Controlled bubble coalescence in direct numerical simulations of two-phase flows

Bubbles in contact coalesce if the liquid film separating them drains in finite time. However, interface-resolved direct numerical simulations (DNS) are limited in capturing the micro- and nanometer-scale physics governing this drainage process and are prone to a grid-sensitive artifact known as numerical coalescence. Numerical coalescence leads to unphysical, instantaneous merging of bubbles when their separation falls below the grid size, resulting in an inaccurate description of bubble interactions in two-phase flows. In this study, we introduce a memory-efficient, multicolor coupled level set and volume-of-fluid (CLSVOF) framework designed to prevent numerical coalescence and enable controlled coalescence in DNS of complex bubbly flows involving large bubble counts and dense configurations. In our framework, colors represent variable spaces associated with distinct level set and volume-of-fluid fields. Bubbles in close proximity are assigned different colors to avoid numerical coalescence, while those allowed to coalesce are assigned the same color. This color reassignment is managed through a robust iterative algorithm that dynamically determines the total number of colors required at each simulation time step, based on the number and spatial distribution of bubbles. Using our framework, we demonstrate accurate controlled coalescence in a cluster of O(10³) bubbles rising to a liquid-gas interface, with prescribed liquid film drainage times. We also showcase our solver’s ability to suppress coalescence in dense bubble plumes entrained beneath a plunging breaking wave. The advancement in this study has important implications for modeling salinity effects, which are known to delay or suppress bulk bubble coalescence in breaking ocean surface waves. Subgrid-scale film drainage models that account for such salinity effects will also be discussed.