A two-way coupled model of particle-laden turbulence

A model for turbulent suspensions involving two-way coupling between a liquid carrier phase and a solid dispersed phase is presented. Closure relations are obtained from particle kinetic theory, with both drag and virtual mass effects taken into account. It is shown that the feedback on the flow due to the particles mainly depends on the particle concentration, the characteristic Stokes numbers, and the density ratio between the particle and liquid phases. Over a broad parameter range, we find that drag coupling gives turbulence damping and an increased streaming velocity. Added mass coupling has the opposite effect. Some of the model predictions are compared with data given in the literature, and with PIV experimental data. It is found that the model is generally consistent with experiments; in particular, when it comes to the observed turbulence damping and drag reduction effects. The model can be used as a stand-alone tool to calculate turbulent stresses, mean velocities and concentration profiles of both phases. Alternatively, it can serve as basis for a reduced parametric model of particle feedback effects on; for example, the eddy viscosity, and thus the pressure drop and superficial speed.