(493c) Prediction of Particle Dynamics Using Random Forcing Model in a Turbulent Particle-Laden Shear Flow

Modeling particle-laden flows has its challenges mainly due to two reasons: the complex coupling between the career phase and the dispersed phase, and due to the multi-scale nature of the problem. Due to the decoupled modeling strategy, Fluctuating Force Simulation (FFS) provided an alternative, which is computationally less expensive than traditional Eulerian-Lagrangian particle-laden DNS solvers. In the backdrop of Fluctuating Force Simulation, the collision rules were developed in the event-driven simulation of inter-particle and wall-particle collisions, assuming the collisions to be hard-sphere, perfectly smooth and elastic, which was somewhat stretching the reality. In this article a much more generalized collision rules are developed taking into account the co-efficient of restitution (e) and roughness factor (β) and considering hard-sphere collisions. In rough collisions, particle rotational motion is taken into account. In this light, in order to consider the effect of local fluid vorticity on particle rotation, torque coupling becomes important. The fluctuations in turbulent fluid vorticity result in fluctuating torque acting on particles. Here the fluctuating torque modelling is developed considering the fluctuating torque as Gaussian random white-noise. The strength of the noise is extracted from rotational velocity diffusivity of unladen fluid-phase obtained through Direct Numerical Simulation. The detail investigation of fluid-phase statistics e.g. velocity and vorticity auto-correlation function, the fluid integral time-scale and translational and rotational diffusivities is carried out through unladen horizintal couette flow DNS.

To capture the particle-phase statistics, simulations runs are performed in horizontal turbulent couette flow in the dilute limit by Fluctuating Force Fluctuating Torque Simulation (F3TS) methodology for heavy particles with St ~ 50 (fluid Integral time-scale is based on the half-channel width and wall-velocity). Under the condition of perfectly smooth β=-1.0 and elastic collisions e=1.0, where the effect of fluctuating velocity and the vorticity field of fluid is dominant on particle-dynamics, it is observed that the F3TS model predicts the particle mean translational velocity ( ) and mean rotational velocity () quiet well. Among the fluctuating quantities, a slight deviation from DNS results is observed for the statistics and . The effect of inelasticity (for e=0.9) is found to be only on the decrease in particle cross-stream fluctuating motion observed through and . The model prediction remains similar to that of the ideal collisions. On the other hand, it is observed that in presence of perfectly rough (β=+1.0) and elastic (e=1.0) collisions, the mean particle angular velocity and particle translational and angular velocity fluctuations increase through increase of roughness induced collisions. Further analysis reveals that the effect of fluctuating torque is necessary to predict span-wise and cross-stream particle rotational mean square velocity. It is worth mentioning that the particle phase velocity statistics clearly show that the wall-particle roughness factor is dominant over inter-particle roughness factor as wall-particle collision frequency is higher than inter-particle collision frequency. This is well captured by the model as well. In presence of roughness, the model found out to be performing better than the previous cases in predicting the mean and mean-square translational and angular velocity components.