validating the frames (resulted from the PTV). Different probability distribution functions were assessed with the Kolmogorov-Smirnov criterion (in 5 percent of the level of confidence) to find the best function which fits the collected data (i.e., the particle velocity). Furthermore, an analysis of the governing parameter for particle entrainment in different transport regimes was conducted. It was found that in a weak transport regime, the particle-bed and higher transport regime, the particle-flow interrelations were the governing factors that make the particle move. It was shown that the probability distribution function is Lognormal for lower particle Reynolds number, and on the other hand, in the higher particle Reynolds number, the Normal distribution best describes the particle velocity. The results of this research also could be applied in similar hydraulic conditions in the eco-hydraulic field, specifically macro-plastic movement as bedload in river courses and Aeolian research. 

کلیدواژه‌ها [English]

  • Bedload
  • Intermittent particle motion
  • Particle Tracking Velocimetry
  • Probability Distribution Function
  • Sediment transport
[1] M.S. Yalin, Mechanics of sediment transport, Pergamon press, Newyork, 2013.
[2] N. Fan, D. Zhong, B. Wu, E. Foufoula‐Georgiou, M. Guala, A mechanistic‐stochastic formulation of bed load particle motions: From individual particle forces to the Fokker‐Planck equation under low transport rates, Journal of Geophysical Research: Earth Surface, 119(3) (2014) 464-482.
[3] C. Ancey, Bedload transport: a walk between randomness and determinism. Part 1. The state of the art, Journal of Hydraulic Research, 58(1) (2020) 1-17.
[4] C. Ancey, Bedload transport: a walk between randomness and determinism. Part 2. Challenges and prospects, Journal of Hydraulic Research, 58(1) (2020) 18-33.
[5] D.J. Furbish, S.L. Fathel, M.W. Schmeeckle, Particle motions and bed load theory: The entrainment forms of the flux and the Exner equation, Gravel-bed Rivers: Processes and Disasters,  (2016).
[6] J. Heyman, F. Mettra, H. Ma, C. Ancey, Statistics of bedload transport over steep slopes: Separation of time scales and collective motion, Geophysical Research Letters, 40(1) (2013) 128-133.
[7] A. Recking, An analysis of nonlinearity effects on bed load transport prediction, Journal of Geophysical Research: Earth Surface, 118(3) (2013) 1264-1281.
[8] J.W. Kirchner, W.E. Dietrich, F. Iseya, H. Ikeda, The variability of critical shear stress, friction angle, and grain protrusion in water‐worked sediments, Sedimentology, 37(4) (1990) 647-672.
[9] A. Shields, Application of similarity principles and turbulence research to bed-load movement, Soil Conservation Service, 1936.
[10] O. Gronz, P.H. Hiller, S. Wirtz, K. Becker, T. Iserloh, M. Seeger, C. Brings, J. Aberle, M.C. Casper, J.B. Ries, Smartstones: A small 9-axis sensor implanted in stones to track their movements, Catena, 142 (2016) 245-251.
[11] M.A. Hassan, H. Voepel, R. Schumer, G. Parker, L. Fraccarollo, Displacement characteristics of coarse fluvial bed sediment, Journal of Geophysical Research: Earth Surface, 118(1) (2013) 155-165.
[12] L. Olinde, J.P. Johnson, Using RFID and accelerometer‐embedded tracers to measure probabilities of bed load transport, step lengths, and rest times in a mountain stream, Water Resources Research, 51(9) (2015) 7572-7589.
[13] W.H. Hager, Du Boys and sediment transport, Journal of Hydraulic Research, 43(3) (2005) 227-233.
[14] S. Dey, Fluvial hydrodynamics, Springer, 2014.
[15] H.A. Einstein, Bedload transport as a probability problem, Sedimentation (reprinted in 1972). Water Resources Publications, Colorado,  (1937) 105-108.
[16] H. Habersack, A. Kreisler, Sediment transport processes, in:  Dating torrential processes on fans and cones, Springer, 2013, pp. 51-73.
[17] C. Ancey, P. Bohorquez, J. Heyman, Stochastic interpretation of the advection‐diffusion equation and its relevance to bed load transport, Journal of Geophysical Research: Earth Surface, 120(12) (2015) 2529-2551.
[18] C. Ancey, J. Heyman, A microstructural approach to bed load transport: mean behaviour and fluctuations of particle transport rates, Journal of Fluid Mechanics, 744 (2014) 129-168.
[19] P. Diplas, C.L. Dancey, A.O. Celik, M. Valyrakis, K. Greer, T. Akar, The role of impulse on the initiation of particle movement under turbulent flow conditions, Science, 322(5902) (2008) 717-720.
[20] D.J. Furbish, P.K. Haff, J.C. Roseberry, M.W. Schmeeckle, A probabilistic description of the bed load sediment flux: 1. Theory, Journal of Geophysical Research: Earth Surface, 117(F3) (2012).
[21] J. Heyman, P. Bohorquez, C. Ancey, Entrainment, motion, and deposition of coarse particles transported by water over a sloping mobile bed, Journal of Geophysical Research: Earth Surface,  (2016).
[22] E. Lajeunesse, L. Malverti, F. Charru, Bed load transport in turbulent flow at the grain scale: Experiments and modeling, Journal of Geophysical Research: Earth Surface, 115(F4) (2010).
[23] J.C. Roseberry, M.W. Schmeeckle, D.J. Furbish, A probabilistic description of the bed load sediment flux: 2. Particle activity and motions, Journal of Geophysical Research: Earth Surface, 117(F3) (2012).
[24] J. Shim, J. Duan, Experimental and theoretical study of bed load particle velocity, Journal of Hydraulic Research, 57(1) (2019) 62-74.
[25] J. Shim, J.G. Duan, Experimental study of bed-load transport using particle motion tracking, International Journal of Sediment Research,  (2016).
[26] M. Valyrakis, P. Diplas, C.L. Dancey, Entrainment of coarse grains in turbulent flows: An extreme value theory approach, Water Resources Research, 47(9) (2011).
[27] M. Valyrakis, P. Diplas, C.L. Dancey, Entrainment of coarse particles in turbulent flows: An energy approach, Journal of Geophysical Research: Earth Surface, 118(1) (2013) 42-53.
[28] M. Valyrakis, P. Diplas, C.L. Dancey, K. Greer, A.O. Celik, Role of instantaneous force magnitude and duration on particle entrainment, Journal of Geophysical Research: Earth Surface, 115(F2) (2010).
[29] J.M. Buffington, D.R. Montgomery, A systematic analysis of eight decades of incipient motion studies, with special reference to gravel‐bedded rivers, Water Resources Research, 33(8) (1997) 1993-2029.
[30] A.O. Celik, P. Diplas, C.L. Dancey, M. Valyrakis, Impulse and particle dislodgement under turbulent flow conditions, Physics of Fluids, 22(4) (2010) 046601.
[31] R. Fernandez Luque, R. Van Beek, Erosion and transport of bed-load sediment, Journal of hydraulic research, 14(2) (1976) 127-144.
[32] J. Bridge, D. Dominic, Bed load grain velocities and sediment transport rates, Water Resources Research, 20(4) (1984) 476-490.
[33] A. Keshavarzy, J. Ball, An application of image processing in the study of sediment motion, Journal of hydraulic research, 37(4) (1999) 559-576.
[34] A. Radice, S. Malavasi, F. Ballio, Solid transport measurements through image processing, Experiments in fluids, 41(5) (2006) 721-734.
[35] M. Houssais, E. Lajeunesse, Bedload transport of a bimodal sediment bed, Journal of Geophysical Research: Earth Surface, 117(F4) (2012).
[36] K. Heays, H. Friedrich, B. Melville, R. Nokes, Quantifying the dynamic evolution of graded gravel beds using particle tracking velocimetry, Journal of Hydraulic Engineering, 140(7) (2014) 04014027.
[37] Z. Wu, D. Furbish, E. Foufoula‐Georgiou, Generalization of hop distance‐time scaling and particle velocity distributions via a two‐regime formalism of bedload particle motions, Water Resources Research, 56(1) (2020) e2019WR025116.
[38] J. Shim, J.G. Duan, Experimental study of bed-load transport using particle motion tracking, International Journal of Sediment Research, 32(1) (2017) 73-81.
[39] R.L. Martin, D.J. Jerolmack, R. Schumer, The physical basis for anomalous diffusion in bed load transport, Journal of Geophysical Research: Earth Surface, 117(F1) (2012).
[40] D. Liu, M. Valyrakis, Preliminary investigation of the transport of small plastic litter along a vegetated riverbank, in:  EGU General Assembly Conference Abstracts, 2017, pp. 14788.
[41] G. Maniatis, T. Hoey, R. Hodge, D. Rickenmann, A. Badoux, Inertial drag and lift forces for coarse grains on rough alluvial beds measured using in-grain accelerometers, Earth Surface Dynamics, 8(4) (2020) 1067-1099.
[42] N.-S. Cheng, A.W.-K. Law, Fluctuations of turbulent bed shear stress, Journal of engineering mechanics, 129(1) (2003) 126-130.
[43] N.-S. Cheng, Influence of shear stress fluctuation on bed particle mobility, Physics of Fluids, 18(9) (2006) 096602.
[44] H. Mouri, A. Hori, M. Takaoka, Large-scale lognormal fluctuations in turbulence velocity fields, Physics of Fluids, 21(6) (2009) 065107.
[45] E. Limpert, W.A. Stahel, M. Abbt, Log-normal distributions across the sciences: keys and clues: on the charms of statistics, and how mechanical models resembling gambling machines offer a link to a handy way to characterize log-normal distributions, which can provide deeper insight into variability and probability—normal or log-normal: that is the question, BioScience, 51(5) (2001) 341-352.
[46] W. Shih, P. Diplas, A unified approach to bed load transport description over a wide range of flow conditions via the use of conditional data treatment, Water Resources Research, 54(5) (2018) 3490-3509.
[47] C. Ancey, I. Pascal, Estimating mean bedload transport rates and their uncertainty, Journal of Geophysical Research: Earth Surface, 125(7) (2020) e2020JF005534.
[48] H. Farhadi, M. Valyrakis, Exploring particle transport dynamics at a range of flow conditions above threshold, in:  Geophysical Research Abstracts, 2019.
[49] T. Pähtz, A.H. Clark, M. Valyrakis, O. Durán, The physics of sediment transport initiation, cessation, and entrainment across aeolian and fluvial environments, Reviews of Geophysics, 58(1) (2020) e2019RG000679.
[50] T. Pähtz, O. Durán, Universal friction law at granular solid-gas transition explains scaling of sediment transport load with excess fluid shear stress, Physical Review Fluids, 3(10) (2018) 104302.