MPS-based axisymmetric particle method for bubble rising with density and pressure discontinuity

Wang, Z. ; Sugiyama, Tomoyuki 

Numerical simulation of gas bubbles rising in liquid is challenging due to high density and viscosity ratios. This study proposes to separately model the liquid and gas phases by the incompressible Moving Particle Semi-implicit (MPS) method and the Weakly Compressible MPS (WCMPS) method. The liquid-gas phase interface is explicitly represented by a series of discrete nodes. By adequately enforcing the stress balance equation on these moving interface nodes, the MPS and WCMPS methods are coupled. Rather than being treated as the volume force, the surface tension is considered as a pressure jump at the interface. Without applying any smoothing or averaging scheme, the density, viscosity and pressure are discontinuous across the interface. The axisymmetric formulation is directly introduced based on the least squares scheme to save computational cost. In addition, a multi-time step algorithm is proposed so that independent time increments can be adopted for different phases. Furthermore, the particle shifting technique is extended to control the multi-spatial resolution dynamically and maintain the particle distribution quasi-isotropic. Several numerical tests, including hydrostatic pressure problems, droplet deformation and bubble rising benchmark are conducted to show the accuracy, efficiency and stability. Finally, validations are performed using experimental results with wide ranges of Reynolds number and Bond number, which dominate the bubble shape.