369774 Turbulence Modeling of Collisional Gas-Particle Flows in Wall-Bounded Risers
Wall-bounded disperse multiphase flows are common in many environmental and industrial applications, and are often turbulent. Some examples include liquid-solid slurry pipelines, solid deposition in marine flows, and foreign debris in gas turbine engines. In vertical risers of circulating fluidized bed (CFB) reactors, strong coupling between the phases leads to the spontaneous generation of dense clusters that fall at the walls of the reactor, while dilute suspensions of particles rise in the central region. Sustained volume fraction and velocity fluctuations caused by the clusters result in the production of fluid-phase turbulent kinetic energy, referred to as cluster-induced turbulence (CIT). Due to the highly multiscale nature of turbulent gas-particle flows, and the wide range of granular flow regimes that may coexist, from near close-packing in clusters to more dilute conditions in the reactor core, turbulence modeling of wall-bounded CIT remains severely limited.
In a recent work by Fox, the exact Reynolds-average (RA) equations were derived for the particle phase in a collisional gas-particle flow. The equations contain unclosed terms due to nonlinearities in the hydrodynamic model, including new constants that arise from correlations between the particle-phase volume fraction and fluid-phase velocity fluctuations. To assess the accuracy of the turbulence model, and determine modeling constants that appear in the unclosed terms, Eulerian-Lagrangian simulations of statistically stationary three-dimensional gas-solid flows in vertical pipes are performed. Special care is given when exchanging data between the phases to decouple the mesh size from the particle diameter, enabling finer meshes for capturing fluid turbulence. The walls of the reactor are modeled using a conservative immersed boundary scheme that is integrated with the Lagrangian particle tracking framework. Recent work has demonstrated the capability of the numerical framework to capture particle clustering in wall-bounded risers with physical characteristics, including descent velocity and mean and fluctuating particle concentration.
To extract useful information consistent with the Eulerian turbulence model, a separation of length scales must be introduced to separate correlated and uncorrelated granular motion. In particular, a clear distinction must be made between the PA granular temperature, which appears in the kinetic theory constitutive relations, and the particle-phase turbulent kinetic energy, which appears in the turbulent transport coefficients. To accomplish this, an adaptive spatial filter is employed on the particle data with an averaging volume that varies with the local particle-phase volume fraction, allowing direct comparisons to be made with the multiphase turbulence model. Radial profiles from the turbulence model are compared with the three-dimensional Eulerian-Lagrangian results, and details on the nature of the unclosed terms are presented.