A novel LES modeling approach for turbulence modulation in particle-laden flows without particles*

In the present work, first, we have performed direct numerical simulations to capture the fluid phase in the Eulerian framework, and the particles are tracked with the Lagrangian approach. The simulations are performed for bulk Reynolds numbers for 3300 and 5600 for a vertical channel flow. The intensity of fluid fluctuations decreases steadily up to a volume fraction, after which a sudden collapse in the fluid fluctuations is observed. An increase in the anisotropy across the fluid fluctuations is observed with an increase in particle volume loading. The local isotropy of small scales and large scales is analyzed across the channel width. It is observed that local isotropy decreases in the near-wall and channel center region with mass loading, which affects the Kolmogorov constant. The Kolmogorov constant is explored via compensated spectra and second-order velocity structure function for particle-laden cases. It is found that the Kolmogorov constant decreases in the near-wall and channel center region, which depicts the particle feedback effect on the fluid phase. From the assumption of local equilibrium, the eddy viscosity in the Smagorinsky model includes the Kolmogorov constant via Smagorinksy coefficient. A decrease in the Kolmogorov constant results in an increase in the Smagorinksy coefficient. Thus, the simulations are performed with the Smagorinksy model with an increase in the Smagorinsky coefficient to predict the turbulence attenuation without considering the particle phase. The simulations capture the decrease in Reynolds stress, wall-normal and spanwise fluctuations, and the sudden collapse in fluid fluctuations similar to the particle-laden cases. Therefore, the present work demonstrates that a priori knowledge of the variation of eddy viscosity may predict the fluid phase dynamics without considering the particle phase simultaneously.