Detailed nonlinear dynamics of the liquid spike development in gaseous medium caused by a three-dimensional Rayleigh-Taylor instability

Previous researches on the single-mode Rayleigh-Taylor (RT) instability were mainly focused on the advancing speed of gaseous bubbles, while few of them shed light on the nonlinear dynamics of the liquid spikes (jets) where the droplets are constantly generated in the liquid atomization case. In this paper, a three-dimensional (3D) numerical simulation on a single-mode RT instability (Atwood number is close to unity) with the focus on the development of the liquid spike was conducted by the Coupled Level-Set and Volume-of-Fluid (CLSVOF) method. Nonlinear dynamic characteristics of the RT instability were then analyzed thoroughly based on the detailed information of pressure and velocity fields obtained from the numerical simulation. The numerical results revealed that a local maximum pressure point, where an equilibrium was achieved between the inertial force and pressure gradient, was formed at the root of liquid spike region caused by the horizontal impinging flow. Combined with the theoretical analysis, the relationships among the steady-state characteristic parameters, the initial perturbation wavelength and the inertial acceleration were established. It is found that the velocity and width of the liquid entering the freed liquid spike at the maximum pressure point exhibit the same characteristics as those of a vertical jet emanating downward from an orifice injector under gravity. Thus, theories concerning the low-speed jet can be used to predict the disintegration behavior of a liquid spike caused by RT instability.