**4. Computational fluid dynamics (CFD)**

Computational Fluid Dynamics (CFD) is a technique which uses conservation principles and rigorous equations of fluid flow (Navier-Stokes) along with specialized turbulence models (k-, k-, SST among others). These models are more accurate and fundamentally more acceptable than empirical ones. The empirical models are approximations that assemble different phenomena to remove a number of unknown parameters. For this reason, these models are not reliable and therefore should not be generalized.

The CFD models can be divided into two groups: the *Eulerian-Eulerian* model in which the gas and solid phases are considered as two interpenetrating continuum flows; and the *Eulerian-Lagrangian* model that consider the gas as a fluid phase and the solids as discrete phase. The *Eulerian-Lagrangian* model calculates the trajectory of each individual particle using Newton's second law. The interaction between particles can be described by the potential energy or the dynamic of collisions. This method has the advantage of knowing exactly the particle trajectory and the system variables. However, this requires high computational effort, higher yet when gas and solid velocity fields are coupled.
