Late-time description of immiscible Rayleigh-Taylor instability: A lattice Boltzmann study

Abstract

In this paper, the late-time description of immiscible Rayleigh-Taylor instability (RTI) in a long duct is investigated over a comprehensive range of the Reynolds numbers (1 ≤ Re ≤ 10000) and Atwood numbers (0.05 ≤ A ≤ 0.7) based on the mesoscopic lattice Boltzmann method. We first reported that the instability with a moderately high Atwood number of 0.7 undergoes a sequence of distinguishing stages at a high Reynolds number, which are termed as the linear growth, saturated velocity growth, reacceleration and chaotic development stages. The spike and bubble at the secondary stage evolve with the constant velocities and their values agree well with the analytical solutions of the potential flow theory. The duration of the spike saturated velocity stage is very shorter than that of the bubble, implying the asymmetric developments between the spike and bubble fronts. Owing to the increasing strengths of the formed vortices, the movements of the spike and bubble are accelerated such that their velocities exceed than the asymptotic values and the evolution of the instability then enters into the reacceleration stage. Lastly, the curves for the spike and bubble velocities have some fluctuations at the chaotic stage and also a complex interfacial structure with large topological change is observed, while it still preserves the symmetry property with respect to the central axis. To determine the nature of the late-time growth, we also calculated the spike and bubble growth rates by using five popular statistical methods and two comparative techniques are recommended, resulting in the spike and bubble growth rates of about 0.13 and 0.022, respectively. When the Reynolds number is gradually reduced, some later stages such as the chaotic and reacceleration stages cannot be reached successively and the structure of the interface in the evolutional process becomes relatively smooth. The influence of the fluid Atwood number is also examined on the late-time RTI development at a large Reynolds number.It is found that the sustaining time for the saturated velocity stage decreases with the Atwood number. The spike late-time growth rate shows an overall increase with the Atwood number, while it has little influence on the bubble growth rate being approximately 0.0215.