Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T14:28:02.076Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of the finite particle size in turbulent wall-bounded flows of dense suspensions

Published online by Cambridge University Press:  22 March 2018

Pedro Costa Open the ORCID record for Pedro Costa [Opens in a new window] ,
Francesco Picano ,
Luca Brandt Open the ORCID record for Luca Brandt [Opens in a new window]  and
Wim-Paul Breugem
Pedro Costa*
Affiliation:
Process and Energy Dpt. – Multiphase Systems, Delft University of Technology, Leeghwaterstraat 21, 2621CA, Delft, The Netherlands
Francesco Picano
Affiliation:
Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131 Padua, Italy
Luca Brandt
Affiliation:
Swedish e-Science Research Centre and Linné FLOW Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
Wim-Paul Breugem
Affiliation:
Process and Energy Dpt. – Multiphase Systems, Delft University of Technology, Leeghwaterstraat 21, 2621CA, Delft, The Netherlands
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We use interface-resolved numerical simulations to study finite-size effects in turbulent channel flow of neutrally buoyant spheres. Two cases with particle sizes differing by a factor of two, at the same solid volume fraction of 20 % and bulk Reynolds number are considered. These are complemented with two reference single-phase flows: the unladen case, and the flow of a Newtonian fluid with the effective suspension viscosity of the same mixture in the laminar regime. As recently highlighted in Costa et al. (Phys. Rev. Lett., vol. 117, 2016, 134501), a particle–wall layer is responsible for deviations of the mesoscale-averaged statistics from what is observed in the continuum limit where the suspension is modelled as a Newtonian fluid with (higher) effective viscosity. Here we investigate in detail the fluid and particle dynamics inside this layer and in the bulk. In the particle–wall layer, the near-wall inhomogeneity has an influence on the suspension microstructure over a distance proportional to the particle size. In this layer, particles have a significant (apparent) slip velocity that is reflected in the distribution of wall shear stresses. This is characterized by extreme events (both much higher and much lower than the mean). Based on these observations we provide a scaling for the particle-to-fluid apparent slip velocity as a function of the flow parameters. We also extend the scaling laws in Costa et al. (Phys. Rev. Lett., vol. 117, 2016, 134501) to second-order Eulerian statistics in the homogeneous suspension region away from the wall. The results show that finite-size effects in the bulk of the channel become important for larger particles, while negligible for lower-order statistics and smaller particles. Finally, we study the particle dynamics along the wall-normal direction. Our results suggest that single-point dispersion is dominated by particle–turbulence (and not particle–particle) interactions, while differences in two-point dispersion and collisional dynamics are consistent with a picture of shear-driven interactions.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 843 , 25 May 2018 , pp. 450 - 478
Copyright
© 2018 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.)

References

Ardekani, M. N., Costa, P., Breugem, W.-P., Picano, F. & Brandt, L. 2017 Drag reduction in turbulent channel flow laden with finite-size oblate spheroids. J. Fluid Mech. 816, 43–70.Google Scholar
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 49–63.Google Scholar
Batchelor, G. K. 1952 The effect of homogeneous turbulence on material lines and surfaces. Proc. R. Soc. Lond. A 213, 349–366.Google Scholar
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41 (03), 545–570.Google Scholar
Biegert, E., Vowinckel, B. & Meiburg, E. 2017 A collision model for grain-resolving simulations of flows over dense, mobile, polydisperse granular sediment beds. J. Comput. Phys. 340, 105–127.Google Scholar
Blanc, F., Lemaire, E., Meunier, A. & Peters, F. 2013 Microstructure in sheared non-Brownian concentrated suspensions. J. Rheology 57 (1), 273–292.Google Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Ann. Rev. Fluid Mech. 20, 111–157.Google Scholar
Breugem, W.-P. 2012 A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows. J. Comput. Phys. 231 (13), 4469–4498.Google Scholar
Brown, E. & Jaeger, H. M. 2014 Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming. Reports on Progress in Physics 77 (4), 046602.Google Scholar
Chouippe, A. & Uhlmann, M. 2015 Forcing homogeneous turbulence in direct numerical simulation of particulate flow with interface resolution and gravity. Phys. Fluids 27 (12), 123301.Google Scholar
Costa, P., Boersma, B. J., Westerweel, J. & Breugem, W.-P. 2015 Collision model for fully resolved simulations of flows laden with finite-size particles. Phys. Rev. E 92 (5), 053012.Google Scholar
Costa, P., Picano, F., Brandt, L. & Breugem, W.-P. 2016 Universal scaling laws for dense particle suspensions in turbulent wall-bounded flows. Phys. Rev. Lett. 117, 134501.Google Scholar
Crowe, C. T., Sharma, M. Pt. & Stock, D. E. 1977 The particle-source-in cell (psi-cell) model for gas-droplet flows. J. Fluids Engng. 99 (2), 325–332.Google Scholar
Dance, S. L. & Maxey, M. R. 2003 Incorporation of lubrication effects into the force-coupling method for particulate two-phase flow. J. Comput. Phys. 189 (1), 212–238.Google Scholar
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.Google Scholar
Einstein, A. 1905 Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik 322 (8), 549–560.Google Scholar
Eshghinejadfard, A., Hosseini, S. A. & Thévenin, D. 2017 Fully-resolved prolate spheroids in turbulent channel flows: a lattice Boltzmann study. AIP Advances 7 (9), 095007.Google Scholar
Fessler, J. R., Kulick, J. D. & Eaton, J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6 (11), 3742–3749.Google Scholar
Foerster, S. F., Louge, M. Y., Chang, H. & Allia, K. 1994 Measurements of the collision properties of small spheres. Phys. Fluids 6 (3), 1108–1115.Google Scholar
Fornari, W., Formenti, A., Picano, F. & Brandt, L. 2016a The effect of particle density in turbulent channel flow laden with finite size particles in semi-dilute conditions. Phys. Fluids 28 (3), 033301.Google Scholar
Fornari, W., Picano, F. & Brandt, L. 2016b Sedimentation of finite-size spheres in quiescent and turbulent environments. J. Fluid Mech. 788, 640–669.Google Scholar
Fornari, W., Picano, F. & Brandt, L. 2018 The effect of polydispersity in a turbulent channel flow laden with finite-size particles. European J. Mech. (B/Fluids) 67, 54–64; (Supplement C).Google Scholar
Guazzelli, E. & Morris, J. F. 2011 A Physical Introduction to Suspension Dynamics, vol. 45. Cambridge University Press.Google Scholar
Hinze, J. O. 1975 Turbulence McGraw-Hill Classic Textbook Reissue Series, vol. 218. McGraw-Hill.Google Scholar
Hunt, M. L., Zenit, R., Campbell, C. S. & Brennen, C. E. 2002 Revisiting the 1954 suspension experiments of RA Bagnold. J. Fluid Mech. 452, 1–24.Google 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.Google Scholar
Kidanemariam, A. G. & Uhlmann, M. 2014 Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, R2.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Lashgari, I., Picano, F., Breugem, W.-P. & Brandt, L. 2014 Laminar, turbulent, and inertial shear-thickening regimes in channel flow of neutrally buoyant particle suspensions. Phys. Rev. Lett. 113, 254502.Google Scholar
Lashgari, I., Picano, F., Breugem, W.-P. & Brandt, L. 2016 Channel flow of rigid sphere suspensions: particle dynamics in the inertial regime. Intl J. Multiphase Flow 78, 12–24.Google Scholar
Lashgari, I., Picano, F., Costa, P., Breugem, W.-P. & Brandt, L. 2017 Turbulent channel flow of a dense binary mixture of rigid particles. J. Fluid Mech. 818, 623–645.Google Scholar
Legendre, D., Zenit, R., Daniel, C. & Guiraud, P. 2006 A note on the modelling of the bouncing of spherical drops or solid spheres on a wall in viscous fluid. Chem. Engng Sci. 61 (11), 3543–3549.Google Scholar
Leighton, D. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.Google Scholar
Loisel, V., Abbas, M., Masbernat, O. & Climent, E. 2013 The effect of neutrally buoyant finite-size particles on channel flows in the laminar-turbulent transition regime. Phys. Fluids 25 (12), 123304.Google Scholar
Lucci, F., Ferrante, A. & Elghobashi, S. 2010 Modulation of isotropic turbulence by particles of taylor length-scale size. J. Fluid Mech. 650, 5–55.Google Scholar
Marchioro, M., Tanksley, M. & Prosperetti, A. 1999 Mixture pressure and stress in disperse two-phase flow. Intl J. Multiphase Flow 25 (6), 1395–1429.Google Scholar
Matas, J.-P., Morris, J. F. & Guazzelli, E. 2003 Transition to turbulence in particulate pipe flow. Phys. Rev. Lett. 90 (1), 014501.Google 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.Google Scholar
Morris, J. F. 2009 A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheologica Acta 48 (8), 909–923.Google Scholar
Örlü, R. & Schlatter, P. 2011 On the fluctuating wall-shear stress in zero pressure-gradient turbulent boundary layer flows. Phys. Fluids 23 (2), 021704.Google 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.Google Scholar
Picano, F., Breugem, W.-P., Mitra, D. & Brandt, L. 2013 Shear thickening in non-Brownian suspensions: an excluded volume effect. Phys. Rev. Lett. 111, 098302.Google Scholar
Pope, S. B.2001. Turbulent flows.Google Scholar
Prosperetti, A. 2015 Life and death by boundary conditions. J. Fluid Mech. 768, 1–4.Google Scholar
Reeks, M. W. 1977 On the dispersion of small particles suspended in an isotropic turbulent fluid. J. Fluid Mech. 83 (03), 529–546.Google Scholar
Roma, A. M., Peskin, C. S. & Berger, M. J. 1999 An adaptive version of the immersed boundary method. J. Comput. Phys. 153 (2), 509–534.Google Scholar
Salazar, J. P. & Collins, L. R. 2009 Two-particle dispersion in isotropic turbulent flows. Ann. Rev. Fluid Mech. 41, 405–432.Google 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.Google Scholar
Sierou, A. & Brady, J. F. 2004 Shear-induced self-diffusion in non-colloidal suspensions. J. Fluid Mech. 506 (1), 285–314.Google Scholar
Soldati, A. & Marchioli, C. 2009 Physics and modelling of turbulent particle deposition and entrainment: review of a systematic study. Intl J. Multiphase Flow 35 (9), 827–839.Google Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.Google Scholar
Ten, C., Andreas, D., Portela, J. J., Louis, M., Van Den, A. & Harry, E. A. 2004 Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. J. Fluid Mech 519, 233–271.Google Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209 (2), 448–476.Google Scholar
Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20 (5), 053305.Google Scholar
Vowinckel, B., Kempe, T. & Fröhlich, J. 2014 Fluid–particle interaction in turbulent open channel flow with fully-resolved mobile beds. Adv. Water Resour. 72, 32–44.Google Scholar
Vreman, A. W. 2016 Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres. J. Fluid Mech. 796, 40–85.Google Scholar
Wang, G., Abbas, M. & Climent, E. 2017 Modulation of large-scale structures by neutrally buoyant and inertial finite-size particles in turbulent Couette flow. Phys. Rev. Fluids 2 (8), 084302.Google Scholar
Wang, L.-P., Peng, C., Guo, Z. & Yu, Z. 2016 Flow modulation by finite-size neutrally buoyant particles in a turbulent channel flow. J. Fluids Engng 138 (4), 041306.Google Scholar
Yang, F.-L. & Hunt, M. L. 2006 Dynamics of particle-particle collisions in a viscous liquid. Phys. Fluids 18 (12), 121506.Google Scholar
Yu, W., Vinkovic, I. & Buffat, M. 2016 Finite-size particles in turbulent channel flow: quadrant analysis and acceleration statistics. J. Turbul. 17 (11), 1048–1071.Google Scholar