Numerical Simulation Study Of Weakly Compressible Rayleigh-Taylor Instability

Rayleigh-Taylor instability(RTI)plays a key role in astrophysics,atmospheric science,inertial confinement fusion,and other scientific and engineering fields.During the evolution process of Rayleigh-Taylor instability,various physical and transport factors have different effects on its evolutionary behavior.Therefore,studying the influence of various factors on the Rayleigh-Taylor instability is also significant for understanding and regulating the evolution of the instability.The smooth particle hydrodynamics(SPH)method,as a meshless and Lagrange type particle method,has unique advantages in simulating complex flows during fluid motion.In this thesis,the evolution process of the Rayleigh-Taylor instability with a weakly compressible fluid is simulated numerically using the SPH method.The simulations were performed systematically for the evolution of the Rayleigh-Taylor instability with different Atwood numbers,different surface tension coefficients,and different dynamic viscosity coefficients.The evolutionary law of each stage of instability development was studied utilizing modal analysis and vortex dynamics analysis.The main results of this thesis are as follows:First,based on the SPH scheme of this work,we simulate the single-mode Rayleigh-Taylor instability with different parameters,and the analysis of the linear growth rate of the instability for different Atwood numbers,different surface tension coefficients,and different viscosity coefficients shows that the Atwood number is positively correlated with the linear growth rate,and both surface tension and viscosity suppress the linear growth rate,and the linear growth rate obtained from the simulation shows good agreement with the Mikaelian’s theoretical predictions.Second,when the dissipative effect of the system is strong,the bubbles’ and the spikes’ velocity of the Rayleigh-Taylor instability will reach a stable value,which is referred to as the terminal velocity.The analysis of the formation mechanism of the terminal velocity in the nonlinear phase from the vortex dynamics shows that behind the formation of the bubble terminal velocity,there exists a dynamic balance between the baroclinic generation term,viscous dissipation term,and the convective transport term of the vorticity.In addition,based on the significant correlation exhibited between the bubble velocity and the vorticity of bubble head,this thesis further modified Sohn’s theoretical model by combining previous theoretical works,and the predicted values of the improved model are in better agreement with the simulation results.Finally,this thesis quantitatively analyzes the effect of the selection of the horizontal dimension of the computational region on the Rayleigh-Taylor instability.The results show that when there are multiple groups of bubble and spike structures in the system,the transfer of flow field energy in the mixing region between d ifferent scales is induced due to the interaction between the neighboring bubble.