| Rayleigh-Taylor(RT)instability is a common phenomenon of interface instability in nature,and widely exists in many natural phenomena and engineering applications.In the past hundred years,Rayleigh-Taylor instability has been actively studied as a fundamental problem of fluid dynamics.With rapid development of computational methods,numerical simulation becomes one of the important methods to study this problem.In order to study the effect of compressibility on Rayleigh-Taylor instability,we numerically simulated the nonlinear evolution of two-dimensional and three-dimensional single-mode RT instability for isothermal background stratification with different isothermal Mach numbers and Atwood numbers(At)using a high-order central compact finite difference scheme.The main research results of this thesis are as follows.The effect of compressibility on two-dimensional single-mode Rayleigh-Taylor instability at different Atwood number is studied.It is found that the initial density stratification caused by compressibility plays a stabilizing role,while the expansion-compression effect of flow plays a destabilizing role.The overall impact of compressibility on the evolutions of RT instability depends on competition between two effects.For the case of small Atwood number,the density difference between the two sides of the interface is small,and the density distribution of the upper and lower layers is nearly symmetrical.The initial density stratification plays a dominant role,and the expansion-compression effect has little influence.With the increase of Atwood number,the stabilization effect of initial density stratification decreases,and the instability caused by expansion-compression effect becomes more significant.The flow structures of bubbles and spikes are quite different at medium Atwood number.The effect of compressibility on the bubble velocity has been reversed at At= 0.5.The bubble velocity in the potential flow stage increases with the increase of compressibility.The effect of compressibility on the bubble velocity is strong at large At.The bubble height is approximately a quadratic function of time at potential flow growth(PFG)stage.The average bubble acceleration is nearly proportional to the square of Mach number at At= 0.9.We study three-dimensional single-mode incompressible Rayleigh-Taylor instability.Bubble velocity and spike velocity are basically the same in two-dimensional and threedimensional simulations before and during the reacceleration stage.However,the vortexstructures are different.After the reacceleration stage,there are some differences between 3D simulation and 2D simulation.At medium and high Reynolds numbers with small Atwood number,the three-dimensional RT instability enters a uniform-acceleration state after reacceleration state until the spike or bubble structure becomes very weak.This stage is caused by the continuous formation of new bubble or spike structure at the top of bubble or spike.At medium Atwood number,the increase of Reynolds number promotes the development of spike.But it has a certain inhibition effect on bubble during and after the reacceleration state.We compare the effects of compressibility on the development of three-dimensional and two-dimensional Rayleigh-Taylor instability.It is found that the influence of compressibility on RT instability is basically the same for bubble and spike velocities.However,with respect to vortex structures or other details,the effect of compressibility is different. |
