A two-phase lattice Boltzmann study on injection filling of cavities with arbitrary shapes

In this paper, a multi-relaxation time (MRT) pseudo-potential based lattice Boltzmann model is implemented to investigate the isothermal injection filling of 2D cavities with arbitrary shapes. The model is capable of handling relatively large density ratios and low viscosities. First, the model is validated by a comparison of the numerical results with those of the experiments reported in the literature for a broken dam problem where a good agreement is observed. Next, the filling process of a rectangular cavity is simulated and effects of the Reynolds and Froude numbers as well as the cavity aspect ratio are investigated. Two filling regimes namely steady and splashing are identified. The formation of gas bubbles are observed in the splashing regime while in the case of steady filling, no bubbles are trapped and the liquid jet fills the cavity smoothly. Furthermore, the threshold Re number for the onset of splashing is evaluated by changing the effective variables. It was found that this threshold Re is increased by a reduction of the cavity aspect ratio (H/L) less than 0.5. Decreasing the Fr number and increasing the ratio D/L also increase the threshold Re for the onset of splashing. In the next case, filling a circular cavity with a solid core is also simulated at relatively low and high Re numbers and results at a Re of 81 are compared with those of the SPH method reported in the literature. Finally, a multi-branch header discharging into eight uniform cavities is studied. It was found that the filling sequence of the branches is different for low and relatively high Re numbers.