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On fluid–particle dynamics in fully developed cluster-induced turbulence

Published online by Cambridge University Press:  07 September 2015

Jesse Capecelatro ,
Olivier Desjardins  and
Rodney O. Fox
Jesse Capecelatro*
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14850, USA
Olivier Desjardins
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14850, USA
Rodney O. Fox
Affiliation:
Department of Chemical and Biological Engineering, 2114 Sweeney Hall, Iowa State University, Ames, IA 50011-2230, USA EM2C-UPR, CNRS 288, Ecole Centrale Paris, Grande Vois des Vignes, 92295 Chatenay Malabry, France
*
†Email address for correspondence: [email protected]
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Abstract

At sufficient mass loading and in the presence of a mean body force (e.g. gravity), an initially random distribution of particles may organize into dense clusters as a result of momentum coupling with the carrier phase. In statistically stationary flows, fluctuations in particle concentration can generate and sustain fluid-phase turbulence, which we refer to as cluster-induced turbulence (CIT). This work aims to explore such flows in order to better understand the fundamental modelling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume-fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters. To this end, a complete description of the two-phase flow is presented in terms of the exact Reynolds-average (RA) equations, and the relevant unclosed terms that are retained in the context of homogeneous gravity-driven flows are investigated numerically. An Eulerian–Lagrangian computational strategy is used to simulate fully developed CIT for a range of Reynolds numbers, where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. The adaptive filtering technique recently introduced in our previous work (Capecelatro et al., J. Fluid Mech., vol. 747, 2014, R2) is used to evaluate the Lagrangian data as Eulerian fields that are consistent with the terms appearing in the RA equations. Results from gravity-driven CIT show that momentum coupling between the two phases leads to significant differences from the behaviour observed in very dilute systems with one-way coupling. In particular, entrainment of the fluid phase by clusters results in an increased mean particle velocity that generates a drag production term for fluid-phase turbulent kinetic energy that is highly anisotropic. Moreover, owing to the compressibility of the particle phase, the uncorrelated components of the particle-phase velocity statistics are highly non-Gaussian, as opposed to systems with one-way coupling, where, in the homogeneous limit, all of the velocity statistics are nearly Gaussian. We also observe that the particle pressure tensor is highly anisotropic, and thus additional transport equations for the separate contributions to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.

JFM classification

Turbulent Flows: Homogeneous turbulence Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 780 , 10 October 2015 , pp. 578 - 635
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© 2015 Cambridge University Press 

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References

Agrawal, K., Loezos, P. N., Syamlal, M. & Sundaresan, S. 2001 The role of meso-scale structures in rapid gas–solid flows. J. Fluid Mech. 445, 151–186.CrossRefGoogle Scholar
Aliseda, A., Cartellier, A., Hainaux, F. & Lasheras, J. C. 2002 Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 468, 77–105.Google Scholar
Anderson, T. B. & Jackson, R. 1967 Fluid mechanical description of fluidized beds. Equations of motion. Ind. Engng Chem. Fundam. 6 (4), 527–539.Google Scholar
Arya, S. P. 1999 Air Pollution Meteorology and Dispersion. Oxford University Press.Google Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Basu, P. & Fraser, S. A. 1991 Circulating Fluidized Bed Boilers: Design and Operations. Butterworth-Heinemann.Google Scholar
Beetstra, R., Van der Hoef, M. A. & Kuipers, J. A. M. 2007 Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres. AIChE J. 53 (2), 489–501.Google Scholar
Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (3), 511–525.Google Scholar
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon.CrossRefGoogle Scholar
Bosse, T., Kleiser, L. & Meiburg, E. 2006 Small particles in homogeneous turbulence: settling velocity enhancement by two-way coupling. Phys. Fluids 18 (2), 027102.Google Scholar
Bridgewater, A. V. 1995 The technical and economical feasibility of biomass gasification for power generation. Fuel 74 (5), 631–653.CrossRefGoogle Scholar
Briley, W. R. & McDonald, H. 1977 Solution of the multidimensional compressible Navier–Stokes equations by a generalized implicit method. J. Comput. Phys. 24 (4), 372–397.Google Scholar
Capecelatro, J. & Desjardins, O. 2013a An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 1–31.Google Scholar
Capecelatro, J. & Desjardins, O. 2013b Eulerian–Lagrangian modeling of turbulent liquid–solid slurries in horizontal pipes. Intl J. Multiphase Flow 55, 64–79.CrossRefGoogle Scholar
Capecelatro, J., Desjardins, O. & Fox, R. O. 2014a Numerical study of collisional particle dynamics in cluster-induced turbulence. J. Fluid Mech. 747, R2, 1–13.Google Scholar
Capecelatro, J., Pepiot, P. & Desjardins, O. 2014b Numerical characterization and modeling of particle clustering in wall-bounded vertical risers. Chem. Engng J. 245, 295–310.Google Scholar
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Gèotechnique 29 (1), 47–65.Google Scholar
Desjardins, O., Blanquart, G., Balarac, G. & Pitsch, H. 2008 High order conservative finite difference scheme for variable density low Mach number turbulent flows. J. Comput. Phys. 227 (15), 7125–7159.CrossRefGoogle Scholar
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.CrossRefGoogle Scholar
Einstein, A. 1906 Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 324 (2), 289–306.Google Scholar
Elghobashi, S. & Truesdell, G. C. 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655–700.Google 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.Google Scholar
Février, P., Simonin, O. & Squires, K. D. 2005 Partitioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study. J. Fluid Mech. 533, 1–46.Google Scholar
Fox, R. O. 2007 Introduction and fundamentals of modeling approaches for polydisperse multiphase flows. In Multiphase Reacting Flows: Modelling and Simulation, pp. 1–40. Springer.Google Scholar
Fox, R. O. 2012 Large-eddy-simulation tools for multiphase flows. Annu. Rev. Fluid Mech. 44, 47–76.Google Scholar
Fox, R. O. 2014 On multiphase turbulence models for collisional fluid–particle flows. J. Fluid Mech. 742, 368–424.Google Scholar
Gibilaro, L. G., Gallucci, K., Di Felice, R. & Pagliai, P. 2007 On the apparent viscosity of a fluidized bed. Chem. Engng Sci. 62 (1–2), 294–300.CrossRefGoogle Scholar
Gidaspow, D. 1994 Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic.Google Scholar
Glasser, B. J., Sundaresan, S. & Kevrekidis, I. G. 1998 From bubbles to clusters in fluidized beds. Phys. Rev. Lett. 81, 1849.CrossRefGoogle Scholar
Good, G. H., Ireland, P. J., Bewley, G. P., Bodenschatz, E., Collins, L. R. & Warhaft, Z. 2014 Settling regimes of inertial particles in isotropic turbulence. J. Fluid Mech. 759, R3.CrossRefGoogle Scholar
Grabowski, W. W. & Wang, L. P. 2013 Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293–324.CrossRefGoogle Scholar
He, Y., Deen, N. G., Annaland, M. S. & Kuipers, J. A. M. 2009 Gas–solid turbulent flow in a circulating fluidized bed riser: experimental and numerical study of monodisperse particle systems. Ind. Engng Chem. Res. 48 (17), 8091–8097.Google Scholar
Helland, E., Occelli, R. & Tadrist, L. 2002 Computational study of fluctuating motions and cluster structures in gas–particle flows. Intl J. Multiphase Flow 28 (2), 199–223.Google Scholar
Hoomans, B. P. B., Kuipers, J. A. M., Briels, W. J. & Van Swaaij, W. P. M. 1996 Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: a hard-sphere approach. Chem. Engng Sci. 51 (1), 99–118.Google Scholar
Hrenya, C. M. & Sinclair, J. L. 1997 Effects of particle-phase turbulence in gas–solid flows. AIChE J. 43 (4), 853–869.CrossRefGoogle Scholar
Igci, Y., Andrews, A. T., Sundaresan, S., Pannala, S. & O’Brien, T. 2008 Filtered two-fluid models for fluidized gas–particle suspensions. AIChE J. 54 (6), 1431–1448.CrossRefGoogle Scholar
Iverson, R. M., Reid, M. E. & LaHusen, R. G. 1997 Debris-flow mobilization from landslides. Annu. Rev. Earth Planet. Sci. 25, 85–138.Google Scholar
Jenkins, J. T. & Savage, S. B. 1983 Theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202.Google Scholar
Kennedy, J. F. 1963 The mechanics of dunes and antidunes in erodible-bed channels. J. Fluid Mech. 16, 521–544.Google Scholar
Kidanemariam, A. G. & Uhlmann, M. 2014 Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, R2.Google Scholar
Koch, D. L. & Hill, R. J. 2001 Inertial effects in suspension and porous-media flows. Annu. Rev. Fluid Mech. 33, 619–647.Google Scholar
Lefebvre, A. 1988 Atomization and Sprays, Combustion: An International Series, vol. 1040. Taylor & Francis.Google Scholar
Li, T., Pannala, S. & Shahnam, M. 2014 CFD simulations of circulating fluidized bed risers, Part II, Evaluation of differences between 2D and 3D simulations. Powder Technol. 254, 115–124.Google Scholar
Lin, S. P. & Reitz, R. D. 1998 Drop and spray formation from a liquid jet. Annu. Rev. Fluid Mech. 30, 85–105.CrossRefGoogle Scholar
Liu, H. & Lu, H. 2009 Numerical study on the cluster flow behavior in the riser of circulating fluidized beds. Chem. Engng J. 150 (2), 374–384.Google Scholar
Liu, X. & Xu, X. 2009 Modelling of dense gas–particle flow in a circulating fluidized bed by distinct cluster method (DCM). Powder Technol. 195 (3), 235–244.CrossRefGoogle Scholar
Lun, C. K., Savage, S. B., Jeffrey, D. J. & Chepuriny, N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140, 223–256.Google Scholar
Marchisio, D. L. & Fox, R. O. 2013 Computational Models for Polydisperse Particulate and Multiphase Systems. Cambridge University Press.CrossRefGoogle Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.Google Scholar
McQuarrie, D. A. 1976 Statistical Mechanics. Harper and Row.Google Scholar
Minier, J., Peirano, E. & Chibbarro, S. 2004 PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas–solid flow. Phys. Fluids 16, 2419.Google Scholar
Minier, J. P. & Peirano, E. 2001 The PDF approach to turbulent polydispersed two-phase flows. Phys. Rep. 352 (1), 1–214.Google Scholar
Noymer, P. D. & Glicksman, L. R. 2000 Descent velocities of particle clusters at the wall of a circulating fluidized bed. Chem. Engng Sci. 55 (22), 5283–5289.CrossRefGoogle Scholar
Ozel, A., Fede, P. & Simonin, O. 2013 Development of filtered Euler–Euler two-phase model for circulating fluidised bed: high resolution simulation, formulation and a priori analyses. Intl J. Multiphase Flow 55, 43–63.Google Scholar
Passalacqua, A., Galvin, J. E., Vedula, P., Hrenya, C. M. & Fox, R. O. 2011 A quadrature-based kinetic model for dilute non-isothermal granular flows. Commun. Comput. Phys. 10, 216–252.Google Scholar
Peirano, E. & Leckner, B. 1998 Fundamentals of turbulent gas–solid flows applied to circulating fluidized bed combustion. Prog. Energy Combust. Sci. 24 (4), 259–296.Google Scholar
Pierce, C. D.2001 Progress-variable approach for large-eddy simulation of turbulent combustion. PhD thesis, Stanford University.Google Scholar
Radl, S. & Sundaresan, S. 2014 A drag model for filtered Euler–Lagrange simulations of clustered gas–particle suspensions. Chem. Engng Sci. 117, 416–425.CrossRefGoogle Scholar
Richards, K. J. 1980 The formation of ripples and dunes on an erodible bed. J. Fluid Mech. 99, 597–618.Google Scholar
Shaffer, F., Gopalan, B., Breault, R. W., Cocco, R., Karri, S. B., Hays, R. & Knowlton, T. 2013 High speed imaging of particle flow fields in CFB risers. Powder Technol. 242, 86–99.Google Scholar
Shah, M. T., Utikar, R. P., Tade, M. O., Evans, G. M. & Pareek, V. K. 2013 Effect of a cluster on gas–solid drag from lattice Boltzmann simulations. Chem. Engng Sci. 102, 365–372.Google Scholar
Shaw, R. A. 2003 Particle–turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183–227.Google Scholar
Shuyan, W., Huanpeng, L., Huilin, L., Wentie, L., Ding, J. & Wei, L. 2005 Flow behavior of clusters in a riser simulated by direct simulation Monte Carlo method. Chem. Engng J. 106 (3), 197–211.Google Scholar
Sommerfeld, M. 2001 Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. Intl J. Multiphase Flow 27 (10), 1829–1858.Google Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids 3, 1169.Google Scholar
Subramaniam, S. 2000 Statistical representation of a spray as a point process. Phys. Fluids 12 (10), 2413–2431.CrossRefGoogle Scholar
Sundaram, S. & Collins, L. R. 1997 Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 335, 75–109.Google 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.Google Scholar
Sundaresan, S. 2003 Instabilities in fluidized beds. Annu. Rev. Fluid Mech. 35, 63–88.Google Scholar
Takahashi, T. 1981 Debris flow. Annu. Rev. Fluid Mech. 13, 57–77.Google Scholar
Tanaka, T., Yonemura, S., Kiribayashi, K. & Tsuji, Y. 1996 Cluster formation and particle-induced instability in gas–solid flows predicted by the DSMC method. JSME Intl J. B 39 (2), 239–245.CrossRefGoogle Scholar
Tenneti, S., Garg, R. & Subramaniam, S. 2011 Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres. Intl J. Multiphase Flow 37 (9), 1072–1092.Google Scholar
Tenneti, S. & Subramaniam, S. 2014 Particle-resolved direct numerical simulation for gas–solid flow model development. Annu. Rev. Fluid Mech. 46, 199–230.Google Scholar
Thomas, D. G. 1965 Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles. J. Colloid Sci. 20 (3), 267–277.Google Scholar
Uhlmann, M. & Doychev, T. 2014 Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion. J. Fluid Mech. 752, 310–348.Google 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.Google Scholar
Xu, Y. & Subramaniam, S. 2010 Effect of particle clusters on carrier flow turbulence: a direct numerical simulation study. Flow Turbul. Combust. 85 (3–4), 735–761.Google Scholar
Yang, T. S. & Shy, S. S. 2003 The settling velocity of heavy particles in an aqueous near-isotropic turbulence. Phys. Fluids 15 (4), 868–880.Google Scholar
Zamansky, R., Coletti, F., Massot, M. & Mani, A. 2014 Radiation induces turbulence in particle-laden fluids. Phys. Fluids 26 (7), 071701.CrossRefGoogle Scholar
Zhang, D. Z. & Prosperetti, A. 1994 Averaged equations for inviscid disperse two-phase flow. J. Fluid Mech. 267, 185–220.Google Scholar