Population balance modeling of polydispersed bubbly flow in continuous casting using average bubble number density approach

A new methodology of average bubble number density (ABND) model for handling the evolution of polydispersed bubbly flow in the slab continuous casting mold is presented and evaluated. The average bubble number density transport equation coupled with the Eulerian-Eulerian two-fluid model is employed to describe size distribution of bubbles. Various interfacial forces including drag force, lift force, virtual mass force, and turbulent dispersion force are incorporated in this model. SST turbulence model is used with extra source terms introduced to account for the interaction between the bubbles and the liquid. The coalescence of bubbles is formulated according to the random collision driven by turbulence and wake entrainment, and the breakage of bubbles is formulated through considering the impact of turbulent eddies. The intermediate peak and core peak behaviors of void fraction inside the submersed entry nozzle (SEN) are captured very well. Comparisons of gas void fraction, liquid flow pattern, and local bubble size distribution profiles with experimental measurements are provided, showing the applicability and accuracy of the ABND approach in modeling the polydispersed bubbly flow in the slab continuous casting mold.