Hostname: page-component-54dcc4c588-54gsr Total loading time: 0 Render date: 2025-09-28T01:45:10.286Z Has data issue: false hasContentIssue false
  • English
  • Français

Particle–fluid–wall interaction of inertial spherical particles in a turbulent boundary layer

Published online by Cambridge University Press:  11 December 2020

Lucia J. Baker Open the ORCID record for Lucia J. Baker [Opens in a new window]  and
Filippo Coletti Open the ORCID record for Filippo Coletti [Opens in a new window]
Lucia J. Baker*
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414, USA
Filippo Coletti
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414, USA
*
†Email address for correspondence: bake0616@umn.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the dynamics of dilute, slightly negatively buoyant, millimetre-size spherical particles fully suspended in a smooth-wall open channel flow. The Reynolds number is $Re_{\tau } = 570$ and the particle Stokes number is ${{\textit {St}}}^{+} = 15$. Particle image velocimetry and tracking are used to obtain simultaneous, time-resolved flow fields and particle trajectories. Particles travel at a lower mean velocity than the fluid: in the log layer this is due to the oversampling of slow fluid regions, but closer to the wall the cause is instantaneous slip between particles and fluid. The particle Reynolds stresses exceed those of the fluid. Near the wall, the particle streamwise diffusivity is larger than the momentum diffusivity, while the opposite is true for the wall-normal component. The particle transport is strongly linked to ejections, while the role of sweeps is marginal, and there is no evidence of turbophoresis. The concentration profile follows a power law with a shallower slope than predicted by equilibrium theories that neglect particle inertia. Upward-/downward-moving particles display positive/negative mean streamwise acceleration due to the particle–fluid slip. The particles that contact the wall are faster than the local fluid both before reaching the wall and after leaving it. Therefore, they are decelerated by drag and pushed downward by shear-induced lift. The durations of wall contact follow exponential distributions with characteristic time scale close to the particle response time. Lift-offs coincide with particles meeting a fluid ejection. These observations emphasize the competing effects of inertia and gravity.

JFM classification

Geophysical and Geological Flows: Sediment transport Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulent boundary layers

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A39
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

‡

Present address: Department of Mechanical and Process Engineering, ETH Zurich, Switzerland.

References

REFERENCES

Adhikari, D. 2013 Volumetric velocity measurement of aquatic predator-prey interactions. PhD thesis, University of Minnesota.Google Scholar
Ancey, C., Böhm, T., Jodeau, M. & Frey, P. 2006 Statistical description of sediment transport experiments. Phys. Rev. E 74 (1), 011302.CrossRefGoogle ScholarPubMed
Ancey, C., Davison, A. C., Böhm, T., Jodeau, M. & Frey, P. 2008 Entrainment and motion of coarse particles in a shallow water stream down a steep slope. J. Fluid Mech. 595, 83–114.CrossRefGoogle Scholar
Ayyalasomayajula, S., Gylfason, A., Collins, L. R., Bodenschatz, E. & Warhaft, Z. 2006 Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence. Phys. Rev. Lett. 97 (14), 144507.CrossRefGoogle ScholarPubMed
Bagnold, R. A. 1936 The movement of desert sand. Proc. R. Soc. Lond. A 157 (892), 594–620.Google Scholar
Bagnold, R. A. 1941 The Physics of Blown Sand and Desert Dunes. Methuen.Google Scholar
Baker, L. J. & Coletti, F. 2019 Experimental study of negatively buoyant finite-size particles in a turbulent boundary layer up to dense regimes. J. Fluid Mech. 866, 598–629.CrossRefGoogle Scholar
Balachandar, S., Liu, K. & Lakhote, M. 2019 Self-induced velocity correction for improved drag estimation in Euler–Lagrange point-particle simulations. J. Comput. Phys. 376, 160–185.CrossRefGoogle Scholar
Bec, J., Biferale, L., Boffetta, G., Celani, A., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2006 Acceleration statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349–358.CrossRefGoogle Scholar
Bendat, J. S. & Piersol, A. G. 2011 Random Data: Analysis and Measurement Procedures, vol. 729. John Wiley & Sons.Google Scholar
Berk, T. & Coletti, F. 2020 Transport of inertial particles in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 903, A18.CrossRefGoogle Scholar
Bernardini, M. 2014 Reynolds number scaling of inertial particle statistics in turbulent channel flows. J. Fluid Mech. 758, R1.CrossRefGoogle Scholar
Brenner, H. 1965 Effect of finite boundaries on the Stokes resistance of an arbitrary particle. J. Fluid Mech. 12 (1), 35–48.CrossRefGoogle Scholar
Cameron, S. M., Nikora, V. I. & Witz, M. J. 2020 Entrainment of sediment particles by very large-scale motions. J. Fluid Mech. 888, A7.CrossRefGoogle Scholar
Capecelatro, J. & Desjardins, O. 2013 An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 1–31.CrossRefGoogle Scholar
Choi, J.-I., Yeo, K. & Lee, C. 2004 Lagrangian statistics in turbulent channel flow. Phys. Fluids 16 (3), 779–793.CrossRefGoogle Scholar
Clift, R., Grace, J. R. & Weber, M. E. 2005 Bubbles, Drops, and Particles. Dover Publications.Google Scholar
Crowe, C. T., Schwarzkopf, J. D., Sommerfeld, M. & Tsuji, Y. 2011 Multiphase Flows with Droplets and Particles. CRC Press.CrossRefGoogle Scholar
Csanady, G. T. 1963 Turbulent diffusion of heavy particles in the atmosphere. J. Atmos. Sci. 20 (3), 201–208.2.0.CO;2>CrossRefGoogle Scholar
De Graaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Ebrahimian, M., Sanders, R. S. & Ghaemi, S. 2019 Dynamics and wall collision of inertial particles in a solid–liquid turbulent channel flow. J. Fluid Mech. 881, 872–905.CrossRefGoogle Scholar
Einstein, H. A. 1950 The Bed-Load Function for Sediment Transportation in Open Channel Flows. US Government Printing Office.Google Scholar
Elghobashi, S. & Truesdell, G. C. 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655–700.CrossRefGoogle Scholar
Fan, N., Singh, A., Guala, M., Foufoula-Georgiou, E. & Wu, B. 2016 Exploring a semimechanistic episodic Langevin model for bed load transport: emergence of normal and anomalous advection and diffusion regimes. Water Resour. Res. 52 (4), 2789–2801.CrossRefGoogle Scholar
Fong, K. O., Amili, O. & Coletti, F. 2019 Velocity and spatial distribution of inertial particles in a turbulent channel flow. J. Fluid Mech. 872, 367–406.CrossRefGoogle Scholar
Gerashchenko, S., Sharp, N. S., Neuscamman, S. & Warhaft, Z. 2008 Lagrangian measurements of inertial particle accelerations in a turbulent boundary layer. J. Fluid Mech. 617, 255–281.CrossRefGoogle Scholar
Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14 (2), 643–652.CrossRefGoogle Scholar
Guala, M., Manes, C., Clifton, A. & Lehning, M. 2008 On the saltation of fresh snow in a wind tunnel: profile characterization and single particle statistics. J. Geophys. Res.: Earth 113, F03024.CrossRefGoogle Scholar
Gualtieri, P., Picano, F., Sardina, G. & Casciola, C. M. 2015 Exact regularized point particle method for multiphase flows in the two-way coupling regime. J. Fluid Mech. 773, 520–561.CrossRefGoogle Scholar
Heyman, J., Bohorquez, P. & Ancey, C. 2016 Entrainment, motion, and deposition of coarse particles transported by water over a sloping mobile bed. J. Geophys. Res.: Earth 121 (10), 1931–1952.CrossRefGoogle Scholar
Horwitz, J. A. K. & Mani, A. 2016 Accurate calculation of Stokes drag for point–particle tracking in two-way coupled flows. J. Comput. Phys. 318, 85–109.CrossRefGoogle Scholar
van Hout, R. 2011 Time-resolved PIV measurements of the interaction of polystyrene beads with near-wall-coherent structures in a turbulent channel flow. Intl J. Multiphase Flow 37 (4), 346–357.CrossRefGoogle Scholar
van Hout, R. 2013 Spatially and temporally resolved measurements of bead resuspension and saltation in a turbulent water channel flow. J. Fluid Mech. 715, 389.CrossRefGoogle Scholar
van Hout, R., Sabban, L. & Cohen, A. 2013 The use of high-speed PIV and holographic cinematography in the study of fiber suspension flows. Acta Mechanica 224 (10), 2263–2280.CrossRefGoogle Scholar
Hurther, D. & Lemmin, U. 2003 Turbulent particle flux and momentum flux statistics in suspension flow. Water Resour. Res. 39 (5), 1139.CrossRefGoogle Scholar
Ireland, P. J. & Desjardins, O. 2017 Improving particle drag predictions in Euler–Lagrange simulations with two-way coupling. J. Comput. Phys. 338, 405–430.CrossRefGoogle Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 433, 329–346.CrossRefGoogle Scholar
Jung, J., Yeo, K. & Lee, C. 2008 Behavior of heavy particles in isotropic turbulence. Phys. Rev. E 77 (1), 016307.CrossRefGoogle ScholarPubMed
Kaftori, D., Hetsroni, G. & Banerjee, S. 1995 a Particle behavior in the turbulent boundary layer. I. Motion, deposition, and entrainment. Phys. Fluids 7 (5), 1095–1106.CrossRefGoogle Scholar
Kaftori, D., Hetsroni, G. & Banerjee, S. 1995 b Particle behavior in the turbulent boundary layer. II. Velocity and distribution profiles. Phys. Fluids 7 (5), 1107–1121.CrossRefGoogle Scholar
Kidanemariam, A. G., Chan-Braun, C., Doychev, T. & Uhlmann, M. 2013 Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction. New J. Phys. 15 (2), 025031.CrossRefGoogle Scholar
Kiger, K. T. & Pan, C. 2002 Suspension and turbulence modification effects of solid particulates on a horizontal turbulent channel flow. J. Turbul. 3 (19), 1–17.CrossRefGoogle Scholar
Kok, J. F., Parteli, E. J. R., Michaels, T. I. & Karam, D. B. 2012 The physics of wind-blown sand and dust. Rep. Prog. Phys. 75 (10), 106901.CrossRefGoogle Scholar
Lajeunesse, E., Malverti, L. & Charru, F. 2010 Bed load transport in turbulent flow at the grain scale: experiments and modeling. J. Geophys. Res.: Earth 115, F04001.CrossRefGoogle Scholar
Lavezzo, V., Soldati, A., Gerashchenko, S., Warhaft, Z. & Collins, L. R. 2010 On the role of gravity and shear on inertial particle accelerations in near-wall turbulence. J. Fluid Mech. 658, 229–246.CrossRefGoogle Scholar
Lee, H. & Balachandar, S. 2010 Drag and lift forces on a spherical particle moving on a wall in a shear flow at finite Re. J. Fluid Mech. 657, 89–125.CrossRefGoogle Scholar
Lee, J. & Lee, C. 2015 Modification of particle-laden near-wall turbulence: effect of Stokes number. Phys. Fluids 27 (2), 023303.CrossRefGoogle Scholar
Lee, J. & Lee, C. 2019 The effect of wall-normal gravity on particle-laden near-wall turbulence. J. Fluid Mech. 873, 475–507.CrossRefGoogle Scholar
Li, J., Wang, H., Liu, Z., Chen, S. & Zheng, C. 2012 An experimental study on turbulence modification in the near-wall boundary layer of a dilute gas-particle channel flow. Exp. Fluids 53 (5), 1385–1403.CrossRefGoogle Scholar
Lin, Z.-W., Shao, X.-M., Yu, Z.-S. & Wang, L.-P. 2017 Effects of finite-size heavy particles on the turbulent flows in a square duct. J. Hydrodyn. 29 (2), 272–282.CrossRefGoogle Scholar
Marchioli, C. 2017 Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches. Acta Mechanica 228 (3), 741–771.CrossRefGoogle Scholar
Marchioli, C. & Soldati, A. 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283–315.CrossRefGoogle Scholar
Mathai, V., Loeffen, L. A. W. M., Chan, T. T. K. & Wildeman, S. 2019 Dynamics of heavy and buoyant underwater pendulums. J. Fluid Mech. 862, 348–363.CrossRefGoogle Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
Mordant, N., Crawford, A. M. & Bodenschatz, E. 2004 Experimental Lagrangian acceleration probability density function measurement. Physica D 193 (1-4), 245–251.CrossRefGoogle Scholar
Nemes, A., Dasari, T., Hong, J., Guala, M. & Coletti, F. 2017 Snowflakes in the atmospheric surface layer: observation of particle–turbulence dynamics. J. Fluid Mech. 814, 592–613.CrossRefGoogle Scholar
Nielsen, P. 1993 Turbulence effects on the settling of suspended particles. J. Sedim. Res. 63 (5), 835–838.Google Scholar
Niño, Y. & Garcia, M. H. 1996 Experiments on particle–turbulence interactions in the near-wall region of an open channel flow: implications for sediment transport. J. Fluid Mech. 326, 285–319.CrossRefGoogle Scholar
Nishimura, K. & Hunt, J. C. R. 2000 Saltation and incipient suspension above a flat particle bed below a turbulent boundary layer. J. Fluid Mech. 417, 77–102.CrossRefGoogle Scholar
Papanicolaou, A. N., Diplas, P., Evaggelopoulos, N. & Fotopoulos, S. 2002 Stochastic incipient motion criterion for spheres under various bed packing conditions. J. Hydraul. Engng ASCE 128 (4), 369–380.CrossRefGoogle Scholar
Petersen, A. J., Baker, L. & Coletti, F. 2019 Experimental study of inertial particles clustering and settling in homogeneous turbulence. J. Fluid Mech. 864, 925–970.CrossRefGoogle Scholar
Picano, F., Breugem, W.-P. & Brandt, L. 2015 Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764, 463–487.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Prandtl, L. 1952 Essentials of Fluid Dynamics: with Applications to Hydraulics, Aeronautics, Meteorology and Other Subjects. Hafner Publishing Company.Google Scholar
Rabencov, B., Arca, J. & van Hout, R. 2014 Measurement of polystyrene beads suspended in a turbulent square channel flow: spatial distributions of velocity and number density. Intl J. Multiphase Flow 62, 110–122.CrossRefGoogle Scholar
Reeks, M. W. 1977 On the dispersion of small particles suspended in an isotropic turbulent fluid. J. Fluid Mech. 83 (3), 529–546.CrossRefGoogle Scholar
Richter, D. H. & Sullivan, P. P. 2014 Modification of near-wall coherent structures by inertial particles. Phys. Fluids 26 (10), 103304.CrossRefGoogle Scholar
Righetti, M. & Romano, G. P. 2004 Particle–fluid interactions in a plane near-wall turbulent flow. J. Fluid Mech. 505, 93–121.CrossRefGoogle Scholar
Rimon, Y. & Cheng, S. I. 1969 Numerical solution of a uniform flow over a sphere at intermediate Reynolds numbers. Phys. Fluids 12 (5), 949–959.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.CrossRefGoogle Scholar
Rouse, H. 1937 Modern conceptions of the mechanics of fluid turbulence. Trans. Am. Soc. Civ. Engng 102, 463–505.Google Scholar
Rouson, D. W. I. & Eaton, J. K. 2001 On the preferential concentration of solid particles in turbulent channel flow. J. Fluid Mech. 428, 149–169.CrossRefGoogle Scholar
Sabban, L. & van Hout, R. 2011 Measurements of pollen grain dispersal in still air and stationary, near homogeneous, isotropic turbulence. J. Aerosol Sci. 42 (12), 867–882.CrossRefGoogle Scholar
Saffman, P. G. T. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22 (2), 385–400.CrossRefGoogle Scholar
Sardina, G., Schlatter, P., Brandt, L., Picano, F. & Casciola, C. M. 2012 Wall accumulation and spatial localization in particle-laden wall flows. J. Fluid Mech. 699, 50–78.CrossRefGoogle Scholar
Shields, A. 1936 Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. PhD thesis, Technical University Berlin.Google Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High–Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Squires, K. D. & Eaton, J. K. 1991 Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 226, 1–35.CrossRefGoogle Scholar
Tanière, Anne & Arcen, Boris 2016 Overview of existing Langevin models formalism for heavy particle dispersion in a turbulent channel flow. Intl J. Multiphase Flow 82, 106–118.CrossRefGoogle Scholar
Tanière, A., Oesterlé, B. & Monnier, J. C. 1997 On the behaviour of solid particles in a horizontal boundary layer with turbulence and saltation effects. Exp. Fluids 23 (6), 463–471.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. s2-20 (1), 196–212.Google Scholar
Tee, Y. H., Barros, D. & Longmire, E. K. 2020 Motion of finite-size spheres released in a turbulent boundary layer. Intl J. Multiphase Flow 133, 103462.CrossRefGoogle Scholar
Voth, G. A., La Porta, A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121–160.CrossRefGoogle Scholar
Wang, G., Abbas, M. & Climent, É. 2017 Modulation of large-scale structures by neutrally buoyant and inertial finite-size particles in turbulent Couette flow. Phys. Rev. Fluids 2 (8), 084302.CrossRefGoogle Scholar
Wang, G., Fong, K. O., Coletti, F., Capecelatro, J. & Richter, D. H. 2019 Inertial particle velocity and distribution in vertical turbulent channel flow: a numerical and experimental comparison. Intl J. Multiphase Flow 120, 103105.CrossRefGoogle Scholar
Wang, L.-P. & Maxey, M. R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68.CrossRefGoogle Scholar
Wang, L.-P. & Stock, D. E. 1993 Dispersion of heavy particles by turbulent motion. J. Atmos. Sci. 50 (13), 1897–1913.2.0.CO;2>CrossRefGoogle Scholar
Wells, M. R. & Stock, D. E. 1983 The effects of crossing trajectories on the dispersion of particles in a turbulent flow. J. Fluid Mech. 136, 31–62.CrossRefGoogle Scholar
Westerweel, J. & Scarano, F. 2005 Universal outlier detection for PIV data. Exp. Fluids 39, 1096–1100.CrossRefGoogle Scholar
Zamansky, R., Vinkovic, I. & Gorokhovski, M. 2011 Acceleration statistics of solid particles in turbulent channel flow. Phys. Fluids 23 (11), 113304.CrossRefGoogle Scholar
Zhao, L. H., Andersson, H. I. & Gillissen, J. J. J. 2010 Turbulence modulation and drag reduction by spherical particles. Phys. Fluids 22 (8), 081702.CrossRefGoogle Scholar
Zhu, H.-Y., Pan, C., Wang, J.-J., Liang, Y.-R. & Ji, X.-C. 2019 Sand-turbulence interaction in a high-Reynolds-number turbulent boundary layer under net sedimentation conditions. Intl J. Multiphase Flow 119, 56–71.CrossRefGoogle Scholar