A Lagrangian Mesh-Free Multi-Phase Model for Simulating Complex Dynamics of Bubbly Flows

Smoothed particle hydrodynamics (SPH) is a Lagrangian, mesh-free numerical method renowned for its ability to handle fluid dynamics problems with large interface deformations and multiphase flow coupling. This study introduces an SPH-based multiphase flow model for simulating bubbly flows involving various immiscible fluids. The model uses a volume-based density discretization equation, ensuring numerical accuracy near interfaces, independent of density ratios, thus maintaining accuracy and stability even at high density ratios. By integrating the Continuous Surface Force method for surface tension into the multiphase SPH model, the study simulates interfacial behavior between phases. The model accurately predicts Laplace pressure differences across interfaces, maintaining interface stability at density ratios up to 100.0. Simulations of single and double bubble ascents elucidate the influence of the Bond number on bubble shape, rising distance, and velocity. As the Bond number increases, bubbles flatten and develop tails, affecting their integrity. The study also simulates multiple bubbles ascents in water, showcasing the model's ability to capture complex interfacial behaviors in bubbly flows, including deformation, adsorption, coalescence, and tearing.