Turbulent dispersion force -- physics, model derivation and evaluation --

Turbulence dispersion has a significant dispersion effect on the migration of bubbles in a vertical flow. Based on a double averaging approach and by adopting the Favre averged velocity, we developed the Favre Averaged Drag (FAD) turbulent dispersion force model for Eulerian simulations of multiphase flows. The model formulation was originally derived from the instant Eulerian model equations as a result of the correlation between the interphase drag and the volume fractions. In this work, a new model derivation from the two-way coupled Lagrangian formulation is provided. This derivation explains the physical mechanism and makes the sense of the double averaging approach straightford. Moreover, the new derivation provides a theoretical foundation for applying the FAD model to the Lagrangian solver, which will significantly increase the computational efficiency.

We also provide a systematic model evaluation based on numerical simulations of bubbly flows in a vertical pipe using both mono- and poly-dispersed flow models. The numerical results for the radial distribution of the gas concentration were compared with the experimental data measured by using the wire-mesh sensor technique. The results confirm that the bubble size and the liquid flow Reynolds number have a strong effect on the turbulent dispersion as is shown in the model derivation.