Abstract
Studying the dynamical behaviors of the liquid spike formed by Rayleigh-Taylor instability is important to understand the mechanisms of liquid atomization process. In this paper, based on the information on the velocity and pressure fields obtained by the coupled-level-set and volume-of- fluid (CLSVOF) method, we describe how a freed spike can be formed from a liquid layer under falling at a large Atwood number. At the initial stage when the surface deformation is small, the amplitude of the surface deformation increases exponentially. Nonlinear effect becomes dominant when the amplitude of the surface deformation is comparable with the surface wavelength (~0.1λ). The maximum pressure point, which results from the impinging flow at the spike base, is essential to generate a liquid spike. The spike region above the maximum pressure point is dynamically free from the bulk liquid layer below that point. As the descending of the maximum pressure point, the liquid elements enter the freed region and elongate the liquid spike to a finger-like shape.
Highlights
When an external acceleration directs from a light fluid to a heavy one, instability takes place on the interface, which is usually called Rayleigh-Taylor (RT) instability
We discuss the major dynamics associated with the spike formation due to RT instability based on the prototype case of A∗= 4.48π3
By using the coupled-level-set and volume-offluid (CLSVOF) method, we numerically studied the mechanisms of the spike formation due to RT instability for a large Atwood number
Summary
When an external acceleration directs from a light fluid to a heavy one, instability takes place on the interface, which is usually called Rayleigh-Taylor (RT) instability. Taylor [8] conducted a linear analysis on the RT instability in the absence of the surface tension and viscosity He derived that the amplitude of the initial disturbance grows exponentially over time. Layzer [10] obtained an approximate analytic solution for the instability of a fluid-vacuum interface in a gravitational field In such case of limited Atwood number (at = (rH − rL ) (rH + rL ) = 1) , where ρH is the density for the heavy fluid and ρL for the light fluid, he find that the bubble velocity is a constant value eventually, which is proportional to (gλ)1/2, where g is the gravitational acceleration. As the first step to study the problem in 3D case, which requires large calculation time, we first pay attention to 2D case in this study
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