Particles-turbulence interaction in stationary, homogeneous, isotropic turbulence

A physical model for the dynamics of a dispersion of solid spherical particles in an incompressible viscous fluid is outlined and used to calculate the turbulence modulation in a stationary, homogeneous and isotropic turbulent flow with particles. Starting from a postulated fluid turbulence spectrum in the absence of particles, the physical model predicts the corresponding fluid turbulence spectrum in the presence of particles and the particles turbulence spectrum as function of frequency and wavenumber. There are two versions of the model. The first one uses a point-force approximation for the particles and takes into account the hydrodynamic interaction between the particles. The second version accounts for the detailed flow around the (finite-diameter) particles, but does not consider their hydrodynamic interaction. The spectra, calculated with the two versions, are used to determine the turbulence intensity of the fluid and particles as function of three relevant dimensionless groups. It is found that in general the differences between the results of the point-particle model and the finite-diameter-particle model are significant. So one has to be careful with point-particle models. The effect of the hydrodynamic interaction between the particles is up to a volume fraction of 0.1 still mostly negligible.