Czasopismo
2018
|
Vol. 66, no. 1
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93--107
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
The present study proposes a model on vertical distribution of streamwise velocity in an open channel turbulent flow through a newly proposed mixing length, which is derived for both clear water and sedimentladen turbulent flows. The analysis is based on a theoretical consideration which explores the effect of density stratification on the streamwise velocity profile. The derivation of mixing length makes use of the diffusion equation where both the sediment diffusivity and momentum diffusivity are taken as a function of height from the channel bed. The damping factor present in the mixing length of sediment-fluid mixture contains velocity and concentration gradients. This factor is capable of describing the dip-phenomenon of velocity distribution. From the existing experimental data of velocity, the mixing length data are calculated. The pattern shows that mixing length increases from bed to the dip-position, having a larger value at dip-position and then decreases up to the water surface with a zero value thereat. The present model agrees well with these data sets and this behavior cannot be described by any other existing model. Finally, the proposed mixing length model is applied to find the velocity distribution in wide and narrow open channels.The derived velocity distribution is compared with laboratory channel data of velocity, and the comparison shows good agreement.
Czasopismo
Rocznik
Tom
Strony
93--107
Opis fizyczny
Bibliogr. 67 poz.
Twórcy
autor
- Department of Basic Sciences and Humanities, IIIT Bhubaneswar, Bhubaneswar, India
autor
- Department of Mathematics, Indian Institute of Technology, Kharagpur, India, manotosh.kumbhakar@gmail.com
autor
- Department of Mathematics, Indian Institute of Technology, Kharagpur, India
Bibliografia
- 1. Absi R (2011) An ordinary differential equation for velocity distribution and dip-phenomenon in open channel flows. J Hydraul Res 49(1):82–89
- 2. Baldock TE, Tomkins MR, Nielsen P, Hughes MG (2004) Settling velocity of sediments at high concentrations. Coast Eng 51(1):91–100
- 3. Ballio F, Tait S (2012) Sediment transport mechanics. Acta Geophys 60(6):1493–1499
- 4. Bialik R, Nikora V, Rowiński P (2012) 3d lagrangian modelling of saltating particles diffusion in turbulent water flow. Acta Geophys 60(6):1639–1660
- 5. Bialik RJ (2011) Particle-particle collision in lagrangian modelling of saltating grains. J Hydraul Res 49(1):23–31
- 6. Bialik RJ (2013) Numerical study of near-bed turbulence structures influence on the initiation of saltating grains movement. J Hydrol Hydromech 61(3):202–207
- 7. Bialik RJ, Nikora VI, Karpiński M, Rowiński PM (2015) Diffusion of bedload particles in open-channel flows: distribution of travel times and second-order statistics of particle trajectories. Environ Fluid Mech 15(6):1281–1292
- 8. Bonakdari H, Larrarte F, Lassabatere L, Joannis C (2008) Turbulent velocity profile in fully-developed open channel flows. Environ Fluid Mech 8:1–17
- 9. Buschmann M, Gad-el Hak M (2005) New mixing-length approach for the mean velocity profile of turbulent boundary layers. J Fluids Eng 127(2):393–396
- 10. Castro-Orgaz O, Giraldez JV, Mateos L, Dey S (2012) Is the von karman constant affected by sediment suspension? J Geophys Res 117(F04002):1–16
- 11. Cellino M, Graf WH (1999) Sediment-laden flow in open-channels under noncapacity and capacity conditions. J Hydraul Eng 125(5):455–462
- 12. Cheng NS (1997) Effect of concentration on settling velocity of sediment particles. J Hydraul Eng 123(8):728–731
- 13. Coleman NL (1981) Velocity profiles with suspended sediment. J Hydraul Res 19(3):211–229
- 14. Coleman NL (1986) Effects of suspended sediment on the open-channel velocity distribution. Water Resour Res 22(10):1377–1384
- 15. Coles DE (1956) The law of the wake in the turbulent boundary layer. J Fluid Mech 1:191–226
- 16. Francis JB (1878) On the cause of the maximum velocity of water flowing in open channels being below the surface. Trans Am Soc Civ Eng 7(1):109–113
- 17. Galbraith RM, Sjolander S, Head M (1977) Mixing length in the wall region of turbulent boundary layers. Aeronaut Q 28(02):97–110
- 18. Graf WH (1971) Hydraulics of sediment transport. McGraw-Hill, New York
- 19. Granville P (1989) A modified van driest formula for the mixing length of turbulent boundary layers in pressure gradients. ASME Trans J Fluids Eng 111:94–97
- 20. Guo J (2006) Self-similarity of mean flow in pipe turbulence. In: 36th AIAA fluid dynamics conferences and exhibit, AIAA paper 2885, San Francisco
- 21. Guo J (2013) Modified log-wake-law for smooth rectangular open channel flow. J Hydraul Res 52(1):121–128
- 22. Guo J, Julien PY (2001) Turbulent velocity profiles in sediment-laden flows. J Hydraul Res 39(1):11–23
- 23. Guo J, Julien PY (2003) Modified log-wake law for turbulent flow in smooth pipes. J Hydraul Res 41(5):493–501
- 24. Hunt JN (1954) The turbulent transport of suspended sediment in open channels. Proc R Soc Lond A 224:322–335
- 25. von Karman T (1930) Mechanische Ähnlichkeit und turbulenz. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen: Mathematisch-physische Klasse, pp 58–76
- 26. Karman VT (1960) see H Schlichting, Boundary layer theory. McGraw-Hill, New York
- 27. Keulegan CH (1938) Laws of turbulence flow in open channels. J Res Natl Bureau Stand 21:707–741
- 28. Kironoto BA, Graf WH (1994) Turbulence characteristics in rough uniform open-channel flow. Proc ICE Water Marit Energy 106(12):333–344
- 29. Kovacs AE (1988) Prandtl’s mixing length concept modified for equilibrium sediment-laden flows. J Hydraul Eng 124(8):803–812
- 30. Kumbhakar M, Kundu S, Ghoshal K (2017) Hindered settling velocity in particle-fluid mixture: a theoretical study using the entropy concept. J Hydraul Eng 143(11):06017019 (1–8)
- 31. Kundu PK (1990) Fluid mechanics. Academic, New York
- 32. Kundu S (2016) Effect of lateral bed roughness variation on particle suspension in open channels. Environ Earth Sci 75(8):1–18
- 33. Kundu S, Ghoshal K (2012) An analytical model for velocity distribution and dip-phenomenon in uniform open channel flows. Int J Fluid Mech Res 39(5):381–395
- 34. Lassabatere L, Pu HJ, Bonakdari H, Joannis C, Larrarte F (2013) Velocity distribution in open channel flows: analytical approach for the outer region. J Hydraul Eng 139(1):37–43
- 35. Launder BE, Priddin C (1973) A comparison of some proposals for the mixing length near a wall. Int J Heat Mass Transf 16(3):700–702
- 36. Lewis W, Gilliland E, Bauer W (1949) Characteristics of fluidized particles. Ind Eng Chem 41:1104–1127
- 37. Lyn DA (1986) Turbulence and turbulent transport in sediment-laden open-channel flows. PhD thesis, California Institute of Technology, California
- 38. Lyn DA (1988) A similarity approach to open-channel sediment laden flows. J Fluid Mech 193(1):1–26
- 39. Mazumder BS, Ghoshal K (2006) Velocity and concentration profiles in uniform sediment-laden flow. Appl Math Model 30:164–176
- 40. Montes JS (1973) Interaction of two dimensional turbulent flow with suspended particles. PhD thesis, Massachusetts Institute of Technology, Cambridge
- 41. Murphy C (1904) Accuracy of stream measurements. Water Supply Irrigation Pap 95:111–112
- 42. Muste M, Patel VC (1997) Velocity profiles for particles and liquid in open-channel flow with suspended sediment. J Hydraul Eng 123(9):742–751
- 43. Muste M, Yu K, Fujita I, Ettema R (2005) Two-phase versus mixed-flow perspective on suspended sediment transport in turbulent channel flows. Water Resour Res 41(W10402). https://doi.org/10.1029/2004WR003595
- 44. Nezu I, Tominaga A, Nakagawa H (1993) Field measurements of secondary currents in straight rivers. J Hydraul Eng 119(5):598–614
- 45. Nishioka M, Iida S (1973) The mixing length derived from krmns similarity hypothesis. Aeronaut Q 24:71–76
- 46. Obermeier F (2006) Prandtl’s mixing length model-revisited. PAMM 6(1):577–578
- 47. Pal D, Ghoshal K (2013) Hindered settling with an apparent particle diameter concept. Adv Water Resour 60:178–187
- 48. Pal D, Ghoshal K (2016) Effect of particle concentration on sediment and turbulent diffusion coefficients in open-channel turbulent flow. Environ Earth Sci 75(18):1245
- 49. Patel VC (1973) A unified view of the law of the wall using mixing-length theory. Aeronaut Q 24(01):55–70
- 50. Prandtl L (1925) Bericht ber untersuchungen zur ausgebildeten turbulenz. Zeitschrift für Angewandte Mathematik und Mechanik 5:136–139
- 51. Prandtl L (1932) Recent results of turbulence research. Technical Memorandum 720, National Advisory Committee for Aeronautics
- 52. Prandtl L (1960) see H Schlichting, Boundary layer theory. McGraw-Hill, New York
- 53. Pu JH (2013) Universal velocity distribution for smooth and rough open channel flows. J Appl Fluid Mech 6(3):413–423
- 54. Richardson JF, Zaki WN (1954) Sedimantation and fluidization part I. Trans Inst Chem Eng 32:35–53
- 55. Rouse H (1937) Modern concepts of the mechanics of turbulence. Trans ASCE 102:463–543
- 56. Rowinski P, Lee SL (1993) Equilibrium profile of suspended sediment concentration. Acta Geophysica Polonica 41(2):163–176
- 57. Sun ZL, Sun ZF, Donahue J (2003) Equilibrium bed-concentration of nonuniform sediment. J Zhejiang Univ Sci 4(2):186–194
- 58. Townsend AA (1961) Equilibrium layers and wall turbulence. J Fluid Mech 11:97–120
- 59. Umeyama M, Gerritsen F (1992a) Velocity distribution in uniform sediment-laden flow. J Hydraul Eng 118(2):229–245
- 60. Umeyama M, Gerritsen F (1992b) Velocity distribution in uniform sediment-laden flow. J Hydraul Eng 118(2):229–245
- 61. Van Driest ER (1956) The problem of aerodynamic heating. Aeronaut Eng Rev 15(10):26–41
- 62. Vanoni VA (1940) Experiments on the transportation of suspended sediment by water. PhD thesis, California Institute of Technology, Pasadina
- 63. Wang X, Qian N (1989) Turbulence characteristics of sediment-laden flows. J Hydraul Eng 115(6):781–799
- 64. Yalin MS (1977) Mechanics of sediment transport, 2nd edn. Pegramon Press, New York
- 65. Yang SQ (2007) Turbulent transfer mechanism in sediment-laden flow. J Geophys Res 112(F01005). https://doi.org/10.1029/2005JF000452
- 66. Yang SQ (2009) Mechanism for initiating secondary currents in channel flows. Can J Civ Eng 36(9):1506–1516CrossRefGoogle Scholar
- 67. Zhiyao S, Tingting W, Fumin X, Ruijie L (2008) A simple formula for predicting settling velocity of sediment particles. Water Sci Eng 1(1):37–43
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-c7598c3a-3d99-4e9b-9ca4-fc265f597780