On generating initial conditions for turbulence models: the case of Rayleigh–Taylor instability turbulent mixing

A new approach to generate initial conditions for RANS simulations of Rayleigh–Taylor (RT) turbulence is presented. The strategy is to provide profiles of turbulent model variables when it is suitable for the turbulence model to be started, and then use these profiles for the turbulence model initialization. The generation of turbulence model variable profiles is achieved with a two-step process. In the first step, a nonlinear modal model assuming small amplitude initial perturbations, incompressible and inviscid fluids is used to track the growth of modes that exist in a given initial perturbation spectrum, and also modes generated by mode interactions. The amplitude development of each mode represents the penetration distance of the light fluid into the heavy fluid (bubble penetration), for a given mode perturbation. The penetration distance of heavy fluid into the light fluid (spike penetration), for a given mode perturbation, is inferred from the bubble's height by an empirical relation valid for small initial amplitudes, and established by DNS simulations that depend on a nondimensional time, and the density contrast (Atwood number). It is hypothesized that the bubble front position of the RT mixing layer can be approximated by the largest penetration distance among all existing modes. The spike front position is approximated in the same fashion. The nonlinear model is evaluated by comparing the bubble front height evolution predicted by the model against the bubble front height predicted by an incompressible implicit large eddy simulations (ILES) code. Comparisons of results for “top-hat” and two-band initial perturbation spectra at Atwood numbers, A_T =0.3 and A_T =0.5 for the former, and A_T =0.01 and A_T =0.5 for the latter, show reasonable agreement. In the second step, the bubble and spike front positions, their derived velocities, and simplified profiles of the mixture fraction distribution of each fluid between the bubble and spike fronts are used with a two-fluid approximation to derive profiles for the turbulence model variables. When initialized with modal model profiles at start time τ₀, (i.e., the time when the turbulence model variable profiles are inferred from the modal model results), the RANS simulations provide at all times τ>τ₀ profiles that show good agreement with ILES simulations. The procedure for determining the time at which the RANS model should be started is a representative use, other parameters can be used depending on the application. In this paper, for the purpose of demonstration of the full strategy, τ₀ is taken as the time at which the mixing layer growth rate parameter α has reached its asymptotic value in the corresponding ILES simulation.     

Rayleigh–Taylor instability at spherical interfaces of incompressible fluids

Rayleigh–Taylor instability(RTI) of three incompressible fluids with two interfaces in spherical geometry is derived analytically. The growth rate on the two interfaces and the perturbation feedthrough coefficients between two spherical interfaces are derived. For low-mode perturbation, the feedthrough effect from outer interface to inner interface is much more severe than the corresponding planar case, while the feedback from inner interface to the outer interface is smaller than that in planar geometry. The low-mode perturbations lead to the pronounced RTI growth on the inner interface of a spherical shell that are larger than the cylindrical and planar results. It is the low-mode perturbation that results in the difference between the RTI growth in spherical and cylindrical geometry. When the mode number of the perturbation is large enough, the results in cylindrical geometry are recovered.     

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.     

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.     

Interface coupling effects of weakly nonlinear Rayleigh–Taylor instability with double interfaces

Taking the Rayleigh–Taylor instability with double interfaces as the research object,the interface coupling effects in the weakly nonlinear regime are studied numerically.The variation of Atwood numbers on the two interfaces and the variation of the thickness between them are taken into consideration.It is shown that,when the Atwood number on the lower interface is small,the amplitude of perturbation growth on the lower interface is positively related with the Atwood number on the upper interface.However,it is negatively related when the Atwood number on the lower interface is large.The above phenomenon is quantitatively studied using an analytical formula and the underlying physical mechanism is presented.     

Nonlinear Rayleigh–Taylor instability of the cylindrical fluid flow with mass and heat transfer

The nonlinear Rayleigh–Taylor stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied. The phases enclosed between two cylindrical surfaces coaxial with mass and heat transfer is derived from nonlinear Ginzburg–Landau equation. The F-expansion method is used to get exact solutions for a nonlinear Ginzburg–Landau equation. The region of solutions is displayed graphically.     

Measurements of Rayleigh–Taylor instability growth of laser-shocked iron–silicon alloy

The Rayleigh–Taylor (RT) instability of liquid iron alloys is important for understanding the core formation mechanism in the Earth. Here we first report the measurement of RT instability growth for a liquid iron–silicon (Fe–Si) alloy, which is one of the major candidate for the material of the Earth’s core, using a high power laser. We optimized the measurement setup and analytical technique to observe the growth of perturbation on an Fe–Si sample surface. The growth of perturbation amplitude on the Fe–Si alloy under high pressure and temperature was successfully observed using in situ X-ray radiography. The growth rate of the RT instability for the Fe–Si alloy on about 1000?GPa was estimated to be 0.3 ns^?1.     

Viscosity,heat conductivity,and Prandtl number effects in the Rayleigh–Taylor Instability

The two-dimensional Rayleigh–Taylor instability problem is simulated with a multiple-relaxation-time discrete Boltzmann model with a gravity term. Viscosity, heat conductivity, and Prandtl number effects are probed from macroscopic and nonequilibrium viewpoints. In the macro sense, both viscosity and heat conduction show a significant inhibitory effect in the reacceleration stage, which is mainly achieved by inhibiting the development of the Kelvin–Helmholtz instability. Before this, the Prandtl number effect is not sensitive. Viscosity, heat conductivity, and Prandtl number effects on nonequilibrium manifestations and the degree of correlation between the nonuniformity and the nonequilibrium strength in the complex flow are systematically investigated.     

Quantum Effects on Rayleigh–Taylor Instability of Incompressible Plasma in a Vertical Magnetic Field

Quantum effects on Rayleigh-Taylor instability of a stratified incompressible plasmas layer under the influence of vertical magnetic field are investigated. The solutions of the linearized equations of motion together with the boundary conditions lead to deriving the relation between square normalized growth rate and square normalized wave number in two algebraic equations and are numerically analyzed. In the case of the real solution of these two equations, they can be combined to generate a single equation. The results show that the presence of vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration.     

Phase Effects of Long-Wavelength Rayleigh–Taylor Instability on the Thin Shell

Taking the long-wavelength Rayleigh-Taylor instability(RTI) on the thin shell of inertial confinement fusion as the research object,a linear analytical model is presented to study the phase effects that are caused by the phase difference of single-mode perturbations on the two interfaces.Its accuracy is tested by numerical simulations.By analyzing the characteristic of this model,it is found that the phase difference does not change the basic RTI structure(only one spike and one bubble in a peri...     

Jet-Like Long Spike in Nonlinear Evolution of Ablative Rayleigh–Taylor Instability

We report the formation of jet-like long spike in the nonlinear evolution of the ablative Rayleigh-Taylor instability （ARTI） experiments by numerical simulations. A preheating model k（T） = KSH[1＋f（T）], where KSH is the Spitzer Harm （SH） electron conductivity and f（T） interprets the preheating tongue effect in the cold plasma ahead of the ablative front [Phys. Rev. E 65 （2002） 57401], is introduced in simulations. The simulation results of the nonlinear evolution of the ARTI are in general agreement with the experiment results. It is found that two factors, i.e., the suppressing of ablative Kelvin Helmholtz instability （AKHI） and the heat flow cone in the spike tips, contribute to the formation of jet-like long spike in the nonlinear evolution of the ARTI.     

Simulation of the Weakly Nonlinear Rayleigh–Taylor Instability in Spherical Geometry

The Rayleigh-Taylor instability at the weakly nonlinear(WN) stage in spherical geometry is studied by numerical simulation.The mode coupling processes are revealed.The results are consistent with the WN model based on parameter expansion,while higher order effects are found to be non-negligible.For Legendre mode perturbation Pn(cos B),the nonlinear saturation amplitude(NS A) of the fundamental mode decreases with the mode number n.When n is large,the spherical NSA is lower than the corresponding...     

Determination of the Kardar–Parisi–Zhang equation from experimental data with a small number of configurations

We introduce an inverse method to determine the parameters of the Kardar–Parisi–Zhang equation corresponding to an evolving interface which requires a small number of configurations as input data. Our approach presents advantages for applications in real world scenarios since it does not require small time intervals between fronts. The method is applied to a restricted solid-on-solid model and a stochastic cellular automata model for fire front propagation.     

The dynamics of the k–ϵ mix model toward its self-similar Rayleigh–Taylor solution

We propose an analysis of the non-linear system of partial differential equations for the k–? model expressing the evolution of a turbulent mixing zone induced by the Rayleigh–Taylor instability. The method developed in this work is based on dynamical system theory. Our objective is to prove the global stability of the self-similar solution and at the same time to investigate the dynamics of transient phases. In fact, it is possible to show the existence of a central manifold allowing to reduce the dimension of the problem to a set of two ordinary differential equations.We establish that this simplified non-linear system globally converges toward a fixed point representing the self-similar solution by application of the Poincaré–Bendixson theorem. In addition, we shed light on the existence of a second fixed point which influences the trajectories in the phase space and leads to a non-physical enhanced growth rate in some cases explicitly detailed.     

Influence of flow shear on localized Rayleigh–Taylor and resistive drift wave instabilities

The impact of velocity shear on the localized solutions of Rayleigh–Taylor (RT) and resistive drift wave (DW) instabilities has been investigated. Slab geometry is used, and the plasma density gradient is assumed to have a finite spatial structure. It demonstrates that the velocity shear has quite different effects on these instabilities: while it stabilizes RT instability and causes tilting of the eddies of equipotential contour, it has a very mild impact on the resistive DW instability and simply shifts the eddies with no tilting.     

Anomalies of the electrical properties and the stability of the double layer at a metal-electrolyte boundary. Characteristics of the capacitance of a double layer with relaxing “plates∝

An electromechanical model of the electric double layer, whose plates are displaced on charging, is proposed; it is shown for the example of this model that the differential capacitance can diverge and become negative. The reasons why these anomalies were not predicted in the well-known models of the double layer are examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 9–15, November 1987.     

Generalisation of the eddy-dissipation concept for jet flames with low turbulence and low Damköhler number

Moderate or intense low oxygen dilution (MILD) combustion has been the focus of a range of fundamental experimental and numerical studies. Reasonable agreement between experimental and numerical investigations, however, requires finite-rate chemistry models and, often, ad hoc model adjustment. To remedy this, an adaptive eddy dissipation concept (EDC) combustion model has previously been developed to target conditions encountered in MILD combustion; however, this model relies on a simplified, pre-defined assumption about the combustion chemistry. The present paper reports a generalised version of the modified EDC model without the need for an assumed, single-step chemical reaction or ad hoc coefficient tuning. The results show good agreement with experimental measurements of two CH₄/H₂ flames in hot coflows, showing improvements over the standard EDC model as well as the previously published modified EDC model. The updated version of the EDC model also demonstrates the capacity to reproduce the downstream transition in flame structure of a MILD jet flame seen experimentally, but which has previously proven challenging to capture computationally. Analyses of the previously identified dominant heat-release reactions provide insight into the structural differences between a conventional autoignitive flame and a flame in the MILD combustion regime, whilst highlighting the requirement for a generalised EDC combustion model.     

Metallic hydrogen with a strong electron–phonon coupling at a pressure of 300–500 GPa

Atomic metallic hydrogen, which has a lattice with the FDDD unit cell symmetry, has been shown to be a stable phase at a hydrostatic pressure of 350–500 GPa. The found structure has a phonon spectrum which is stable with respect to decay. The structural, electronic, phonon, etc., characteristics of normal metallic phases of hydrogen at a pressure of 350–500 GPa have been ab initio calculated.     

Numerical simulation of the evolution of unstable disturbances of various modes and initial stages of the laminar-turbulent transition in the boundary layer at the freestream Mach number М = 6

Direct numerical simulations of linear and nonlinear stages of the evolution of unstable disturbances of various modes and initial stages of the laminar-turbulent transition in the boundary layer on a flat plate at the freestream Mach number M = 6 are performed on the basis of full unsteady Navier–Stokes equations for a compressible gas. A considerable effect of three-dimensional unstable disturbances on initiation of the laminar-turbulent transition is demonstrated.