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

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 † Email address for correspondence: jsc359@cornell.edu On fluid-particle dynamics in cluster-induced turbulence 579 to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.

Experimental data for code validation: Horizontal air jets in a semicircular fluidized bed of Geldart Group D particles

“…43 Used extensively in other fields, 44,45 a verification and validation (V&V) framework including UQ has only recently emerged within the gas-solid multiphase CFD community. 60,61 Thus, by controlling the particle count (N p < 10 5 in this set of experiments, which is comparable to previous validation studies in more idealized systems), we ensure efficient turnover and acceptable expense in computational resources for obtaining simulation results. This system is widely used in engineering processes to aid fluidization 53,54 and solid mixing, 55 to introduce gas reactants 56 or to perform particle attrition.…”

“…[57][58][59] While similar complex experiments have been widely reported, such systems typically contain on the order of N p 10 10 particles, far exceeding the current capability of DEM which only recently has been able to achieve N p 10 7 to 10 8 particles using state-of-the-art computers and parallelization. 60,61 Thus, by controlling the particle count (N p < 10 5 in this set of experiments, which is comparable to previous validation studies in more idealized systems), we ensure efficient turnover and acceptable expense in computational resources for obtaining simulation results. The bed pressure drop is reported for each operating condition as a time-averaged mean value and standard deviation.…”

Scale‐dependent nonequilibrium features in a bubbling fluidized bed

“…27,66 Moreover, it is a critical parameter in the kinetic theory of granular flow. To further understand their dynamic behavior and in particular the transition between them, it is necessary to investigate the different spatial configurations of particles in these two phases.…”

“…Breault et al 25 proposed a time scale criterion according to the analogy between molecular gases and fluidized particles to tell apart the turbulent kinetic energy of particles from the granular temperature in a riser. 27 Although these definitions or criteria have been proposed, very little is known about quantitative properties of dynamical heterogeneity in a gas-fluidized bed with respect to the time and length scales, e.g., the scale dependence of non-Gaussian velocity distribution and the other macroscopic variables. 27 Although these definitions or criteria have been proposed, very little is known about quantitative properties of dynamical heterogeneity in a gas-fluidized bed with respect to the time and length scales, e.g., the scale dependence of non-Gaussian velocity distribution and the other macroscopic variables.…”

Turbophoresis in forced inhomogeneous turbulence

“…Clustering of particles is also found in simulations where the feedback from the particles to the flow is included, see, e.g., refs. [33,34]. In those cases, gravity may also play an important role, i.e., horizontal and vertical pipes may show different clustering phenomena, see e.g., refs.…”