A Statistical Analysis Towards Modelling the Fluctuating Torque on Particles in Particle-laden Turbulent Shear Flow

TL;DR

This study investigates the rotational dynamics of inertial particles in turbulent shear flow, proposing a Langevin-type model for fluctuating torque based on DNS data and statistical analysis.

Contribution

It introduces a novel approach to model particle rotational acceleration using a Gaussian white noise Langevin model informed by DNS-derived fluid angular velocity correlations.

Findings

Particle rotational acceleration distribution can be modeled as Gaussian white noise.

The model's strength is estimated from fluid angular velocity correlations.

The approach improves understanding of particle-fluid rotational interactions.

Abstract

Dynamics of the particle phase in a particle laden turbulent flow is highly influenced by the fluctuating velocity and vorticity field of the fluid phase. The present work mainly focuses on exploring the possibility of applying a Langevin type of random torque model to predict the rotational dynamics of the particle phase. Towards this objective, direct numerical simulations (DNS) have been carried out for particle laden turbulent shear flow with Reynolds number, $Re_\delta=750$ in presence of sub-Kolmogorov sized inertial particles (Stokes number >>1). The inter-particle and wall-particle interactions have also been considered to be elastic. From the particle equation of rotational motion, we arrive at the expression where the fluctuating angular acceleration fluctuation $\alpha'_i$ of the particle is expressed as the ratio of a linear combination of fluctuating rotational velocities of particle $\omega'_i$ and fluid angular velocity $\Omega'_i$ to the particle rotational relaxation time $\tau_r$. The analysis was done using p.d.f plots and Jensen-Shannon Divergence based method to assess the similarity of the particle net rotational acceleration distribution $f(\alpha'_i)$, with (i) the distributions of particle acceleration component arising from fluctuating fluid angular velocity computed in the particle-Largrangian frame $f(\Omega'_i/\tau_r)_{pl}$, (ii) fluctuating particle angular velocity $f(\omega'_i/\tau_r)_{pl}$, and (iii) the fluid angular velocity $(\Omega'_i/\tau_r)_{e}$, computed in the fluid Eulerian grids. The analysis leads to the conclusion that $f(\alpha'_i)$ can be modeled with a Gaussian white noise using a pre-estimated strength which can be calculated from the temporal correlation of $(\Omega'_i/\tau_r)_{e}$.