Particles-turbulence interaction in stationary, homogeneous, isotropic turbulence (original) (raw)

A physical model for the dynamics of a dispersion of solid spherical particles in an incompressible viscous¯uid is outlined and used to calculate the turbulence modulation in a stationary, homogeneous and isotropic turbulent¯ow with particles. Starting from a postulated¯uid turbulence spectrum in the absence of particles, the physical model predicts the corresponding¯uid 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 ®rst 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¯ow around the (®nite-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¯uid and particles as function of three relevant dimensionless groups. It is found that in general the dierences between the results of the point-particle model and the ®nite-diameter-particle model are signi®cant. So one has to be careful with point-particle models. The eect of the hydrodynamic interaction between the particles is up to a volume fraction of 0.1 still mostly negligible.