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Turbulent channel flow of dense suspensions of neutrally buoyant spheres

Published online by Cambridge University Press:  08 January 2015

Francesco Picano ,
Wim-Paul Breugem  and
Luca Brandt
Francesco Picano*
Affiliation:
SeRC (Swedish e-Science Research Centre) and Linné FLOW Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131 Padua, Italy
Wim-Paul Breugem
Affiliation:
Aero and Hydrodynamics Laboratory, Delft University of Technology, Leeghwaterstraat 21, NL-2628 CA Delft, The Netherlands
Luca Brandt
Affiliation:
SeRC (Swedish e-Science Research Centre) and Linné FLOW Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: francesco.picano@unipd.it
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Abstract

Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct numerical simulation (DNS) are performed in the range of volume fractions ${\it\Phi}=0{-}0.2$ with an immersed boundary method (IBM) used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Kármán constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect if just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction investigated here, ${\it\Phi}=0.2$, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high ${\it\Phi}$ and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Complex Fluids: Suspensions Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 463 - 487
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Copyright
© 2015 Cambridge University Press 

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References

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 (1160), 49–63.Google Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41 (03), 545–570.CrossRefGoogle Scholar
Batchelor, G. K. & Green, J. T. 1972 The determination of the bulk stress in a suspension of spherical particles to order C2. J. Fluid Mech. 56 (03), 401–427.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2007 Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98 (8), 84502.CrossRefGoogle ScholarPubMed
Bellani, G., Byron, M. L., Collignon, A. G., Meyer, C. R. & Variano, E. A. 2012 Shape effects on turbulent modulation by large nearly neutrally buoyant particles. J. Fluid Mech. 712, 41–60.CrossRefGoogle Scholar
Benzi, R., Sbragaglia, M., Succi, S., Bernaschi, M. & Chibbaro, S. 2009 Mesoscopic lattice Boltzmann modeling of soft-glassy systems: theory and simulations. J. Chem. Phys. 131 (10), 104903.CrossRefGoogle Scholar
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107 (18), 188301.CrossRefGoogle ScholarPubMed
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. (B/Fluids) 47, 80–96; Enok Palm Memorial Volume.CrossRefGoogle Scholar
Bray, A. J. 2002 Theory of phase-ordering kinetics. Adv. Phys. 51 (2), 481–587.CrossRefGoogle Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3), 242–251.CrossRefGoogle 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.CrossRefGoogle Scholar
Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.CrossRefGoogle Scholar
Celani, A., Mazzino, A., Muratore-Ginanneschi, P. & Vozella, L. 2009 Phase-field model for the Rayleigh–Taylor instability of immiscible fluids. J. Fluid Mech. 622, 115–134.CrossRefGoogle Scholar
Clausen, J. R., Reasor, D. A. & Aidun, C. K. 2011 The rheology and microstructure of concentrated non-colloidal suspensions of deformable capsules. J. Fluid Mech. 685, 202–234.CrossRefGoogle Scholar
De Angelis, E., Casciola, C. M. & Piva, R. 2002 DNS of wall turbulence: dilute polymers and self-sustaining mechanisms. Comput. Fluids 31 (4), 495–507.CrossRefGoogle Scholar
Einstein, A. 1906 Eine neue bestimmung der moleküldimensionen. Ann. Phys. 324 (2), 289–306.CrossRefGoogle Scholar
Einstein, A. 1911 Berichtigung zu meiner arbeit: eine neue bestimmung der moleküldimensionen. Ann. Phys. 339 (3), 591–592.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: turbulence modification. Phys. Fluids A 5 (7), 1790–1801.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315–329.CrossRefGoogle Scholar
Gualtieri, P., Picano, F., Sardina, G. & Casciola, C. M. 2013 Clustering and turbulence modulation in particle-laden shear flow. J. Fluid Mech. 715, 134–162.CrossRefGoogle Scholar
Guazzelli, É. & Morris, J. F. 2011 A Physical Introduction to Suspension Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Homann, H., Bec, J. & Grauer, R. 2013 Effect of turbulent fluctuations on the drag and lift forces on a towed sphere and its boundary layer. J. Fluid Mech. 721, 155–179.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
Kidanemariam, A. G. & Uhlmann, M. 2014 Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, R2.CrossRefGoogle 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.CrossRefGoogle Scholar
Kulick, J. D., Fessler, J. R. & Eaton, J. K. 1994 Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277, 109–134.CrossRefGoogle Scholar
Kulkarni, P. M. & Morris, J. F. 2008a Pair-sphere trajectories in finite-Reynolds-number shear flow. J. Fluid Mech. 596, 413–435.CrossRefGoogle Scholar
Kulkarni, P. M. & Morris, J. F. 2008b Suspension properties at finite Reynolds number from simulated shear flow. Phys. Fluids 20, 040602.CrossRefGoogle Scholar
Ladd, A. J. C. & Verberg, R. 2001 Lattice-Boltzmann simulations of particle–fluid suspensions. J. Stat. Phys. 104 (5–6), 1191–1251.CrossRefGoogle Scholar
Lambert, R. A., Picano, F., Breugem, W.-P. & Brandt, L. 2013 Active suspensions in thin films: nutrient uptake and swimmer motion. J. Fluid Mech. 733, 528–557.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Li, Y., McLaughlin, J. B., Kontomaris, K. & Portela, L. 2001 Numerical simulation of particle-laden turbulent channel flow. Phys. Fluids 13 (10), 2957–2967.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Magaletti, F., Picano, F., Chinappi, M., Marino, L. & Casciola, C. M. 2013 The sharp-interface limit of the Cahn–Hilliard/Navier–Stokes model for binary fluids. J. Fluid Mech. 714, 95–126.CrossRefGoogle Scholar
Marchioro, M., Tankslay, M. & Prosperetti, A. 1999 Mixture pressure and stress in disperse two-phase flow. Intl J. Multiphase Flow 25, 1395–1429.CrossRefGoogle Scholar
Matas, J.-P., Morris, J. F. & Guazzelli, E. 2003 Transition to turbulence in particulate pipe flow. Phys. Rev. Lett. 90 (1), 014501.CrossRefGoogle ScholarPubMed
Morris, J. F. 2009 A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol. Acta 48 (8), 909–923.CrossRefGoogle Scholar
Naso, A. & Prosperetti, A. 2010 The interaction between a solid particle and a turbulent flow. New J. Phys. 12 (3), 033040.CrossRefGoogle Scholar
Pan, Y. & Banerjee, S. 1996 Numerical simulation of particle interactions with wall turbulence. Phys. Fluids 8 (10), 2733–2755.CrossRefGoogle 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 (9), 098302.CrossRefGoogle ScholarPubMed
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Reeks, M. W. 1983 The transport of discrete particles in inhomogeneous turbulence. J. Aerosol Sci. 14 (6), 729–739.CrossRefGoogle Scholar
Sardina, G., Picano, F., Schlatter, P., Brandt, L. & Casciola, C. M. 2011 Large scale accumulation patterns of inertial particles in wall-bounded turbulent flow. Flow Turbul. Combust. 86 (3–4), 519–532.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 (1), 50–78.CrossRefGoogle Scholar
Shao, X., Wu, T. & Yu, Z. 2012 Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number. J. Fluid Mech. 693, 319–344.CrossRefGoogle Scholar
Sierou, A. & Brady, J. F. 2002 Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46 (5), 1031–1056.CrossRefGoogle 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.CrossRefGoogle Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3 (5), 1169–1178.CrossRefGoogle Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.CrossRefGoogle Scholar
Stone, P. A., Waleffe, F. & Graham, M. D. 2002 Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows. Phys. Rev. Lett. 89 (20), 208301.CrossRefGoogle Scholar
Sundaram, S. & Collins, L. R. 1999 A numerical study of the modulation of isotropic turbulence by suspended particles. J. Fluid Mech. 379, 105–143.CrossRefGoogle Scholar
Takagi, S., Oguz, H. N., Zhang, Z. & Prosperetti, A. 2003 Physalis: a new method for particle simulation: part II: two-dimensional Navier–Stokes flow around cylinders. J. Comput. Phys. 187 (2), 371–390.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.CrossRefGoogle Scholar
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y.-J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169 (2), 708–759.CrossRefGoogle Scholar
Virk, P. S. 1975 Drag reduction fundamentals. J. Am. Inst. Chem. Engng 21 (4), 625–656.CrossRefGoogle 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.CrossRefGoogle Scholar
Wagner, N. J. & Brady, J. F. 2009 Shear thickening in colloidal dispersions. Phys. Today 62 (10), 27–32.CrossRefGoogle Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883–900.CrossRefGoogle Scholar
Yeo, K., Dong, S., Climent, E. & Maxey, M. R. 2010 Modulation of homogeneous turbulence seeded with finite size bubbles or particles. Intl J. Multiphase Flow 36 (3), 221–233.CrossRefGoogle Scholar
Yeo, K. & Maxey, M. R. 2010a Dynamics of concentrated suspensions of non-colloidal particles in Couette flow. J. Fluid Mech. 649, 205–231.CrossRefGoogle Scholar
Yeo, K. & Maxey, M. R. 2010b Simulation of concentrated suspensions using the force-coupling method. J. Comput. Phys. 229 (6), 2401–2421.CrossRefGoogle Scholar
Yeo, K. & Maxey, M. R. 2011 Numerical simulations of concentrated suspensions of monodisperse particles in a Poiseuille flow. J. Fluid Mech. 682, 491–518.CrossRefGoogle Scholar
Yu, Z., Wu, T., Shao, X. & Lin, J. 2013 Numerical studies of the effects of large neutrally buoyant particles on the flow instability and transition to turbulence in pipe flow. Phys. Fluids 25, 043305.CrossRefGoogle Scholar
Zarraga, I. E., Hill, D. A. & Leighton, D. T. 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44 (2), 185–220.CrossRefGoogle Scholar
Zhang, Q. & Prosperetti, A. 2010 Physics-based analysis of the hydrodynamic stress in a fluid–particle system. Phys. Fluids 22, 033306.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