Turbulence modulation by settling inertial aerosols in Eulerian-Eulerian and Eulerian-Lagrangian simulations of homogeneously sheared turbulence

Settling inertial aerosols dispersed at high enough concentration modulate the structure of the suspending turbulent flow. The present study addresses this modulation in a canonical flow, which is homogeneously sheared turbulence (HST). Eulerian-Eulerian (EE) and Eulerian-Lagrangian (EL) simulations are conducted in the semidilute regime, i.e., such that the particulate phase is sufficiently dilute to neglect particle-particle interaction but sufficiently concentrated to be strongly coupled with the carrier flow. Four cases are considered for which the Stokes number based on the Kolmogorov timescale is St(eta) = 0.06 or 0.19 and mass loading is M = 0.125 or 0.5. Turbulence is initialized with a Taylor microscale Reynolds number Re-lambda,Re-0 = 29 and is strongly sheared, resulting in a shear number S-0* = 27. Simulations of the suspension with St(eta) = 0.06 and M = 0.125 show no turbulence modification compared with single-phase HST. However, when the mass loading is increased to M = 0.5 the aerosols cluster, despite their small inertia, and measurably modify the carrier flow. These aerosols enhance turbulence in the carrier phase, causing an increase of the growth rates of the turbulent kinetic energy (TKE) and dissipation rate among other effects. The opposite behavior emerges when the Stokes number is St(eta) = 0.19. These aerosols cause the attenuation of turbulence by reducing the growth rates of the TKE and dissipation rate in HST. This attenuation is weaker for the larger mass loading case M = 0.5 due to stronger forcing by the particles on the gas in the gravity direction. Turbulence modulation in the EE simulation is verified to hold excellent agreement with EL simulations. In the former approach, simulating a few integral lengths of turbulence leads to a large number of Lagrangian particles, up to 1.7 x 10(9) particles in the present work. Eulerian-Eulerian simulations are performed with a positivity-preserving kinetic-based formulation that assumes an anisotropic-Maxwellian distribution of the subgrid particle velocity probability distribution function. The excellent agreement with EL simulations shows that this EE simulation strategy is a robust and predictive method in the semidilute regime.