Numerical investigation on the mechanism of ligament formation aroused by Rayleigh–Taylor instability

Ligament formation aroused by the Rayleigh–Taylor (R-T) instability is crucial to the secondary atomization of fuel drops in the internal combustion engine because it is a transition stage for a continuous bulk liquid to generate discrete droplets. In this paper, based on the detailed numerical data on the pressure and velocity fields, we investigated the mechanisms of how a ligament is generated from the interface due to a constant external acceleration. It is found that the maximum pressure location, which is formed due to the horizontal colliding flow from the trough portions, is a typical nonlinear characteristic and plays an essential role in ligament generation. The ligament above the maximum pressure location grows freely from the bottom bulk fluid region. In the nonlinear development of the interface deformation, the flow near the ligament root region reaches a steady state, in which the trough interface is discovered to retain a sinusoidal shape with a constant amplitude and descend at a constant velocity. The steady quantities, such as the dimensionless trough bottom descending velocity, U*, amplitude of the trough surface, δ₀*, and the distance between the maximum pressure location and the trough bottom point, ξ*, are demonstrated. The effects of the Bond number and Reynolds number on the nonlinear dynamics during the ligament formation process are also discussed in this paper.