Skip to main content Accessibility help
×
Home

A direct numerical investigation of two-way interactions in a particle-laden turbulent channel flow

  • Cheng Peng (a1) (a2), Orlando M. Ayala (a3) and Lian-Ping Wang (a1) (a2)

Abstract

Understanding the two-way interactions between finite-size solid particles and a wall-bounded turbulent flow is crucial in a variety of natural and engineering applications. Previous experimental measurements and particle-resolved direct numerical simulations revealed some interesting phenomena related to particle distribution and turbulence modulation, but their in-depth analyses are largely missing. In this study, turbulent channel flows laden with neutrally buoyant finite-size spherical particles are simulated using the lattice Boltzmann method. Two particle sizes are considered, with diameters equal to 14.45 and 28.9 wall units. To understand the roles played by the particle rotation, two additional simulations with the same particle sizes but no particle rotation are also presented for comparison. Particles of both sizes are found to form clusters. Under the Stokes lubrication corrections, small particles are found to have a stronger preference to form clusters, and their clusters orientate more in the streamwise direction. As a result, small particles reduce the mean flow velocity less than large particles. Particles are also found to result in a more homogeneous distribution of turbulent kinetic energy (TKE) in the wall-normal direction, as well as a more isotropic distribution of TKE among different spatial directions. To understand these turbulence modulation phenomena, we analyse in detail the total and component-wise volume-averaged budget equations of TKE with the simulation data. This budget analysis reveals several mechanisms through which the particles modulate local and global TKE in the particle-laden turbulent channel flow.

Copyright

Corresponding author

Email address for correspondence: lwang@udel.edu

References

Hide All
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.10.1146/annurev.fluid.010908.165243
Botto, L. & Prosperetti, A. 2012 A fully resolved numerical simulation of turbulent flow past one or several spherical particles. Phys. Fluids 24 (1), 013303.10.1063/1.3678336
Bouzidi, M., Firdaouss, M. & Lallemand, P. 2001 Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys. Fluids 13 (11), 34523459.10.1063/1.1399290
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20 (1), 111157.10.1146/annurev.fl.20.010188.000551
Brändle de Motta, J. C., Breugem, W.-P., Gazanion, B., Estivalezes, J.-L., Vincent, S. & Climent, E. 2013 Numerical modelling of finite-size particle collisions in a viscous fluid. Phys. Fluids 25 (8), 083302.10.1063/1.4817382
Brändle de Motta, J. C., Costa, P., Derksen, J. J., Peng, C., Wang, L.-P., Breugem, W.-P., Estivalezes, J. L., Vincent, S., Climent, E., Fede, P. et al. 2019 Assessment of numerical methods for fully resolved simulations of particle-laden turbulent flows. Comput. Fluids 179, 114.10.1016/j.compfluid.2018.10.016
Brändle de Motta, J. C., Estivalezes, J.-L., Climent, E. & Vincent, S. 2016 Local dissipation properties and collision dynamics in a sustained homogeneous turbulent suspension composed of finite size particles. Intl J. Multiphase Flow 85, 369379.10.1016/j.ijmultiphaseflow.2016.07.003
Breugem, W.-P. 2010 A combined soft-sphere collision/immersed boundary method for resolved simulations of particulate flows. In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting Collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels, pp. 23812392. American Society of Mechanical Engineers.
Burton, T. M. & Eaton, J. K. 2005 Fully resolved simulations of particle-turbulence interaction. J. Fluid Mech. 545, 67111.10.1017/S0022112005006889
Caiazzo, A. 2008 Analysis of lattice Boltzmann nodes initialisation in moving boundary problems. Intl J. Comput. Fluid Dyn. 8 (1–4), 310.10.1504/PCFD.2008.018074
du Cluzeau, A., Bois, G. & Toutant, A. 2019 Analysis and modelling of Reynolds stresses in turbulent bubbly up-flows from direct numerical simulations. J. Fluid Mech. 866, 132168.10.1017/jfm.2019.100
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 (13), 134501.10.1103/PhysRevLett.117.134501
Crowe, C. T., Schwarzkopf, J. D., Sommerfeld, M. & Tsuji, Y. 2011 Multiphase Flows With Droplets and Particles. CRC Press.10.1201/b11103
Eaton, J. K. 2009 Two-way coupled turbulence simulations of gas-particle flows using point-particle tracking. Intl J. Multiphase Flow 35 (9), 792800.10.1016/j.ijmultiphaseflow.2009.02.009
Elghobashi, S. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I. Turbulence modification. Phys. Fluids 5 (7), 17901801.10.1063/1.858854
Eshghinejadfard, A., Abdelsamie, A., Hosseini, S. A. & Thévenin, D. 2017 Immersed boundary lattice Boltzmann simulation of turbulent channel flows in the presence of spherical particles. Intl J. Multiphase Flow 96, 161172.10.1016/j.ijmultiphaseflow.2017.07.011
Feng, Z.-G. & Michaelides, E. E. 2005 Proteus: a direct forcing method in the simulations of particulate flows. J. Comput. Phys. 202 (1), 2051.10.1016/j.jcp.2004.06.020
Feng, Z.-G. & Michaelides, E. E. 2009 Robust treatment of no-slip boundary condition and velocity updating for the lattice-Boltzmann simulation of particulate flows. Comput. Fluids 38 (2), 370381.10.1016/j.compfluid.2008.04.013
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315329.10.1063/1.1532731
Gao, H., Li, H. & Wang, L.-P. 2013 Lattice Boltzmann simulation of turbulent flow laden with finite-size particles. Comput. Maths. Applics. 65 (2), 194210.10.1016/j.camwa.2011.06.028
Glowinski, R., Pan, T.-W., Hesla, T. I. & Joseph, D. D. 1999 A distributed lagrange multiplier/fictitious domain method for particulate flows. Intl J. Multiphase Flow 25 (5), 755794.10.1016/S0301-9322(98)00048-2
Gore, R. A. & Crowe, C. T. 1989 Effect of particle size on modulating turbulent intensity. Intl J. Multiphase Flow 15 (2), 279285.10.1016/0301-9322(89)90076-1
Gupta, A., Clercx, H. J. H. & Toschi, F. 2018 Computational study of radial particle migration and stresslet distributions in particle-laden turbulent pipe flow. Eur. Phys. J. E 41 (3), 34.10.1140/epje/i2018-11638-3
Hall, D. 1988 Measurements of the mean force on a particle near a boundary in turbulent flow. J. Fluid Mech. 187, 451466.10.1017/S0022112088000515
Joseph, G.2003 Collisional dynamics of macroscopic particles in a viscous fluid. PhD thesis, California Institute of Technology, Pasadena, CA.
Kajishima, T., Takiguchi, S., Hamasaki, H. & Miyake, Y. 2001 Turbulence structure of particle-laden flow in a vertical plane channel due to vortex shedding. JSME Intl J. 44 (4), 526535.10.1299/jsmeb.44.526
Kataoka, I. & Serizawa, A. 1989 Basic equations of turbulence in gas–liquid two-phase flow. Intl J. Multiphase Flow 15 (5), 843855.10.1016/0301-9322(89)90045-1
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.10.1017/S0022112087000892
Kulick, J. D., Fessler, J. R. & Eaton, J. K. 1994 Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277, 109134.10.1017/S0022112094002703
Kurose, R. & Komori, S. 1999 Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183206.10.1017/S0022112099004164
Kussin, J. & Sommerfeld, M. 2002 Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness. Exp. Fluids 33 (1), 143159.10.1007/s00348-002-0485-9
Lammers, P., Beronov, K. N., Volkert, R., Brenner, G. & Durst, F. 2006 Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow. Comput. Fluids 35, 11371153.10.1016/j.compfluid.2005.10.002
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), 35433549.10.1016/j.ces.2005.12.028
Li, Y., McLaughlin, J. B., Kontomaris, K. & Portela, L. 2001 Numerical simulation of particle-laden turbulent channel flow. Phys. Fluids 13 (10), 29572967.10.1063/1.1396846
Lucci, F., Ferrante, A. & Elghobashi, S. 2010 Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 555.10.1017/S0022112009994022
Maxey, M. R. 2017 Simulation methods for particulate flows and concentrated suspensions. Annu. Rev. Fluid Mech. 49, 171193.10.1146/annurev-fluid-122414-034408
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883889.10.1063/1.864230
Mei, R. 1992 An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Intl J. Multiphase Flow 18 (1), 145147.10.1016/0301-9322(92)90012-6
Mollinger, A. M. & Nieuwstadt, F. T. M. 1996 Measurement of the lift force on a particle fixed to the wall in the viscous sublayer of a fully developed turbulent boundary layer. J. Fluid Mech. 316, 285306.10.1017/S0022112096000547
Pan, Y. & Banerjee, S. 1997 Numerical investigation of the effects of large particles on wall-turbulence. Phys. Fluids 9 (12), 37863807.10.1063/1.869514
Paris, A. D.2001 Turbulence attenuation in a particle-laden channel flow. PhD thesis, Stanford University, CA.
Peng, C., Geneva, N., Guo, Z. & Wang, L.-P. 2018 Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method. J. Comput. Phys. 357, 1642.10.1016/j.jcp.2017.11.040
Peng, C., Teng, Y., Hwang, B., Guo, Z. & Wang, L.-P. 2016 Implementation issues and benchmarking of lattice Boltzmann method for moving rigid particle simulations in a viscous flow. Comput. Maths Applics. 72 (2), 349374.10.1016/j.camwa.2015.08.027
Peng, C. & Wang, L.-P. 2018 Direct numerical simulations of turbulent pipe flow laden with finite-size neutrally buoyant particles at low flow Reynolds number. Acta Mechanica 230, 517539.
Picano, F., Breugem, W.-P. & Brandt, L. 2015 Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764, 463487.10.1017/jfm.2014.704
Prosperetti, A. & Tryggvason, G. 2009 Computational Methods for Multiphase Flow. Cambridge University Press.
Reeks, M. W. 1983 The transport of discrete particles in inhomogeneous turbulence. J. Aero. Sci. 14 (6), 729739.10.1016/0021-8502(83)90055-1
Saffman, P. G. T. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22 (2), 385400.10.1017/S0022112065000824
Santarelli, C., Roussel, J. & Fröhlich, J. 2016 Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel. Chem. Engng Sci. 141, 4662.10.1016/j.ces.2015.10.013
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, 319344.10.1017/jfm.2011.533
Squires, K. D. & Eaton, J. K. 1990 Particle response and turbulence modification in isotropic turbulence. Phys. Fluids 2 (7), 11911203.10.1063/1.857620
Tanaka, T. & Eaton, J. K. 2008 Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Phys. Rev. Lett. 101 (11), 114502.10.1103/PhysRevLett.101.114502
Tanaka, T. & Eaton, J. K. 2010 Sub-Kolmogorov resolution partical image velocimetry measurements of particle-laden forced turbulence. J. Fluid Mech. 643, 177206.10.1017/S0022112009992023
Tao, S., Hu, J. & Guo, Z. 2016 An investigation on momentum exchange methods and refilling algorithms for lattice Boltzmann simulation of particulate flows. Comput. Fluids 133, 114.10.1016/j.compfluid.2016.04.009
Ten Cate, A., Derksen, J. J., Portela, L. M. & Van Den Akker, H. E. A. 2004 Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. J. Fluid Mech. 519, 233271.10.1017/S0022112004001326
Ten Cate, A., Nieuwstad, C. H., Derksen, J. J. & Van den Akker, H. E. A. 2002 Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity. Phys. Fluids 14 (11), 40124025.10.1063/1.1512918
Tenneti, S. & Subramaniam, S. 2014 Particle-resolved direct numerical simulation for gas-solid flow model development. Annu. Rev. Fluid Mech. 46, 199230.10.1146/annurev-fluid-010313-141344
Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20 (5), 053305.10.1063/1.2912459
Uhlmann, M. & Chouippe, A. 2017 Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence. J. Fluid Mech. 812, 9911023.10.1017/jfm.2016.826
Vreman, A. W. 2015 Turbulence attenuation in particle-laden flow in smooth and rough channels. J. Fluid Mech. 773, 103136.10.1017/jfm.2015.208
Vreman, A. W. 2016 Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres. J. Fluid Mech. 796, 4085.10.1017/jfm.2016.228
Vreman, A. W. & Kuerten, J. G. M. 2018 Turbulent channel flow past a moving array of spheres. J. Fluid Mech. 856, 580632.10.1017/jfm.2018.715
Wang, L.-P., Ardila, O. G. C., Ayala, O., Gao, H. & Peng, C. 2016a Study of local turbulence profiles relative to the particle surface in particle-laden turbulent flows. J. Fluids Engng 138 (4), 041307.
Wang, L.-P., Peng, C., Guo, Z. & Yu, Z. 2016b Flow modulation by finite-size neutrally buoyant particles in a turbulent channel flow. J. Fluids Engng 138 (4), 041306.
Wang, L.-P., Peng, C., Guo, Z. & Yu, Z. 2016c Lattice Boltzmann simulation of particle-laden turbulent channel flow. Comput. Fluids 124, 226236.10.1016/j.compfluid.2015.07.008
Wen, B., Zhang, C., Tu, Y., Wang, C. & Fang, H. 2014 Galilean invariant fluid–solid interfacial dynamics in lattice Boltzmann simulations. J. Comput. Phys. 266, 161170.10.1016/j.jcp.2014.02.018
Wu, T., Shao, X. & Yu, Z. 2011 Fully resolved numerical simulation of turbulent pipe flows laden with large neutrally-buoyant particles. J. Hydrodyn. 23 (1), 2125.10.1016/S1001-6058(10)60083-2
Xu, Y. & Subramaniam, S. 2010 Effect of particle clusters on carrier flow turbulence: a direct numerical simulation study. Flow, Turbul. Combust. 85 (3), 735761.10.1007/s10494-010-9298-8
Yang, F.-L. & Hunt, M. L. 2006 Dynamics of particle–particle collisions in a viscous liquid. Phys. Fluids 18 (12), 121506.10.1063/1.2396925
Yu, Z., Lin, Z., Shao, X. & Wang, L.-P. 2017 Effects of particle-fluid density ratio on the interactions between the turbulent channel flow and finite-size particles. Phys. Rev. E 96, 033102.
Zeng, L., Balachandar, S., Fischer, P. & Najjar, F. 2008 Interactions of a stationary finite-sized particle with wall turbulence. J. Fluid Mech. 594, 271305.10.1017/S0022112007009056
Zhao, W. & Yong, W.-A. 2017 Single-node second-order boundary schemes for the lattice Boltzmann method. J. Comput. Phys. 329 (6), 115.10.1016/j.jcp.2016.10.049
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed