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A simple approach to simulate the size distribution of suspended sediment

부유사 입경분포 모의를 위한 간편법

  • Kwon, Minhyuck (Department of Civil Engineering, Chungnam National University) ;
  • Byun, Jisun (K-water Research Institute, Korea Water Resources Corportation) ;
  • Son, Minwoo (Department of Civil Engineering, Chungnam National University)
  • 권민혁 (충남대학교 토목공학과) ;
  • 변지선 (한국수자원공사 K-water 연구원) ;
  • 손민우 (충남대학교 토목공학과)
  • Received : 2024.04.23
  • Accepted : 2024.05.07
  • Published : 2024.05.31

Abstract

Numerous prior studies have delineated the size distribution of noncohesive sediment in suspension, focusing on mean size and standard deviation. However, suspensions comprise a heterogeneous mixture of sediment particles of varying sizes. The transport dynamics of suspended sediment in turbulent flow are intimately tied to settling velocities calculated based on size and density. Consequently, understanding the grain size distribution becomes paramount in comprehending sediment transport phenomena for noncohesive sediment. This study aims to introduce a straightforward modeling approach for simulating the grain size distribution of suspended sediment amidst turbulence. Leveraging insights into the contrast between cohesive and noncohesive sediment, we have meticulously revised a stochastic flocculation model originally designed for cohesive sediment to aptly simulate the grain size distribution of noncohesive sediment in suspension. The efficacy of our approach is corroborated through a meticulous comparison between experimental data and the grain size distribution simulated by our newly proposed model. Through numerical simulations, we unveil that the modulation of grain size distribution of suspended sediment is contingent upon the sediment transport capacity of the carrier fluid. Hence, we deduce that our simplified approach to simulating the grain size distribution of suspended sediment, integrated with a sediment transport model, serves as a robust framework for elucidating the pivotal bulk properties of sediment transport.

많은 연구에서 비점착성 부유사의 입경분포를 평균입경와 표준편차를 이용해 묘사한다. 그러나 부유사는 크기가 다른 많은 입자의 혼합물로 구성되어 있다. 난류조건에서 부유사의 이동은 크기와 밀도로부터 계산된 침강속도에 영향을 받는다. 따라서 비점착성 부유사의 이동을 이해하려면 입경 분포를 보다 정량적으로 고려하는 것이 중요하다. 본 연구의 목적은 난류조건에서 부유사의 입경분포를 모의할 수 있는 간편한 모형화 방법을 제시하는 것이다. 점착성 유사와 비점착성 유사의 차이에 대한 이해를 바탕으로, 점착성 부유사를 위한 추계학적 응집 모형을 비점착성 유사의 입경분포 모의에 적합하도록 수정하였다. 본 연구에서 제안하는 간편법의 적용성을 살펴보기 위해 선행연구의 실험자료에 적용하여 모의 결과와 비교하였다. 수치 모의의 결과를 통해 본 연구에서 제안한 모형이 실험값에서 나타나는 주요한 특성을 모사할 수 있다는 점을 확인하였다. 이를 바탕으로 유사 이동 모형을 사용하여 부유사 입경분포를 모의하는 접근 방식이 부유사 입경분포의 중요한 특성을 이해하기에 효과적이라는 결론을 얻었다.

Keywords

Acknowledgement

이 논문은 2024년도 정부(교육부)의 재원으로 한국연구재단의 지원을 받아 수행된 기초연구사업임(2021R1I1A3060354).

References

  1. Bagnold, R.A. (1966). An approach to the sediment transport problem from general physics. US Government Printing Office, Washington, D.C., U.S. 
  2. Beverage, J.P., and Culbertson, J.K. (1964). "Hyper-concentrations of suspended sediment." Journal of the Hydraulics Division, Vol. 90, No. 6, pp. 117-128.  https://doi.org/10.1061/JYCEAJ.0001128
  3. Box, G.E., and Muller, M.E. (1958). "A note on the generation of random normal deviates." The Annals of Mathematical Statistics, Vol. 29, No. 2, pp. 610-611.  https://doi.org/10.1214/aoms/1177706645
  4. Byun, J., and Son, M. (2020). "On the relationship between turbulent motion and bimodal size distribution of suspended flocs." Estuarine, Coastal and Shelf Science, Vol. 245, 106938. 
  5. Cao, Z., Pender, G., and Meng, J. (2006). "Explicit formulation of the Shields diagram for incipient motion of sediment." Journal of Hydraulic Engineering, Vol. 132, No. 10, pp. 1097-1099.  https://doi.org/10.1061/(ASCE)0733-9429(2006)132:10(1097)
  6. Friedman, G.M. (1962). "On sorting, sorting coefficients, and the lognormality of the grain-size distribution of sandstones." The Journal of Geology, Vol. 70, No. 6, pp. 737-753.  https://doi.org/10.1086/jg.70.6.30066373
  7. Gelfenbaum, G., and Smith, J.D. (1986). "Experimental evaluation of a generalized suspended-sediment transport theory." Shelf Sands and Sandstones, Edited by Knight, R.J., and Mclean, J.R., Canadian Society of Petroleum Geologists Memoir II, Alberta, Canada, pp. 133-144. 
  8. Gentle, J.E. (2003). Random number generation and Monte Carlo methods. Springer Science & Business Media, NY, U.S. 
  9. Ghosh, J.K., and Mazumder, B.S. (1981). Size distribution of suspended particles-unimodality, symmetry and lognormality. Proceedings in Statistical Distributions in Scientific Work, Springer, Dordrecht, Netherlands, pp. 21-32. 
  10. Ghosh, J.K., Mazumder, B.S., and Sengupta, S. (1981). "Methods of computation of suspended load from bed materials and flow parameters." Sedimentology, Vol. 28, No. 6, pp. 781-791.  https://doi.org/10.1111/j.1365-3091.1981.tb01942.x
  11. Graf, W.H. (1984). Hydraulics of sediment transport. Water Resources Publication, CO, U.S. 
  12. Hsu, T.J., Traykovski, P.A., and Kineke, G.C. (2007). "On modeling boundary layer and gravity-driven fluid mud transport." Journal of Geophysical Research: Oceans, Vol. 112, No. C4, C04011. 
  13. Hunt, J.N. (1954). "The turbulent transport of suspended sediment in open channels." Proceedings of the Royal Society of London, Vol. 224, No. 1158, pp. 322-335. 
  14. Khelifa, A., and Hill, P.S. (2006). "Models for effective density and settling velocity of flocs." Journal of Hydraulic Research, Vol. 44, No. 3, pp. 390-401.  https://doi.org/10.1080/00221686.2006.9521690
  15. Kleinhans, M.G., and van Rijn, L.C. (2002). "Stochastic prediction of sediment transport in sand-gravel bed rivers." Journal of Hydraulic Engineering, Vol. 128, No. 4, pp. 412-425.  https://doi.org/10.1061/(ASCE)0733-9429(2002)128:4(412)
  16. Kuhnle, R.A. (1993). "Fluvial transport of sand and gravel mixtures with bimodal size distributions." Sedimentary Geology, Vol. 85, No. 1-4, pp. 17-24.  https://doi.org/10.1016/0037-0738(93)90072-D
  17. Kuhnle, R.A., and Wren, D.G. (2009). "Size of suspended sediment over dunes." Journal of Geophysical Research: Earth Surface, Vol. 114, No. F2, F02020. 
  18. Launder, B.E., and Sharma, B.I. (1974). "Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc." Letters in Heat and Mass Transfer, Vol. 1, pp. 131-138. 
  19. Law, B.A., Hill, P.S., Milligan, T.G., Curran, K.J., Wiberg, P.L., and Wheatcroft, R.A. (2008). "Size sorting of fine-grained sediments during erosion: Results from the western Gulf of Lions." Continental Shelf Research, Vol. 28, No. 15, pp. 1935-1946.  https://doi.org/10.1016/j.csr.2007.11.006
  20. Lisle, I.G., Rose, C.W., Hogarth, W.L., Hairsine, P.B., Sander, G.C., and Parlange, J.Y. (1998). "Stochastic sediment transport in soil erosion." Journal of Hydrology, Vol. 204, No. 1-4, pp. 217-230.  https://doi.org/10.1016/S0022-1694(97)00123-6
  21. Man, C., and Tsai, C.W. (2007). "Stochastic partial differential equation-based model for suspended sediment transport in surface water flows." Journal of Engineering Mechanics, Vol. 133, No. 4, pp. 422-430.  https://doi.org/10.1061/(ASCE)0733-9399(2007)133:4(422)
  22. Mazumder, B.S. (1994). "Grain size distribution in suspension from bed materials." Sedimentology, Vol. 41, No. 2, pp. 271-277.  https://doi.org/10.1111/j.1365-3091.1994.tb01405.x
  23. Mazumder, B.S., Ghoshal, K., and Dalal, D.C. (2005). "Influence of bed roughness on sediment suspension: experimental and theoretical studies." Journal of Hydraulic Research, Vol. 43, No. 3, pp. 245-257.  https://doi.org/10.1080/00221680509500119
  24. Mehta, A.J. (2013). An introduction to hydraulics of fine sediment transport (Vol. 38). World Scientific Publishing Company, Singapore. 
  25. Middleton, G.V. (1976). "Hydraulic interpretation of sand size distributions." The Journal of Geology, Vol. 84, No. 4, pp. 405-426.  https://doi.org/10.1086/628208
  26. Miller, M.C., McCave, I.N., and Komar, P. (1977). "Threshold of sediment motion under unidirectional currents." Sedimentology, Vol. 24, No. 4, pp. 507-527.  https://doi.org/10.1111/j.1365-3091.1977.tb00136.x
  27. Pal, D., and Ghoshal, K. (2014a). "Mathematical model on grain-size distribution in suspension over sand-gravel bed." Journal of Hydrology, Vol. 511, pp. 640-647.  https://doi.org/10.1016/j.jhydrol.2014.01.035
  28. Pal, D., and Ghoshal, K. (2014b). "Effect of bed roughness on grainsize distribution in an open channel flow." Journal of Hydro-environment Research, Vol. 8, No. 4, pp. 441-451.  https://doi.org/10.1016/j.jher.2013.09.001
  29. Purkait, B. (2002). "Patterns of grain-size distribution in some point bars of the Usri River, India." Journal of Sedimentary Research, Vol. 72, No. 3, pp. 367-375.  https://doi.org/10.1306/091001720367
  30. Richardson, J.F., and Zaki, W.N. (1954). "Sedimentation and fluidisation, Part 1." Transactions of American Institute of Chemical Engineers, Vol. 31, pp. 35-53. 
  31. Samaga, B.R., Ranga Raju, K.G., and Garde, R.J. (1986). "Suspended load transport of sediment mixtures." Journal of Hydraulic Engineering, Vol. 112, No. 11, pp. 1019-1034.  https://doi.org/10.1061/(ASCE)0733-9429(1986)112:11(1019)
  32. Sengupta, S. (1975). "Size-sorting during suspension transportation-lognormality and other characteristics." Sedimentology, Vol. 22, No. 2, pp. 257-273.  https://doi.org/10.1111/j.1365-3091.1975.tb00293.x
  33. Sengupta, S. (1979). "Grain-size distribution of suspended load in relation to bed materials and flow velocity." Sedimentology, Vol. 26, No. 1, pp. 63-82.  https://doi.org/10.1111/j.1365-3091.1979.tb00338.x
  34. Shaw, S.B., Makhlouf, R., Walter, M.T., and Parlange, J.Y. (2008). "Experimental testing of a stochastic sediment transport model." Journal of Hydrology, Vol. 348, No. 3-4, pp. 425-430.  https://doi.org/10.1016/j.jhydrol.2007.10.014
  35. Shi, Z.H., Fang, N.F., Wu, F.Z., Wang, L., Yue, B.J., and Wu, G.L. (2012). "Soil erosion processes and sediment sorting associated with transport mechanisms on steep slopes." Journal of Hydrology, Vol. 454, pp. 123-130.  https://doi.org/10.1016/j.jhydrol.2012.06.004
  36. Son, M., and Hsu, T.J. (2008). "Flocculation model of cohesive sediment using variable fractal dimension." Environmental Fluid Mechanics, Vol. 8, No. 1, pp. 55-71.  https://doi.org/10.1007/s10652-007-9050-7
  37. Son, M., and Hsu, T.J. (2011). "The effects of flocculation and bed erodibility on modeling cohesive sediment resuspension." Journal of Geophysical Research: Oceans, Vol. 116, No. C3, C03021. 
  38. Son, M., Byun, J., Kim, S.U., and Chung, E.S. (2016). "Effect of particle size on calibration of Schmidt number." Journal of Coastal Research, Vol. 75, No. sp1, pp. 148-152.  https://doi.org/10.2112/SI75-30.1
  39. Sun, D., Bloemendal, J., Rea, D.K., van den berghe, J., Jiang, F., An, Z., and Su, R. (2002). "Grain-size distribution function of polymodal sediments in hydraulic and aeolian environments, and numerical partitioning of the sedimentary components." Sedimentary Geology, Vol. 152, No. 3-4, pp. 263-277.  https://doi.org/10.1016/S0037-0738(02)00082-9
  40. Sundborg, A. (1956). "The river Klaralven a study of fluvial processes." Geografiska Annaler, Vol. 38, No. 2-3, pp. 125-316. 
  41. Tanner, W.F. (1964). "Modification of sediment size distributions." Journal of Sedimentary Research, Vol. 34, No. 1, pp. 156-164.  https://doi.org/10.1306/74D710A0-2B21-11D7-8648000102C1865D
  42. van Rijn, L.C. (1984). "Sediment transport, part II: Suspended load transport." Journal of Hydraulic Engineering, Vol. 110, No. 11, pp. 1613-1641.  https://doi.org/10.1061/(ASCE)0733-9429(1984)110:11(1613)
  43. Visher, G.S. (1969). "Grain size distributions and depositional processes." Journal of Sedimentary Research, Vol. 39, No. 3, pp. 1074-1106. 
  44. Winterwerp, J.C. (1998). "A simple model for turbulence induced flocculation of cohesive sediment." Journal of Hydraulic Research, Vol. 36, No. 3, pp. 309-326.  https://doi.org/10.1080/00221689809498621
  45. Wright, S., and Parker, G. (2004). "Flow resistance and suspended load in sand-bed rivers: Simplified stratification model." Journal of Hydraulic Engineering, Vol. 130, No. 8, pp. 796-805.  https://doi.org/10.1061/(ASCE)0733-9429(2004)130:8(796)
  46. Wu, B., Molinas, A., and Julien, P.Y. (2004). "Bed-material load computations for nonuniform sediments." Journal of Hydraulic Engineering, Vol. 130, No. 10, pp. 1002-1012. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:10(1002)