Diffusion-inertia Model for Two-phase Turbulent Flows and its Implementation into OpenFOAM

The existing strategies of modelling turbulent two-phase flows can be subdivided into two groups depending on the Lagrangian tracking and Eulerian continuum approaches for handling the particulate phase. In the framework of the Lagrangian method, the particles are assumed to encounter a series of turbulent eddies randomly, and the macroscopic particle properties are determined by solving stochastic equations along separate trajectories. As a consequence, such a method requires tracking of a very large number of particle trajectories to achieve a statistically invariant solution. Thus, this technique, especially when coupling with DNS or LES for the computation of fluid turbulence, provides a very useful research tool of investigating particle-laden flows, but it can be too expensive for engineering calculations. The Eulerian method deals with the particulate phase in much the same manner as with the carrier fluid phase. Therefore, the two-fluid modelling technique is computationally very efficient, as it allows us to use the governing equations of the same type for both phases. In addition, the description of fine particles does not cause great difficulties because the problem of the transport of particles with vanishing response times reduces to the turbulent diffusion of a passive impurity. Overall, the Lagrangian tracking and Eulerian continuum modelling methods complement each other. Each method has its advantages and, consequently, its own field of application. The Lagrangian method is more applicable for the nonequilibrium flows (e.g., high-inertia particles, dilute dispersed media), while the Eulerian method is preferable for the flows which are close to equilibrium (e.g., low-inertia particles, dense dispersed media). Thereby the particulate phase simultaneously combines the properties of continuum medium and discrete particles.