Rayleigh-Taylor instability under multi-mode perturbation: Discrete Boltzmann modeling with tracers

The two-dimensional Rayleigh-Taylor Instability (RTI) under multi-mode perturbation in compressible flow is probed via the Discrete Boltzmann Modeling (DBM) with tracers. The distribution of tracers provides clear boundaries between light and heavy fluids in the position space. Besides, the position-velocity phase space offers a new perspective for understanding the flow behavior of RTI with intuitive geometrical correspondence. The effects of viscosity, acceleration, compressibility, and Atwood number on the mixing of material and momentum and the mean non-equilibrium strength at the interfaces are investigated separately based on both the mixedness defined by the tracers and the non-equilibrium strength defined by the DBM. The mixedness increases with viscosity during early stage but decreases with viscosity at the later stage. Acceleration, compressibility, and Atwood number show enhancement effects on mixing based on different mechanisms. After the system relaxes from the initial state, the mean non-equilibrium strength at the interfaces presents an initially increasing and then declining trend, which is jointly determined by the interface length and the macroscopic physical quantity gradient. We conclude that the four factors investigated all significantly affect early evolution behavior of an RTI system, such as the competition between interface length and macroscopic physical quantity gradient. The results contribute to the understanding of the multi-mode RTI evolutionary mechanism and the accompanied kinetic effects.     

Linear Growth of Rayleigh-Taylor Instability of Two Finite-Thickness Fluid Layers

The linear growth of Rayleigh-Taylor instability(RTI) of two superimposed finite-thickness fluids in a gravitational field is investigated analytically. Coupling evolution equations for perturbation on the upper, middle and lower interfaces of the two stratified fluids are derived. The growth rate of the RTI and the evolution of the amplitudes of perturbation on the three interfaces are obtained by solving the coupling equations. It is found that the finite-thickness fluids reduce the growth rate of perturbation on the middle interface. However, the finite-thickness effect plays an important role in perturbation growth even for the thin layers which will cause more severe RTI growth. Finally, the dependence of the interface position under different initial conditions are discussed in some detail.     

Theory of surface tension and its application to simple fluids

We consider a liquid-vapor interface in thermal equilibrium. The tangential component of the pressure tensor is supposed to depend explicitly upon the position and the density profile. Under this hypothesis the mechanical definition of surface tension becomes a finite summation ofN+1 terms related directly to the local compressibility. When the inhomogeneous compressibility equation is considered, the theory provides a microscopic expression of the surface tension coefficient. A calculation for argon near the critical point is done; the agreement with experiment is satisfactory.     

工质变比热对不可逆Otto循环性能的影响

用有限时间热力学的方法分析空气标准Otto循环,由数值计算给出了存在不可逆损失和工质变比热时循环功率与压缩比、效率与压缩比以及功率和效率的特性关系,分析了工质变比热对不可逆Otto循环性能的影响特点,通过分析可知工质变比热特性对不可逆Otto循环性能有较大影响,在实际循环分析中应该予以考虑,本文所得结果对实际内燃机的设计有一定的指导意义。     

Effects of Rayleigh-Taylor instabilities on turbulent premixed flames in a curved rectangular duct

Large-eddy simulations are used to demonstrate the effects of Rayleigh-Taylor instabilities (RTIs) on constant-pressure, turbulent premixed flames stabilized in a curved rectangular duct. A splitter plate of constant radius separates a reactant and pilot stream such that the flame stabilizes in the mixing layer between the two streams. Centrifugal acceleration due to the duct curvature induces the RTI, increasing the mixing of the higher-density reactant stream with the lower-density pilot stream. In both non-reacting and reacting flows, the resulting mixing layer thickness grows at rates comparable to those in unconfined RTIs until the flame occupies approximately half of the duct, at which point the duct walls limit the growth rate. The conservative equations are modified with artificial body forces to negate the centrifugal effect (and the RTI) to isolate the impact of the curved geometry. A comparison between the flames with and without the RTI shows that the RTI increases the turbulent flame speed primarily through increased flame surface area. The RTI also increases the range of local flame stretches and curvatures. The increased turbulent flame speed and growth rates due to RTI suggest a viable mechanism to increase turbulent flame speed in gas turbine engines though the application of flow path curvature.     

Effect of initial phase on the Rayleigh—Taylor instability of a finite-thickness fluid shell

Rayleigh—Taylor instability (RTI) of finite-thickness shell plays an important role in deep understanding the characteristics of shell deformation and material mixing. The RTI of a finite-thickness fluid layer is studied analytically considering an arbitrary perturbation phase difference on the two interfaces of the shell. The third-order weakly nonlinear (WN) solutions for RTI are derived. It is found the main feature (bubble-spike structure) of the interface is not affected by phase difference. However, the positions of bubble and spike are sensitive to the initial phase difference, especially for a thin shell (kd<1), which will be detrimental to the integrity of the shell. Furthermore, the larger phase difference results in much more serious RTI growth, significant shell deformation can be obtained in the WN stage for perturbations with large phase difference. Therefore, it should be considered in applications where the interface coupling and perturbation phase effects are important, such as inertial confinement fusion.     

Instabilities responsible for magnetic turbulence in laboratory rotating plasma

Instabilities responsible for magnetic turbulence in laboratory rotating plasma are investigated. It is shown that the plasma compressibility gives a new driving mechanism in addition to the known Velikhov effect due to the negative rotation frequency gradient. This new mechanism is related to the perpendicular plasma pressure gradient, while the density gradient gives an additional drive depending also on the pressure gradient. It is shown that these new effects can manifest themselves even in the absence of the equilibrium magnetic field, which corresponds to nonmagnetic instabilities.     

工质变比热条件下内燃机循环普适特性

用有限时间热力学的方法分析空气标准不可逆内燃机循环,导出了考虑工质变比热情况下,存在摩擦及传热损失时,由两个加热过程、两个放热过程和两个绝热过程组成的普适的空气标准不可逆内燃机循环的功率与压缩比、效率与压缩比以及功率和效率的最佳特性关系,同时由数值计算分析了工质变比热和循环过程对循环性能的影响特点,比较了工质恒、变比热时循环性能差异。所得结果包含了不可逆往复式Diesel、Otto、Brayton、Atkinson、Dual和Miller 循环的性能特性。     

可压缩与不可压缩流体中Rayleigh Taylor不稳定性的比较

 对比研究了可压缩与不可压缩流体的Rayleigh Taylor不稳定性小扰动阶段的增长速率，其中，压力是密度的任意单值函数，这个函数也即是可压缩流体的状态方程。研究表明：在相同密度分布条件下，可压缩流体的界面扰动增长速率总是比相应的不可压缩流体的界面增长率大，其相对增长率随扰动波长的增加而增大，随两种介质的声速减小而增大，在长波和易压缩流体中，相对增长率可达0.8以上。因此，在某些条件下，流体可压缩性对Rayleigh Taylor不稳定性的影响是不能忽略的。     

激光烧蚀RT不稳定性线性增长率和非线性行为的数值研究

 给出了不同情况下多种波长的烧蚀瑞利 泰勒不稳定性线性增长率的二维计算结果，并与Takabe公式和Sanz公式进行了比较，最后给出了单模激光烧蚀RTI非线性发展行为的数值结果。线性增长率的二维计算结果很好验证了Sanz公式，表明β值应是2，不是3。当烧蚀速度较大或烧蚀面较宽时，用Takabe公式估计的烧蚀RTI线性增长率与二维计算值明显不符。     

Nonlinear Rayleigh–Taylor instability of two superposed magnetic fluids under parallel rotation and a normal magnetic field

The Rayleigh–Taylor instability (RTI) of a ferrofluid has been the subject of recent research, because of its implications on the stability of stellar and planetary interiors. This paper analyzes the effects of rotation and magnetic field on nonlinear RTI of two superposed ferrofluids. It is considered that the system is subjected to uniform parallel rotation and normal magnetic field. Surface tension acts at the interface. The method of multiple scales is utilized to obtain the solutions and dispersion relations are obtained for the nonlinear problem of RTI of magnetic fluids. Finally the stability of the problem is discussed.     

Lattice Boltzmann study of three-dimensional immiscible Rayleigh–Taylor instability in turbulent mixing stage

In this paper, we numerically studied the late-time evolutional mechanism of three-dimensional (3D) single-mode immiscible Rayleigh–Taylor instability (RTI) by using an improved lattice Boltzmann multiphase method implemented on graphics processing units. The influences of extensive dimensionless Reynolds numbers and Atwood numbers on phase interfacial dynamics, spike and bubble growth were investigated in details. The longtime numerical experiments indicate that the development of 3D singlemode RTI with a high Reynolds number can be summarized into four different stages: linear growth stage, saturated velocity growth stage, reacceleration stage and turbulent mixing stage. A series of complex interfacial structures with large topological changes can be observed at the turbulent mixing stage, which always preserve the symmetries with respect to the middle axis for a low Atwood number, and the lines of symmetry within spike and bubble are broken as the Atwood number is increased. Five statistical methods for computing the spike and bubble growth rates were then analyzed to reveal the growth law of 3D single-mode RTI in turbulent mixing stage. It is found that the spike late-time growth rate shows an overall increase with the Atwood number, while the bubble growth rate experiences a slight decrease with the Atwood number at first and then basically maintains a steady value of around 0.1. When the Reynolds number decreases, the later stages cannot be reached gradually and the evolution of phase interface presents a laminar flow state.     

Xe adsorption on Ag(111): Experiment

Precise structural and thermodynamic studies of Xe adsorbed on Ag(111) are made using low-energy diffraction. Spacings are measured relative to those of bulk adsorbed film. Effective equilibrium experiments are done using a directed gas beam and cryopumping. The density of only that gas in the coherently diffracting area is measured by the attenuation of the Ag(01) beam. With decreasing temperature at fixed gas flux one observes the sequential of 2D gas, monolayer, bilayer and bulk films. The effective pressure of the impinging gas is determined from the known bulk vapor pressure so bypassing absolute pressure measurements. The phase diagram, lattice spacings in the film at equilibrium and at zero pressure, latent heats of adsorption and isosteric heats are determined.     

Effects of the initial perturbations on the Rayleigh–Taylor–Kelvin–Helmholtz instability system

The effects of initial perturbations on the Rayleigh–Taylor instability (RTI), Kelvin–Helmholtz instability (KHI), and the coupled Rayleigh–Taylor–Kelvin–Helmholtz instability (RTKHI) systems are investigated using a multiple-relaxation-time discrete Boltzmann model. Six different perturbation interfaces are designed to study the effects of the initial perturbations on the instability systems. It is found that the initial perturbation has a significant influence on the evolution of RTI. The sharper the interface, the faster the growth of bubble or spike. While the influence of initial interface shape on KHI evolution can be ignored. Based on the mean heat flux strength D_3,1, the effects of initial interfaces on the coupled RTKHI are examined in detail. The research is focused on two aspects: (i) the main mechanism in the early stage of the RTKHI, (ii) the transition point from KHI-like to RTI-like for the case where the KHI dominates at earlier time and the RTI dominates at later time. It is found that the early main mechanism is related to the shape of the initial interface, which is represented by both the bilateral contact angle θ₁ and the middle contact angle θ₂. The increase of θ₁ and the decrease of θ₂ have opposite effects on the critical velocity. When θ₂ remains roughly unchanged at 90 degrees, if θ₁ is greater than 90 degrees (such as the parabolic interface), the critical shear velocity increases with the increase of θ₁, and the ellipse perturbation is its limiting case; If θ₁ is less than 90 degrees (such as the inverted parabolic and the inverted ellipse disturbances), the critical shear velocities are basically the same, which is less than that of the sinusoidal and sawtooth disturbances. The influence of inverted parabolic and inverted ellipse perturbations on the transition point of the RTKHI system is greater than that of other interfaces: (i) For the same amplitude, the smaller the contact angle θ₁, the later the transition point appears; (ii) For the same interface morphology, the disturbance amplitude increases, resulting in a shorter duration of the linear growth stage, so the transition point is greatly advanced.     

Investigation of thermodynamic properties of cerium dioxide by statistical moment method

The thermodynamic properties of the cerium dioxide (CeO₂) are studied using the statistical moment method, including the anharmonicity effects of thermal lattice vibrations. The free energy, linear thermal expansion coefficient, bulk modulus, specific heats at the constant volume and those at the constant pressure, C_V and C_P, are derived in closed analytic forms in terms of the power moments of the atomic displacements. The temperature dependence of the thermodynamic quantities of cerium dioxide is calculated using three different interatomic potentials. The influence of dipole polarization effects on the thermodynamic properties and thermodynamic stability of cerium dioxide have been studied in detail.     

Rayleigh-Taylor不稳定性弱非线性阶段界面效应对谐波的影响

为了更好地理解不同空间坐标系下流体界面对Rayleigh-Taylor（RT）不稳定性弱非线性阶段谐波的影响,文章采用3阶小扰动展开法,解析研究了球坐标空间经典RT不稳定性弱非线性阶段谐波的演化规律,并和柱坐标空间以及直角坐标空间相应结果进行了对比研究.当球坐标系和直角坐标系中RT不稳定性界面扰动波长相同,球坐标系中初始扰动半径为无穷大时（即球坐标下RT不稳定性初始扰动半径相对于扰动波长为无穷大时）,球坐标下RT不稳定性前4次谐波的结果和直角坐标系下的相应结果相同.研究表明:由初始界面曲率引起的Bell-Plesset（BP）效应和空间效应（直角坐标空间、柱坐标空间和球坐标空间）对谐波发展有较大的影响.即在不同正交曲线坐标系下,不同曲率的流体界面效应对RT不稳定性谐波发展有较大的影响.对于柱坐标空间和球坐标空间,2阶对0次谐波的反馈加强了界面向内收缩.研究还表明:界面效应增加了2次谐波的负反馈,然而,对于基模和3次谐波却有不同的影响.      

A new pressure formulation for gas-compressibility dampening in bubble dynamics models

We formulated a pressure equation for bubbles performing nonlinear radial oscillations under ultrasonic high pressure amplitudes. The proposed equation corrects the gas pressure at the gas–liquid interface on inertial bubbles. This pressure formulation, expressed in terms of gas-Mach number, accounts for dampening due to gas compressibility during the violent collapse of cavitation bubbles and during subsequent rebounds. We refer to this as inhomogeneous pressure, where the gas pressure at the gas–liquid interface can differ to the pressure at the centre of the bubble, in contrast to homogenous pressure formulations that consider that pressure inside the bubble is spatially uniform from the wall to the centre. The pressure correction was applied to two bubble dynamic models: the incompressible Rayleigh–Plesset equation and the compressible Keller and Miksis equation. This improved the predictions of the nonlinear radial motion of the bubble vs time obtained with both models. Those simulations were also compared with other bubble dynamics models that account for liquid and gas compressibility effects. It was found that our corrected models are in closer agreement with experimental data than alternative models. It was concluded that the Rayleigh–Plesset family of equations improve accuracy by using our proposed pressure correction.     

Quantum effects on the Rayleigh–Taylor instability of stratified plasma in the presence of suspended particles

The effects of quantum correction on the Rayleigh–Taylor instability (RTI) in stratified plasma layer have been investigated in the presence of suspended particles. A general dispersion relation is obtained from the linearized set of quantum hydrodynamic (QHD) equations. Two particular cases of suspended particle parameters (f ^? and α ₀) with and without quantum corrections are analysed. The condition of RTI is derived while the stability of the system is discussed by applying Routh–Hurwitz (RH) criterion in the polynomial equation. The results show that, in the absence of quantum term, the relaxation frequency of the suspended particles has a destabilizing effect, while the mass concentration of the suspended particles has a stabilizing effect on the growth rates of RTI. In the presence of the quantum term, the relaxation frequency of the suspended particle yields to the stability behaviour on the growth rates of RTI.     

Adiabatic electron thermal pressure fluctuations in tokamak plasmas

Electron thermal pressure fluctuations measured in the edge plasma of the Texas Experimental Tokamak Upgrade are a fundamental component of plasma turbulence on both sides of the velocity shear layer. The ratio of specific heats, estimated from fluctuations in electron temperature and electron number density measured simultaneously at the same electrode, indicates that observed fluctuations are adiabatic. The observations are made by means of a novel Langmuir probe technique, the time domain triple-probe method, which concurrently measures multiple plasma properties at each of two electrodes with the temporal and the spatial resolution required to estimate thermodynamic properties in a turbulent plasma.     

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.