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Two-phase flow insights into open-channel flows with suspended particles of different densities

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Abstract

The effect of particle density on the turbulent open-channel flow carrying dilute particle suspensions is investigated using two specific gravities and three concentrations of solid particles. The particles, identical in size and similar in shape, were natural sand and a neutrally buoyant plastic. The particles were fully suspended, and formed no particle streaks on the channel’s bed. Accordingly, the changes in the flow are attributed to the interactions between suspended particles and flow turbulence structures. Measurements were obtained by means of image velocimetry enabling simultaneous, but distinct, measurement of liquid and particle velocities. The experimental results show that, irrespective of particle specific gravity, particle suspension influences bulk velocity of flow and the Kármán coefficient, while friction velocity essentially remains constant. The results also show that particles in suspension modify local water turbulence over the flow depth, but in ways not accurately predicted using the customary parameters for characterizing turbulence modification.

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Abbreviations

C :

Depth averaged sediment concentration

D 50 :

Median diameter of sediment particle

D s :

Sediment particle diameter

D + s :

Dimensionless sediment particle diameter \({\left( {\equiv {D_s u_\ast}\mathord{\left/ {\vphantom {{D_s u_\ast }\nu }}\right.\kern-\nulldelimiterspace}\nu }\right)}\)

Fr:

Froude number

N :

Total number of particles

N + :

Number of upward-moving particles

N − :

Number of downward-moving particles

q s :

Total unit sediment discharge

U :

Mean streamwise velocity

V :

Mean vertical velocity

\({\overline{U}}\) :

Depth averaged streamwise velocity of water

\({{\overline{U}_s}}\) :

Depth averaged streamwise velocity of sediment

u L :

Average velocity lag

u * :

Shear velocity

u′:

Root-mean square of fluctuation component of streamwise velocity\({\left({\equiv \sqrt {\overline {{u}'{u}'}} }\right)}\)

V MLT :

Equivalent vertical velocity by McLaughlin and Tiederman

υ ′:

Root-mean square of fluctuation component of vertical velocity\({\left( {\equiv \sqrt {\overline {{\upsilon }'{\upsilon }'}} }\right)}\)

υ s :

Fall velocity of sediment particle

v :

Kinematic viscosity of water

h :

Flow depth

y :

Distance from the channel bed

y + :

Dimensionless distance from the channel bed \({\left( {\equiv {yu_\ast }\mathord{\left/ {\vphantom {{yu_\ast }\nu }}\right.\kern-\nulldelimiterspace}\nu }\right)}\)

Re:

Reynolds number

Re p :

Particle Reynolds number

\({{\varepsilon _m}}\) :

Turbulent momentum diffusion coefficient

St :

Stokes number

λ T :

Taylor microscale

ξ:

The rate of turbulent energy dissipation

\({{\kappa}}\) :

von Kármán coefficient/constant

τ p :

Particle response time

τ f :

Representative flow time scale

τ K :

Kolmogorov time scale \({\left( {\equiv \sqrt {\nu \mathord{\left/{\vphantom {\nu \xi }}\right. \kern-\nulldelimiterspace}\xi }}\right)}\)

ℓ e :

Length scale of the energy containing eddies

η:

Dimensionless height \({\left( {\equiv y \mathord{\left/ {\vphantom {yh}}\right. \kern-\nulldelimiterspace} h}\right)}\)

References

  1. Hanratty TJ, Theofanous T, Delhaye J-M, Eaton J, McLaughlin J, Prosperetti A et al (2003) Workshop findings. Int J Multiph Flow 29(7): 1047–1059. doi:10.1016/S0301-9322(03)00068-5

    Article  CAS  Google Scholar 

  2. Kaftori D, Hetsroni G, Banerjee S (1995) Particle behavior in the turbulent boundary layer. I. Motion, deposition, and entrainment. Phys Fluids 7(5): 1095–1106. doi:10.1063/1.868551

    Article  CAS  Google Scholar 

  3. Kaftori D, Hetsroni G, Banerjee S (1995) Particle behavior in the turbulent boundary layer. II. Velocity and distribution profiles. Phys Fluids 7(5): 1107–1121. doi:10.1063/1.868552

    Article  CAS  Google Scholar 

  4. Kiger KT, Pan C (2002) Suspension and turbulence modification effects of solid particlulates on a horizontal turbulent channel flow. J Turbul 19(3): 1–21. doi:10.1088/1468-5248/3/1/019

    Article  Google Scholar 

  5. Muste M, Yu K, Fujita I, Ettema R (2005) Traditional versus two-phase perspective on turbulent channel flows with suspended sediment. Water Resour Res 41(10), W10402, 22 p

  6. Taniere A, Oesterle B, Monnier JC (1997) On the behaviour of solid particles in a horizontal boundary layer with turbulence and saltation effects. Exp Fluids 23(6): 463–471. doi:10.1007/s003480050136

    Article  Google Scholar 

  7. Tsuji Y, Morikawa Y (1982) LDV measurements of an air-solid two-phase flow in a horizontal pipe. J Fluid Mech 120: 385–409. doi:10.1017/S002211208200281X

    Article  Google Scholar 

  8. Elghobashi SE, Abou-Arab TW (1983) Two-equation turbulence model for two-phase flows. Phys Fluids 26(4): 931–938. doi:10.1063/1.864243

    Article  Google Scholar 

  9. Rashidi MG, Hetsroni G, Banerjee S (1990) Particle–turbulence interaction in a boundary layer. Int J Multiph Flow 16(6): 935–949. doi:10.1016/0301-9322(90)90099-5

    Article  CAS  Google Scholar 

  10. Gore RA, Crowe CT (1991) Modulation of turbulence by a dispersed phase. J Fluids Eng ASME 113: 304–307. doi:10.1115/1.2909497

    Article  CAS  Google Scholar 

  11. Rogers CB, Eaton J (1991) The effect of small particles on fluid turbulence in a flat-plate turbulent boundary layer in air. Phys Fluids A(3): 928–937

    Google Scholar 

  12. Yarin LP, Hetsroni G (1994) Turbulence intensity in dilute two-phase flows-3: the particles–turbulence interaction in dilute two-phase flow. Int J Multiph Flow 20(1): 27–44. doi:10.1016/0301-9322(94)90004-3

    Article  CAS  Google Scholar 

  13. Crowe CT, Sommerfeld M, Tsuji Y (1998) Multiphase flows with droplets and particles. Academic Press, London

    Google Scholar 

  14. Hetsroni G (1989) Particles–turbulence interaction. Int J Multiph Flow 15(5): 735–746. doi:10.1016/0301-9322(89)90037-2

    Article  CAS  Google Scholar 

  15. Kaftori D, Hetsroni G, Banerjee S (1998) The effect of particles on wall turbulence. Int J Multiph Flow 24(3): 359–386. doi:10.1016/S0301-9322(97)00054-2

    Article  CAS  Google Scholar 

  16. Pedinottti S, Mariotti G, Banerjee S (1992) Direct simulation of particle behavior in the wall region of turbulent flows in horizontal channels. Int J Multiph Flow 18(6): 927–941. doi:10.1016/0301-9322(92)90068-R

    Article  Google Scholar 

  17. Wang Q, Squires KD, Chen M, McLaughlin JB (1997) On the role of the lift force in turbulence simulations of particle deposition. Int J Multiph Flow 23(4): 749–763. doi:10.1016/S0301-9322(97)00014-1

    Article  CAS  Google Scholar 

  18. Boivin M, Simonin O, Squires KD (2000) On the prediction of gas–solid flows with two-way coupling using LES. Phys Fluids 12(8): 2080–2090. doi:10.1063/1.870453

    Article  CAS  Google Scholar 

  19. Rouson DWI, Eaton JK (2001) On the preferential concentration of solid particles in turbulent channel flow. J Fluid Mech 428: 149–169. doi:10.1017/S0022112000002627

    Article  CAS  Google Scholar 

  20. Zedler EA, Street RL (2001) Large-eddy simulation of sediment transport: currents over ripples. J Hydraul Eng 127(6): 444–452. doi:10.1061/(ASCE)0733-9429(2001)127:6(444)

    Article  Google Scholar 

  21. Scotti A, Piomelli U (2002) Turbulence models in pulsating flows. AIAA J 40(3): 537–544

    Article  Google Scholar 

  22. Vanoni VA (1946) Transportation of suspended sediment by water. Trans ASCE 111: 67–133

    Google Scholar 

  23. Bennett S, Bridge JS, Best JL (1998) Fluid and sediment dynamics of upper stage plane beds. J Geophys Res 103(C1): 1239–1274. doi:10.1029/97JC02764

    Article  Google Scholar 

  24. 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. doi:10.1061/(ASCE)0733-9429(1997)123:9(742)

    Article  Google Scholar 

  25. Best J, Bennett S, Bridge JS, Leeder M (1997) Turbulence modulation and particle velocities over flat sand beds at low transport rates. J Hydraul Eng 123(12): 1118–1129. doi:10.1061/(ASCE)0733-9429(1997)123:12(1118)

    Article  Google Scholar 

  26. Kiger KT, Pan C (2000) PIV technique for the simultaneous measurement of dilute two-phase flows. J Fluid Eng ASME 122: 811–818. doi:10.1115/1.1314864

    Article  Google Scholar 

  27. Righetti M, Romano GP (2004) Particle–fluid interactions in a plane near-wall turbulent flow. J Fluid Mech 505: 93–121. doi:10.1017/S0022112004008304

    Article  CAS  Google Scholar 

  28. Dietrich WE (1982) Settling velocity of natural particles. Water Resour Res 18(6): 1615–1626. doi:10.1029/WR018i006p01615

    Article  Google Scholar 

  29. Rouse H (1937) Nomogram for the settling velocity of spheres. National Research Council, Washington, DC

    Google Scholar 

  30. Yu K (2004) Particle tracking of suspended-sediment velocities in open-channel flow. Ph.D. dissertation, University of Iowa, Iowa City, IA

  31. Muste M, Fujita I, Kruger A (1998) Experimental comparison of two laser-based velocimeters for flows with alluvial sand. Exp Fluids 24: 273–284. doi:10.1007/s003480050174

    Article  Google Scholar 

  32. Khalitov DA, Longmire EK (2002) Simultaneous two-phase PIV by two-parameter phase discrimination. Exp Fluids 32(2): 252–268. doi:10.1007/s003480100356

    Article  CAS  Google Scholar 

  33. Cowen EA, Monismith SG (1997) A hybrid digital particle tracking technique. Exp Fluids 22: 199–211. doi:10.1007/s003480050038

    Article  CAS  Google Scholar 

  34. Ferziger JH, Peric M (1996) Computational methods for fluid dynamics. Springer, Berlin

    Google Scholar 

  35. White FM (1991) Viscous fluid flow. McGraw-Hill, Inc., New York

    Google Scholar 

  36. Durst F, Melling A, Whitelaw JH (1981) Principles and practice of laser-Doppler anemometry, 2nd edn. Academic Press, Inc., San Diego, CA

    Google Scholar 

  37. Balakrishnan M, Dancey CL (1998) Laser Doppler velocimetry velocity bias in turbulent open channel flow. AIAA J 36(8): 1544–1546

    Article  CAS  Google Scholar 

  38. McLaughlin DK, Tiederman WG (1973) Biasing correction for individual realization of laser anemometer measurements in turbulent flows. Phys Fluids 16(12): 2082–2088. doi:10.1063/1.1694269

    Article  Google Scholar 

  39. Hinze JO (1959) Turbulence. McGraw-Hill Book Company, Inc., New York

    Google Scholar 

  40. Nezu I, Nakagawa H (1993) Turbulence in open-channel flows. A. A. Balkema, Rotterdam

    Google Scholar 

  41. Einstein HA, Chien N (1955) Effect of heavy sediment concentration near the bed on the velocity and sediment distribution. Institute of Engineering Research, University of California, Berkeley

    Google Scholar 

  42. Elata C, Ippen AT (1961) The dynamics of open channel flow with suspensions of neutrally buoyant particles. Technical Report No. 45, Hydrodynamics Laboratory, Massachusetts Institute of Technology

  43. Lyn DA (1991) Resistance in flat-bed sediment-laden flows. J Hydraul Eng 117(1): 94–114. doi:10.1061/(ASCE)0733-9429(1991)117:1(94)

    Article  Google Scholar 

  44. Wang X, Qian N (1989) Turbulence characteristics of sediment-laden flows. J Hydraul Eng 115(6): 781–799

    Google Scholar 

  45. Graf WH, Cellino M (2002) Suspension flows in open channels: experimental study. J Hydraul Res 40(4): 435–447

    Google Scholar 

  46. Coleman NL (1986) Effects of suspended sediment on the open-channel velocity distribution. Water Resour Res 22(10): 1377–1384. doi:10.1029/WR022i010p01377

    Article  Google Scholar 

  47. Umeyama M, Gerritsen F (1992) Velocity distribution in uniform sediment-laden flow. J Hydraul Eng 118(2): 229–245. doi:10.1061/(ASCE)0733-9429(1992)118:2(229)

    Article  Google Scholar 

  48. Guo J, Julien PY (2001) Turbulence velocity profiles in sediment-laden flows. J Hydraul Res 39(1): 11–23

    Google Scholar 

  49. Kulick JD, Fessler JR, Eaton JK (1994) Particle response and turbulence modification in fully developed channel flow. J Fluid Mech 277: 109–134. doi:10.1017/S0022112094002703

    Article  Google Scholar 

  50. Sumer BM, Deigaard R (1981) Particle motions near the bottom in turbulent flow in open channel: Part 2. J Fluid Mech 109: 311–337. doi:10.1017/S0022112081001092

    Article  CAS  Google Scholar 

  51. Wei T, Wilmarth WW (1991) Examination of v-velocity fluctuations in a turbulent channel flow in the context of sediment transport. J Fluid Mech 223: 241–252. doi:10.1017/S0022112091001416

    Article  Google Scholar 

  52. Bouvard M, Petkovic S (1985) Vertical dispersion of spherical, heavy particles in turbulent open channel flow. J Hydraul Res 23(1): 5–19

    Google Scholar 

  53. Wang D (2000) On the spatial structure of low-speed streaks and particle motion in the wall region of turbulent open channel flow. Ph.D. thesis, Tsinghua University (in Chinese)

  54. Kaufmann A, Simonin O, Poinsot T, Helie J (2002) Dynamics of dispersion in Eulerian-Eulerian DNS of Two-Phase Flows. In: Proceedings, Center for Turbulence, Stanford University, Stanford, CA, pp 381-392

  55. Vance MW, Squires KD, Simonin O (2004) Properties of the particle velocity-field in gas-solid turbulent channel flow. In: Proceedings of the 5th international conference on multiphase flows, Yokohama, Japan

  56. Bernard-Michel G, Monavon A, Lhuiller D, Abdo D, Simon H (2002) Particle velocity fluctuations and correlation lenghts in dilute sedimenting suspensions. Phys Fluids 14: 2339–2349. doi:10.1063/1.1483302

    Article  CAS  Google Scholar 

  57. Tsinober A (2003) Nonlocality in turbulence. In: Gyr A, Kinzelbach W (eds) Sedimentation and sediment transport. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  58. Abbott JE, Francis JRD (1977) Saltation and suspension trajectories of solid grains in a water stream. Philos Trans R Soc Lond A 284(1321): 225–254. doi:10.1098/rsta.1977.0009

    Article  Google Scholar 

  59. Foucaut J-M, Stanislas M (1997) Experimental study of saltating particle trajectories. Exp Fluids 22: 321–326. doi:10.1007/s003480050054

    Article  Google Scholar 

  60. Bagnold RA (1966) An approach to the sediment transport problem from general physics, U.S.G.S. Paper 422-I:37

  61. Lyn DA (1988) A similarity approach to turbulent sediment-laden flows in open channels. J Fluid Mech 193: 1–26. doi:10.1017/S0022112088002034

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. IIHR-Hydroscience & Engineering, The University of Iowa, 302E Maxwell C. Stanley Hydraulics Laboratory, Iowa City, IA, 52242-1585, USA

    M. Muste

  2. Department of Civil Engineering, Dong-Eui University, Busan, Korea

    K. Yu

  3. Department of Architecture and Civil Engineering, Kobe University, Kobe, Japan

    I. Fujita

  4. College of Engineering and Applied Science, The University of Wyoming, Laramie, WY, USA

    R. Ettema

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  1. M. Muste
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  2. K. Yu
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Correspondence to M. Muste.

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Muste, M., Yu, K., Fujita, I. et al. Two-phase flow insights into open-channel flows with suspended particles of different densities. Environ Fluid Mech 9, 161–186 (2009). https://doi.org/10.1007/s10652-008-9102-7

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