Multimode Rayleigh-Taylor Instability Research Articles

Effects of Atwood number and stratification parameter on compressible multi-mode Rayleigh–Taylor instability

This study numerically analyzes the two-dimensional (2D) compressible multi-mode Rayleigh–Taylor instability at different Atwood numbers (At) and stratification parameters (Sr), corresponding to the different levels of flow compressibility. It is found that the growth of bubble thickness is suppressed with the increase in Sr due to the density stratification at small At, whereas it is enhanced at large At, because of the expansion and compression motions. The ratio of the bubble to spike thickness increases with the increase in Sr at any At. The effects of the flow compressibility on the molecular mixing fraction, Taylor Reynolds number, turbulent Mach number, and velocity divergence statistics are similar at different Atwood numbers. The expansion and compression motions are enhanced by increasing the Sr and At. The expansion motions are relatively strong in the mixing layer, whereas the compression motions are prevalent outside the mixing layer, which may form a force promoting the upward movement of the bubble. The profiles of mean concentration, mean temperature, and root mean square of velocities can overlap with each other at different stratification parameters after normalization, which demonstrates the self-similarity of the 2D compressible Rayleigh–Taylor (RT) turbulence. The density stratification weakens the conversion from potential energy to kinetic energy, while the flow compressibility enhances the pressure-dilatation work at large values of Sr. The present results can help in the development of theoretical models of compressible RT turbulence.

Numerical simulation of single- and multi-mode Rayleigh–Taylor instability with surface tension in two dimensions

In this paper, we study the long-time evolutions of the single- and multi-mode Rayleigh–Taylor instability with surface tension in two dimensions by using the vortex sheet model. Applying a spectrally accurate numerical method, we investigate the effects of surface tension and density jump on the instability in various regimes of parameters. Complex phenomena of pinching, capillary waves, elongation, and roll-up appear at the interfaces. For a single-mode interface, surface tension retards the growths of bubble and spike. The effect of surface tension on the bubble and spike velocity is generally small but is large for a spike of an infinite density ratio. For multi-mode interfaces, we focus on an infinite density ratio. We show that bubbles grow with the scaling law h=αAgt2 even in the presence of surface tension, while spikes follow the scaling law weakly. It is found that both the growth rates of bubbles and spikes decrease with surface tension and the growth rate of spikes decreases larger than that of bubbles. The growth rate of the bubble front is in agreements with results of previous numerical simulations and experiments.

Analysis of Rayleigh–Taylor instability at high Atwood numbers using fully implicit, non-dissipative, energy-conserving large eddy simulation algorithm

Large eddy simulation of three-dimensional, multi-mode Rayleigh–Taylor instability at high Atwood numbers is performed using a recently developed, kinetic energy-conserving, non-dissipative, fully implicit, finite volume algorithm. The algorithm was especially designed for simulating low-Mach number, variable density/viscosity, transitional, and turbulent flows. No interface capturing mechanism is required. Buoyancy and heat transfer effects can be handled without relying on the Boussinesq assumption. Because of this feature, unlike the pure incompressible ones, it does not suffer from the loss of physical accuracy at high Atwood and Rayleigh numbers. In this study, the mixing phenomenon in Rayleigh–Taylor instability and the effects of high Atwood numbers on the development of the flow are investigated using various diagnostics such as local mole fractions, bubble and spike penetration lengths and growth rates, mixing efficiencies, Taylor micro-scales, and corresponding Reynolds numbers and energy ratios. Additionally, some important terms of the Reynolds stress transport equation are also introduced, such as Reynolds stresses (and their anisotropies) and turbulent production. Results show that Rayleigh–Taylor instability at high Atwood numbers is characterized by rapid development of instability due to the increasing growth rates and higher velocities of spike fronts, larger asymmetry in the mixing region, denser interactions in the non-linear phase, and changes in bubble and spike morphologies. It is also found that interactions of spike-fronts with their surroundings are the primary mechanisms of turbulent production and transition to turbulence. However, late time mean flow measures such as energy ratio and mixedness are not significantly affected. A scaling relation between the spike to bubble penetration ratio and the heavy to light density ratio is also provided.

Weakly nonlinear multi-mode Rayleigh-Taylor instability in two-dimensional spherical geometry

A weakly nonlinear model is proposed for the multi-mode incompressible Rayleigh-Taylor instability in two-dimensional spherical geometry. The second-order solutions are derived, which can be applied to arbitrary small initial perturbations. The cosine-type and the Gaussian-type perturbations are discussed in detail. The growth of perturbations at the pole and that at the equator are compared, and the geometry effect is analyzed. It is found that the initial identical perturbation at the pole and the equator in the cross-sectional view will grow asymmetrically. In the linear regime, the perturbation amplitudes at the pole grow faster than those at the equator due to the different topologies. The geometry effect accelerates the ingoing motion and slows down the outgoing motion in the weakly nonlinear regime. This effect is stronger at the pole than that at the equator.

Numerical study of Rayleigh-Taylor instability by using smoothed particle hydrodynamics

In this paper, we present a smoothed particle hydrodynamics (SPH) method for modeling multiphase flows. The multiphase SPH method includes a corrective discretization scheme for density approximation around the fluid interface to treat large density ratio, a small repulsive force between particles from different phases to prevent particles from unphysically penetrating fluid interface, and a newly-developed hyperbolic-shaped kernel function to remove possible stress instability. This multiphase SPH method is then used to study the single-and multi-mode Rayleigh-Taylor instability problems. A comparison between our results with the results from existing literature shows that our results are obviously better than most available results from other SPH simulations. The present results are close to those by Grenier et al. while the present multiphase SPH method is simpler and easier to implement than that in the work by Grenier et al. (Grenier, et al. 2009 J. Comput. Phys. 228 8380). For the single-mode Rayleigh-Taylor instability, the evolutions of the interface pattern and vortex structures, and the penetration depth each as a function of time are investigated. For the multi-mode Rayleigh-Taylor instability, the merging of small structures into a large structure during the evolution of the interface is studied. The horizontal average density and the penetration each as a function of height are also studied.

Mixed miscible-immiscible fluid flow modelling with incompressible SPH framework

A divergence-free Incompressible Smoothed Particle Hydrodynamics (ISPH) framework is developed for modelling multifluid immiscible/miscible flows. The numerical model considers Navier-Stokes equation along with scalar-transport equation to represent flow characteristics. Pure divergence free ISPH algorithm is used to solve Navier-Stokes momentum equation. Scalar transport equation is solved based on the nature of the fluid particles represented in terms of colour indicator (ϕ). Fixed ghost particles are utilized for simulating slip boundary. Proposed model is validated against three analytical/experimental results: (a) immiscible Rayleigh-Taylor Instability (b) lock-exchange non-Boussinesq flow (c) miscible gravity current with low density ratio. The model can capture Kelvin-Helmholtz instabilities generated at the interface. the framework is capable of capturing density-dependent flow with low to high density ratio alike. The capability of the developed model in general multifluid system is demonstrated for two cases (a) miscible multimode Rayleigh-Taylor Instability and (b) mixed miscible-immiscible fluid flow simulation.

Conceptual design of a Rayleigh–Taylor experiment to study bubble merger in two dimensions on NIF

A preliminary design of an experiment meant to investigate the evolution of multimode Rayleigh–Taylor instability (RT) is presented. This experiment is intended to provide a direct measurement of the two-dimensional bubble front evolution in the hydrodynamic regime. RT growth for the proposed design has been analyzed using one-dimensional direct numerical simulations in Hyades and models of self-similar behavior. The models predictions are compared to results obtained in two-dimensional Dafna numerical simulations, with good agreement. The proposed design assures a significant bubble-merging process (∼3–4 bubble merger generations). The design takes advantage of the National Ignition Facility (NIF) capabilities to provide a large enough laser spot area (∼0.5–1 cm2), along with a low-enough drive that preheat effects remain small.

High-fidelity interface tracking in compressible flows: Unlimited anchored adaptive level set

The interface-capturing-fidelity issue of the level set method is addressed wholly within the Eulerian framework. Our aim is for a practical and efficient way to realize the expected benefits of grid resolution and high order schemes. Based on a combination of structured adaptive mesh refinement (SAMR), rather than quad/octrees, and on high-order spatial discretization, rather than the use of Lagrangian particles, our method is tailored to compressible flows, while it provides a potentially useful alternative to the particle level set (PLS) for incompressible flows. Interesting salient features of our method include (a) avoidance of limiting (in treating the Hamiltonian of the level set equation), (b) anchoring the level set in a manner that ensures no drift and no spurious oscillations of the zero level during PDE-reinitialization, and (c) a non-linear tagging procedure for defining the neighborhood of the interface subject to mesh refinement. Numerous computational results on a set of benchmark problems (strongly deforming, stretching and tearing interfaces) demonstrate that with this approach, implemented up to 11th order accuracy, the level set method becomes essentially free of mass conservation errors and also free of parasitic interfacial oscillations, while it is still highly efficient, and convenient for 3D parallel implementation. In addition, demonstration of performance in fully-coupled simulations is presented for multimode Rayleigh–Taylor instability (low-Mach number regime) and shock-induced, bubble-collapse (highly compressible regime).

Modal model for the nonlinear multimode Rayleigh–Taylor instability

A modal model for the Rayleigh–Taylor (RT) instability, applicable at all stages of the flow, is introduced. The model includes a description of nonlinear low-order mode coupling, mode growth saturation, and post-saturation mode coupling. It is shown to significantly extend the range of applicability of a previous model proposed by Haan, to cases where nonlinear mode generation is important. Using the new modal model, we study the relative importance of mode coupling at late nonlinear stages and resolve the difference between cases in which mode generation assumes a dominant role, leading to the late time inverse cascade of modes and loss of memory of initial conditions, and cases where mode generation is not important and memory of initial conditions is retained. Effects of finite density ratios (Atwood number A<1) are also included in the model and the difference between various measures of the mixing zone penetration depth for A<1 is discussed.

Nonlinear evolution of multimode Rayleigh–Taylor instability in two and three dimensions

The nonlinear evolution of the Rayleigh–Taylor instability from multimode initial perturbations is studied by two complementary approaches. First, a statistical-mechanics bubble-merger model is presented, that enables determination of the late-time scaling properties based on single-mode and two-bubble interaction physics. The results for Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) bubble and spike front penetrations are given, as well as scaling laws for mixing under a time-dependent driving acceleration. The second approach is a modal model, in which nonlinear mode coupling and saturation are included in an equation for effective modes that describe the mixed region. The importance of mode coupling in the generation of large structure that dominates the late stage evolution, and the relative importance of long-wavelength components in the initial perturbation spectra on the late-stage evolution are studied. Finally, multimode RT instability in three dimensions is studied by both full-scale simulations and the modal model. The effect and late-stage memory loss of different aspect ratios in the initial perturbation are demonstrated.