Skip to main content Accessibility help
×
Home

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

  • Jesse Capecelatro (a1), Olivier Desjardins (a1) and Rodney O. Fox (a2) (a3)

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.

Copyright

Corresponding author

Email address for correspondence: jsc359@cornell.edu

References

Hide All
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, 151186.
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, 77105.
Anderson, T. B. & Jackson, R. 1967 Fluid mechanical description of fluidized beds. Equations of motion. Ind. Engng Chem. Fundam. 6 (4), 527539.
Arya, S. P. 1999 Air Pollution Meteorology and Dispersion. Oxford University Press.
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.
Basu, P. & Fraser, S. A. 1991 Circulating Fluidized Bed Boilers: Design and Operations. Butterworth-Heinemann.
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), 489501.
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), 511525.
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon.
Bosse, T., Kleiser, L. & Meiburg, E. 2006 Small particles in homogeneous turbulence: settling velocity enhancement by two-way coupling. Phys. Fluids 18 (2), 027102.
Bridgewater, A. V. 1995 The technical and economical feasibility of biomass gasification for power generation. Fuel 74 (5), 631653.
Briley, W. R. & McDonald, H. 1977 Solution of the multidimensional compressible Navier–Stokes equations by a generalized implicit method. J. Comput. Phys. 24 (4), 372397.
Capecelatro, J. & Desjardins, O. 2013a An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 131.
Capecelatro, J. & Desjardins, O. 2013b Eulerian–Lagrangian modeling of turbulent liquid–solid slurries in horizontal pipes. Intl J. Multiphase Flow 55, 6479.
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.
Capecelatro, J., Pepiot, P. & Desjardins, O. 2014b Numerical characterization and modeling of particle clustering in wall-bounded vertical risers. Chem. Engng J. 245, 295310.
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Gèotechnique 29 (1), 4765.
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), 71257159.
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169209.
Einstein, A. 1906 Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 324 (2), 289306.
Elghobashi, S. & Truesdell, G. C. 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655700.
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315329.
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, 146.
Fox, R. O. 2007 Introduction and fundamentals of modeling approaches for polydisperse multiphase flows. In Multiphase Reacting Flows: Modelling and Simulation, pp. 140. Springer.
Fox, R. O. 2012 Large-eddy-simulation tools for multiphase flows. Annu. Rev. Fluid Mech. 44, 4776.
Fox, R. O. 2014 On multiphase turbulence models for collisional fluid–particle flows. J. Fluid Mech. 742, 368424.
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), 294300.
Gidaspow, D. 1994 Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic.
Glasser, B. J., Sundaresan, S. & Kevrekidis, I. G. 1998 From bubbles to clusters in fluidized beds. Phys. Rev. Lett. 81, 1849.
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.
Grabowski, W. W. & Wang, L. P. 2013 Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293324.
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), 80918097.
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), 199223.
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), 99118.
Hrenya, C. M. & Sinclair, J. L. 1997 Effects of particle-phase turbulence in gas–solid flows. AIChE J. 43 (4), 853869.
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), 14311448.
Iverson, R. M., Reid, M. E. & LaHusen, R. G. 1997 Debris-flow mobilization from landslides. Annu. Rev. Earth Planet. Sci. 25, 85138.
Jenkins, J. T. & Savage, S. B. 1983 Theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187202.
Kennedy, J. F. 1963 The mechanics of dunes and antidunes in erodible-bed channels. J. Fluid Mech. 16, 521544.
Kidanemariam, A. G. & Uhlmann, M. 2014 Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, R2.
Koch, D. L. & Hill, R. J. 2001 Inertial effects in suspension and porous-media flows. Annu. Rev. Fluid Mech. 33, 619647.
Lefebvre, A. 1988 Atomization and Sprays, Combustion: An International Series, vol. 1040. Taylor & Francis.
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, 115124.
Lin, S. P. & Reitz, R. D. 1998 Drop and spray formation from a liquid jet. Annu. Rev. Fluid Mech. 30, 85105.
Liu, H. & Lu, H. 2009 Numerical study on the cluster flow behavior in the riser of circulating fluidized beds. Chem. Engng J. 150 (2), 374384.
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), 235244.
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, 223256.
Marchisio, D. L. & Fox, R. O. 2013 Computational Models for Polydisperse Particulate and Multiphase Systems. Cambridge University Press.
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441465.
McQuarrie, D. A. 1976 Statistical Mechanics. Harper and Row.
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.
Minier, J. P. & Peirano, E. 2001 The PDF approach to turbulent polydispersed two-phase flows. Phys. Rep. 352 (1), 1214.
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), 52835289.
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, 4363.
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, 216252.
Peirano, E. & Leckner, B. 1998 Fundamentals of turbulent gas–solid flows applied to circulating fluidized bed combustion. Prog. Energy Combust. Sci. 24 (4), 259296.
Pierce, C. D.2001 Progress-variable approach for large-eddy simulation of turbulent combustion. PhD thesis, Stanford University.
Radl, S. & Sundaresan, S. 2014 A drag model for filtered Euler–Lagrange simulations of clustered gas–particle suspensions. Chem. Engng Sci. 117, 416425.
Richards, K. J. 1980 The formation of ripples and dunes on an erodible bed. J. Fluid Mech. 99, 597618.
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, 8699.
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, 365372.
Shaw, R. A. 2003 Particle–turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183227.
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), 197211.
Sommerfeld, M. 2001 Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. Intl J. Multiphase Flow 27 (10), 18291858.
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids 3, 1169.
Subramaniam, S. 2000 Statistical representation of a spray as a point process. Phys. Fluids 12 (10), 24132431.
Sundaram, S. & Collins, L. R. 1997 Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 335, 75109.
Sundaram, S. & Collins, L. R. 1999 A numerical study of the modulation of isotropic turbulence by suspended particles. J. Fluid Mech. 379, 105143.
Sundaresan, S. 2003 Instabilities in fluidized beds. Annu. Rev. Fluid Mech. 35, 6388.
Takahashi, T. 1981 Debris flow. Annu. Rev. Fluid Mech. 13, 5777.
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), 239245.
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), 10721092.
Tenneti, S. & Subramaniam, S. 2014 Particle-resolved direct numerical simulation for gas–solid flow model development. Annu. Rev. Fluid Mech. 46, 199230.
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), 267277.
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, 310348.
Wang, L. P. & Maxey, M. R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 2768.
Xu, Y. & Subramaniam, S. 2010 Effect of particle clusters on carrier flow turbulence: a direct numerical simulation study. Flow Turbul. Combust. 85 (3–4), 735761.
Yang, T. S. & Shy, S. S. 2003 The settling velocity of heavy particles in an aqueous near-isotropic turbulence. Phys. Fluids 15 (4), 868880.
Zamansky, R., Coletti, F., Massot, M. & Mani, A. 2014 Radiation induces turbulence in particle-laden fluids. Phys. Fluids 26 (7), 071701.
Zhang, D. Z. & Prosperetti, A. 1994 Averaged equations for inviscid disperse two-phase flow. J. Fluid Mech. 267, 185220.
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