Rayleigh-Taylor Bubbles Research Articles

Lagrangian investigation of the interface dynamics in single-mode Rayleigh–Taylor instability

We apply Lagrangian particle tracking to the two-dimensional single-mode Rayleigh–Taylor (RT) instability to study the dynamical evolution of fluid interface. At the onset of the nonlinear RT stage, we select three ensembles of tracer particles located at the bubble tip, at the spike tip, and inside the spiral of the mushroom structure, which cover most of the interfacial region as the instability develops. Conditional statistics performed on the three sets of particles and over different RT evolution stages, such as the trajectory curvature, velocity, and acceleration, reveals the temporal and spatial flow patterns characterizing the single-mode RT growth. The probability density functions of tracer particle velocity and trajectory curvature exhibit scalings compatible with local flow topology, such as the swirling motion of the spiral particles. Large-scale anisotropy of RT interfacial flows, measured by the ratio of horizontal to vertical kinetic energy, also varies for different particle ensembles arising from the differing evolution patterns of the particle acceleration. In addition, we provide direct evidence to connect the RT bubble re-acceleration to its interaction with the transported fluid from the spike side, due to the shear driven Kelvin–Helmholtz instability. Furthermore, we reveal that the secondary RT instability inside the spiral, which destabilizes the spiraling motion and induces complex flow structures, is generated by the centrifugal acceleration.

Multimode Hydrodynamic Instability Growth of Preimposed Isolated Defects in Ablatively Driven Foils.

The Nike KrF laser facility was used to study the evolution of isolated defects with characteristic sizes of <1 to 10s of μm in laser-accelerated plastic foils. The experimental platform permitted, for the first time, the systematic study of localized perturbation growth, which is inherently multimode, through ablative Richtmyer-Meshkov and Rayleigh-Taylor stages and into the strongly nonlinear regime. Initial target defects were relatively large amplitude, but spatially localized, and emulated tent, fill-tube, and other nonuniformities that are present in inertial confinement fusion capsules. Face-on x-ray radiography indicated initial growth of the perturbation in both depth and width, followed by its apparent closure due to oblique spike growth. Hollow jetlike profiles of laterally expanding, rising, Rayleigh-Taylor bubbles were observed on the rear surface of the target from each isolated defect. Radiation hydrodynamic simulations provided insight into the mechanism of the closure and other features of the bubble and spike evolution specific to isolated defects.

The [formula omitted]s and [formula omitted]s in Rayleigh–Taylor and Richtmyer–Meshkov instabilities

The alphas (αb, αs) and thetas (θb, θs) are the essential parameters describing the asymptotic growth behavior of the mixing layer driven by Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities at the interface between the fluids. Extensive simulations and experiments have been conducted in the determination of these parameters. The results depend on numerical algorithms, resolutions, and the accuracy of experimental measurements. In this article, we present a unique relationship between the alphas and thetas by applying a simple buoyancy-drag mixing model. Our first main result is that, for the same fluids, these parameters are not independent because they are fundamentally connected by physics principles and they all are functions of the drag coefficients of the fluids. As a consequence, the alphas and thetas are intrinsically coupled. All are functions of any single one of these. Our second main result is that the RT bubble growth rate (αb) is determined by the bubble competition process – a merger model – at the edge of the mixing layer. Together, these two main results determine all the alphas and thetas by strictly theoretical reasoning. Applications to both hydro and laser driven experiments at OMEGA are presented.

Dynamic evolution of Rayleigh-Taylor bubbles from sinusoidal, W-shaped, and random perturbations.

Implicit large eddy simulations of two-dimensional Rayleigh-Taylor instability at different density ratios (i.e., Atwood number A=0.05, 0.5, and 0.9) are conducted to investigate the late-time dynamics of bubbles. To produce a flow field full of bounded, semibounded, and chaotic bubbles, three problems with distinct perturbations are simulated: (I) periodic sinusoidal perturbation, (II) isolated W-shaped perturbation, and (III) random short-wave perturbations. The evolution of height h, velocity v, and diameter D of the (dominant) bubble with time t are formulated and analyzed. In problem I, during the quasisteady stage, the simulations confirm Goncharov's prediction of the terminal speed v_{∞}=Frsqrt[Agλ/(1+A)], where Fr=1/sqrt[3π]. Moreover, the diameter D at this stage is found to be proportional to the initial perturbation wavelength λ as D≈λ. This differed from Daly's simulation result of D=λ(1+A)/2. In problem II, a W-shaped perturbation is designed to produce a bubble environment similar to that of chaotic bubbles in problem III. We obtain a similar terminal speed relationship as above, but Fr is replaced by Fr_{w}≈0.63. In problem III, the simulations show that h grows quadratically with the bubble acceleration constant α≡h/(Agt^{2})≈0.05, and D expands self-similarly with a steady aspect ratio β≡D/h≈(1+A)/2, which differs from existing theories. Therefore, following the mechanism of self-similar growth, we derive a relationship of β=4α(1+A)/Fr_{w}^{2} to relate the evolution of chaotic bubbles in problem III to that of semibounded bubbles in problem II. The validity of this relationship highlights the fact that the dynamics of chaotic bubbles in problem III are similar to the semibounded isolated bubbles in problem II, but not to that of bounded periodic bubbles in problem I.

The physics of long- and intermediate-wavelength asymmetries of the hot spot: Compression hydrodynamics and energetics

The effect of asymmetries on the performance of inertial confinement fusion implosions is investigated. A theoretical model is derived for the compression of distorted hot spots, and quantitative estimates are obtained using hydrodynamic simulations. The asymmetries are divided into low (ℓ&amp;lt;6) and intermediate (6&amp;lt;ℓ&amp;lt;40) modes by comparison of the mode wavelength with the hot-spot radius and the thermal-diffusion scale length. Long-wavelength modes introduce substantial nonradial motion, whereas intermediate-wavelength modes involve more cooling by thermal losses. It is found that for distorted hot spots, the measured neutron-averaged properties can be very different from the real hydrodynamic conditions. This is because mass ablation driven by thermal conduction introduces flows in the Rayleigh–Taylor bubbles that results in pressure variations, in addition to temperature variations between the bubbles and the neutron-producing region. The differences are less pronounced for long-wavelength asymmetries since the bubbles are relatively hot and sustain fusion reactions. The yield degradation—with respect to the symmetric case—results primarily from a reduction in the hot-spot pressure for low modes and from a reduction in burn volume for intermediate modes. A general expression is found relating the pressure degradation to the residual shell energy and the flow within the hot spot (i.e., the total residual energy).

Numerical study of particle-induced Rayleigh-Taylor instability: Effects of particle settling and entrainment

In this study, we investigate Rayleigh-Taylor instability in which the density stratification is caused by the suspension of particles in liquid flows using the conventional single-phase model and Euler-Lagrange (EL) two-phase model. The single-phase model is valid only when the particles are small and number densities are large, such that the continuum approximation applies. The present single-phase results show that the constant settling of the particle concentration restricts the lateral development of the vortex ring, which results in a decrease of the rising speed of the Rayleigh-Taylor bubbles. The EL model enables the investigation of particle-flow interaction and the influence of particle entrainment, resulting from local non-uniformity in the particle distribution. We compare bubble dynamics in the single-phase and EL cases, and our results show that the deviation between the two cases becomes more pronounced when the particle size increases. The main mechanism responsible for the deviation is particle entrainment, which can only be resolved in the EL model. We provide a theoretical argument for the small-scale local entrainment resulting from the local velocity shear and non-uniformity of the particle concentration. The theoretical argument is supported by numerical evidence. Energy budget analysis is also performed and shows that potential energy is released due to the interphase drag and buoyant effect. The buoyant effect, which results in the transformation of potential energy into kinetic energy and shear dissipation, plays a key role in settling enhancement. We also find that particle entrainment increases the shear dissipation, which in turn enhances the release of potential energy.

Combined Effect of Viscosity, Surface Tension and Compressibility on Rayleigh-Taylor Bubble Growth Between Two Fluids

The combined effect of viscosity, surface tension, and the compressibility on the nonlinear growth rate of Rayleigh-Taylor (RT) instability has been investigated. For the incompressible case, it is seen that both viscosity and surface tension have a retarding effect on RT bubble growth for the interface perturbation wave number having a value less than three times of a critical value (kc=(ρh-ρl)g/T, T is the surface tension). For the value of wave number greater than three times of the critical value, the RT induced unstable interface is stabilized through damped nonlinear oscillation. In the absence of surface tension and viscosity, the compressibility has both a stabilizing and destabilizing effect on RTI bubble growth. The presence of surface tension and viscosity reduces the growth rate. Above a certain wave number, the perturbed interface exhibits damped oscillation. The damping factor increases with increasing kinematic viscosity of the heavier fluid and the saturation value of the damped oscillation depends on the surface tension of the perturbed fluid interface and interface perturbation wave number. An approximate expression for asymptotic bubble velocity considering only the lighter fluid as a compressible one is presented here. The numerical results describing the dynamics of the bubble are represented in diagrams.

Multiscale Nested Simulations of Rayleigh–Taylor Instabilities in Ionospheric Flows

Nested numerical simulations of ionospheric plasma density structures associated with nonlinear evolution of the Rayleigh–Taylor (RT) instability in equatorial spread F (ESF) are presented. The numerical implementation of the nested model uses a spatial discretization with a C grid staggering configuration where normal velocities of ions and electrons are staggered one-half grid length from the density of charged particles. The advection of charged particles is computed with a fifth order accurate in space weighted essentially nonoscillatory (WENO) scheme. The continuity equation is integrated using a third-order Runge–Kutta (RK) time integration scheme. The equation for the electric potential is solved at each time step with a multigrid method. For the limited area and nested simulations, the lateral boundary conditions are treated via implicit relaxation applied in buffer zones where the density of charged particles for each nest is relaxed to that obtained from the parent domain. The high resolution in targeted regions offered by the nested model was able to resolve secondary RT instabilities, and to improve the resolution of the primary RT bubble compared to the coarser large domain model. The computational results are validated by conducting a large domain simulation where the resolution is increased everywhere.

Observation of Self-Similarity in the Magnetic Fields Generated by the Ablative Nonlinear Rayleigh-Taylor Instability

Magnetic fields generated by the nonlinear Rayleigh-Taylor growth of laser-seeded three-dimensional broadband perturbations were measured in laser-accelerated planar targets using ultrafast proton radiography. The experimental data show self-similar behavior in the growing cellular magnetic field structures. These observations are consistent with a bubble competition and merger model that predicts the time evolution of the number and size of the bubbles, linking the cellular magnetic field structures with the Rayleigh-Taylor bubble and spike growth.

Flame dynamics and consideration of deflagration-to-detonation transition in central gravitational field

Expanding reaction fronts are central to many terrestrial processes as well as such cosmic phenomena as the thermonuclear combustion in supernovae. While in terrestrial conditions the effect of intrinsic flamefront instabilities is generally believed to be supplementary to, say, external turbulence and chamber dynamics, at the astrophysical scale the role of flamefront instabilities in the flame acceleration is presumably dominant. Moreover, while in terrestrial systems we focus mainly on the hydrodynamic, Darrieus–Landau (DL) instability, the Rayleigh–Taylor (RT), body-force instability could be a key issue for astrophysical flames because of the enormous gravity and the associated large scales. Consequently, if RT effects dominate over DL effects, the globally-spherical flamefront can be replaced by an expanding bubble with a non-spherical shape, possibly that of digit “8”. In the present work we have developed a self-similar formulation describing a globally-spherical expanding flamefront corrugated due to the DL instability in a central gravitation field. The associated scenario of the flame acceleration, the evolution of the upstream flow, and the instant when a gas parcel ahead of the flamefront first explodes, hence initiating the deflagration-to-detonation transition (DDT), as well as the radial coordinate of this parcel, are determined. We have also compared the effects of DL and RT instabilities, estimating whether a globally-spherical, DL-corrugated flamefront is subsequently terminated by the formation of RT bubbles. It is shown how the instant of such a transition and the relevant global flame radius are coupled to various flame and flow parameters.

On bubble and spike oscillations in a dusty gas Rayleigh-Taylor instability

AbstractThe Multiphase Buoyancy-Drag model recently formulated in Balakrishnan &amp; Menon, Laser and Particle Beams, 2011 is applied to investigate the (1) rise of dusty gas Rayleigh-Taylor bubbles into a pure gas and (2) fall of pure gas Rayleigh-Taylor spikes into a region of particles. It is demonstrated that for these two scenarios, the bubble or spike amplitude oscillates about the dusty gas/pure gas interface. The ratio of the bubble or spike amplitudes on the pure gas side to the dusty gas side, asymptotes to a constant that depends only on the initial Atwood number, A, the multiphase Atwood number, Am, and the initial wavelength of the perturbation, λo. For the same Am, the ratio decreases with A for oscillating bubbles, and vice versa for oscillating spikes.

The bubble velocity research of Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers

We generalize the Layzer's bubble model to the cases of two-dimensional and three-dimensional analytical models of an arbitrary interface Atwood number and obtain self-consistent equations. The generalized model provides a continuous bubble evolution from the earlier exponential growth to the nonlinear regime. The asymptotic bubble velocities are obtained for the Rayleigh-Taylor(RT) and Richtmyer-Meshkov(RM) instabilities. We also report on the two-dimensional and the three-dimensional analytical expressions for the evolution of the RT bubble velocity.

Quantitative modeling of bubble competition in Richtmyer-Meshkov instability

We present a quantitative model for the evolution of single and multiple bubbles in the Richtmyer-Meshkov (RM) instability. The higher-order solutions for a single-mode bubble are obtained, and distinctions between RM and Rayleigh-Taylor bubbles are investigated. The results for multiple-bubble competition from the model shows that the higher-order correction to the solution of the bubble curvature has a large influence on the growth rate of the RM bubble front. The model predicts that the bubble front of RM mixing grows as h approximately ttheta with theta approximately (0.3-0.35)+/-0.02 .

Surface tension in incompressible Rayleigh–Taylor mixing flow

We study the effect of surface tension on the incompressible Rayleigh–Taylor instability. We modify Goncharov's local analysis [1] to consider the surface tension effect on the Rayleigh–Taylor bubble velocity. The surface tension damps the linear instability and reduces the nonlinear terminal bubble velocity. We summarize the development of a finite-volume, particle-level-set, two-phase flow solver with an adaptive Cartesian mesh, and results from convergence and validation studies of this two-phase flow solver are provided. We use this code to simulate the single-mode, viscous Rayleigh–Taylor instability with surface tension, and good agreement in terminal bubble velocity is found when compared with analytic results. We also simulate the immiscible Rayleigh–Taylor instability with random initial perturbations. The ensuing mixing flow is characterized by the effective mixing rate and the flow anisotropy. Surface tension tends to reduce the effective mixing rate and homogenizes the Rayleigh–Taylor mixing flow. Finally, we provide a scaling argument for detecting the onset of the quadratic, self-similar Rayleigh–Taylor growth.

Single-mode dynamics of the Rayleigh-Taylor instability at any density ratio

The behavior of a periodic array of Rayleigh-Taylor bubbles (and spikes) of wavelength lambda is investigated at different density ratios using three-dimensional numerical simulations. The scaled bubble and spike velocities (v(b,s)/sqrt[Aglambda/2]), are found to vary with the Atwood number A, and are compared with recent potential flow theories. Simulations at different grid resolutions reveal that the convergence rates of bubble velocities improve with increasing A, while the converse holds true for spike velocities. The asymptotic radius of curvature at the bubble tip is found to be independent of A, consistent with potential flow theory. These results are useful in validating potential flow theory models of the nonlinear stage of the Rayleigh-Taylor instability.

Density dependence of a Zufiria-type model for Rayleigh–Taylor bubble fronts

We present the analytic model for the evolution of bubbles of arbitrary density ratio in Rayleigh-Taylor and Richtmyer-Meshkov instabilities. The model is the generalization of Zufiria's potential theory, which is based on the velocity potential with a point source and previously applied only for the interface of infinite density ratio. The analytic expressions for asymptotic solutions of bubbles are obtained. The predictions from the Zufiria model agree well with the numerical results not only for the bubble velocity, but also for the bubble curvature. It is found that the asymptotic curvature of a Richtmyer-Meshkov bubble is smaller than that of a Rayleigh-Taylor bubble for all Atwood numbers.

Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities.

The vortex method is applied to simulations of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities. The numerical results from the vortex method agree well with analytic solutions and other numerical results. The bubble velocity in the RT instability converges to a constant limit, and in the RM instability, the bubble and spike have decaying growth rates, except for the spike of infinite density ratio. For both RT and RM instabilities, bubbles attain constant asymptotic curvatures. It is found that, for the same density ratio, the RT bubble has slightly larger asymptotic curvature than the RM bubble. The vortex sheet strength of the RM interface has different behavior than that of the RT interface. We also examine the validity of theoretical models by comparing the numerical results with theoretical predictions.

Wedge and conic singularities on the free surface of a fluid: The dynamics of rayleigh-taylor bubbles and bubbles near the wall of an inclined tube

Wedge and conic singularities on the free surface of a fluid: The dynamics of rayleigh-taylor bubbles and bubbles near the wall of an inclined tube

Dynamics of two-dimensional Rayleigh–Taylor bubbles for fluids with a finite density contrast

We study the motion of a two-dimensional coherent structure of bubbles and spikes in the Rayleigh–Taylor instability for fluids with a finite density contrast in the case of a small amplitude initial perturbation. The theoretical and numerical solutions for the system of conservation laws are found, and the dynamics of the bubble shape and velocity in the nonlinear regime is described. Good agreement between theory and simulations is achieved. A comparison to earlier models is performed.

Rayleigh–Taylor spike evaporation

Laser-based experiments have shown that Rayleigh–Taylor (RT) growth in thin, perturbed copper foils leads to a phase dominated by narrow spikes between thin bubbles. These experiments were well modeled and diagnosed until this “ spike” phase, but not into this spike phase. Experiments were designed, modeled, and performed on the OMEGA laser [T. R. Boehly, D. L. Brown, R. S. Craxton et al., Opt. Commun. 133, 495 (1997)] to study the late-time spike phase. To simulate the conditions and evolution of late time RT, a copper target was fabricated consisting of a series of thin ridges (spikes in cross section) 150 μm apart on a thin flat copper backing. The target was placed on the side of a scale-1.2 hohlraum with the ridges pointing into the hohlraum, which was heated to 190 eV. Side-on radiography imaged the evolution of the ridges and flat copper backing into the typical RT bubble and spike structure including the “ mushroom-like feet” on the tips of the spikes. RAGE computer models [R. M. Baltrusaitis, M. L. Gittings, R. P. Weaver, R. F. Benjamin, and J. M. Budzinski, Phys. Fluids 8, 2471 (1996)] show the formation of the “ mushrooms,” as well as how the backing material converges to lengthen the spike. The computer predictions of evolving spike and bubble lengths match measurements fairly well for the thicker backing targets but not for the thinner backings.