Forcing homogeneous turbulence in DNS of particulate flow with interface resolution and gravity

TL;DR

This paper develops a method to generate homogeneous turbulence in DNS of settling particles under gravity, using a specific forcing scheme and immersed-boundary method, and analyzes the effects of gravity on particle dynamics.

Contribution

It introduces a turbulence forcing scheme that allows for physical-space evaluation and investigates the impact of gravity on particle settling and flow statistics.

Findings

Results at zero gravity match experimental and numerical data.

Gravity reduces average settling velocity and alters acceleration statistics.

Lagrangian auto-correlations are affected by gravity.

Abstract

We consider the case of finite-size spherical particles which are settling under gravity in a homogeneous turbulent background flow. Turbulence is forced with the aid of the random forcing method of Eswaran and Pope [Comput. Fluids, 16(3):257-278, 1988], while the solid particles are represented with an immersed-boundary method. The forcing scheme is used to generate isotropic turbulence in vertically elongated boxes in order to warrant better decorrelation of the Lagrangian signals in the direction of gravity. Since only a limited number of Fourier modes are forced, it is possible to evaluate the forcing field directly in physical space, thereby avoiding full-size transforms. The budget of box-averaged kinetic energy is derived from the forced momentum equations. Medium-sized simulations for dilute suspensions at low Taylor-scale Reynolds number $Re_\lambda=65$, small density ratio $\rho_p/\rho_f=1.5$ and for two Galileo numbers $Ga=0$ and 120 are carried out over long time intervals in order to exclude the possibility of slow divergence. It is shown that the results at zero gravity are fully consistent with previous experimental measurements and available numerical reference data. Specific features of the finite-gravity case are discussed with respect to a reduction of the average settling velocity, the acceleration statistics and the Lagrangian auto-correlations.