A Lagrangian probability-density-function model for turbulent particle-laden channel flow in the dense regime

Modeling particle-laden turbulent flows at high volume fractions requires accounting for the coupling between phases. The latter is often a sensitive point, and proper closure of the exchange and production terms due to the presence of particles is not straightforward. In the present work, a Lagrangian probability-density-function model developed for homogeneous cluster-induced turbulence is extended to a channel flow. The key features are consistent two-way coupling and the decomposition of the particle velocity into spatially correlated and uncorrelated components, which is crucial for dense flows and which allows dealing with collisions from a statistical point of view. A numerical scheme for the coupled solution of the stochastic differential equations for the particles and a Reynolds-stress model for the fluid is developed. Tests with tracer particles without two-way coupling are done to assess the validity and the consistency of the numerical scheme. Finally, two sets of numerical simulations with particles with different diameters in a turbulent channel flow at a shear Reynolds of R e τ = 300 are reported. The effect of two-way coupling by varying the mass loading of the dispersed phase in the mass-loading range φ = 0–2 is analyzed, and the results are compared to previous Eulerian–Lagrangian and Eulerian–Eulerian direct-numerical simulation (DNS) studies. Mean velocities and turbulent kinetic energy show good agreement with DNS, especially regarding the trend with respect to mass loading. Consistent with prior work, increased mass loading causes a drastic reduction of turbulent kinetic energy in the range φ = 0–2.