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, 151–185.

Anderson, T. B. & Jackson, R.
1967
Fluid mechanical description of fluidized beds. Equations of motion. Ind. Engng Chem. Fundam.
6 (4), 527–539.

Balachandar, S. & Eaton, J. K.
2010
Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech.
42, 111–133.

Capecelatro, J. & Desjardins, O.
2013
An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys.
238, 1–31.

Capecelatro, J. & Desjardins, O.
2015
Mass loading effects on turbulence modulation by particle clustering in dilute and moderately dilute channel flows. J. Fluids Engng
137, 1–8.

Capecelatro, J., Desjardins, O. & Fox, R. O.
2014a
Numerical study of collisional particle dynamics in cluster-induced turbulence. J. Fluid Mech.
747, R2.

Capecelatro, J., Desjardins, O. & Fox, R. O.
2015
On fluid–particle dynamics in fully developed cluster-induced turbulence. J. Fluid Mech.
780, 578–635.

Capecelatro, J., Desjardins, O. & Fox, R. O.
2016a
Strongly coupled fluid-particle flows in vertical channels. I. Reynolds-averaged two-phase statistics. Phys. Fluids
28, 033306.

Capecelatro, J., Desjardins, O. & Fox, R. O.
2016b
Strongly coupled fluid-particle flows in vertical channels. II. Turbulence modeling. Phys. Fluids
28, 033307.

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.

Cundall, P. A. & Strack, O. D. L.
1979
A discrete numerical model for granular assemblies. Geotechnique
29 (1), 47–65.

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.

Dritselis, C. D.
2016
Direct numerical simulation of particle-laden turbulent channel flows with two-and four-way coupling effects: budgets of Reynolds stress and streamwise enstrophy. Fluid Dyn. Res.
48 (1), 015507.

Fessler, J. R., Kulick, J. D. & Eaton, J. K.
1994
Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids
6 (11), 3742–3749.

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.

Fox, R. O.
2014
On multiphase turbulence models for collisional fluid–particle flows. J. Fluid Mech.
742, 368–424.

García-Villalba, M., Kidanemariam, A. G. & Uhlmann, M.
2012
DNS of vertical plane channel flow with finite-size particles: voronoi analysis, acceleration statistics and particle-conditioned averaging. Intl J. Multiphase Flow
46, 54–74.

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.

Glasser, B. J., Sundaresan, S. & Kevrekidis, I. G.
1998
From bubbles to clusters in fluidized beds. Phys. Rev. Lett.
81, 1849.

Gualtieri, P., Battista, F. & Casciola, C. M.
2017
Turbulence modulation in heavy-loaded suspensions of tiny particles. Phys. Rev. Fluids
2 (3), 034304.

Gualtieri, P., Picano, F., Sardina, G. & Casciola, C. M.
2013
Clustering and turbulence modulation in particle-laden shear flows. J. Fluid Mech.
715, 134–162.

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.

Jenkins, J. T. & Savage, S. B.
1983
A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech.
130, 187–202.

Kim, J., Moin, P. & Moser, R.
1987
Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech.
177, 133–166.

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.

Lashgari, I., Picano, F., Breugem, W. P. & Brandt, L.
2016
Channel flow of rigid sphere suspensions: particle dynamics in the inertial regime. Intl J. Multiphase Flow
78, 12–24.

Lashgari, I., Picano, F., Costa, P., Breugem, W. P. & Brandt, L.
2017
Turbulent channel flow of a dense binary mixture of rigid particles. J. Fluid Mech.
818, 623–645.

Marchioli, C. & Soldati, A.
2002
Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech.
468, 283–315.

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.

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 (1), 216–252.

Picano, F., Breugem, W. P. & Brandt, L.
2015
Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech.
764, 463–487.

Picciotto, M., Marchioli, C. & Soldati, A.
2005
Characterization of near-wall accumulation regions for inertial particles in turbulent boundary layers. Phys. Fluids
17, 098101.

Pitton, E., Marchioli, C., Lavezzo, V., Soldati, A. & Toschi, F.
2012
Anisotropy in pair dispersion of inertial particles in turbulent channel flow. Phys. Fluids
24 (7), 073305.

Pope, S. B.
2000
Turbulent Flows. Cambridge University Press.

Richter, D. H.
2015
Turbulence modification by inertial particles and its influence on the spectral energy budget in planar Couette flow. Phys. Fluids
27 (6), 063304.

Rouson, D. W. I. & Eaton, J. K.
2001
On the preferential concentration of solid particles in turbulent channel flow. J. Fluid Mech.
428, 149–169.

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, 46–62.

Tanaka, M.
2017
Effect of gravity on the development of homogeneous shear turbulence laden with finite-size particles. J. Turbul.
18, 1–36.

Tenneti, S., Garg, R., Hrenya, C. M., Fox, R. O. & Subramaniam, S.
2010
Direct numerical simulation of gas–solid suspensions at moderate Reynolds number: quantifying the coupling between hydrodynamic forces and particle velocity fluctuations. Powder Technol.
203 (1), 57–69.

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.

Vreman, A. W.
2007
Turbulence characteristics of particle-laden pipe flow. J. Fluid Mech.
584, 235–279.

Vreman, B., Geurts, B. J., Deen, N. G., Kuipers, J. A. M. & Kuerten, J. G. M.
2009
Two-and four-way coupled Euler–Lagrangian large-eddy simulation of turbulent particle-laden channel flow.. Flow Turbul. Combust.
82 (1), 47–71.

Wang, Q. & Squires, K. D.
1996
Large eddy simulation of particle-laden turbulent channel flow. Phys. Fluids
8, 1207–1223.

Yamamoto, Y., Potthoff, M., Tanaka, T., Kajishima, T. & Tsuji, Y.
2001
Large-eddy simulation of turbulent gas–particle flow in a vertical channel: effect of considering inter-particle collisions. J. Fluid Mech.
442, 303–334.

Zhao, L., Andersson, H. I. & Gillissen, J. J.
2013
Interphasial energy transfer and particle dissipation in particle-laden wall turbulence. J. Fluid Mech.
715, 32–59.