Finite element discretization and iterative solution techniquea for multiphase flows in gas-liquid reactors

A mathematical model for gas-liquid flows subject to mass transfer and chemical reactions is presented. It is shown that bubble-induced buoyancy resembles natural convection and can readily be incorporated into an incompressible flow solver by using an analog of the Boussinesq approximation. Extra transport equations with nonlinear source terms are introduced to describe the evolution of scalar quantities. A segregated algorithm is proposed for the numerical treatment of the resulting PDE system. The Navier-Stokes equations are solved by a projection-like method based on the Pressure Schur Complement approach. Novel high-resolution finite element schemes of FCT and TVD type are employed for the discretization of unstable convective terms. Numerical results for a number of prototypical gas-liquid reactor configurations illustrate the performance of the developed simulation tools. Key Words: computational fluid dynamics; bubble columns; airlift loop reactors finite elements; incompressible flow solvers; high-resolution scheme