Study On Single-mode Rayleiy-Taylor Instability Based On Lattice Boltzmann Method

Rayleigh-Taylor instability(RTI)phenomenon is widely present in nature and engineering applications.In this paper,the lattice Boltzmann method is used to study the immiscible single-mode RTI in the long micro-channel.The late-time growth of the RTI is explored and the influences of several factors including Reynolds number,Atwood number,surface tension on interfacial dynamics and developments of spike and bubble are analyzed.First,this paper study the effect of Reynolds number at a medium high Atwood number.Numerical simulation results show that the development of single-mode RTI at a high Reynolds number will go through four different stages,including the linear growth,saturated velocity growth,reacceleration and chaotic development stages.In the second stage,the velocity of spike and bubble is kept at a stable value,which is consistent with the analysis result of potential flow theory.The duration of the spike saturated velocity stage is shorter than that of the bubble,implying the asymmetric developments between the spike and bubble fronts.Then,in the instability development process,the vortex strength increases with time,leading to the spike and bubble velocity exceeding the potential flow theory's asymptotic solution,and the instability growth enters 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.To reveal the law of the late instable growth,We used five different statistical methods mentioned in the literature to calculate spike and bubble growth rates and compare the differences.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.Based on the above,we continue to examine the effects of fluid Atwood number,interfacial tension and initial disturbance on the late-time development of single-mode RTI at a high Reynolds number.Results show that the sustaining time for the saturated velocity stage decreases with the Atwood number,and the spike late-time growth rate increases with the Atwood number,while the bubble growth rate seems to be indepedence of the Atwood number.As for the effect of surface tension,it is shown that increasing surface tension can effectively reduce the complexity of phase interface structure in the evolution process,and the discrete droplet formation caused by phase interface rupture in the later instable phase can be inhibited.Further,it is found that increasing the surface tension can promote and then inhibit the growth of bubble amplitude,and there is no obvious difference between the spike amplitude growth curves for small surface tensions.When the surface tension increases to a certain value,its inhibitory effect on spike amplitude can be obviously observed.At a small Atwood number,the spike growth rate gradually decreases with the increase of surface tension.And at a large Atwood number,the growth rate of bubble and spike shows a law of first promotion and then inhibition.We also studied the critical surface tension of RTI under different Atwood numbers.The results of numerical calculation and theoretical analysis are consistent with each other,and the critical surface tension increases with Atwood number.For the initial disturbance,the decrease of the disturbance amplitude will lead to the deceleration of the growth in the linear stage.When the initial disturbance is very small,the bubble growth rate significantly decrease,while the growth rate of spikes will not change much.