The effects of back-reaction on turbulence modulation in shear flows: a new exact regularized point-particle method

Particles advected by turbulent flows spread non uniformly and form small scale aggregates known as clusters where their local concentration is much higher than it is in nearby rarefaction regions. Recently it has been shown that the addition of a mean flow, through its large scale anisotropy, induces a preferential orientation of the clusters whose directionality can even increase in the smallest scales. Such finding opens new issues in presence of large mass loads, when the momentum exchange between the two phases becomes significant and the back-reaction of the particles on the carrier flow cannot be neglected. These aspects are addressed by direct numerical simulations data of particle laden homogeneous shear flows in the two-way coupling regime. Particles with Stokes number of order one induce an energy depletion of the classical inertial scales and the amplitude increase of the smallest ones where the particle back-reaction pumps energy into the turbulent eddies. We find that increased mass loads results in a broadening of the energy co-spectrum extending the range of scales driven by anisotropic production mechanisms. Such results are obtained in the context of the classical "particle in cell" method. To go beyond this approach we propose a new methodology to model particle laden two phase flows. The method is based on the exact unsteady Stokes solution around a point-particle and is intended to provide a physically consistent picture of the momentum exchange between the carrier and disperse phase.