Multilevel modelling of dispersed multiphase flows

Dispersed multiphase flows are frequently encountered in a variety of industrially important processes in the petroleum, chemical, metallurgical and energy industries. Scale-up of equipment involving dispersed multiphase flows is quite difficult which is mainly due to the inherent complexity of the prevailing flow phenomena (formation of bubbles and clusters in gas-particle flows). Especially during the last decade significant research efforts have been made in both academic and industrial research laboratories to study dispersed multiphase flows using detailed microbalance models (1 to 3). Despite current limitations it has become clear that this approach offers a powerful complementary strategy parallel to careful experimentation and it is therefore anticipated that the role of modelling based on detailed microbalance models for design and operation of multiphase chemical reactors will significantly expand in the near future. In this paper the concept of multilevel modelling will be highlighted with which flow phenomena at different spatial and temporal scales can be studied. In addition some illustrative results will be presented which highlight current modelling capabilities in the area of dispersed gas-liquid and gas-solid two-phase flows. Broadly speaking three different classes of models can be distinguished, each with its own specific advantages and disadvantages, namely models suited to study multiphase flows at the microscopic, mesoscopic and macroscopic level. It should be stressed here that "particle" corresponds to dispersed elements such as solid particles, droplets or bubbles. Lattice Boltzmann models are useful to study flow phenomena at the microscopic level and can be used to develop closure laws for fluid-particle interaction needed in continuum models. Due to current limitations of computer capacity the lattice Boltzmann approach is limited to study the collective motion of 1000 suspended particles. Discrete particle models are useful to study flow phenomena at the mesoscopic level and can be used to develop closure laws for particle-particle and particle-wall interactions needed in continuum models. In the discrete particle approach one does not attempt to resolve the flow field at subparticle level and at present therefore far more (typically 100 000) particles can be allowed in the computation. As a logical consequence the closure laws for fluid-particle interaction have to be specified which can be obtained from the lattice Boltzmann model. Finally the knowledge obtained on the basis of the lattice Boltzmann model (closures for fluid-particle interaction) and the discrete particle model (closures for particle-particle and particle-wall interactions) can be implemented in continuum models which are useful to study flow phenomena at the macroscopic level.