Forcing homogeneous turbulence in direct numerical simulation of particulate flow with interface resolution and gravity

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 [“An examination of forcing in direct numerical simulations of turbulence,” 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 Reλ = 65, small density ratio ρp/ρf = 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.