Turbulent dispersion of bubbles in poly-dispersed gas-liquid flows in a vertical pipe

The turbulence of the liquid phase has a signi cant dispersion e ect on the migration of bubbles in a vertical ow. Based on a double averaging approach and by adopting the Favre averaged velocity, a generalized model, called the Favre Averaged Drag (FAD) Model, was developed for the turbulent dispersion force for Eulerian simulations of multiphase ows [Burns et al., 2004]. The model formulation was originally derived from the instant Eulerian model equations as a result of the correlation between the inter phase drag and the volume fractions. In this work, a new model derivation from the two-way coupled Lagrangian formulation is provided. This derivation makes the sense of the double averaging approach straightforward. Moreover, the new derivation provides a theoretical foundation for applying the FAD model to the Lagrangian solver, which will signi cantly increase the computational e ciency. We also provide validation and evaluation for this model by numerical and experimental investigations of bubbly ows in a vertical pipe. The experimental data were obtained by using the wire-mesh sensor technique. The computations were carried out by applying poly-dispersed models. The emphasis is to examine the model applicability under various ow conditions including bubbly ows with a wall peak and a core peak of the gas volume fraction, ows in the transition region between them, and in the nely dispersed ow regime. The e ect of the drag force model on the turbulent dispersion force was also examined.