A statistical analysis of velocity and acceleration fluctuations of inertial particles in particle-laden turbulent Couette flow

Abstract

Dynamics of the particle phase in a particle-laden turbulent flow is strongly influenced by the fluctuating velocity and vorticity field of the fluid phase. The present work mainly focuses on exploring the statistics of velocity and acceleration of the particle phase in a particle-laden turbulent Couette flow. Direct numerical simulations have been performed for particle-laden turbulent Couette flow with two different Reynolds numbers, Reδ=750 and 1300, in the presence of sub-Kolmogorov sized inertial particles for multiple Stokes numbers (Stokes number ≫1). The inter-particle and wall-particle interactions have also been considered to be elastic. We report the distribution functions for the linear and rotational velocities and accelerations in the presence of particle roughness. From the particle equation of rotational motion, we arrive at the expression where the fluctuating angular acceleration αi′ of the particle is expressed as the ratio of a linear combination of fluctuating rotational velocities of particle (ωi′) and fluid angular velocity (Ωi′) to the particle rotational relaxation time τr. The analysis is done using probability density function plots and Jensen–Shannon divergence-based method to assess the similarity between the particle net rotational acceleration distributions f(αi′), with (i) the distributions of particle acceleration component arises from fluctuating fluid angular velocity computed in the particle-Lagrangian frame f((Ω′i/τr)pl), (ii) fluctuating particle angular velocity f(ω′i/τr), and (iii) the fluid angular velocity f((Ω′i/τr)e) computed in the fluid Eulerian grids. The analysis leads to the conclusion that for a wide range of Reynolds and Stokes numbers, f(αi′) can be represented with a Gaussian white noise with a pre-estimated strength that can be calculated from the temporal decorrelation correlation of fluid-phase angular velocity fluctuations at Eulerian grid (Ω′i/τr)e.