Numerical Study Of The Rayleigh-Taylor Instability Between Two Immiscible Fluids

Rayleigh-Taylor instability(RTI)is widely found in astrophysics,geophysics,and engineering.Due to the complex interface dynamics,topological changes and the span of space-time scale,the understanding of its late evolution law and its influence mechanism has not been perfected.In this paper,an advanced phase-field lattice Boltzmann method based on the multiple-relaxation-time collision model is used to simulate the immiscible single-mode Rayleigh-Taylor instability with a moderate Atwoods number in a long tube,and we systematically analyze the effect of the Reynolds number on the interfacial dynamics and the late-time development stages of interface disturbance.The highest Reynolds number in the current simulation reaches up to 10000.The numerical results show that the Reynolds number significantly affects the development of the instability.For high Reynolds numbers,the instability undergoes a sequence of different growth stages,which include the linear growth,saturated velocity growth,reacceleration,and chaotic mixing stages.In the linear growth stage,the developments of the bubble and spike conform to the classical linear growth theory,and it is shown that the growth rate increases with the Reynolds number.In the second stage,the bubble and spike evolve with the constant velocities,and the numerical prediction for spike velocity is found to be slightly larger than the solution of the potential flow theory proposed by Goncharov [Phys:Rev:Lett: 88(2002)134502],which can be attributed to the formation of vortices in the proximity of the spike tip.In addition,it is found that increasing the Reynolds number reduces the bubble saturated velocity,which then is smaller than the solution of the potential model.The nonlinear evolutions of the bubble and spike induce the Kelvin–Helmholtz instability,producing many vortex structures with different scales.Due to the interactions among the vortices,the instability eventually enters into the chaotic mixing stage,where the interfaces undergo the roll-up at multiple layers,sharp deformation,and chaotic breakup,forming a very complicated topology structure.Furthermore,we also measured the bubble and spike accelerations and find that the dimensionless values fluctuates around the constants of 0.045 and 0.233,indicating a mean quadratic growth.And for low Reynolds numbers,the heavy fluid will fall down in the form of the spike,and the interface in the whole process becomes very smooth without the appearances of the roll-up and vortices.The late-time evolutional stages such as the reacceleration and chaotic mixing cannot also be observed.Furthermore,we also numerically studied the late evolution of multimode RTI in microchannels,and analyzed the effects of Reynolds number on interface dynamics and the amplitude of bubbles and spikes under low Atwood numbers.Compared with the singlemode case,the mutual competition and interaction between modes makes the evolution mechanism of multi-mode RTI more complicated.The effect of the Reynolds number on the evolutional interfacial dynamics and bubble/spike amplitudes is first investigated by considering its wide range from 100 up to a high value of 30000.It is found that increasing the Reynolds number could accelerate the instability development.For sufficiently large Reynolds numbers,a sequence of distinguishing stages in the immiscible RTI can be observed,which includes the linear growth,saturated velocity growth,and chaotic development stages.At late stage,the RTI induces a complex topology structure of the interface,and a mass of dissociative drops can be significantly observed in the system.The accelerations of the bubble and spike front are also measured,and it is reported that their normalized values at late time are respectively approximate to the constant values of around 0.025 and 0.027,exhibiting a terminally quadratic growth.As the Reynolds number is reduced to small ones,the multiple disturbances of the RTI are found to merge into a larger one at initial stage.Then the evolutional interfaces display the patterns familiar from the single-mode RTI.The phase interfaces in the whole process become very smoothed without the appearance of the breakup phenomenon,and the spike and bubble velocities at late time approaches constant values.Further,we also analyze the effects of the initial conditions in terms of the perturbation wavelength and amplitude,and it is found that the instability undergoes a faster growth at the intermediate stage for a larger wavelength,while the late-time bubble and spike growth rates are insensitive to the changes of the initially perturbed wavelength and amplitude,showing a law of selfsimilarity.