A consistent multiphase SPH approximation for bubble rising with moderate Reynolds numbers

Phenomena involving bubble flow have an important role in numerous applications such as mixing, separation, filtration and cooling. When two different phases are treated as liquids–gas, the surface tension and buoyancy must be taken into account. An alternative is proposed to simulate flow for two or more phases, using bubbles formation and the Navier–Stokes equations in a Lagrangian formalism via smoothed particle hydrodynamics (SPH). It is a mesh-free method useful for applications with interface flow. Therefore, we have presented a set of numerical methodologies for SPH in multiphases. Surface tension interface is modeled using the continuum surface force (CSF) method. In order to avoid tension instability and interface penetrations, a background pressure based on the initial pressure between phases is included in the formulation. This model is implemented inside the prediction–correction of time upgrade scheme. Examples of bubble rising around the fluid due to the gravitational force are rarely analyzed in the SPH literature, especially to parameterize density, viscosity, surface coefficient, particle size and boundary conditions. Thus, this work focus on the analysis of these parameters and their effects on the morphology, displacement and velocity of the bubble simulations. Finally, results demonstrate a good numerical stability and adequate multiphase description.