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Particle–particle drag force in inertial bidisperse gas–particle suspensions

Published online by Cambridge University Press:  23 November 2022

Fan Duan Open the ORCID record for Fan Duan [Opens in a new window] ,
Yaxiong Yu ,
Xiao Chen  and
Qiang Zhou Open the ORCID record for Qiang Zhou [Opens in a new window]
Fan Duan
Affiliation:
School of Chemical Engineering and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China
Yaxiong Yu
Affiliation:
School of Chemical Engineering and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China
Xiao Chen
Affiliation:
School of Chemical Engineering and Technology, Xi'an Jiaotong University, Xi'an 710049, PR China
Qiang Zhou*
Affiliation:
State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
*
†Email address for correspondence: [email protected]
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Abstract

Particle-resolved direct numerical simulations are employed to investigate the particle–particle drag force in the bidisperse gas–particle suspensions where the particles are smooth and the single-particle velocity distribution function is Maxwellian. The particle Reynolds number ranges from 6.7 to 123.8, and in this range the particle inertia is high enough that the lubrication force is not essential. It is found that the relation derived by the kinetic theory of granular flow (KTGF) highly overestimates the particle–particle drag force. This is because the pre-collision velocities of colliding particles are not completely uncorrelated with each other. From the time sequence of collision events, it is observed that the particle pair that has just collided will probably collide again after a short time due to the restriction of the particle motion in dense suspensions. Since the post-collision velocities of the first collision cannot relax entirely in such a short time, the relative velocity before the subsequent collision is statistically smaller than the domain-averaged relative velocity. Consequently, the particle–particle drag force is over-predicted when the domain-averaged relative velocity is used. For this reason, this work assumes that the particle–particle drag force is determined by the relative velocity within a local region near large particles. When the local region is set to be the spherical shells centred on the centres of large particles and with an outer radius of a mean free path of small particles, the KTGF-based relation can reasonably predict the particle–particle drag force.

JFM classification

Multiphase and Particle-laden Flows: Fluidized beds Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 952 , 10 December 2022 , A11
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Ashcroft, N.W. & Langreth, D.C. 1967 Structure of binary liquid mixtures. I. Phys. Rev. 156, 685.CrossRefGoogle Scholar
Beetstra, R., van der Hoef, M.A. & Kuipers, J.A.M. 2007 Numerical study of segregation using a new drag force correlation for polydisperse systems derived from lattice-Boltzmann simulations. Chem. Engng Sci. 62, 246–255.CrossRefGoogle Scholar
Benyahia, S. 2008 Verification and validation study of some polydisperse kinetic theories. Chem. Engng Sci. 63, 5672–5680.CrossRefGoogle Scholar
Brandle 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.CrossRefGoogle Scholar
Bressel, L., Wolter, J. & Reich, O. 2015 Particle sizing in highly turbid dispersions by photon density wave spectroscopy: bidisperse systems. J. Quant. Spectrosc. Radiat. Transfer 162, 213–220.CrossRefGoogle Scholar
Caflisch, R.E. & Luke, J.H.C. 1985 Variance in the sedimenting speed of a suspension. Phys. Fluids 28, 759–760.CrossRefGoogle Scholar
Chao, Z.X., Wang, Y.F., Jakobsen, J.P., Fernandino, M. & Jakobsen, H.A. 2011 Derivation and validation of a binary multi-fluid Eulerian model for fluidized beds. Chem. Engng Sci. 66, 3605–3616.CrossRefGoogle Scholar
Chapman, S. & Cowling, T.G. 1970 The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases. Cambridge University Press.Google Scholar
Chen, Y.P., Mei, Y.F. & Wang, W. 2017 Kinetic theory of binary particles with unequal mean velocities and non-equipartition energies. Physica A 469, 293–304.CrossRefGoogle Scholar
Duan, F., Zhao, L., Chen, X. & Zhou, Q. 2020 Fluid–particle drag and particle-particle drag in low-Reynolds-number bidisperse gas-solid suspensions. Phys. Fluids 32, 113311.CrossRefGoogle Scholar
Feitosa, K. & Menon, N. 2002 Breakdown of energy equipartition in a 2D binary vibrated granular gas. Phys. Rev. Lett. 88, 198301.CrossRefGoogle Scholar
Fullmer, W.D. & Hrenya, C.M. 2017 The clustering instability in rapid granular and gas-solid flows. Annu. Rev. Fluid Mech. 49, 485–510.CrossRefGoogle Scholar
Fullmer, W.D., Liu, G., Yin, X. & Hrenya, C.M. 2017 Clustering instabilities in sedimenting fluid-solid systems: critical assessment of kinetic-theory-based predictions using direct numerical simulation data. J. Fluid Mech. 823, 433–469.CrossRefGoogle Scholar
Galvin, J.E., Dahl, S.R. & Hrenya, C.M. 2005 On the role of non-equipartition in the dynamics of rapidly flowing granular mixtures. J. Fluid Mech. 528, 207–232.CrossRefGoogle Scholar
Garg, R., Galvin, J., Li, T. & Pannala, S. 2012 Documentation of open-source MFIX-DEM software for gas-solids flows. https://mfix.netl.doe.gov/doc/mfix-archive/mfix_current_documentation/dem_doc_2012-1.pdf.CrossRefGoogle Scholar
Garzo, V. 2015 Stability of freely cooling granular mixtures at moderate densities. Chaos, Solitons Fractals 81, 497–509.CrossRefGoogle Scholar
Garzo, V. 2019 Granular Gaseous Flows: A Kinetic Theory Approach to Granular Gaseous Flows. Springer Nature.CrossRefGoogle Scholar
Garzo, V., Dufty, J.W. & Hrenya, C.M. 2007 Enskog theory for polydisperse granular mixtures. Part 1. Navier-Stokes order transport. Phys. Rev. E 76, 031303.CrossRefGoogle Scholar
Glansdorff, P. 1962 Solution of the Boltzmann equations for strong shock waves by the two-fluid model. Phys. Fluids 5, 371.CrossRefGoogle Scholar
Guazzelli, E. & Hinch, E.J. 2011 Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech. 43, 87–116.CrossRefGoogle Scholar
Guazzelli, E. & Morris, J. 2012 A Physical Introduction to Suspensions Dynamics. Cambridge University Press.Google Scholar
Hill, R.J., Koch, D.L. & Ladd, A.J.C. 2001 The first effects of fluid inertia on flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 213–241.CrossRefGoogle Scholar
Iddir, H. & Arastoopour, H. 2005 Modeling of multitype particle flow using the kinetic theory approach. AIChE J. 51 (6), 1620–1632.CrossRefGoogle Scholar
Jenkins, J.T. & Mancini, F. 1987 Balance laws and constitutive relations for plane flows of a dense, binary mixture of smooth, nearly elastic, circular disks. J. Appl. Mech. 54 (1), 27–34.CrossRefGoogle Scholar
Jenkins, J.T. & Mancini, F. 1989 Kinetic theory for binary mixtures of smooth, nearly elastic spheres. Phys. Fluids A 1 (12), 2050–2057.CrossRefGoogle Scholar
Koch, D.L. 1990 Kinetic theory for a monodisperse gas-solid suspension. Phys. Fluids A: Fluid Dyn. 2 (10), 1711–1723.CrossRefGoogle Scholar
Koch, D.L. & Hill, R.J. 2001 Inertial effects in suspension and porous media flow. Annu. Rev. Fluid Mech. 33, 619.CrossRefGoogle Scholar
Koch, D.L. & Sangani, A.S. 1999 Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. J. Fluid Mech. 400, 229–263.CrossRefGoogle Scholar
Ladd, A.J.C. 1996 Hydrodynamic screening in sedimenting suspensions of non-Brownian spheres. Phys. Rev. Lett. 76, 1392.CrossRefGoogle ScholarPubMed
Lebowitz, J.L. 1964 Exact solution of generalized Percus-Yevick equation for a mixture of hard spheres. Phys. Rev. A 133, 895–899.CrossRefGoogle Scholar
Liu, P. & Hrenya, C.M. 2018 Cluster-induced deagglomeration in dilute gravity-driven gas-solid flows of cohesive grains. Phys. Rev. Lett. 121, 238001.CrossRefGoogle ScholarPubMed
Lun, C.K.K. 1991 Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres. J. Fluid Mech. 233, 539–559.CrossRefGoogle Scholar
Lun, C.K.K., Savage, S.B., Jeffrey, D.J. & Chepurniy, N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223–256.CrossRefGoogle Scholar
Marchisio, D.L. & Fox, R.O. 2013 Computational Models for Polydisperse Particulate and Multiphase Systems. Cambridge University Press.CrossRefGoogle Scholar
Mehrabadi, M. & Subramaniam, S. 2017 Mechanism of kinetic energy transfer in homogeneous bidisperse gas-solid flow and its implications for segregation. Phys. Fluids 29, 020714.CrossRefGoogle Scholar
Mehrabadi, M., Tenneti, S. & Subramaniam, S. 2016 Importance of the fluid-particle drag model in predicting segregation in bidisperse gas-solid flow. Intl J. Multiphase Flow 86, 99–114.CrossRefGoogle Scholar
Montanero, J.M. & Garzo, V. 2003 Energy nonequipartition in a sheared granular mixture. Mol. Sim. 29, 357–362.CrossRefGoogle Scholar
Nguyen, N.Q. & Ladd, A.J.C. 2002 Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys. Rev. E 66, 046708.CrossRefGoogle ScholarPubMed
Simeonov, J.A. & Calantoni, J. 2012 Modeling mechanical contact and lubrication in direct numerical simulations of colliding particles. Intl J. Multiphase Flow 46, 38–53.CrossRefGoogle Scholar
Solsvik, J. & Manger, E. 2021 Kinetic theory models for granular mixtures with unequal granular temperature: hydrodynamic velocity. Phys. Fluids 33, 043321.CrossRefGoogle Scholar
Songprawat, S. & Gidaspow, D. 2010 Multiphase flow with unequal granular temperatures. Chem. Engng Sci. 65, 1134–1143.CrossRefGoogle Scholar
Syamlal, M. 1987 The particle-particle drag term in a multiparticle model of fluidization. Topical Rep. DOE/MC 21353 2373, NTIS/DE 87006500.Google Scholar
Tsuji, Y., Kawaguchi, T. & Tanaka, T. 1993 Discrete particle simulation of two-dimensional fluidized bed. Powder Technol. 77, 79–87.CrossRefGoogle Scholar
Zaichik, L.I., Fede, P., Simonin, O. & Alipchenkov, V.M. 2009 Statistical models for predicting the effect of bidisperse particle collisions on particle velocities and stresses in homogeneous anisotropic turbulent flows. Intl J. Multiphase Flow 46, 38–53.Google Scholar
Zhao, L., Chen, X. & Zhou, Q. 2021 Inhomogeneous drag models for gas-solid suspensions based on sub-grid quantities. Powder Technol. 385, 170–184.CrossRefGoogle Scholar
Zhao, B.D. & Wang, J.W. 2020 A note on the kinetic theory of polydisperse granular flow. Chem. Engng Sci. 223, 115730.CrossRefGoogle Scholar
Zhao, B.D. & Wang, J.W. 2021 Kinetic theory of polydisperse gas-solid flow: Navier-Stokes transport coefficients. Phys. Fluids 33, 103322.CrossRefGoogle Scholar
Zhou, Q. & Fan, L.S. 2014 A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows. J. Comput. Phys. 268, 269–301.CrossRefGoogle Scholar
Zhou, Q. & Fan, L.S. 2015 a Direct numerical simulation of low-Reynolds-number flow past arrays of rotating spheres. J. Fluid Mech. 765, 396–423.CrossRefGoogle Scholar
Zhou, Q. & Fan, L.S. 2015 b Direct numerical simulation of moderate-Reynolds number flow past arrays of rotating spheres. Phys. Fluids 27 (7), 073306.CrossRefGoogle Scholar
Zhou, Z.Y., Kuang, S.B., Chu, K.W. & Yu, A.B. 2010 Discrete particle simulation of particle-fluid flow: model formulations and their applicability. J. Fluid Mech. 661, 482–510.CrossRefGoogle Scholar
Zhu, H.P., Zhou, Z.Y., Yang, R.Y. & Yu, A.B. 2007 Discrete particle simulation of particulate systems: theoretical developments. Chem. Engng Sci. 62, 3378–3396.CrossRefGoogle Scholar