Dynamics of particle-laden turbulent Couette flow. Part2: Modified fluctuating force model (M-FFS)

TL;DR

This paper investigates the turbulence behavior in particle-laden turbulent Couette flow, revealing a critical volume fraction where turbulence sharply diminishes, and introduces a modified fluctuating force model to better predict particle-fluid interactions in high volume fractions.

Contribution

The paper develops a modified fluctuating force simulation (M-FFS) that accurately captures turbulence attenuation and particle statistics beyond the critical volume fraction, improving upon previous models.

Findings

Turbulence intensity drops sharply beyond a critical particle volume fraction.

Higher collision frequency transfers momentum across directions, flattening velocity profiles.

M-FFS accurately predicts particle statistics in high volume fraction regimes.

Abstract

Two-way coupled DNS simulation of particle-laden turbulent Couette-flow [1], in the volume fraction regime $\phi>10^{-4}$, showed a discontinuous decrease of turbulence intensity beyond a critical volume fraction $\phi_{cr}\sim7.875\times10^{-4}$. Due to the presence of high inertial particles, the drastic reduction of shear production of turbulence is found to be the main cause for the discontinuous attenuation of turbulence. In this article, particle-phase statistics is explored. The two-way coupled DNS reveal that the mean-square velocity profiles in cross-stream (y) and span-wise (z) directions are flat and increase with $\phi$ as the higher frequency of collision helps in transferring streamwise momentum to span-wise and wall-normal directions. Whereas, streamwise fluctuations decrease and tend become flatter with increase in loading. In the regime with $\phi>\phi_{cr}$, the particle velocity fluctuations drive the fluid phase velocity fluctuations. Additionally it is observed that one-way coupled DNS and Fluctuating Force Simulation (FFS) [2] are capable to predict the particle phase statistics with reasonable accuracy in the regime $\phi<\phi_{cr}$ where wall-particle collision time and inter-particle collision time is lesser than viscous relaxation time of the particles. For, $\phi>\phi_{cr}$, a significant error in the prediction from one-way coupled DNS and FFS is observed due to the limitation of FFS in capturing the turbulence attenuation and the change in mean fluid velocity profile. A modified FFS model (M-FFS) is successfully developed in this article with modified mean fluid velocity profile and zero-diffusivity.