Deriving closures for bubbly flows using direct numerical simulations

CFD modeling of dispersed multiphase flows can be quite challenging because of the wide range of time- and length-scales involved. A modern methodology to bridge the different scales is multi-scale modeling, which involves applying different (types of) models to describe phenomena prevailing at different time and length scales. This approach requires however, closure equations for the unresolved sub-grid phenomena in the higher level models. These closures can in principle be obtained from analytical theory, experiments and direct numerical simulations (DNS), each with their own strong and weak points. Analytical theory is limited to idealized situations, for instance spherical bubbles in the limit of high Reynolds numbers, while experiments are timeconsuming, costly and easily influenced by disturbances and contaminations and often not all relevant quantities can be measured simultaneously and with the desired accuracy. A third and relatively new path is to use DNS, which is not restricted to any idealized situation nor suffers from experimental difficulties. One of the strongest points is the freedom to change any of the physical properties or other parameters (geometry, operating parameters, etc.) at will and study their influence independently at great detail, having all the information on all variables (such as flow field, pressure field, etc.) available. The objective of this thesis was to improve a 3D Front Tracking model and to use it to obtain closures for the drag, lift and virtual mass forces acting on single bubbles rising in an initially quiescent infinite liquid. Using periodic boundary conditions, also the influence of neighboring bubbles (referred to as ‘swarm effects’) on the drag force was studied. In addition, dedicated experiments have been performed to validate the numerical results for the drag and lift forces acting on single bubbles