Turbulent wall-bounded flows exhibit a wide range of regimes with significant interaction between scales. The fluid dynamics associated with single-phase channel flows is predominantly characterized by the Reynolds number. Meanwhile, vastly different behaviour exists in particle-laden channel flows, even at a fixed Reynolds number. Vertical turbulent channel flows seeded with a low concentration of inertial particles are known to exhibit segregation in the particle distribution without significant modification to the underlying turbulent kinetic energy (TKE). At moderate (but still low) concentrations, enhancement or attenuation of fluid-phase TKE results from increased dissipation and wakes past individual particles. Recent studies have shown that denser suspensions significantly alter the two-phase dynamics, where the majority of TKE is generated by interphase coupling (i.e.  drag) between the carrier gas and clusters of particles that fall near the channel wall. In the present study, a series of simulations of vertical particle-laden channel flows with increasing mass loading is conducted to analyse the transition from the dilute limit where classical mean-shear production is primarily responsible for generating fluid-phase TKE to high-mass-loading suspensions dominated by drag production. Eulerian–Lagrangian simulations are performed for a wide range of particle loadings at two values of the Stokes number, and the corresponding two-phase energy balances are reported to identify the mechanisms responsible for the observed transition.

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.