Specific heat ratio effects of compressible Rayleigh–Taylor instability studied by discrete Boltzmann method

Rayleigh–Taylor (RT) instability widely exists in nature and engineering fields. How to better understand the physical mechanism of RT instability is of great theoretical significance and practical value. At present, abundant results of RT instability have been obtained by traditional macroscopic methods. However, research on the thermodynamic non-equilibrium (TNE) effects in the process of system evolution is relatively scarce. In this paper, the discrete Boltzmann method based on non-equilibrium statistical physics is utilized to study the effects of the specific heat ratio on compressible RT instability. The evolution process of the compressible RT system with different specific heat ratios can be analyzed by the temperature gradient and the proportion of the non-equilibrium region. Firstly, as a result of the competition between the macroscopic magnitude gradient and the non-equilibrium region, the average TNE intensity first increases and then reduces, and it increases with the specific heat ratio decreasing; the specific heat ratio has the same effect on the global strength of the viscous stress tensor. Secondly, the moment when the total temperature gradient in y direction deviates from the fixed value can be regarded as a physical criterion for judging the formation of the vortex structure. Thirdly, under the competition between the temperature gradients and the contact area of the two fluids, the average intensity of the non-equilibrium quantity related to the heat flux shows diversity, and the influence of the specific heat ratio is also quite remarkable.     

Thermodynamic Nonequilibrium Features in Binary Diffusion

Diffusion is a ubiquitous physical phenomenon where thermodynamic nonequilibrium effects(TNEs) are outstanding issues. In this work, we employ the discrete Boltzmann method to investigate the TNEs in the dynamic process of binary diffusion. The main features of the distribution function in velocity space are recovered and discussed.It is found that, with the decreasing gradients of macroscopic quantities(such as density, concentration, velocity, etc.),both the local and global TNEs decrease with the time but increase with the relaxation time in a power law, respectively.     

超声速流体Kelvin-Helmholtz不稳定性速度梯度效应研究

利用加权本质上无振荡（WENO）方法模拟超声速流体Kelvin-Helmholtz（KH）不稳定性,研究速度梯度对KH不稳定性线性增长率和后期非线性演化的影响.模拟发现超声速流体中的速度梯度对KH不稳定性具有较强的致稳作用,给出了包含速度梯度致稳的线性增长率经验公式.数值模拟和经验公式符合得很好.模拟给出了清晰的流场密度等值线,这说明WENO方法模拟超声速流体KH不稳定性具有较好的界面变形捕捉能力.模拟结果表明速度梯度影响KH涡的演化,在给定密度梯度的情况下速度梯度越大KH涡的横向尺度越小. 关键词： Kelvin-Helmholtz不稳定性 超声速流体 速度梯度     

Kinetic Simulation of Nonequilibrium Kelvin-Helmholtz Instability

The recently developed discrete Boltzmann method(DBM), which is based on a set of uniform linear evolution equations and has high parallel efficiency, is employed to investigate the dynamic nonequilibrium process of Kelvin-Helmholtz instability(KHI). It is found that, the relaxation time always strengthens the global nonequilibrium(GNE), entropy of mixing, and free enthalpy of mixing. Specifically, as a combined effect of physical gradients and nonequilibrium area, the GNE intensity first increases but decreases during the whole life-cycle of KHI. The growth rate of entropy of mixing shows firstly reducing, then increasing, and finally decreasing trends during the KHI process. The trend of the free enthalpy of mixing is opposite to that of the entropy of mixing. Detailed explanations are:(i) Initially,binary diffusion smooths quickly the sharp gradient in the mole fraction, which results in a steeply decreasing mixing rate.(ii) Afterwards, the mixing process is significantly promoted by the increasing length of material interface in the evolution of the KHI.(iii) As physical gradients are smoothed due to the binary diffusion and dissipation, the mixing rate reduces and approaches zero in the final stage. Moreover, with the increasing Atwood number, the global strength of viscous stresses on the heavy(light) medium reduces(increases), because the heavy(light) medium has a relatively small(large) velocity change. Furthermore, for a smaller Atwood number, the peaks of nonequilibrium manifestations emerge earlier, the entropy of mixing and free enthalpy of mixing change faster, because the KHI initiates a higher growth rate.     

可压流体Rayleigh-Taylor不稳定性的离散Boltzmann模拟

使用离散Boltzmann模型模拟了可压流体系统中多模初始情况下的Rayleigh-Taylor不稳定性.该离散Boltzmann模型等效于一个Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.通过模拟Riemann问题:Sod激波管、冲击波碰撞和热Couette流问题验证模型的有效性,所得数值结果与解析解一致.利用该模型对界面间断随机多模初始扰动的可压Rayleigh-Taylor不稳定性进行数值模拟研究,得到不稳定性界面演化过程的基本图像.由于黏性和热传导共同作用,一开始扰动界面被"抹平",演化较慢;随着模式互相耦合而减少,演化开始加速,并经历非线性小扰动阶段和不规则非线性阶段,而后发展成典型的"蘑菇状",后期进入湍流混合阶段.由于扰动模式的耦合与发展,轻重流体的重力势能、压缩能与动能相互转化,系统先是趋于热动平衡态,而后偏离热动平衡态以线性形式增长,接着再次趋于热动平衡态,最后慢慢远离热动平衡态.