Lattice Boltzmann Simulation Of Turbulent Mixing Growth In Multimode Rayleigh-Taylor Instability

Rayleigh-Taylor(RT)instability,as a kind of fluid instability,widely exists in natural science and engineering.In this paper,the lattice Boltzmann method based on phase field theory is used to study the multi-mode RT instability of incompressible immiscible phases in slender channels.First,we study the influence of Reynolds number on the evolution of the mixed interface of immiscible incompressible multimode RT instability and the amplitude,velocity and acceleration coefficient of bubble and spike at a small Atwood number,the results show that the evolution of multi-mode RT instability can be divided into exponential growth stage,nonlinear stage and turbulent mixing stage at medium and high Reynolds numbers.In the third stage,the RT instability induced a drastic change in the interface topology at the late stage of evolution,and then the interface broke up and a large number of discrete droplets appeared in the mixed interface,the instability develops to the turbulent mixing stage.The acceleration coefficients of bubble and Spike at the later stage of evolution were also calculated.It can be concluded that there is indeed a secondary growth of the mixing layer at the later stage of evolution,and the values of the acceleration coefficients of spike and bubble were stable at 0.022 and 0.025 respectively.At low Reynolds numbers,the multimode perturbations of RT instability merge to form a single mode,and then the dynamic behavior of the phase interface is similar to that of the single-mode RT instability,it is a laminar flow state in which heavy and light fluids permeate each other.In addition,the effects of the amplitude and wavelength of the Atwood number,the initial disturbance at the interface and the surface tension on the evolution of multimode RT instability at high Reynolds number(Re = 10000)are also studied.The numerical results show that Atwood number has a significant effect on the multimode RT instability.When Atwood number is increasing,the evolution of spike and bubble became more and more asymmetric,and the amplitude and acceleration of spike increased rapidly,but the acceleration coefficient of bubble basically maintained at 0.025 ± 0.005,this trend is consistent with the results of previous experiments,and the acceleration coefficient of the bubble and the spike under different Atwood number satisfies the quantization relation measured in the experiment.The numerical results show that the increase of the amplitude and wavelength of the initial disturbance can promote the development of the instability,but have little influence on the secondary growth of the mixing layer(the acceleration coefficient of late evolution is described)in the later stage of evolution,the loss of self-similarity in memory of initial conditions.For the surface tension,increasing the surface tension will reduce the number of discrete droplets and the degree of interface confusion.In addition,the growth coefficient of surface tension at the late stage of evolution showed a tendency of promoting first and then restraining.