Finite element simulation of turbulent bubbly flows in gas-liquid reactors

A mathematical model for turbulent gas-liquid flows is presented. It is shown that bubble-induced buoyancy resembles natural convection and can be readily incorporated into an incompressible flow solver by using an analog of the Boussinesq approximation. Extra transport equations are introduced to describe the evolution of the gas holdup and compute the turbulent eddy viscosity in the framework of a generalized k − ε model. A robust solution strategy based on nested iterations is proposed for the numerical treatment of the resulting PDE system. The incompressible Navier-Stokes equations are solved by a discrete projection scheme from the family of Pressure Schur Complement methods. High-resolution finite element schemes designed on the basis of algebraic flux correction are employed for the discretization of convective terms. Numerical results for prototypical gas-liquid reactor configurations illustrate the performance of the developed simulation tools.