Understanding the Rayleigh-Taylor instability through 1D and 3D simulations
Mikhaeil, Mark; Denissen, Nicholas; Ranjan, Devesh
2015-11-01
A series of Rayleigh-Taylor instability numerical simulations were completed using the Arbitrary Lagrangian-Eulerian hydrocode FLAG developed at Los Alamos National Laboratory. One-dimensional simulations employed a Reynolds-averaged Navier-Stokes approach with turbulence closure models selected from the Besnard-Harlow-Rauenzahn family of models. Growth rate parameters and turbulence statistics are derived from these simulations and compared between closure models. Variations from experimental results are explored and used to validate the models. The effect of density ratio on the bubble-spike growth rate asymmetry is also investigated. High resolution three-dimensional large eddy simulations (LES) are also completed and presented. LES were initialized using a multi-modal perturbation prescribed from experimental data collected at the Georgia Institute of Technology multi-layer Gas Tunnel facility. Turbulence statistics are gathered by averaging many simulations started with different initial conditions. Late time development is compared to Gas Tunnel experimental results and previous LES.
Fraschetti, Federico; Ballet, Jean; Decourchelle, Anne
2010-01-01
Context: The Rayleigh-Taylor instabilities generated by the deceleration of a supernova remnant during the ejecta-dominated phase are known to produce finger-like structures in the matter distribution which modify the geometry of the remnant. The morphology of supernova remnants is also expected to be modified when efficient particle acceleration occurs at their shocks. Aims: The impact of the Rayleigh-Taylor instabilities from the ejecta-dominated to the Sedov-Taylor phase is investigated over one octant of the supernova remnant. We also study the effect of efficient particle acceleration at the forward shock on the growth of the Rayleigh-Taylor instabilities. Methods: We modified the Adaptive Mesh Refinement code RAMSES to study with hydrodynamic numerical simulations the evolution of supernova remnants in the framework of an expanding reference frame. The adiabatic index of a relativistic gas between the forward shock and the contact discontinuity mimics the presence of accelerated particles. Results: The ...
Rayleigh-Taylor Instability in Viscoelastic Fluids
Joshi, Amey
2013-01-01
In this paper I analyze the onset of Rayleigh-Taylor instability between two linear viscoelastic fluids assuming that the perturbations at the interface are small. In the first half, the paper analyzes a stratified viscoelastic fluid in which I prove that the perturbations rise or fall exponentially without oscillating. The second half of the paper examines the effect of electric and magnetic fields on viscoelastic fluids. I show that it is possible to choose electric or magnetic field gradie...
Rayleigh-Taylor instability in compressible fluids
Sturtevant, B. (California Inst. of Tech., Pasadena, CA (USA). Graduate Aeronautical Labs.)
1990-11-05
This is a report of the progress during the past year of the shock-tube study of the Richtmyer-Meshkov instability, initiated under the sponsorship of the Lawrence Livermore National Laboratory in September, 1982. The purpose of this research program, as stated in the original proposal, is: to investigate the nonlinear processes initiated by shock wave interaction with gas-gas interfaces. In particular, the nonlinear stage of shock-initiated Rayleigh-Taylor instability, the secondary instabilities (e.g., Kelvin-Helmholtz instability) arising therefrom and the concomitant mixing of the two fluids are of interest.''
Curvature suppresses the Rayleigh-Taylor instability
Trinh, Philippe H; Hammoud, Naima; Howell, Peter D; Chapman, S Jonathan; Stone, Howard A
2014-01-01
The dynamics of a thin liquid film on the underside of a curved cylindrical substrate is studied. The evolution of the liquid layer is investigated as the film thickness and the radius of curvature of the substrate are varied. A dimensionless parameter (a modified Bond number) that incorporates both geometric parameters, gravity, and surface tension is identified, and allows the observations to be classified according to three different flow regimes: stable films, films with transient growth of perturbations followed by decay, and unstable films. Experiments and theory confirm that, below a critical value of the Bond number, curvature of the substrate suppresses the Rayleigh-Taylor instability.
Rayleigh-Taylor instability in elastic solids.
Piriz, A R; Cela, J J López; Cortázar, O D; Tahir, N A; Hoffmann, D H H
2005-11-01
We present an analytical model for the Rayleigh-Taylor instability that allows for an approximate but still very accurate and appealing description of the instability physics in the linear regime. The model is based on the second law of Newton and it has been developed with the aim of dealing with the instability of accelerated elastic solids. It yields the asymptotic instability growth rate but also describes the initial transient phase determined by the initial conditions. We have applied the model to solid/solid and solid/fluid interfaces with arbitrary Atwood numbers. The results are in excellent agreement with previous models that yield exact solutions but which are of more limited validity. Our model allows for including more complex physics. In particular, the present approach is expected to lead to a more general theory of the instability that would allow for describing the transition to the plastic regime. PMID:16383751
Georges, G.; Breil, J.; Ribeyre, X.; Le Bel, E.
2015-12-01
Several astronomical flows can be studied thanks to the gas dynamics equations under the Lagrangian formalism. Here we propose to study the plerion dynamic, i.e. supernova remnants blown-up by a central pulsar as well as the Rayleigh-Taylor Instability (RTI) development at the inner interface of this gas shell. The scheme used is a multi-dimensional second order cell-centered Lagrangian scheme. It satisfies the Geometric Conservation Law (GCL), a semi-discrete entropy inequality and it conserves globally the momentum and the total energy. The convergence of the scheme towards the analytical solution is tested for the plerion test case and in the case of an axi-symmetric perturbation. Finally, the scheme is used to study the perturbation growth on the shell inner face perturbed with spherical harmonics.
The Rotating Rayleigh-Taylor Instability
Scase, Matthew M; Hill, Richard J A
2016-01-01
The effect of rotation upon the classical two-layer Rayleigh-Taylor instability is considered theoretically and compared with previous experimental results. In particular we consider a two-layer system with an axis of rotation that is perpendicular to the interface between the layers. In general we find that a wave mode's growth rate may be reduced by rotation. We further show that in some cases, unstable axisymmetric wave modes may be stabilized by rotating the system above a critical rotation rate associated with the mode's wavelength, the Atwood number and the flow's aspect ratio. We compare our theory with experiments conducted in a magnetic field using 'heavy' diamagnetic and 'light' paramagnetic fluids and present comparisons between the theoretical predictions and experimental observations.
Rayleigh-Taylor Instability in Viscoelastic Fluids
Joshi, Amey
2013-01-01
In this paper I analyze the onset of Rayleigh-Taylor instability between two linear viscoelastic fluids assuming that the perturbations at the interface are small. In the first half, the paper analyzes a stratified viscoelastic fluid in which I prove that the perturbations rise or fall exponentially without oscillating. The second half of the paper examines the effect of electric and magnetic fields on viscoelastic fluids. I show that it is possible to choose electric or magnetic field gradient such that the effective acceleration due to gravity is zero. If a heavy Newtonian fluid rests on top of a lighter Newtonian fluid such a choice of field gradient would have rendered the arrangement stable. If the fluids are viscoelastic, I show that a similar arrangement is unstable.
Kinetic Simulations of Rayleigh-Taylor Instabilities
Sagert, Irina; Bauer, Wolfgang; Colbry, Dirk; Howell, Jim; Staber, Alec; Strother, Terrance
2014-09-01
We report on an ongoing project to develop a large scale Direct Simulation Monte Carlo code. The code is primarily aimed towards applications in astrophysics such as simulations of core-collapse supernovae. It has been tested on shock wave phenomena in the continuum limit and for matter out of equilibrium. In the current work we focus on the study of fluid instabilities. Like shock waves these are routinely used as test-cases for hydrodynamic codes and are discussed to play an important role in the explosion mechanism of core-collapse supernovae. As a first test we study the evolution of a single-mode Rayleigh-Taylor instability at the interface of a light and a heavy fluid in the presence of a gravitational acceleration. To suppress small-wavelength instabilities caused by the irregularity in the separation layer we use a large particle mean free path. The latter leads to the development of a diffusion layer as particles propagate from one fluid into the other. For small amplitudes, when the instability is in the linear regime, we compare its position and shape to the analytic prediction. Despite the broadening of the fluid interface we see a good agreement with the analytic solution. At later times we observe the development of a mushroom like shape caused by secondary Kelvin-Helmholtz instabilities as seen in hydrodynamic simulations and consistent with experimental observations.
Kinetic Simulations of Rayleigh-Taylor Instabilities
Sagert, Irina; Colbry, Dirk; Howell, Jim; Staber, Alec; Strother, Terrance
2014-01-01
We report on an ongoing project to develop a large scale Direct Simulation Monte Carlo code. The code is primarily aimed towards applications in astrophysics such as simulations of core-collapse supernovae. It has been tested on shock wave phenomena in the continuum limit and for matter out of equilibrium. In the current work we focus on the study of fluid instabilities. Like shock waves these are routinely used as test-cases for hydrodynamic codes and are discussed to play an important role in the explosion mechanism of core-collapse supernovae. As a first test we study the evolution of a single-mode Rayleigh-Taylor instability at the interface of a light and a heavy fluid in the presence of a gravitational acceleration. To suppress small-wavelength instabilities caused by the irregularity in the separation layer we use a large particle mean free path. The latter leads to the development of a diffusion layer as particles propagate from one fluid into the other. For small amplitudes, when the instability is i...
Experimental Investigation of the Rayleigh-Taylor Instability
White, Jeremy
2011-12-01
A series of experiments have been carried out to study the behavior of the Rayleigh-Taylor instability. The experiments cover a wide range of Atwood (A = (rho2-rho1)/(rho 2-rho1)) numbers, 0.28 ≤ A ≤ 1 using immiscible fluids, with Reynolds numbers spanning four orders of magnitude, ˜ 10 ≤ Re ≤ 10000. Multiple 2D interface shapes have been studied along with a single 3D configuration. The unique properties of magnetorheological fluids are exploited to generate well defined, static initial conditions for both single and multi-mode sinusoidal perturbations as well as isolated wavelengths of single-mode perturbations protruding from flat interfaces. The magnetic properties of the fluid are used to hold these shapes static prior to running, as well as to suspend them above a lighter fluid to allow gravity to provide acceleration to drive the mixing. The 2D experimental results corroborate some of the limitations of the non-linear analytical models, which have been recently investigated numerically, as well as observed in 3D experiments, but not reported in 2D experiments before. The unbounded growth of the Rayleigh-Taylor spikes at late times has been experimentally confirmed for both the 3D condition, where this is predicted to occur for all Atwood numbers, and for the A = 1 limit in the 2D configuration. Preliminary testing with multi-mode interface shapes with high viscosity, high surface tension MR fluids demonstrate the feasibility of extending this unique experimental technique to the more complicated multi-mode/broadband initial conditions more commonly present in applications. Further extension to lower viscosity and surface tension MR fluids for higher Reynolds number flows has proven difficult with the experimental design, yet has revealed the future changes that will be needed to apply this unique experimental idea to the study of the turbulent mix regime. Finally, 3D simulations using the 2D experimental conditions have demonstrated the importance
Synchrotron Magnetic Fields from Rayleigh-Taylor Instability in Supernovae
Duffell, Paul
2016-01-01
Synchrotron emission from a supernova necessitates a magnetic field, but it is unknown how strong the relevant magnetic fields are, and what mechanism generates them. In this study, we perform high-resolution numerical gas dynamics calculations to determine the growth of turbulence due to Rayleigh-Taylor instability, and the resulting kinetic energy in turbulent fluctuations, to infer the strength of magnetic fields amplified by this turbulence. We find that Rayleigh-Taylor instability can produce turbulent fluctuations strong enough to amplify magnetic fields to a few percent of equipartition with the thermal energy. This turbulence stays concentrated near the reverse shock, but averaging this magnetic energy throughout the shocked region (weighting by emissivity) sets the magnetic fields at a minimum of 0.3 percent of equipartition. This suggests a minimum effective magnetic field strength ($\\epsilon_B > 0.003$) which should be present in all interacting supernovae.
Rayleigh-Taylor instability between two stable stratifications
Wykes, Megan S Davies
2012-01-01
These fluid dynamics video sequences show two Rayleigh-Taylor instability experiments. The first video sequence shows an experiment where two layers of uniform density are arranged such that the density of the upper layer is greater than the density of the lower. The unstable interface between the two layers is initially supported by a stainless steel barrier. With the removal of the barrier, Rayleigh-Taylor instability results in the creation of a mixing region, which grows with time. This growth accelerates until the mixing region fills the entire tank. The second sequence shows Rayleigh-Taylor instability when it is confined between two stable stratifications. Although initially the growth of the mixing region accelerates, the stable stratification slows the growth of the instability and brings it to a halt before it can fill the tank. The stratifications are constructed of fresh and salt water and both experiments have the same Atwood number. Visualisation of the upper surface of the mixing layer was achi...
Effects of interfacial curvature on Rayleigh-Taylor instability
Krechetnikov, Rouslan
2008-01-01
In this work a non-trivial effect of the interfacial curvature on the stability of accelerated interfaces, such as liquid rims, is uncovered. The new stability analysis, based on operator and boundary perturbation theories, reveals and quantifies influence of the interfacial curvature on the growth rate and on the wavenumber selection of the Rayleigh-Taylor instability. The systematic approach developed here also provides a rigorous generalization of the widely used \\textit{ad hoc} idea, due ...
Viscous Potential Flow Analysis of Electrohydrodynamic Rayleigh-Taylor Instability
Awasthi Mukesh Kumar; Yadav Dhananjay; G.S. Agrawal
2014-01-01
A linear analysis of Rayleigh-Taylor instability in the presence of tangential electric field has been carried out using viscous potential flow theory. In viscous potential flow theory, viscosity is not zero but viscous term in the Navier- Stokes equation is zero as vorticity is zero. Viscosity enters through normal stress balance and tangential stresses are not considered in viscous flow theory. A dispersion relation has been obtained and stability criterion has been given in the terms of cr...
Kinetic Simulations of Rayleigh-Taylor Instabilities
Sagert, Irina; Bauer, Wolfgang; Colbry, Dirk; Howell, Jim; Staber, Alec; Strother, Terrance
2014-01-01
We report on an ongoing project to develop a large scale Direct Simulation Monte Carlo code. The code is primarily aimed towards applications in astrophysics such as simulations of core-collapse supernovae. It has been tested on shock wave phenomena in the continuum limit and for matter out of equilibrium. In the current work we focus on the study of fluid instabilities. Like shock waves these are routinely used as test-cases for hydrodynamic codes and are discussed to play an important role ...
Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability
Yan, R.; Aluie, H. [Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627 (United States); Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14627 (United States); Betti, R. [Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627 (United States); Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14627 (United States); Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (United States); Sanz, J. [E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Madrid 28040 (Spain); Liu, B.; Frank, A. [Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (United States)
2016-02-15
The nonlinear evolution of the single-mode ablative Rayleigh-Taylor instability is studied in three dimensions. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the three-dimensional (3D) terminal bubble velocity greatly exceeds both the two-dimensional (2D) value and the classical 3D bubble velocity. Unlike in 2D, the 3D short-wavelength bubble velocity does not saturate. The growing 3D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes to the ablated plasma filling the bubble volume.
Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability
Yan, R. [Univ. of Rochester, Rochester, NY (United States); Betti, R. [Univ. of Rochester, Rochester, NY (United States); Sanz, J. [Univ. Politecnica de Madrid, Madrid (Spain); Aluie, H. [Univ. of Rochester, Rochester, NY (United States); Liu, B. [Univ. of Rochester, Rochester, NY (United States); Frank, A. [Univ. of Rochester, Rochester, NY (United States)
2016-02-02
The nonlinear evolution of the single-mode ablative Rayleigh-Taylor instability is studied in three dimensions. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the three-dimensional (3D) terminal bubble velocity greatly exceeds both the two-dimensional (2D) value and the classical 3D bubble velocity. Unlike in 2D, the 3D short-wavelength bubble velocity does not saturate. The growing 3D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. As a result, the vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes to the ablated plasma filling the bubble volume.
Effects of interfacial curvature on Rayleigh-Taylor instability
Krechetnikov, Rouslan
2008-01-01
In this work a non-trivial effect of the interfacial curvature on the stability of accelerated interfaces, such as liquid rims, is uncovered. The new stability analysis, based on operator and boundary perturbation theories, reveals and quantifies influence of the interfacial curvature on the growth rate and on the wavenumber selection of the Rayleigh-Taylor instability. The systematic approach developed here also provides a rigorous generalization of the widely used \\textit{ad hoc} idea, due to Layzer [Astrophys. J. \\textbf{122}, 1-12 (1955)], of approximating the potential velocity field near the interface.
Theoretical and Experimental Studies of Magneto-Rayleigh-Taylor Instabilities
Magneto-Rayleigh-Taylor instability (MRT) is important to magnetized target fusion, wire-array z-pinches, and equation-of-state studies using flyer plates or isentropic compression. It is also important to the study of the crab nebula. The investigators performed MRT experiments on thin foils, driven by the mega-ampere linear transformer driver (LTD) facility completed in their laboratory. This is the first 1-MA LTD in the USA. Initial experiments on the seeding of MRT were performed. Also completed was an analytic study of MRT for a finite plasma slab with arbitrary magnetic fields tangential to the interfaces. The effects of magnetic shear and feedthrough were analyzed
Theoretical and Experimental Studies of Magneto-Rayleigh-Taylor Instabilities
Lau, Yue Ying [University of Michigan, Ann Arbor, MI (United States); Gilgenbach, Ronald [University of Michigan, Ann Arbor, MI (United States)
2013-07-07
Magneto-Rayleigh-Taylor instability (MRT) is important to magnetized target fusion, wire-array z-pinches, and equation-of-state studies using flyer plates or isentropic compression. It is also important to the study of the crab nebula. The investigators performed MRT experiments on thin foils, driven by the mega-ampere linear transformer driver (LTD) facility completed in their laboratory. This is the first 1-MA LTD in the USA. Initial experiments on the seeding of MRT were performed. Also completed was an analytic study of MRT for a finite plasma slab with arbitrary magnetic fields tangential to the interfaces. The effects of magnetic shear and feedthrough were analyzed.
The Inhibition of the Rayleigh-Taylor Instability by Rotation.
Baldwin, Kyle A; Scase, Matthew M; Hill, Richard J A
2015-01-01
It is well-established that the Coriolis force that acts on fluid in a rotating system can act to stabilise otherwise unstable flows. Chandrasekhar considered theoretically the effect of the Coriolis force on the Rayleigh-Taylor instability, which occurs at the interface between a dense fluid lying on top of a lighter fluid under gravity, concluding that rotation alone could not stabilise this system indefinitely. Recent numerical work suggests that rotation may, nevertheless, slow the growth of the instability. Experimental verification of these results using standard techniques is problematic, owing to the practical difficulty in establishing the initial conditions. Here, we present a new experimental technique for studying the Rayleigh-Taylor instability under rotation that side-steps the problems encountered with standard techniques by using a strong magnetic field to destabilize an otherwise stable system. We find that rotation about an axis normal to the interface acts to retard the growth rate of the instability and stabilise long wavelength modes; the scale of the observed structures decreases with increasing rotation rate, asymptoting to a minimum wavelength controlled by viscosity. We present a critical rotation rate, dependent on Atwood number and the aspect ratio of the system, for stabilising the most unstable mode. PMID:26130005
Rayleigh-Taylor instability with finite current relaxation
Silveira, F. E. M.; Orlandi, H. I.
2016-04-01
In this work, we explore the influence of perturbative wavelengths, shorter than those usually considered, on the growth rate of the Rayleigh-Taylor modes. Therefore, we adopt an extended form of Ohm's law which includes a finite relaxation time of the current density due to inertial effects of charged species in the plasma. The restoring force density that acts upon charged species close to the mode rational surface takes into account a new term which is usually neglected with respect to the motional electromotive force. We find that the width of the resistive layer can be interpreted in terms of the "height" of free fall in a constant gravitational field, in the Alfvén time interval. We also show that the charged species must fall "down" in the constant gravitational field in order that the static state of equilibrium of the system becomes unstable to the linear perturbation. Through the principle of conservation of energy, we find a general formula which gives the growth rate γ of the Rayleigh-Taylor modes. When the new term becomes negligible with respect to the motional electromotive force, we recover the standard result of the Rayleigh-Taylor instability, which establishes that γ scales with the plasma resistivity η as γ ˜ η 1 / 3 . However, in the opposite limiting situation, we find that γ does not depend any longer on the plasma resistivity and scales now with the electron number density n e as γ ˜ ne - 1 / 2 . Further developments of our theory may contribute to improve our understanding on the excitation mechanisms of resistive plasma instabilities by transient phenomena such as shock waves.
Linear analysis of incompressible Rayleigh-Taylor instability in solids.
Piriz, A R; Cela, J J López; Tahir, N A
2009-10-01
The study of the linear stage of the incompressible Rayleigh-Taylor instability in elastic-plastic solids is performed by considering thick plates under a constant acceleration that is also uniform except for a small sinusoidal ripple in the horizontal plane. The analysis is carried out by using an analytical model based on the Newton second law and it is complemented with extensive two-dimensional numerical simulations. The conditions for marginal stability that determine the instability threshold are derived. Besides, the boundary for the transition from the elastic to the plastic regime is obtained and it is demonstrated that such a transition is not a sufficient condition for instability. The model yields complete analytical solutions for the perturbation amplitude evolution and reveals the main physical process that governs the instability. The theory is in general agreement with the numerical simulations and provides useful quantitative results. Implications for high-energy-density-physics experiments are also discussed. PMID:19905434
Rayleigh-Taylor instability of viscous fluids with phase change
Kim, Byoung Jae; Kim, Kyung Doo
2016-04-01
Film boiling on a horizontal surface is a typical example of the Rayleigh-Taylor instability. During the film boiling, phase changes take place at the interface, and thus heat and mass transfer must be taken into consideration in the stability analysis. Moreover, since the vapor layer is not quite thick, a viscous flow must be analyzed. Existing studies assumed equal kinematic viscosities of two fluids, and/or considered thin viscous fluids. The purpose of this study is to derive the analytical dispersion relation of the Rayleigh-Taylor instability for more general conditions. The two fluids have different properties. The thickness of the vapor layer is finite, but the liquid layer is thick enough to be nearly semi-infinite in view of perturbation. Initially, the vapor is in equilibrium with the liquid at the interface, and the direction of heat transfer is from the vapor side to the liquid side. In this case, the phase change has a stabilizing effect on the growth rate of the interface. When the vapor layer is thin, there is a coupled effect of the vapor viscosity, phase change, and vapor thickness on the critical wave number. For the other limit of a thick vapor, both the liquid and vapor viscosities influence the critical wave number. Finally, the most unstable wavelength is investigated. When the vapor layer is thin, the most unstable wavelength is not affected by phase change. When the vapor layer is thick, however, it increases with the increasing rate of phase change.
The Magnetic Rayleigh-Taylor Instability in Astrophysical Disks
Contopoulos, Ioannis; Papadopoulos, Dimitrios
2016-01-01
This is our first study of the magnetic Rayleigh-Taylor instability at the inner edge of an astrophysical disk around a central back hole. We derive the equations governing small-amplitude oscillations in general relativistic ideal magnetodydrodynamics and obtain a criterion for the onset of the instability. We suggest that static disk configurations where magnetic field is held by the disk material are unstable around a Schwarzschild black hole. On the other hand, we find that such configurations are stabilized by the spacetime rotation around a Kerr black hole. We obtain a crude estimate of the maximum amount of poloidal magnetic flux that can be accumulated around the center, and suggest that it is proportional to the black hole spin. Finally, we discuss the astrophysical implications of our result for the theoretical and observational estimations of the black hole jet power.
Viscous Potential Flow Analysis of Electrohydrodynamic Rayleigh-Taylor Instability
Awasthi Mukesh Kumar
2014-01-01
Full Text Available A linear analysis of Rayleigh-Taylor instability in the presence of tangential electric field has been carried out using viscous potential flow theory. In viscous potential flow theory, viscosity is not zero but viscous term in the Navier- Stokes equation is zero as vorticity is zero. Viscosity enters through normal stress balance and tangential stresses are not considered in viscous flow theory. A dispersion relation has been obtained and stability criterion has been given in the terms of critical value of electric field. It has been observed that tangential electric field influences stability of the system. A comparison between the results obtained by viscous potential analysis and inviscid potential flow has been made and found that viscosity reduces the growth of instability.
Experimental investigation of turbulent mixing by Rayleigh-Taylor instability
A key feature of compressible turbulent mixing is the generation of vorticity via the ∇px ∇(1/ρ) term. This source of vorticity is also present in incompressible flows involving the mixing of fluids of different density, for example Rayleigh-Taylor unstable flows. This paper gives a summary of an experimental investigation of turbulent mixing at a plane boundary between two fluids, of densities ρ1, and ρ2. (ρ1 > ρ2) due to Rayleigh-Taylor instability. The two fluids are near incompressible and mixing occurs when an approximately constant acceleration, g, is applied normal to the interface with direction from fluid 2 to fluid 1. Full details of the experimental programme are given in a set of three reports. Some of the earlier experiments are also described by Read. Previous experimental work and much of the theoretical research has concentrated on studying the growth of the instability from a single wavelength perturbation rather than turbulent mixing. Notable exceptions are published in the Russian literature. A related process, turbulent mixing induced by the passage of shock waves though an interface between fluids of different density is described by Andronov et al. The major purpose of the experiments described here was to study the evolution of the instability from small random perturbations where it is found that large and larger structures appear as time proceeds. A novel technique was used to provide the desired acceleration. The two fluids were enclosed in a rectangular tank, the lighter fluid 2 initially resting on top of the denser fluid 1. One or more rocket motors were then used to drive the tank vertically downwards. The aim of the experimental programme is to provide data for the calibration of a turbulence model used to predict mixing in real situations
Magnetic curvature driven Rayleigh-Taylor instability revisited
O. A. Pokhotelov
2011-02-01
Full Text Available The problem of incomplete finite ion Larmor radius (FLR stabilization of the magnetic curvature driven Rayleigh-Taylor instability (RTI in low beta plasma with homogeneous ion temperature is investigated. For this purpose a model hydrodynamic description of nonlinear flute waves with arbitrary spatial scales compared to the ion Larmor radius is developed. It is shown that the RTI is not stabilized by FLR effects in a plasma with cold electrons when the ratio of characteristic spatial scale of the plasma inhomogeneity to local effective radius of curvature of the magnetic field lines is larger than 1/4. The crucial role in the absence of the complete FLR stabilization plays the contribution of the compressibility of the polarization part of the ion velocity.
Experimental investigation of the classical Rayleigh-Taylor instability
Budil, K.S.; Remington, B.A.; Peyser, T.A.; Mikaelian, K.O.; Rubenchik, A.M.; Berning, M.; Wood-Vasey, M.W.
1996-05-21
The evolution of the Rayleigh-Taylor (RT) instability in a compressible medium has been investigated at an accelerating embedded interface and at the ablation front in a series of experiments on the Nova laser. The x-ray drive generated in a gold hohlraum ablatively accelerated a planar target consisting of a doped plastic pusher backed by a higher density titanium payload with perturbations placed at the plastic-Ti interface. The targets were diagnosed by face-on and side-on radiography. In previous work focusing on single mode perturbations, wavelengths as short as 10 m have been observed to grow strongly at the embedded interface. Here multimode perturbations consisting of either 2, 10 or 20 modes superposed in phase have been investigated.
Non-equilibrium Thermodynamics of Rayleigh-Taylor Instability
Sengupta, Tapan K.; Sengupta, Aditi; Sengupta, Soumyo; Bhole, Ashish; Shruti, K. S.
2016-04-01
Here, the fundamental problem of Rayleigh-Taylor instability (RTI) is studied by direct numerical simulation (DNS), where the two air masses at different temperatures, kept apart initially by a non-conducting horizontal interface in a 2D box, are allowed to mix. Upon removal of the partition, mixing is controlled by RTI, apart from mutual mass, momentum, and energy transfer. To accentuate the instability, the top chamber is filled with the heavier (lower temperature) air, which rests atop the chamber containing lighter air. The partition is positioned initially at mid-height of the box. As the fluid dynamical system considered is completely isolated from outside, the DNS results obtained without using Boussinesq approximation will enable one to study non-equilibrium thermodynamics of a finite reservoir undergoing strong irreversible processes. The barrier is removed impulsively, triggering baroclinic instability by non-alignment of density, and pressure gradient by ambient disturbances via the sharp discontinuity at the interface. Adopted DNS method has dispersion relation preservation properties with neutral stability and does not require any external initial perturbations. The complete inhomogeneous problem with non-periodic, no-slip boundary conditions is studied by solving compressible Navier-Stokes equation, without the Boussinesq approximation. This is important as the temperature difference between the two air masses considered is high enough (Δ T = 70 K) to invalidate Boussinesq approximation. We discuss non-equilibrium thermodynamical aspects of RTI with the help of numerical results for density, vorticity, entropy, energy, and enstrophy.
Rayleigh-Taylor instability experiments in cryogenic deuterium
Hansen, J. F.; Smalyuk, V. A.
2005-10-01
We report on experiments under way at the Omega laser, using cryogenic deuterium to study Rayleigh-Taylor instabilities in laser targets. These instabilities are important in astrophysical situations (e.g., mixing of the different shells during a supernova explosion) and in inertial fusion (during the compression stage of a fusion target). They can be studied in small (˜1 mm) shock tubes filled with one heavy and one light material, with an interface between the two materials that is machined to seed the instability. A high-energy laser (˜5 kJ) drives a shock from the heavy to the light material. The evolution of the interface is studied using gated x-ray cameras, where x-ray illumination is obtained from additional laser beams focused on metal backlighter foils. Traditionally the heavy material is CH (1 g/cm^3) doped with I or Br for improved contrast, while the light material is a low-density (˜0.1 g/cm^3) C foam. The goal of the current experiments is to determine if contrast can be improved even further by replacing the foam with cryogenic deuterium, which has a density similar to the foam, but a lower x-ray opacity allowing clearer images, including images taken at late times in the evolution. Work performed under the auspices of the Department of Energy by the Lawrence Livermore National Laboratory under contract number W-7405-ENG-48.
Rayleigh Taylor instability of two superposed compressible fluids in un-magnetized plasma
Sharma, P. K.; Tiwari, A.; Argal, S.; Chhajlani, R. K.
2014-09-01
The linear Rayleigh Taylor instability of two superposed compressible Newtonian fluids is discussed with the effect of surface tension which can play important roles in space plasma. As in both the superposed Newtonian fluids, the system is stable for potentially stable case and unstable for potentially unstable case in the present problem also. The equations of the problem are solved by normal mode method and a dispersion relation is obtained for such a system. The behaviour of growth rate is examined in the presence of surface tension and it is found that the surface tension has stabilizing influence on the Rayleigh Taylor instability of two superposed compressible fluids. Numerical analysis is performed to show the effect of sound velocity and surface tension on the growth rate of Rayleigh Taylor instability. It is found that both parameters have stabilizing influence on the growth rate of Rayleigh Taylor instability.
Magneto-Rayleigh-Taylor instability in solid media
Sun, Y. B. [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China); School of Physical Science and Technology, Lanzhou University, Lanzhou 73000 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Piriz, A. R., E-mail: roberto.piriz@uclm.es [E.T.S.I. Industriales (Spain); CYTEMA (Spain); Instituto de Investigaciones Energéticas, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)
2014-07-15
A linear analysis of the magneto-Rayleigh-Taylor instability at the interface between a Newtonian fluid and an elastic-plastic solid is performed by considering a uniform magnetic B{sup →}, parallel to the interface, which has diffused into the fluid but not into the solid. It is found that the magnetic field attributes elastic properties to the viscous fluid which enhance the stability region by stabilizing all the perturbation wavelengths shorter than λ{sub 0}∝B{sup 2} for any initial perturbation amplitude. Longer wavelengths are stabilized by the mechanical properties of the solid provided that the initial perturbation wavelength is smaller than a threshold value determined by the yield strength and the shear modulus of the solid. Beyond this threshold, the amplitude grows initially with a growth rate reduced by the solid strength properties. However, such properties do not affect the asymptotic growth rate which is only determined by the magnetic field and the fluid viscosity. The described physical situation intends to resemble some of the features present in recent experiments involving the magnetic shockless acceleration of flyers plates.
Magneto-Rayleigh-Taylor instability in solid media
Sun, Y. B.; Piriz, A. R.
2014-07-01
A linear analysis of the magneto-Rayleigh-Taylor instability at the interface between a Newtonian fluid and an elastic-plastic solid is performed by considering a uniform magnetic B →, parallel to the interface, which has diffused into the fluid but not into the solid. It is found that the magnetic field attributes elastic properties to the viscous fluid which enhance the stability region by stabilizing all the perturbation wavelengths shorter than λ 0 ∝ B 2 for any initial perturbation amplitude. Longer wavelengths are stabilized by the mechanical properties of the solid provided that the initial perturbation wavelength is smaller than a threshold value determined by the yield strength and the shear modulus of the solid. Beyond this threshold, the amplitude grows initially with a growth rate reduced by the solid strength properties. However, such properties do not affect the asymptotic growth rate which is only determined by the magnetic field and the fluid viscosity. The described physical situation intends to resemble some of the features present in recent experiments involving the magnetic shockless acceleration of flyers plates.
The role of Rayleigh-Taylor instabilities in filament threads
Terradas, J; Ballester, J L
2012-01-01
Many solar filaments and prominences show short-lived horizontal threads lying parallel to the photosphere. In this work the possible link between Rayleigh-Taylor instabilities and thread lifetimes is investigated. This is done by calculating the eigenmodes of a thread modelled as a Cartesian slab under the presence of gravity. An analytical dispersion relation is derived using the incompressible assumption for the magnetohydrodynamic (MHD) perturbations. The system allows a mode that is always stable, independently of the value of the Alfv\\'en speed in the thread. The character of this mode varies from being localised at the upper interface of the slab when the magnetic field is weak, to having a global nature and resembling the transverse kink mode when the magnetic field is strong. On the contrary, the slab model permits another mode that is unstable and localised at the lower interface when the magnetic field is weak. The growth rates of this mode can be very short, of the order of minutes for typical thr...
Three-Dimensional Single-Mode Nonlinear Ablative Rayleigh-Taylor Instability
Yan, R.; Betti, R.; Sanz, J.; Liu, B.; Frank, A.
2015-11-01
The nonlinear evolution of the ablative Rayleigh-Taylor (ART) instability is studied in three dimensions for conditions relevant to inertial confinement fusion targets. The simulations are performed using our newly developed code ART3D and an astrophysical code AstroBEAR. The laser ablation can suppress the growth of the short-wavelength modes in the linear phase but may enhance their growth in the nonlinear phase because of the vortex-acceleration mechanism. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the bubble velocity grows faster than predicted in the classical 3-D theory. When compared to 2-D results, 3-D short-wavelength bubbles grow faster and do not reach saturation. The unbounded 3-D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes into the ablated plasma filling the bubble volume. A density plateau is observed inside a nonlinear ART bubble and the plateau density is higher for shorter-wavelength modes. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
Large-eddy-simulation of 3-dimensional Rayleigh-Taylor instability in incompressible fluids
WANG; Lili
2002-01-01
［1］Sharp, D. H., An overview of Rayleigh-Taylor instability, Physica D, 1984, 12: 3-18.［2］Baker, G. R., Meiron, D. I., Orszag, S. A., Vortex simulation of the Rayleigh-Taylor instability, Phys. Fluids, 1980, 23: 1485-1490.［3］Tryggvason, G., Numerical simulations of the Rayleigh-Taylor instability, J. Comput. Phys., 1988, 75: 253-282.［4］Mulder, W., Osher, S., Sethian, J., Computing interface motion in compressible gas dynamics, J. Comput. Phys., 1992, 100: 209-228.［5］Osher, S., Sethian, J., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Compput. Phys., 1988, 79(1): 12-49.［6］Li, X. L., Study of three-dimensional Rayleigh-Taylor instability in compressible fluids through level set method and parallel computation, Phys. Fluids, 1993, A(5): 1904-1913.［7］Holmes, R. L, Grove, J. W., Sharp, D. H., Numerical investigation of Richtmyer-Meshkov instability using front tracking, J. Fluid Mech., 1995, 301: 51-64.［8］Gardner, C., Glimm, J., McBryan, O. et al., The dynamics of bubble growth for Rayleigh-Taylor unstable interfaces, Phys. Fluids, 1988, 31: 447-465.［9］He Xiaoyi, Chen Shiyi, Zhang Raoyang, A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability, J. Comput Phys., 1999, 152: 642-663.［10］Li, X. L., Jin, B. X., Glimm, J., Numerical study for the three-dimensional Rayleigh-Taylor instability through the TVD/AC scheme and parallel computation, J. Comput. Phys., 1996, 126: 343-355.［11］Taylor, G. I., The stability of liquid surface when accelerated in a direction perpendicular to their planes, I, Proc. Roy. Soc., London, 1950, A201: 192-196.［12］Abarzhi, S. I., Stable steady flow in the Rayleigh-Taylor instability, Phs. Rev. Lett., 1998, 81: 337-340.［13］Zhang, Q., The motion of single-mode Rayleigh-Taylor unstable interfaces, IMPACT Comput. Sci. Eng., 1991, 3: 277-389.［14］Deardorff. J. W
Suppressing the Rayleigh-Taylor instability with a rotating magnetic field
Rannacher, D
2006-01-01
The Rayleigh-Taylor instability of a magnetic fluid superimposed on a non-magnetic liquid of lower density may be suppressed with the help of a spatially homogeneous magnetic field rotating in the plane of the undisturbed interface. Starting from the complete set of Navier-Stokes equations for both liquids a Floquet analysis is performed which consistently takes into account the viscosities of the fluids. Using experimentally relevant values of the parameters we suggest to use this stabilization mechanism to provide controlled initial conditions for an experimental investigation of the Rayleigh-Taylor instability.
The 'anelastic' approximation allows us to filter the acoustic waves thanks to an asymptotic development of the Navier-Stokes equations, so increasing the averaged time step, during the numerical simulation of hydrodynamic instabilities development. So, the anelastic equations for a two fluid mixture in case of Rayleigh-Taylor instability are established.The linear stability of Rayleigh-Taylor flow is studied, for the first time, for perfect fluids in the anelastic approximation. We define the Stokes problem resulting from Navier-Stokes equations without the non linear terms (a part of the buoyancy is considered); the ellipticity is demonstrated, the Eigenmodes and the invariance related to the pressure are detailed. The Uzawa's method is extended to the anelastic approximation and shows the decoupling speeds in 3D, the particular case k = 0 and the spurious modes of pressure. Passing to multi-domain allowed to establish the transmission conditions.The algorithms and the implementation in the existing program are validated by comparing the Uzawa's operator in Fortran and Mathematica languages, to an experiment with incompressible fluids and results from anelastic and compressible numerical simulations. The study of the influence of the initial stratification of both fluids on the development of the Rayleigh-Taylor instability is initiated. (author)
Unstable normal mode for Rayleigh--Taylor instability in viscous fluids
The character of the growth rates of the normal modes for Rayleigh--Taylor instability of superposed incompressible, viscous fluids is analyzed in terms of appropriately scaled dimensionless parameters and a particularly simple representation of the Rayleigh--Taylor dispersion relation. The chief feature that emerges is that the scaled growth rate is remarkably insensitive to the values of fluid densities and viscosities. To within a few percent, the physical growth rate depends only on the surface tension, the density-weighted average viscosity, and the effective acceleration. Approximate formulae for the most unstable wavenumber and the corresponding maximum growth rate are given
A numerical and analytical investigation of Rayleigh-Taylor instability in a solid tungsten plate
The Rayleigh-Taylor instability response of an elastic-plastic tungsten plate is investigated by numerical experiments and an approximate modal analysis. The so-called ''minimum amplitude'' instability criteria derived from plasticity analyses is shown to be incomplete as a general indicator of instability or stability at very large driving pressures. Model equations are derived which are able to reproduce the basic qualitative features of the observed instability response given by the numerical calculations. 11 refs., 29 figs
Intuitive calculation of the relativistic Rayleigh-Taylor instability linear growth rate
Bret, A.
2011-01-01
The Rayleigh-Taylor instability is a key process in many fields of Physics ranging from astrophysics to inertial confinement fusion. It is usually analyzed deriving the linearized fluid equations, but the physics behind the instability is not always clear. Recent works on this instability allow for an very intuitive understanding of the phenomenon and for a straightforward calculation of the linear growth rate. In this Letter, it is shown that the same reasoning allows for a direct derivation...
Results are reported from the first experiments to explore the evolution of the Rayleigh-Taylor (RT) instability from intentionally three-dimensional (3D) initial conditions at an embedded, decelerating interface in a high-Reynolds-number flow. The experiments used ∼5 kJ of laser energy to produce a blast wave in polyimide and/or brominated plastic having an initial pressure of ∼50 Mbars. This blast wave shocked and then decelerated the perturbed interface between the first material and lower-density C foam. This caused the formation of a decelerating interface with an Atwood number ∼2/3, producing a long-term positive growth rate for the RT instability. The initial perturbations were a 3D perturbation in an 'egg-crate' pattern with feature spacings of 71 μm in two orthogonal directions and peak-to-valley amplitudes of 5 μm. The resulting RT spikes appear to overtake the shock waves, moving at a large fraction of the predeceleration, 'free-fall' velocity. This result was unanticipated by prior simulations and models
Investigation of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities
Riccardo Bonazza, Mark Anderson, Jason Oakley
2006-11-03
The present research program is centered on the experimental and numerical study of two instabilities that develop at the interface between two different fluids when the interface experiences an impulsive or a constant acceleration. The instabilities, called the Richtmyer-Meshkov and Rayleigh-Taylor instability, respectively, adversely affect target implosion in experiments aimed at the achievement of nuclear fusion by inertial confinement by causing the nuclear fuel contained in a target and the shell material to mix, leading to contamination of the fuel, yield reduction or no ignition at all. The laboratory experiments summarized in this report include shock tube experiments to study a shock-accelerated bubble and a shock-accelerated 2-D sinusoidal interface; and experiments based on the use of magnetorheological fluids for the study of the Rayleigh-Taylor instability. Computational experiments based on the shock tube experimental conditions are also reported.
Adams, Colin Stuart [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)
2015-01-15
The Rayleigh-Taylor instability causes mixing in plasmas throughout the universe, from micron-scale plasmas in inertial confinement fusion implosions to parsec-scale supernova remnants. The evolution of this interchange instability in a plasma is influenced by the presence of viscosity and magnetic fields, both of which have the potential to stabilize short-wavelength modes. Very few experimental observations of Rayleigh-Taylor growth in plasmas with stabilizing mechanisms are reported in the literature, and those that are reported are in sub-millimeter scale plasmas that are difficult to diagnose. Experimental observations in well-characterized plasmas are important for validation of computational models used to make design predictions for inertial confinement fusion efforts. This dissertation presents observations of instability growth during the interaction between a high Mach-number, initially un-magnetized plasma jet and a stagnated, magnetized plasma. A multi-frame fast camera captures Rayleigh-Taylor-instability growth while interferometry, spectroscopy, photodiode, and magnetic probe diagnostics are employed to estimate plasma parameters in the vicinity of the collision. As the instability grows, an evolution to longer mode wavelength is observed. Comparisons of experimental data with idealized magnetohydrodynamic simulations including a physical viscosity model suggest that the observed instability evolution is consistent with both magnetic and viscous stabilization. These data provide the opportunity to benchmark computational models used in astrophysics and fusion research.
Mitigation Effect of Finite Larmor Radius on Rayleigh-Taylor Instability in Z-Pinch Implosions
邱孝明; 黄林; 简广德
2002-01-01
Based on the framework of magnetohydrodynamic theory, a simple model is proposed to study the mitigation effect of finite Larmor radius on the Rayleigh-Taylor instability in Z-pinch implosions. In this model, taking account of Ti ≥ Te in Z-pinch implosions we believe that the magnetohydrodynamic plasma responds to a perturbation (～ exp [i (k. x - ωt)]) at frequency (ω + ik2⊥ρ2iΩi) instead of frequency ω, where k2⊥ρ2i is due to the finite Larmor radius effects expressed from the generalkinetic theory of magnetized plasma. Therefore the linearized continuity and momentum equations for the perturbed mass-density and velocity include the finite Larmor radius effects. The calculations indicate that, in the wavenumber region of interest, the finite Larmor radius effects can mitigate the Rayleigh-Taylor instability in Z-pinch implosions.
LI Zhang-Guo; LIU Qiu-Sheng; LIU Rong; HU Wei; DENG Xin-Yu
2009-01-01
A computational simulation is conducted to investigate the influence of Rayleigh-Taylor instability on liquid propellant reorientation flow dynamics for the tank of CZ-3A launch vehicle series fuel tanks in a low-gravity environment. The volume-of-fluid (VOF) method is used to simulate the free surface flow of gas-liquid. The process of the liquid propellant reorientation started from initially fiat and curved interfaces are numerically studied. These two different initial conditions of the gas-liquid interface result in two modes of liquid flow. It is found that the Rayleigh-Taylor instability can be reduced evidently at the initial gas-liquid interface with a high curve during the process of liquid reorientation in a low-gravity environment.
Bel`kov, S.A.; Bondarenko, S.V.; Vinokurov, O.A.; Kochemasov, G.G.; Mkhitarian, L.S.
1996-09-01
This report presents the research results for the time point when the Rayleigh-Taylor instability converts to the nonlinear stage as well as the computational results for the interaction of two modes of Rayleigh-Taylor instability when initial perturbations are concentrated at the ablation front (problem (a)) and on the rear side (problem (b)) of the plane target. As was shown in the report for the first phase, for a target of 3 {mu}m thick the existence time of the nonlinear stage is extremely low and does not allow to track the evolution pattern. In it was shown that the plane target with {Delta}{sub 0}=5 {mu}m is more preferable for this goal. Therefore all the computations presented here relate to the target with the indicated thickness. The laser pulse parameters are remained unchanged J{sub L}=10{sup 15} W/cm{sup 2}, {lambda}=0.35 {mu}m.
Study on Electrohydrodynamic Rayleigh-Taylor Instability with Heat and Mass Transfer
Mukesh Kumar Awasthi
2014-01-01
Full Text Available The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.
Suppression of Rayleigh-Taylor instability in Z-pinch loads with tailored density profiles
A load structure with a tailored density profile which delays the onset of the Rayleigh-Taylor instability development in imploding Z-pinches by inverting acceleration of the magnetic field/plasma interface was proposed and studied numerically. This approach makes it possible to start gas-puff implosions from large radii (like 8 cm) and produce a significant K-shell yield with current pulse duration of 250 ns and longer. (author). 3 figs., 7 refs
Di Lucchio, Laura
2012-01-01
One of the most important problems in inertial confinement fusion is how to find a way to mitigate the onset of the Rayleigh-Taylor instability which arises in the ablation front during the compression. In this thesis it is studied in detail the possibility of using for such a purpose the well-known mechanism of dynamic stabilization, already applied to other dynamical systems such as the inverted pendulum. In this context, a periodic acceleration superposed to the background gravity generat...
Rayleigh-Taylor finger instability mixing in hydrodynamic shell convection models
Mocak, Miroslav; Mueller, Ewald
2010-01-01
Mixing processes in stars driven by composition gradients as a result of the Rayleigh-Taylor instability are not anticipated. They are supported only by hydrodynamic studies of stellar convection. We find that such mixing occurs below the bottom edge of convection zones in our multidimensional hydrodynamic shell convection models. It operates at interfaces created by off-center nuclear burning, where less dense gas with higher mean molecular weight is located above denser gas with a lower mea...
Direct numerical simulations of type Ia supernovae flames II: The Rayleigh-Taylor instability
A Type Ia supernova explosion likely begins as a nuclear runaway near the center of a carbon-oxygen white dwarf. The outward propagating flame is unstable to the Landau-Darrieus, Rayleigh-Taylor, and Kelvin-Helmholtz instabilities, which serve to accelerate it to a large fraction of the speed of sound. We investigate the Rayleigh-Taylor unstable flame at the transition from the flamelet regime to the distributed-burning regime, around densities of 10e7 gm/cc, through detailed, fully resolved simulations. A low Mach number, adaptive mesh hydrodynamics code is used to achieve the necessary resolution and long time scales. As the density is varied, we see a fundamental change in the character of the burning--at the low end of the density range the Rayleigh-Taylor instability dominates the burning, whereas at the high end the burning suppresses the instability. In all cases, significant acceleration of the flame is observed, limited only by the size of the domain we are able to study. We discuss the implications of these results on the potential for a deflagration to detonation transition
This paper describes experiments exploring the three-dimensional (3D) Rayleigh-Taylor instability at a blast-wave-driven interface. This experiment is well scaled to the He/H interface during the explosion phase of SN1987A. In the experiments, ∼5 kJ of energy from the Omega laser was used to create a planar blast wave in a plastic disk, which is accelerated into a lower-density foam. These circumstances induce the Richtmyer-Meshkov instability and, after the shock passes the interface, the system quickly becomes dominated by the Rayleigh-Taylor instability. The plastic disk has an intentional pattern machined at the plastic/foam interface. This perturbation is 3D with a basic structure of two orthogonal sine waves with a wavelength of 71 μm and an amplitude of 2.5 μm. Additional long-wavelength modes with a wavelength of either 212 or 424 μm are added onto the single-mode pattern. The addition of the long-wavelength modes was motivated by the results of previous experiments where material penetrated unexpectedly to the shock front, perhaps due to an unintended structure. The current experiments and simulations were performed to explore the effects of this unintended structure; however, we were unable to reproduce the previous results.
Andrei, A. Ivanov
2001-06-15
In this thesis we're studying both the general case of the 'classic' Rayleigh-Taylor instability (in incompressible fluids) and more specific cases of the instabilities of Rayleigh-Taylor type in magnetized plasmas, in the liners or wire array implosions etc. We have studied the influence of the Hall diffusion of magnetic field on the growth rate of the instability. We have obtained in this work a self-similar solution for the widening of the initial profile of the magnetic field and for the wave of the penetration of magnetic field. After that the subsequent evolution of the magnetic field in plasma opening switches (POS) has been examined. We have shown the possibility of the existence of a strong rarefaction wave for collisional and non-collisional cases. This wave can explain the phenomenon of the opening of POS. The effect of the suppression of Rayleigh-Taylor instability by forced oscillations of the boundary between two fluids permits us to propose some ideas for the experiments of inertial fusion. We have considered the general case of the instability, in other words - two incompressible viscous superposed fluids in a gravitational field. We have obtained an exact analytical expression for the growth rate and then we have analyzed the influence of the parameters of external 'pumping' on the instability. These results can be applied to a wide range of systems, starting from classic hydrodynamics and up to astrophysical plasmas. The scheme of wire arrays has become recently a very popular method to obtain a high power X-radiation or for a high quality implosion in Z-pinches. The experimental studies have demonstrated that the results of implosion are much better for the case of multiple thin wires situated cylindrically than in a usual liner scheme. We have examined the problem modeling the stabilization of Rayleigh-Taylor instability for a wire array system. The reason for instability suppression is the regular spatial modulation of
Two- and three-dimensional behavior of Rayleigh-Taylor and Kelvin-Helmholtz instabilities
Two- and three-dimensional behavior of the Rayleigh-Taylor (R-T) and Kelvin-Helmholts (K-H) instabilities is examined with a newly developed hydrodynamic code CIP (Cubic Interpolated Pseudoparticle). The mushroom structure owing to the K-H instability is quite different in two and three dimensions. The simulation without gravity show a similar behavior and hence this difference between two and three dimensions does not originate from the R-T instability. This difference cannot be explained by a linear analysis on the K-H instability also. (author)
Experimental techniques for measuring Rayleigh-Taylor instability in inertial confinement fusion
Rayleigh-Taylor (RT) instability is one of the major concerns in inertial confinement fusion (ICF) because it amplifies target modulations in both acceleration and deceleration phases of implosion, which leads to shell disruption and performance degradation of imploding targets. This article reviews experimental results of the RT growth experiments performed on OMEGA laser system, where targets were driven directly with laser light. RT instability was studied in the linear and nonlinear regimes. The experiments were performed in acceleration phase, using planar and spherical targets, and in deceleration phase of spherical implosions, using spherical shells. Initial target modulations consisted of two-dimensional (2D) pre-imposed modulations, and 2D and three-dimensional (3D) modulations imprinted on targets by the nonuniformities in laser drive. In planar geometry, the nonlinear regime was studied using 3D modulations with broadband spectra near nonlinear saturation levels. In acceleration-phase, the measured modulation Fourier spectra and nonlinear growth velocities are in good agreement with those predicted by Haan's model (Haan 1989 Phys. Rev. A 39 5812). In a real-space analysis, the bubble merger was quantified by a self-similar evolution of bubble size distributions (Oron et al 2001 Phys. Plasmas 8 2883). The 3D, inner-surface modulations were measured to grow throughout the deceleration phase of spherical implosions. RT growth rates are very sensitive to the drive conditions, therefore they can be used to test and validate drive physics in hydrodynamic codes used to design ICF implosions. Measured growth rates of pre-imposed 2D target modulations below nonlinear saturation levels were used to validate nonlocal thermal electron transport model in laser-driven experiments.
Rayleigh-Taylor (RT) instability is one of the major concerns in inertial confinement fusion (ICF) because it amplifies target modulations in both acceleration and deceleration phases of implosion, which leads to shell disruption and performance degradation of imploding targets. This article reviews experimental results of the RT growth experiments performed on OMEGA laser system, where targets were driven directly with laser light. RT instability was studied in the linear and nonlinear regimes. The experiments were performed in acceleration phase, using planar and spherical targets, and in deceleration phase of spherical implosions, using spherical shells. Initial target modulations consisted of 2-D pre-imposed modulations, and 2-D and 3-D modulations imprinted on targets by the non-uniformities in laser drive. In planar geometry, the nonlinear regime was studied using 3-D modulations with broadband spectra near nonlinear saturation levels. In acceleration-phase, the measured modulation Fourier spectra and nonlinear growth velocities are in good agreement with those predicted by Haan's model (Haan S W 1989 Phys. Rev. A 39 5812). In a real-space analysis, the bubble merger was quantified by a self-similar evolution of bubble size distributions (Oron D et al 2001 Phys. Plasmas 8, 2883). The 3-D, inner-surface modulations were measured to grow throughout the deceleration phase of spherical implosions. RT growth rates are very sensitive to the drive conditions, therefore they can be used to test and validate drive physics in hydrodynamic codes used to design ICF implosions. Measured growth rates of pre-imposed 2-D target modulations below nonlinear saturation levels were used to validate non-local thermal electron transport model in laser-driven experiments.
Analytical and numerical analysis of finite amplitude Rayleigh-Taylor instability
Meiron, D.I.; Saffman, P.G.
1987-09-18
We summarize the results obtained in the last year. These include a simple model of bubble competition in Rayleigh-Taylor unstable flows which gives results which are in good agreement with experiment. In addition the model has been compared with two dimensional numerical simulations of inviscid Rayleigh-Taylor instability using the cloud-in-cell method. These simulations can now be run into the late time regime and can track the competition of as many as ten bubbles. The improvement in performance over previous applications of the cloud-in-cell approach is due to the application of finite difference techniques designed to handle shock-like structures in the vorticity of the interface which occur at late times. We propose to extend the research carried thus far to Rayleigh-Taylor problems in three dimensional and convergent geometries as well as to two-fluid instabilities in which interface roll-up is observed. Finally we present a budget for the fiscal year 1987-1988. 6 refs.
Analytical and numerical analysis of finite amplitude Rayleigh-Taylor instability
We summarize the results obtained in the last year. These include a simple model of bubble competition in Rayleigh-Taylor unstable flows which gives results which are in good agreement with experiment. In addition the model has been compared with two dimensional numerical simulations of inviscid Rayleigh-Taylor instability using the cloud-in-cell method. These simulations can now be run into the late time regime and can track the competition of as many as ten bubbles. The improvement in performance over previous applications of the cloud-in-cell approach is due to the application of finite difference techniques designed to handle shock-like structures in the vorticity of the interface which occur at late times. We propose to extend the research carried thus far to Rayleigh-Taylor problems in three dimensional and convergent geometries as well as to two-fluid instabilities in which interface roll-up is observed. Finally we present a budget for the fiscal year 1987-1988. 6 refs
Granular Rayleigh-Taylor Instability: Experiments and Simulations
Vinningland, Jan Ludvig; Johnsen, Oistein; Flekkoy, Eirik G.; Toussaint, Renaud; Maloy, Knut Jorgen
2007-01-01
A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later s...
Intuitive calculation of the relativistic Rayleigh-Taylor instability linear growth rate
Bret, A
2011-01-01
The Rayleigh-Taylor instability is a key process in many fields of Physics ranging from astrophysics to inertial confinement fusion. It is usually analyzed deriving the linearized fluid equations, but the physics behind the instability is not always clear. Recent works on this instability allow for an very intuitive understanding of the phenomenon and for a straightforward calculation of the linear growth rate. In this Letter, it is shown that the same reasoning allows for a direct derivation of the relativistic expression of the linear growth rate for an incompressible fluid.
Stabilization of Rayleigh-Taylor instability in a non-Newtonian incompressible complex plasma
Garai, S.; Janaki, M. S.; Chakrabarti, N. [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata - 700 064 (India); Banerjee, D. [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India)
2015-03-15
The stabilization of Rayleigh-Taylor (RT) instability is investigated in a non-Newtonian unmagnetized dusty plasma with an experimentally verified model of shear flow rate dependent viscosity. It has been found that non-Newtonian property has also a significant role in stabilization of RT instability along with velocity shear stabilization in the short wavelength regime. The effect of the non-Newtonian parameters is more profound in the higher velocity shear rate regime. A detailed study is reported on the role of non-Newtonian effect on RT instability with conventional dust fluid equations using standard numerical eigenvalue analysis.
Theoretical and numerical studies of Rayleigh-Taylor instabilities in magnetized plasmas
The instabilities of Rayleigh-Taylor type are considered in the thesis. The topic of the thesis was inspired by recent advances in the physics of plasma compression, especially with the aid of systems like Z-pinch. Rayleigh-Taylor instability (RTI) plays an important role in the evolution of magnetized plasmas in these experiments, as well as in stellar plasmas and classic fluids. For the phenomena concerning the nuclear fusion the RTI is very often the factor limiting the possibility of compression. In the current work we try to examine in detail the characteristic features of the instabilities of this type in order to eliminate their detrimental influence. In this thesis we are studying both the general case of the 'classic' Rayleigh-Taylor instability (in incompressible fluids) and more specific cases of the instabilities of Rayleigh-Taylor type in magnetized plasmas, in the liners or wire array implosions etc. We have studied the influence of the Hall diffusion of magnetic field on the growth rate of the instability. We have obtained in this work a self-similar solution for the widening of the initial profile of the magnetic field and for the wave of the penetration of magnetic field. After that the subsequent evolution of the magnetic field in plasma opening switches (POS) has been examined. We have shown the possibility of the existence of a strong rarefaction wave for collisional and non-collisional cases. This wave can explain the phenomenon of the opening of POS. The effect of the suppression of Rayleigh-Taylor instability by forced oscillations of the boundary between two fluids permits us to propose some ideas for the experiments of inertial fusion. We have considered the general case of the instability, in other words, two incompressible viscous superposed fluids in a gravitational field. We have obtained an exact analytical expression for the growth rate and then we have analyzed the influence of the parameters of external 'pumping' on the instability
Theoretical and numerical study of Rayleigh-Taylor instabilities in magnetized plasmas
In this thesis we're studying both the general case of the 'classic' Rayleigh-Taylor instability (in incompressible fluids) and more specific cases of the instabilities of Rayleigh-Taylor type in magnetized plasmas, in the liners or wire array implosions etc. We have studied the influence of the Hall diffusion of magnetic field on the growth rate of the instability. We have obtained in this work a self-similar solution for the widening of the initial profile of the magnetic field and for the wave of the penetration of magnetic field. After that the subsequent evolution of the magnetic field in plasma opening switches (POS) has been examined. We have shown the possibility of the existence of a strong rarefaction wave for collisional and non-collisional cases. This wave can explain the phenomenon of the opening of POS. The effect of the suppression of Rayleigh-Taylor instability by forced oscillations of the boundary between two fluids permits us to propose some ideas for the experiments of inertial fusion. We have considered the general case of the instability, in other words - two incompressible viscous superposed fluids in a gravitational field. We have obtained an exact analytical expression for the growth rate and then we have analyzed the influence of the parameters of external 'pumping' on the instability. These results can be applied to a wide range of systems, starting from classic hydrodynamics and up to astrophysical plasmas. The scheme of wire arrays has become recently a very popular method to obtain a high power X-radiation or for a high quality implosion in Z-pinches. The experimental studies have demonstrated that the results of implosion are much better for the case of multiple thin wires situated cylindrically than in a usual liner scheme. We have examined the problem modeling the stabilization of Rayleigh-Taylor instability for a wire array system. The reason for instability suppression is the regular spatial modulation of the surface plasma
Rayleigh-Taylor Instability in Elastoplastic Solids: A Local Catastrophic Process
Maimouni, I.; Goyon, J.; Lac, E.; Pringuey, T.; Boujlel, J.; Chateau, X.; Coussot, P.
2016-04-01
We show that the Rayleigh-Taylor instability in elastoplastic solids takes the form of local perturbations penetrating the material independently of the interface size, in contrast with the theory for simple elastic materials. Then, even just beyond the stable domain, the instability abruptly develops as bursts rapidly moving through the other medium. We show that this is due to the resistance to penetration of a finger which is minimal for a specific finger size and drops to a much lower value beyond a small depth (a few millimeters).
A visualization study of Rayleigh-Taylor instability of flames generated by sudden acceleration
Ma, L.; Yao, X.; Chomiak, J. [Chalmers Univ. of Technology, Goeteborg (Sweden). Dept. of Thermo- and Fluid Dynamics
1996-07-01
The Rayleigh-Taylor instability phenomenon occurs in flames when the pressure in the products is higher than in the mixture. The development of this phenomenon in premixed flames was investigated experimentally. A square glass tube for standard flammability limit studies and a methane air mixture were used in the experiment. The flame was accelerated by a falling piston and flame shapes and positions were recorded. Results showed that sudden acceleration does not induce small scale instabilities of flame, contrary to predictions of existing linear theories. The accelerated flames form large scale bubbles which propagate with constant speed relative to the gas. 20 refs., 6 figs.
Lattice Boltzmann simulation of three-dimensional Rayleigh-Taylor instability.
Liang, H; Li, Q X; Shi, B C; Chai, Z H
2016-03-01
In this paper, the three-dimensional (3D) Rayleigh-Taylor instability (RTI) with low Atwood number (A(t)=0.15) in a long square duct (12W × W × W) is studied by using a multiple-relaxation-time lattice Boltzmann (LB) multiphase model. The effect of the Reynolds number on the interfacial dynamics and bubble and spike amplitudes at late time is investigated in detail. The numerical results show that at sufficiently large Reynolds numbers, a sequence of stages in the 3D immiscible RTI can be observed, which includes the linear growth, terminal velocity growth, reacceleration, and chaotic development stages. At late stage, the RTI induces a very complicated topology structure of the interface, and an abundance of dissociative drops are also observed in the system. The bubble and spike velocities at late stage are unstable and their values have exceeded the predictions of the potential flow theory [V. N. Goncharov, Phys. Rev. Lett. 88, 134502 (2002)]. The acceleration of the bubble front is also measured and it is found that the normalized acceleration at late time fluctuates around a constant value of 0.16. When the Reynolds number is reduced to small values, some later stages cannot be reached sequentially. The interface becomes relatively smoothed and the bubble velocity at late time is approximate to a constant value, which coincides with the results of the extended Layzer model [S.-I. Sohn, Phys. Rev. E 80, 055302(R) (2009)] and the modified potential theory [R. Banerjee, L. Mandal, S. Roy, M. Khan, and M. R. Guptae, Phys. Plasmas 18, 022109 (2011)]. In our simulations, the Graphics Processing Unit (GPU) parallel computing is also used to relieve the massive computational cost. PMID:27078453
Reckinger, Scott James [Montana State Univ., Bozeman, MT (United States); Livescu, Daniel [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vasilyev, Oleg V. [Univ. of Colorado, Boulder, CO (United States)
2016-09-02
A comprehensive numerical methodology has been developed that handles the challenges introduced by considering the compressive nature of Rayleigh-Taylor instability (RTI) systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification dependent vorticity production [1]. The computational framework is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis.
Proton Beam Fast Ignition Fusion: Synergy of Weibel and Rayleigh-Taylor Instabilities
Stefan, V. Alexander
2011-04-01
The proton beam generation and focusing in fast ignition inertial confinement fusion is studied. The spatial and energy spread of the proton beam generated in a laser-solid interaction is increased due to the synergy of Weibel and Rayleigh-Taylor instabilities. The focal spot radius can reach 100 μm, which is nearly an order of magnitude larger than the optimal value. The energy spread decreases the beam deposition energy in the focal spot. Under these conditions, ignition of a precompressed DT fuel is achieved with the beam powers much higher than the values presently in consideration. Work supported in part by NIKOLA TESLA Laboratories (Stefan University), La Jolla, CA.
Combined effect of horizontal magnetic field and vorticity on Rayleigh Taylor instability
Banerjee, Rahul
2016-01-01
In this research, the height, curvature and velocity of the bubble tip in Rayleigh-Taylor instability at arbitrary Atwood number with horizontal magnetic field are investigated. To support the earlier simulation and experimental results, the vorticity generation inside the bubble is introduced. It is found that, in early nonlinear stage, the temporal evolution of the bubble tip parameters depend essentially on the strength and initial perturbation of the magnetic field, although the asymptotic nature coincides with the non magnetic case. The model proposed here agrees with the previous linear, nonlinear and simulation observations.
Casner, A.; Galmiche, D.; Huser, G.; Jadaud, J.P.; Richard, A.; Liberatore, S.; Vandenboomgaerde, M. [CEA Bruyeres-le-Chatel, 91 (France)
2009-07-01
The mastering of the development of hydrodynamic instabilities like Rayleigh-Taylor instabilities is an important milestone on the way to perform efficient laser implosions. The complexity of these instabilities implies an experimental validation of the theoretical models and their computer simulations. An experimental platform involving the Omega laser has allowed us to perform indirect drive with rugby-shaped hohlraums. The experiments have validated the growth of 2- and 3-dimensional initial defects as predicted by theory. We have shown that the 3-dimensional defect saturates for an higher amplitude than the 2-dimensional one does. The experiments have been made by using a plastic shell doped with Germanium (CH:Ge). (A.C.)
TWO-DIMENSIONAL BLAST-WAVE-DRIVEN RAYLEIGH-TAYLOR INSTABILITY: EXPERIMENT AND SIMULATION
This paper shows results from experiments diagnosing the development of the Rayleigh-Taylor instability with two-dimensional initial conditions at an embedded, decelerating interface. Experiments are performed at the Omega Laser and use ∼5 kJ of energy to create a planar blast wave in a dense, plastic layer that is followed by a lower density foam layer. The single-mode interface has a wavelength of 50 μm and amplitude of 2.5 μm. Some targets are supplemented with additional modes. The interface is shocked then decelerated by the foam layer. This initially produces the Richtmyer-Meshkov instability followed and then dominated by Rayleigh-Taylor growth that quickly evolves into the nonlinear regime. The experimental conditions are scaled to be hydrodynamically similar to SN1987A in order to study the instabilities that are believed to occur at the He/H interface during the blast-wave-driven explosion phase of the star. Simulations of the experiment were performed using the FLASH hydrodynamics code.
As shown elsewhere an ablatively imploded shell is hydrodynamically unstable, the dominant instability being the well known Rayleigh-Taylor instability with growth rate γ = √Akg where k = 2π/λ is the wave number, g is the acceleration and A the Attwood number (ρhi - ρlo)/(ρhi + ρlo) where ρhi is the density of the heavier fluid and ρlo is the density of the lighter fluid. A theoretical understanding of ablative stabilization has gradually evolved, confirmed over the last five years by experiments. The linear growth is very well understood with excellent agreement between experiment and simulation for planar geometry with wavelengths in the region of 30--100μm. There is an accurate, albeit phenomenological dispersion relation. The non-linear growth has been measured and agrees with calculations. In this lecture, the authors go into the fundamentals of the Rayleigh-Taylor instability and the experimental measurements that show it is stabilized sufficiently by ablation in regimes relevant to ICF
Jian Guangde; Huang Lin; Qiu Xiaoming
2005-01-01
The assembling stabilizing effect of the finite Larmor radius (FLR) and the sheared axial flow (SAF) on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible finite Larmor radius magnetohydrodynamic (MHD) equations. The finite Larmor radius effects are introduced in the momentum equation with the sheared axial flow through an anisotropic ion stress tensor. In this paper a linear mode equation is derived that is valid for arbitrary kL, where k is the wave number and L is the plasma shell thickness. Numerical solutions are presented. The results indicate that the short-wavelength modes of the RayleighTaylor instability are easily stabilized by the individual effect of the finite Larmor radius or the sheared axial flow. The assembling effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability, and the unstable region can be compressed considerably.
This paper is devoted to an investigation of Quantum effects and magnetic field effects on the Rayleigh Taylor instability of two superposed incompressible fluids in bounded porous medium. The Quantum magneto hydrodynamic equations are solved by using normal mode method and a dispersion relation is obtained. The dispersion relation is derived for the case where plasma is bounded by two rigid planes z = 0 and z = h. The Rayleigh Taylor instability growth rate and stability condition of the medium is discussed in the presence of quantum effect, magnetic field, porosity and permeability. It is found that the magnetic field and medium porosity have stabilizing influence while permeability has destabilizing influence on the Rayleigh Taylor instability. (author)
Nonlinear evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities
Dimonte, G
1998-11-01
Scaled experiments on the nonlinear evolution of the Rayleigh- Taylor (RT) and Richtmyer-Meshkov (RM) instabilities are described under a variety, of conditions that occur in nature. At high Reynolds number, the mixing layer grows self-similarly - {alpha}{sub i}Agt{sup 2} for a constant acceleration (g), and as a power law t{sup {theta}{sub i}} for impulsive accelerations U{delta}(t) at low and high Mach numbers. The growth coefficients {alpha}{sub i} and {theta}{sub i} exponents are measured over a comprehensive range of Atwood numbers A. The RT instability is also investigated with Non- Newtonian materials which are independently characterized. A critical wavelength and amplitude for instability is observed associated with the shear modulus and tensile yield of the material. The results are applicable from supernova explosions to geophysical flows subject to these hydrodynamic instabilities.
Development of Richtmyer-Meshkov and Rayleigh-Taylor Instability in presence of magnetic field
Khan, Manoranjan; Banerjee, Rahul; Roy, Sourav; Gupta, M R
2011-01-01
Fluid instabilities like Rayleigh-Taylor,Richtmyer-Meshkov and Kelvin-Helmholtz instability can occur in a wide range of physical phenomenon from astrophysical context to Inertial Confinement Fusion(ICF).Using Layzer's potential flow model, we derive the analytical expressions of growth rate of bubble and spike for ideal magnetized fluid in R-T and R-M cases. In presence of transverse magnetic field the R-M and R-T instability are suppressed or enhanced depending on the direction of magnetic pressure and hydrodynamic pressure. Again the interface of two fluid may oscillate if both the fluids are conducting. However the magnetic field has no effect in linear case.
Gauglitz, Phillip A.; Wells, Beric E.; Buchmiller, William C.; Rassat, Scot D.
2013-03-21
In Hanford underground waste storage tanks, a typical waste configuration is settled beds of waste particles beneath liquid layers. The settled beds are typically composed of layers, and these layers can have different physical and chemical properties. One postulated configuration within the settled bed is a less-dense layer beneath a more-dense layer. The different densities can be a result of different gas retention in the layers or different degrees of settling and compaction in the layers. This configuration can experience a Rayleigh-Taylor (RT) instability where the less dense lower layer rises into the upper layer. Previous studies of gas retention and release have not considered potential buoyant motion within a settle bed of solids. The purpose of this report is to provide a review of RT instabilities, discuss predictions of RT behavior for sediment layers, and summarize preliminary experimental observations of RT instabilities in simulant experiments.
Morgan, Robert; Jacobs, Jeffrey
2014-11-01
Experiments are presented in which a diffuse interface between two gases is accelerated to become Rayleigh-Taylor unstable. The initially flat interface is generated by the opposing flow of two test gases at matched volumetric flow rates exiting through small holes in the test section. A random, three-dimensional interface perturbation is forced using a loudspeaker. The interface is then accelerated by an expansion wave which is generated by the rupturing of a diaphragm separating the heavy gas from a vacuum tank evacuated to ~0.01 atm. The expansion wave generates a large (of order 1000 g), non-constant acceleration acting on the interface causing the Rayleigh-Taylor instability to develop. Planar Mie scattering is employed to visualize the flow using a planar laser sheet generated at the top of the apparatus, which illuminates smoke particles seeded in the heavy gas. The scattered light is then recorded using a CMOS camera operating at 12 kHz. The mixing layer width is obtained from an ensemble of experiments and the turbulent growth parameter α is extracted and compared with previous experiments and simulations.
Stabilization of Viscosity on Rayleigh-Taylor Instability in Z Pinches
邱孝明; 黄林; 简广德
2004-01-01
On the basis of incompressible viscid magnetohydrodynamic equations, a formula is developed to study the mitigation of viscosity on the Rayleigh-Taylor instability in Z pinches. The results indicate that in the whole wavenumber region, the viscosity effect can mitigate the instability. In addition, we compare the viscosity effect with the finite Larmor radius effect [Chin. Phys. Lett. 19 (2002) 217], and the calculation results show that in the temperature region of interest, the former is stronger than the latter. Moreover, for heavy wire-array implosion the viscosity effect is stronger than the finite Larmor radius one, because the former is proportional to m1/2i and the latter is independent of mi.
The effect of normal electric field on the evolution of immiscible Rayleigh-Taylor instability
Tofighi, Nima; Ozbulut, Murat; Feng, James J.; Yildiz, Mehmet
2016-04-01
Manipulation of the Rayleigh-Taylor instability using an external electric field has been the subject of many studies. However, most of these studies are focused on early stages of the evolution. In this work, the long-term evolution of the instability is investigated, focusing on the forces acting on the interface between the two fluids. To this end, numerical simulations are carried out at various electric permittivity and conductivity ratios as well as electric field intensities using Smoothed Particle Hydrodynamics method. The electric field is applied in parallel to gravity to maintain unstable evolution. The results show that increasing top-to-bottom permittivity ratio increases the rising velocity of the bubble while hindering the spike descent. The opposite trend is observed for increasing top-to-bottom conductivity ratio. These effects are amplified at larger electric field intensities, resulting in narrower structures as the response to the excitation is non-uniform along the interface.
Two-dimensional (r-z) magnetohydrodynamic simulations of the electromagnetic implosion of metallic foil plasmas show, for certain initial configurations, a tendency to develop large-amplitude perturbations characteristic of the hydromagnetic Rayleigh-Taylor instability. These perturbations develop at the plasma magnetic field interface for plasma configurations where the density gradient scale length, the characteristic dimension for the instability, is short. The effects on the plasma dynamics of the implosion will be discussed for several initial foil configurations. In general, the growth rates and linear mode structure are found to be influenced by the plasma shell thickness and density gradient scale length, in agreement with theory. The most destructive modes are found to be those with wavelengths of the order of the plasma shell thickness
Self-similar solutions describing the evolution of rounding nonlinear waves in a nonuniform plasma and the dynamics of final amplitude drops under Rayleigh-Taylor instability of rotating shallow water are constructed. 4 refs.; 2 figs.; 2 tabs
Self-consistent cutoff wave number of the ablative Rayleigh--Taylor instability
The cutoff wave number of the ablative Rayleigh--Taylor instability is calculated self-consistently by including the effects of finite thermal conduction. The derived cutoff wave number is quite different from the one obtained with the incompressible fluid (∇·v=0) or sharp boundary models, and it is strongly dependent on thermal conductivity (K∼Tν) and the Froude number (Fr). The derivation is carried out for values of ν>1, Fr>1, and it is valid for some regimes of interest to direct and indirect-drive inertial confinement fusion (ICF). The analytic formula for the cutoff wave number is in excellent agreement with the numerical results of Kull [Phys. Fluids B 1, 170 (1989)]. copyright 1995 American Institute of Physics
Non-linear Evolution of Rayleigh-Taylor Instability in a Radiation Supported Atmosphere
Jiang, Yan-Fei; Stone, James
2012-01-01
The non-linear regime of Rayleigh-Taylor instability (RTI) in a radiation supported atmosphere, consisting of two uniform fluids with different densities, is studied numerically. We perform simulations using our recently developed numerical algorithm for multi-dimensional radiation hydrodynamics based on a variable Eddington tensor as implemented in Athena, focusing on the regime where scattering opacity greatly exceeds absorption opacity. We find that the radiation field can reduce the growth and mixing rate of RTI, but this reduction is only significant when radiation pressure significantly exceeds gas pressure. Small scale structures are also suppressed in this case. In the non-linear regime, dense fingers sink faster than rarefied bubbles can rise, leading to asymmetric structures about the interface. By comparing the calculations that use a variable Eddington tensor (VET) versus the Eddington approximation, we demonstrate that anisotropy in the radiation field can affect the non-linear development of RTI...
The magnetic Rayleigh-Taylor instability for inviscid and viscous fluids
Chambers, K.; Forbes, L. K.
2011-05-01
The Rayleigh-Taylor instability arises whenever two fluids with different densities are arranged such that the heavier fluid sits above the lighter fluid, with a sharp interface in between. The magnetic Rayleigh-Taylor instability has the further complication due to the presence of a magnetic field throughout both media. The two fluids in question may also have differing magnetic properties, such as the magnetic permeability. When the fluids in consideration are in fact plasmas comprised of charged particles, induced currents, magnetic fields, and Lorentz forces can all act in ways that will affect the stability of the system. Stable base flows exist for the 2D case, and small sinusoidal disturbances to the base flow will grow in the unstable scenario. The numerical method described in this paper calculates the growth of the interface in the nonlinear regime, since closed form solutions are obtained only in the linear approximation. Through the analysis of both the fluid and magnetic vorticities and streamfunctions, the simulated results can be explained from the principles of magnetohydrodynamics. A range of simulations is presented, looking at cases with different initial conditions, cases with strong and weak magnetic fields, and cases with magnetic fields oriented at different angles relative to the interface of the two fluids. It is shown in particular how different initial conditions give rise to outcomes that are very different in terms of the geometry of the interface between the two fluids, primarily the differences between a single mode disturbance and a multimode disturbance to the interface at time t = 0.
The magnetic Rayleigh-Taylor instability for inviscid and viscous fluids
The Rayleigh-Taylor instability arises whenever two fluids with different densities are arranged such that the heavier fluid sits above the lighter fluid, with a sharp interface in between. The magnetic Rayleigh-Taylor instability has the further complication due to the presence of a magnetic field throughout both media. The two fluids in question may also have differing magnetic properties, such as the magnetic permeability. When the fluids in consideration are in fact plasmas comprised of charged particles, induced currents, magnetic fields, and Lorentz forces can all act in ways that will affect the stability of the system. Stable base flows exist for the 2D case, and small sinusoidal disturbances to the base flow will grow in the unstable scenario. The numerical method described in this paper calculates the growth of the interface in the nonlinear regime, since closed form solutions are obtained only in the linear approximation. Through the analysis of both the fluid and magnetic vorticities and streamfunctions, the simulated results can be explained from the principles of magnetohydrodynamics. A range of simulations is presented, looking at cases with different initial conditions, cases with strong and weak magnetic fields, and cases with magnetic fields oriented at different angles relative to the interface of the two fluids. It is shown in particular how different initial conditions give rise to outcomes that are very different in terms of the geometry of the interface between the two fluids, primarily the differences between a single mode disturbance and a multimode disturbance to the interface at time t = 0.
Numerical study on Rayleigh-Taylor instabilities in the lightning return stroke
The Rayleigh-Taylor (R-T) instabilities are important hydrodynamics and magnetohydrodynamics (MHD) phenomena that are found in systems in high energy density physics and normal fluids. The formation and evolution of the R-T instability at channel boundary during back-flow of the lightning return stroke are analyzed using the linear perturbation theory and normal mode analysis methods, and the linear growth rate of the R-T instability in typical condition for lightning return stroke channel is obtained. Then, the R-T instability phenomena of lightning return stroke are simulated using a two-dimensional Eulerian finite volumes resistive radiation MHD code. The numerical results show that the evolution characteristics of the R-T instability in the early stage of back-flow are consistent with theoretical predictions obtained by linear analysis. The simulation also yields more evolution characteristics for the R-T instability beyond the linear theory. The results of this work apply to some observed features of the return stroke channel and further advance previous theoretical and experimental work
Numerical study on Rayleigh-Taylor instabilities in the lightning return stroke
Chen, Qiang, E-mail: cq0405@126.com [National Key Laboratory of Electromagnetic Environment and Electro-optical Engineering, PLA University of Science and Technology, Nanjing 210007 (China); Luoyang Electronic Equipment Testing Center, Luoyang 471000 (China); Chen, Bin, E-mail: emcchen@163.com; Shi, Lihua; Yi, Yun [National Key Laboratory of Electromagnetic Environment and Electro-optical Engineering, PLA University of Science and Technology, Nanjing 210007 (China); Wang, Yangyang [Department of Electro-optical Engineering, Electronic Engineering Institute of PLA, Hefei 230037 (China)
2015-09-15
The Rayleigh-Taylor (R-T) instabilities are important hydrodynamics and magnetohydrodynamics (MHD) phenomena that are found in systems in high energy density physics and normal fluids. The formation and evolution of the R-T instability at channel boundary during back-flow of the lightning return stroke are analyzed using the linear perturbation theory and normal mode analysis methods, and the linear growth rate of the R-T instability in typical condition for lightning return stroke channel is obtained. Then, the R-T instability phenomena of lightning return stroke are simulated using a two-dimensional Eulerian finite volumes resistive radiation MHD code. The numerical results show that the evolution characteristics of the R-T instability in the early stage of back-flow are consistent with theoretical predictions obtained by linear analysis. The simulation also yields more evolution characteristics for the R-T instability beyond the linear theory. The results of this work apply to some observed features of the return stroke channel and further advance previous theoretical and experimental work.
Numerical study on Rayleigh-Taylor instabilities in the lightning return stroke
Chen, Qiang; Chen, Bin; Shi, Lihua; Yi, Yun; Wang, Yangyang
2015-09-01
The Rayleigh-Taylor (R-T) instabilities are important hydrodynamics and magnetohydrodynamics (MHD) phenomena that are found in systems in high energy density physics and normal fluids. The formation and evolution of the R-T instability at channel boundary during back-flow of the lightning return stroke are analyzed using the linear perturbation theory and normal mode analysis methods, and the linear growth rate of the R-T instability in typical condition for lightning return stroke channel is obtained. Then, the R-T instability phenomena of lightning return stroke are simulated using a two-dimensional Eulerian finite volumes resistive radiation MHD code. The numerical results show that the evolution characteristics of the R-T instability in the early stage of back-flow are consistent with theoretical predictions obtained by linear analysis. The simulation also yields more evolution characteristics for the R-T instability beyond the linear theory. The results of this work apply to some observed features of the return stroke channel and further advance previous theoretical and experimental work.
Chou, Yi-Ju; Shao, Yun-Chuan
2016-04-01
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.
Simulating the Rayleigh-Taylor instability in polymer fluids with dissipative particle dynamics
Li, Yanggui; Geng, Xingguo; Zhuang, Xin; Wang, Lihua; Ouyang, Jie
2016-04-01
The Rayleigh-Taylor (RT) instability that occurs in the flow of polymer fluids is numerically investigated with dissipative particle dynamics (DPD) method at the mesoscale particle level. For modeling two-phase flow, the Flory-Huggins parameter is introduced to model binary fluids. And the polymer chains in fluids are described by the modified FENE model that depicts both the elastic tension and the elastic repulsion between the adjacent beads with bond length as the equilibrium length of one segment. Besides, a bead repulsive potential is employed to capture entanglements between polymer chains. Through our model and numerical simulation, we research the dynamics behaviors of the RT instability in polymer fluid medium. Furthermore, we also explore the effects of polymer volume concentration, chain length, and extensibility on the evolution of RT instability. These simulation results show that increasing any of the parameters, concentration, chain length, and extensibility, the saturation length of spikes becomes longer, and the two polymer fluids have less mixture. On the contrary, for the case of low concentration, or short chain, or small extensibility, the spikes easily split and break up, and the RT instability pattern evolves into chaotic structure. These observations indicate that the polymer and its properties drastically modify the RT instability pattern.
Adams, Colin S; Hsu, Scott C
2014-01-01
We present time-resolved observations of Rayleigh-Taylor-instability growth at the interface between an unmagnetized plasma jet colliding with a stagnated, magnetized plasma. The observed instability growth time ($\\sim 10$ $\\mu$s) is consistent with the estimated linear Rayleigh-Taylor growth rate calculated using experimentally inferred values of density ($\\sim 10^{14}$ cm$^{-3}$) and acceleration ($10^9$ m/s$^2$). The observed instability wavelengths ($\\gtrsim 1$ cm) are consistent with stabilization of short wavelengths by a magnetic field of the experimentally measured magnitude ($\\sim 15$ G) and direction. Comparisons of data with idealized magnetohydrodynamic simulations including a physical viscosity model suggest that the observed instability evolution is consistent with both magnetic and viscous stabilization.
Investigation of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities
Riccardo Bonazza
2006-03-09
The present research program is centered on the experimental and numerical study of two instabilities that develop at the interface between two different fluids when the interface experiences an impulsive or a constant acceleration. The instabilities, called the Richtmyer-Meshkov and Rayleigh-Taylor instability, respectively (RMI and RTI), adversely affect target implosion in experiments aimed at the achievement of nuclear fusion by inertial confinement by causing the nuclear fuel contained in a target and the ablated shell material to mix, leading to contamination of the fuel, yield reduction or no ignition at all. Specifically, our work is articulated in three main directions: study of impulsively accelerated spherical gas inhomogeneities; study of impulsively accelerated 2-D interfaces; study of a liquid interface under the action of gravity. The objectives common to all three activities are to learn some physics directly from our experiments and calculations; and to develop a database at previously untested conditions to be used to calibrate and verify some of the computational tools being developed within the RTI/RMI community at the national laboratories and the ASCI centers.
Steiner, Adam; Yager-Elorriaga, David; Patel, Sonal; Jordan, Nicholas; Gilgenbach, Ronald; Lau, Y. Y.
2015-11-01
The electrothermal instability (ETI) and magneto-Rayleigh Taylor instability (MRT) are important in the implosion of metallic liners, such as magnetized liner implosion fusion (MagLIF). The MAIZE linear transformer driver (LTD) at the University of Michigan generates 200 ns risetime-current pulses of 500 to 600 kA into Al foil liners to study plasma instabilities and implosion dynamics, most recently MRT growth on imploding cylindrical liners. A full circuit model of MAIZE, along with I-V measurements, yields time-resolved load inductance. This has enabled measurements of an effective current-carrying radius to determine implosion velocity and plasma-vacuum interface acceleration. Measurements are also compared to implosion data from 4-time-frame laser shadowgraphy. Improved resolution measurements on the laser shadowgraph system have been used to examine the liner interface early in the shot to examine surface perturbations resulting from ETI for various seeding conditions. Fourier analysis examines the growth rates of wavelength bands of these structures to examine the transition from ETI to MRT. This work was supported by the U.S. DoE through award DE-SC0012328. S.G. Patel is supported by Sandia National Labs. D.A. Yager is supported by NSF fellowship grant DGE 1256260.
Effect of FLR and rotation on the Rayleigh-Taylor instability of two component plasma
The problem of Rayleigh-Taylor (R-T) instability of superposed magnetized fluids is investigated in a partially ionized medium. The fluid has ionized and neutralized particles components interacting with each other by collisions. The effect of rotation in the horizontal directions also included in this R-T problem. The usual magnetohydrodynamic equations are modified for finite Larmor radius corrections which is in the form of tensor. The permeability of medium is also included in the equation. The relevant linearized perturbation equation are taken and using normal mode analysis the general relation is obtained. The dispersion relation for two superimposed fluids of different densities is derived. The dispersion relation shows that the growth rate of unstable system is reduced due to FLR corrections, rotation and collisional frequency of the neutrals. The dispersions relation gives no effect of magnetic field because horizontal magnetic field has no role in the R-T instability. The condition of instability remains unaffected by the permeability of porous medium, pressure of neutral particles in the fluids and rotation. (author)
Hydrodynamic Scaling of the Deceleration-Phase Rayleigh-Taylor Instability
Bose, A.; Nora, R.; Woo, K.; Betti, R.
2013-10-01
A 2-D study of the deceleration-phase Rayleigh-Taylor (RT) growth is carried out to assess how the yield-over-clean (YOC) varies in hydro-equivalent implosions. Hydro-equivalent implosions exhibit equal implosion velocity, adiabat, and laser intensity. The YOC indicates the effects of hydrodynamic instabilities on inertial fusion capsule implosions. While the classical RT instability follows the laws of hydrodynamic similarity (the same growth factor for hydro-equivalent implosions), the effects of ablation and thermal transport in the hot spot cause a deviation from similarity. We present analytic and numerical calculations of the RT growth factors in hydro-equivalent implosions with target sizes varying from typical OMEGA to NIF-scale targets. Theoretical scaling suggests that the deceleration-phase Atwood number and ablation velocity is different for OMEGA and the NIF, yielding growth factors that are dependent on the target size. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944 and DE-FC02-04ER54789 (Fusion Science Center).
Magnetic Rayleigh-Taylor instability mitigation in large-diameter gas puff Z-pinch implosions
Recently, a new approach for efficiently generating K-shell x-rays in large-diameter, long-implosion time, structured argon gas Z-pinches has been demonstrated based on a 'pusher-stabilizer-radiator' model. In this paper, direct observations of the Rayleigh-Taylor instability mitigation of a 12-cm diameter, 200-ns implosion time argon Z-pinch using a laser shearing interferometer (LSI) and a laser wavefront analyzer (LWA) are presented. Using a zero-dimensional snowplow model, the imploding plasma trajectories are calculated with the driver current waveforms and the initial mass distributions measured using the planar laser induced fluorescence method. From the LSI and LWA images, the plasma density and trajectory during the implosion are measured. The measured trajectory agrees with the snowplow calculations. The suppression of hydromagnetic instabilities in the ''pusher-stabilizer-radiator'' structured loads, leading to a high-compression ratio, high-yield Z-pinch, is discussed. For comparison, the LSI and LWA images of an alternative load (without stabilizer) show the evolution of a highly unstable Z-pinch
Gupta, M R; Roy, Sourav; Khan, Manoranjan
2011-01-01
The effect of magnetic field on the nonlinear growth rate of Rayleigh-Taylor instability induced two fluid interfacial structures has been investigated. The magnetic field is assumed to be parallel to the plane of the two fluid interface and acts in a direction perpendicular to the wave vector. If magnetic field is restricted only to either side of the interface the growth rate may be depressed (may almost disappear) or be enhanced depending on whether the magnetic pressure on the interface opposes the instability driving pressure difference g({\\rho}h - {\\rho}l)y or acts in the same direction. If magnetic field is present on both sides of the two fluid interface, stabilization may also take place in the sense that the surface of separation undulates periodically when the force due to magnetic pressure on two sides are such as to act in opposite direction. This result differs from the classical linear theory result which predicts that the magnetic field parallel to the surface has no influence on the growth ra...
Linear theory of Rayleigh-Taylor instability growth at a density profile which varies exponentially between regions of constant density is discussed in detail. The exact theory provides an approximate but conservative simple formula for the growth constant and it shows that a hitherto widely used theory erroneously underestimates the growth constant. A simple but effective ''synthetical model'' of nonlinear bubble growth is obtained from a synthesis of linear theory and constant terminal bubble speed. It is applied to pusher shell break-up in an inertial confinement fusion pellet to determine the maximum allowable initial perturbations and the most dangerous wavelength. In a situation typical of heavy ion drivers it is found that the allowable initial perturbations are increased by a few orders of magnitude by the gradual density transition and another order of magnitude by nonlinear saturation of the bubble speed. The gradual density transition also shifts the most dangerous wavelength from about once to about four times the minimum pusher shell thickness. The following topics are treated briefly: Reasons conflicting with use of the synthetical model to decide whether the pusher shell in a certain simulation will be broken up; other nonlinear theories available in the literature; further realistic effects that might aggravate instability growth. (orig.)
This thesis deals with the dynamics of accelerated ablative front spreading in Inertial Confinement Fusion experiments. ICF is designed for the implosion of a deuterium-tritium spherical target. The outer shell, the ablator, is irradiated providing a high level pressure inside the target. During this first stage, the ablation front propagating inwards is perturbed by hydrodynamics instabilities, which can prevent the fusion reaction in the decelerated stage. We propose here a study on Rayleigh-Taylor instabilities during ablation process, in the two dimensional case. In order to obtain a numerical solution, we perform an asymptotic analysis in the limit of a high temperature ratio, between the remaining cold ablator and the hot ablated plasma. This study is divided in two steps. First, the thermo-diffusive part of the set of equations is approximated by a Hele-Shaw model, which is then perturbed by the hydrodynamics part. Using a vortex method, we have to solve the advection of a vortical sheet moving with the ablation front. We compute the numerical solution on an Eulerian mesh coupled with a marker method. The thermal part is computed by implementing the Fat Boundary Method, recently developed. The hydrodynamic part is obtained from a Finite Volume scheme. (author)
Martinez, D. A.; Smalyuk, V. A.; Kane, J. O.; Casner, A.; Liberatore, S.; Masse, L. P.
2015-05-01
We investigate on the National Ignition Facility the ablative Rayleigh-Taylor instability in the transition from weakly nonlinear to highly nonlinear regimes. A planar plastic package with preimposed two-dimensional broadband modulations is accelerated for up to 12 ns by the x-ray drive of a gas-filled Au radiation cavity with a radiative temperature plateau at 175 eV. This extended tailored drive allows a distance traveled in excess of 1 mm for a 130 μ m thick foil. Measurements of the modulation optical density performed by x-ray radiography show that a bubble-merger regime for the Rayleigh-Taylor instability at an ablation front is achieved for the first time in indirect drive. The mutimode modulation amplitudes are in the nonlinear regime, grow beyond the Haan multimode saturation level, evolve toward the longer wavelengths, and show insensitivity to the initial conditions.
Rimbert, Nicolas
2010-01-01
The question whether liquid atomization (or pulverization) resorts to instability dynamics (through refinements of Rayleigh-Plateau, Rayleigh-Taylor or Kelvin-Helmholtz mechanism) or to turbulent cascades similar to Richardson and Kolmogorov first ideas seems to be still open. In this paper, we report experimental evidences that both mechanisms are needed to explain the spray drop PDF obtained from an industrial nozzle. Instability of Rayleigh-Taylor kind governs the size of the largest droplets while the smallest ones obey a PDF given by a turbulent cascading mechanism resulting in a log-L\\'evy stable law of stability parameter close to 1.68. This value, very close to the inverse of the Flory exponent, can be related to a recent model for intermittency modeling stemming from self-avoiding random vortex stretching.
Martinez, David
2015-11-01
We investigate on the National Ignition Facility (NIF) the ablative Rayleigh-Taylor (RT) instability in the transition from linear to highly nonlinear regimes. This work is part of the Discovery Science Program on NIF and of particular importance to indirect-drive inertial confinement fusion (ICF) where careful attention to the form of the rise to final peak drive is calculated to prevent the RT instability from shredding the ablator in-flight and leading to ablator mixing into the cold fuel. The growth of the ablative RT instability was investigated using a planar plastic foil with pre-imposed two-dimensional broadband modulations and diagnosed using x-ray radiography. The foil was accelerated for 12ns by the x-ray drive created in a gas-filled Au radiation cavity with a radiative temperature plateau at 175 eV. The dependence on initial conditions was investigated by systematically changing the modulation amplitude, ablator material and the modulation pattern. For each of these cases bubble mergers were observed and the nonlinear evolution of the RT instability showed insensitivity to the initial conditions. This experiment provides critical data needed to validate current theories on the ablative RT instability for indirect drive that relies on the ablative stabilization of short-scale modulations for ICF ignition. This paper will compare the experimental data to the current nonlinear theories. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC.
Viscous effects on the Rayleigh-Taylor instability with background temperature gradient
Gerashchenko, S
2016-01-01
The growth rate of the compressible Rayleigh-Taylor instability is studied in the presence of a background temperature gradient, $\\Theta$, using a normal mode analysis. The effect of $\\Theta$ variation is examined for three interface types corresponding to combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous and viscous-inviscid) at different Atwood numbers, $At$, and, when at least one of the fluids' viscosity is non-zero, as a function of the Grashof number. For the general case, the resulting ordinary differential equations are solved numerically; however, dispersion relations for the growth rate are presented for several limiting cases. An analytical solution is found for the inviscid-inviscid interface and the corresponding dispersion equation for the growth rate is obtained in the limit of a large $\\Theta$. For the viscous-inviscid case, a dispersion relation is derived in the incompressible limit and $\\Theta=0$. Compared to $\\Theta=0$ case, the role of $\\Theta0$ (col...
Evolution of mixing width induced by general Rayleigh-Taylor instability
Zhang, You-sheng; He, Zhi-wei; Gao, Fu-jie; Li, Xin-liang; Tian, Bao-lin
2016-06-01
Turbulent mixing induced by Rayleigh-Taylor (RT) instability occurs ubiquitously in many natural phenomena and engineering applications. As the simplest and primary descriptor of the mixing process, the evolution of mixing width of the mixing zone plays a notable role in the flows. The flows generally involve complex varying acceleration histories and widely varying density ratios, two dominant factors affecting the evolution of mixing width. However, no satisfactory theory for predicting the evolution has yet been established. Here a theory determining the evolution of mixing width in general RT flows is established to reproduce, first, all of the documented experiments conducted for diverse (i.e., constant, impulsive, oscillating, decreasing, increasing, and complex) acceleration histories and all density ratios. The theory is established in terms of the conservation principle, with special consideration given to the asymmetry of the volume-averaged density fields occurring in actual flows. The results reveal the sensitivity or insensitivity of the evolution of a mixing front of a neighboring light or heavy fluid to the degree of asymmetry and thus explain the distinct evolutions in two experiments with the same configurations.
Numerical Experiments with a Turbulent Single-Mode Rayleigh-Taylor Instability
Cloutman, L.D.
2000-04-01
Direct numerical simulation is a powerful tool for studying turbulent flows. Unfortunately, it is also computationally expensive and often beyond the reach of the largest, fastest computers. Consequently, a variety of turbulence models have been devised to allow tractable and affordable simulations of averaged flow fields. Unfortunately, these present a variety of practical difficulties, including the incorporation of varying degrees of empiricism and phenomenology, which leads to a lack of universality. This unsatisfactory state of affairs has led to the speculation that one can avoid the expense and bother of using a turbulence model by relying on the grid and numerical diffusion of the computational fluid dynamics algorithm to introduce a spectral cutoff on the flow field and to provide dissipation at the grid scale, thereby mimicking two main effects of a large eddy simulation model. This paper shows numerical examples of a single-mode Rayleigh-Taylor instability in which this procedure produces questionable results. We then show a dramatic improvement when two simple subgrid-scale models are employed. This study also illustrates the extreme sensitivity to initial conditions that is a common feature of turbulent flows.
Rayleigh-Taylor instability in non-uniform magnetized rotating strongly coupled viscoelastic fluid
Prajapati, R. P.
2016-02-01
The Rayleigh-Taylor instability (RTI) in an incompressible strongly coupled viscoelastic fluid is investigated considering the effects of inhomogeneous magnetic field, density gradient, and uniform rotation. The generalized hydrodynamic equations have been formulated, and linear dispersion relation is derived taking appropriate density and magnetic field profiles for the considered system. The gravity induced stable and unstable configurations of RTI are analyzed in hydrodynamic and kinetic limits. In the kinetic limit, shear wave modified dispersion relation and the condition of RTI are derived in terms of magnetic-viscoelastic Mach number and viscoelastic Froude number. The criteria of RTI and critical wavenumber for the growth of RTI to be unstable are estimated numerically for white dwarf and inertial confinement fusion target. It is observed that magnetic field, rotation, and viscoelastic effects play a significant role in the suppression of RTI in these systems. The stabilizing influence of magnetic field, rotation, and magnetic-viscoelastic Mach number while the destabilizing influence of viscoelastic Froude on the growth rate of RTI number is observed graphically. The growth rate of RTI decreases faster in kinetic limit as compared to the hydrodynamic limit.
Reckinger, Scott J.; Livescu, Daniel; Vasilyev, Oleg V.
2016-05-01
An investigation of compressible Rayleigh-Taylor instability (RTI) using Direct Numerical Simulations (DNS) requires efficient numerical methods, advanced boundary conditions, and consistent initialization in order to capture the wide range of scales and vortex dynamics present in the system, while reducing the computational impact associated with acoustic wave generation and the subsequent interaction with the flow. An advanced computational framework is presented that handles the challenges introduced by considering the compressive nature of RTI systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification dependent vorticity production. The foundation of the numerical methodology described here is the wavelet-based grid adaptivity of the Parallel Adaptive Wavelet Collocation Method (PAWCM) that maintains symmetry in single-mode RTI systems to extreme late-times. PAWCM is combined with a consistent initialization, which reduces the generation of acoustic disturbances, and effective boundary treatments, which prevent acoustic reflections. A dynamic time integration scheme that can handle highly nonlinear and potentially stiff systems, such as compressible RTI, completes the computational framework. The numerical methodology is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis.
A numerical study of Rayleigh-Taylor instability in aluminum and steel plates
The SCRAM code is applied to the study of Rayleigh-Taylor instability in metal plates, and comparisons of these computer results are made with experimental data for 1100-O aluminum, 6061-T6 aluminum and 304 stainless steel. Various models for the pressure, temperature, and strain-rate dependencies of the flow stress are compared in the computer calculations. The coefficients that are required in these models to give good agreement with the experimental results are generally close to values that were determined from previous experimental comparisons. The sensitivity of the computed results to modeling parameters, to variations in the hardening modulus, and to the amplitude and wavelength of the perturbations in the plate surface is examined. Very little growth in amplitude occurs if either the initial amplitude or the wavelength is sufficiently small. The growth rate increases monotonically with increasing initial amplitude. There appears to exist a wavelength of maximum growth, such that the growth rate increases rapidly with wavelength up to this wavelength, but then decreases slowly as the wavelength is further increased
Bubble merger model for the nonlinear Rayleigh-Taylor instability driven by a strong blast wave
A bubble merger model is presented for the nonlinear evolution of the Rayleigh-Taylor instability driven by a strong blast wave. Single bubble motion is determined by an extension of previous buoyancy-drag models extended to the blast-wave-driven case, and a simple bubble merger law in the spirit of the Sharp-Wheeler model allows for the generation of larger scales. The blast-wave-driven case differs in several respects from the classical case of incompressible fluids in a uniform gravitational field. Because of material decompression in the rarefaction behind the blast front, the asymptotic bubble velocity and the merger time depend on time as well as the transverse scale and the drive. For planar blast waves, this precludes the emergence of a self-similar regime independent of the initial conditions. With higher-dimensional blast waves, divergence restores the properties necessary for the establishment of the self-similar state, but its establishment requires a very high initial characteristic mode number and a high Mach number for the incident blast wave
The purpose of this research program is to investigate fluid dynamic instabilities and mixing initiated by the interaction of shock waves with interfaces between light and heavy gases. In particular, the nonlinear stage of shock-initiated Rayleigh-Taylor instability (also known as the Richtmeyer-Meshkov instability), the secondary instabilities (e.g., the Kelvin-Helmholtz instability) arising therefrom and the resulting mixing of the two gases are of interest. This report describes activities during the performance period 1 October 1985 to 30 September 1986
Ramaprabhu, Praveen; Karkhanis, Varad; Banerjee, Rahul; Varshochi, Hilda; Khan, Manoranjan; Lawrie, Andrew; Variable g RT Collaboration
2015-11-01
From detailed numerical simulations of the single-mode Rayleigh-Taylor (RT) instability driven by time-varying acceleration histories, we report on several findings of relevance to the performance of Inertial Confinement Fusion capsules. The incompressible, Direct Numerical Simulations (DNS) were performed in two- and three-dimensions, and over a range of density ratios of the fluid combinations (characterized by the Atwood number). We have investigated several acceleration histories, including acceleration profiles g(t) of the general form tn, with n > -2. For the 2D flow, results from numerical simulations are compared with a potential flow model developed and reported as part of this work. When the simulations are extended to three dimensions, bubble and spike growth rates are in agreement with an extension to the drag buoyancy model with modifications for time-dependent acceleration histories. We have come up with simple analytic solutions to the Drag Buoyancy model for variable g flows, and compared the solution with the 2D and 3D DNS results. This work was supported in part by the (U.S.) Department of Energy (DOE) under Contract No. DE-AC52-06NA2-5396.
Smitherman, D.P.
1998-04-01
Eight beams carrying a shaped pulse from the NOVA laser were focused into a hohlraum with a total energy of about 25 kJ. A planar foil was placed on the side of the hohlraum with perturbations facing away from the hohlraum. All perturbations were 4 {micro}m in amplitude and 50 {micro}m in wavelength. Three foils of pure aluminum were shot with thicknesses and pulse lengths respectively of 86 {micro}m and 2. 2 ns, 50 {micro}m and 4.5 ns, and 35 {micro}m with both 2.2 ns and 4. 5 ns pulses. Two composite foils constructed respectively of 32 and 84 {micro}m aluminum on the ablative side and 10 {micro}m beryllium on the cold surface were also shot using the 2.2 ns pulse. X-ray framing cameras recorded perturbation growth using both face- and side-on radiography. The LASNEX code was used to model the experiments. A shock wave interacted with the perturbation on the cold surface generating growth from a Richtmyer-Meshkov instability and a strong acoustic mode. The cold surface perturbation fed-out to the Rayleigh-Taylor unstable ablation surface, both by differential acceleration and interface coupling, where it grew. A density jump did not appear to have a large effect on feed-out from interface coupling. The Rayleigh-Taylor instability`s vortex pairs overtook and reversed the direction of flow of the Richtmyer-Meshkov vortices, resulting in the foil moving from a sinuous to a bubble and spike configuration. The Rayleigh-Taylor instability may have acted as an ablative instability on the hot surface, and as a classical instability on the cold surface, on which grew second and third order harmonics.
Ramaprabhu, P; Karkhanis, V; Banerjee, R; Varshochi, H; Khan, M; Lawrie, A G W
2016-01-01
From nonlinear models and direct numerical simulations we report on several findings of relevance to the single-mode Rayleigh-Taylor (RT) instability driven by time-varying acceleration histories. The incompressible, direct numerical simulations (DNSs) were performed in two (2D) and three dimensions (3D), and at a range of density ratios of the fluid combinations (characterized by the Atwood number). We investigated several acceleration histories, including acceleration profiles of the general form g(t)∼t^{n}, with n≥0 and acceleration histories reminiscent of the linear electric motor experiments. For the 2D flow, results from numerical simulations compare well with a 2D potential flow model and solutions to a drag-buoyancy model reported as part of this work. When the simulations are extended to three dimensions, bubble and spike growth rates are in agreement with the so-called level 2 and level 3 models of Mikaelian [K. O. Mikaelian, Phys. Rev. E 79, 065303(R) (2009)10.1103/PhysRevE.79.065303], and with corresponding 3D drag-buoyancy model solutions derived in this article. Our generalization of the RT problem to study variable g(t) affords us the opportunity to investigate the appropriate scaling for bubble and spike amplitudes under these conditions. We consider two candidates, the displacement Z and width s^{2}, but find the appropriate scaling is dependent on the density ratios between the fluids-at low density ratios, bubble and spike amplitudes are explained by both s^{2} and Z, while at large density differences the displacement collapses the spike data. Finally, for all the acceleration profiles studied here, spikes enter a free-fall regime at lower Atwood numbers than predicted by all the models. PMID:26871165
Nonlinear Rayleigh--Taylor instability of the cylindrical fluid flow with mass and heat transfer
ALY R SEADAWY; K EL-RASHIDY
2016-08-01
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 exactsolutions for a nonlinear Ginzburg--Landau equation. The region of solutions is displayed graphically.
Seo, Han; Moon, Sung Bo; Bang, In Cheol [Ulsan National Institute of Science and Technology, Ulsan (Korea, Republic of)
2013-10-15
In the present study, the observation of RT instability wavelength with one-dimensional horizontal wire surface is studied in the pressurized wire pool boiling facility to show the relation between RT instability wavelength and CHF or MHF. The pressure effect is considered instead of using different working fluids. The observation of RT instability wavelength at different system pressure with bare Ni-Cr wire (0.5 mm dia) was studied. The CHF using R-123 refrigerant was enhanced according with higher system pressure. There was a tendency that RT instability wavelength was decreased when CHF and MHF is increased. The measurement value of wavelength in the experiment is less than the predicted wavelength equation. Different wire radius and system pressures should be conducted with bare wire surface to establish the fundamental data for the experiment of nano-coated wire. The analysis of minimum heat flux based on unstable wavelength (RT instability wavelength) has been studied to quantify the available experimental data. The experiments were studied using different inorganic fluids. To quantify the data, the dimensionless terms such as radius and minimum heat flux were considered. Nowadays, nanofluids and depositions of nano-particle on heater surface have been used to enhance of thermal margin in terms of critical heat flux (CHF) and boiling heat transfer. The enhancement of thermal margin is described as surface wettability, thermal activity (effusivity), and the change Rayleigh-Taylor (RT) instability wavelength due to deposition of nanoparticles which could make the surface as porous structure. In our research group, the change of RT instability wavelength using a simple condensation method was studied because the graphene-oxide deposition layer did not show the surface wettability improvement. Based on the enhancement of CHF studies, Lee et al. proposed the change of Rayleigh-Taylor instability wavelength could explain all the methods of CHF enhancement on pool
Mokler, Matthew; Jacobs, Jeffrey
2014-11-01
Incompressible Rayleigh-Taylor instability experiments are presented in which two stratified liquids having Atwood number of 0.2 are accelerated in a vertical linear induction motor driven drop tower. A test sled having only vertical freedom of motion contains the experiment tank and visualization equipment. The sled is positioned at the top of the tower within the linear induction motors and accelerated downward causing the initially stable interface to be unstable and allowing the Rayleigh-Taylor instability to develop. Forced and unforced experiments are conducted using an immiscible liquid combination. Forced initial perturbations are produced by vertically oscillating the test sled prior to the start of acceleration. The interface is visualized using a 445 nm laser light source that illuminates a fluorescent dye mixed in one of the fluids and aluminum oxide particles dispersed in both fluids. The laser beam is synchronously swept across the fluorescent fluid, at the frame rate of the camera, exposing a single plane of the interface. The resulting images are recorded using a monochromatic high speed video camera. Time dependent velocity and density fields are obtained from the recorded images allowing for 2D full field measurements of turbulent kinetic energy and turbulent mass transport.
Initial value problem for Rayleigh--Taylor instability of viscous fluids
The initial value problem associated with the development of small amplitude disturbances in Rayleigh--Taylor unstable, viscous, incompressible fluids is studied. Solutions to the linearized equations of motion which satisfy general initial conditions are obtained in terms of Fourier--Laplace transforms of the hydrodynamic variables, without restriction on the density or viscosity of either fluid. When the two fluids have equal kinematic viscosities, these transforms can be inverted explicitly to express the fluid variables as integrals of Green's functions multiplied by initial data. In addition to normal modes, a set of continuum modes, not treated explicitly in the literature, makes an important contribution to the development of the fluid motion
Zhou, M. L.; Liu, B.; Hu, R. H.; Shou, Y. R.; Lin, C.; Lu, H. Y.; Lu, Y. R.; Gu, Y. Q.; Ma, W. J.; Yan, X. Q.
2016-08-01
In the case of a thin plasma slab accelerated by the radiation pressure of an ultra-intense laser pulse, the development of Rayleigh-Taylor instability (RTI) will destroy the acceleration structure and terminate the acceleration process much sooner than theoretical limit. In this paper, a new scheme using multiple Gaussian pulses for ion acceleration in a radiation pressure acceleration regime is investigated with particle-in-cell simulation. We found that with multiple Gaussian pulses, the instability could be efficiently suppressed and the divergence of the ion bunch is greatly reduced, resulting in a longer acceleration time and much more collimated ion bunch with higher energy than using a single Gaussian pulse. An analytical model is developed to describe the suppression of RTI at the laser-plasma interface. The model shows that the suppression of RTI is due to the introduction of the long wavelength mode RTI by the multiple Gaussian pulses.
Henry de Frahan, M. T. [Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA; Belof, J. L. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Cavallo, R. M. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Raevsky, V. A. [Russian Federal Nuclear Center-VNIIEF, Sarov 607188, Russia; Ignatova, O. N. [Russian Federal Nuclear Center-VNIIEF, Sarov 607188, Russia; Lebedev, A. [Russian Federal Nuclear Center-VNIIEF, Sarov 607188, Russia; Ancheta, D. S. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; El-dasher, B. S. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Florando, J. N. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Gallegos, G. F. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Johnsen, E. [Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA; LeBlanc, M. M. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA
2015-06-14
A recent collaboration between LLNL and VNIIEF has produced a set of high explosive driven Rayleigh-Taylor strength data for beryllium. Design simulations using legacy strength models from Steinberg-Lund and Preston-Tonks-Wallace (PTW) suggested an optimal design that would delineate between not just different strength models, but different parameters sets of the PTW model. Application of the models to the post-shot results, however, shows close to classical growth. We characterize the material properties of the beryllium tested in the experiments. We also discuss recent efforts to simulate the data using the legacy strength models as well as the more recent RING relaxation model developed at VNIIEF. Finally, we present shock and ramp-loading recovery experiments conducted as part of the collaboration.
Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner
This paper analyzes the coupling of magneto-Rayleigh-Taylor (MRT), sausage, and kink modes in an imploding cylindrical liner, using ideal MHD. A uniform axial magnetic field of arbitrary value is included in each region: liner, its interior, and its exterior. The dispersion relation is solved exactly, for arbitrary radial acceleration (-g), axial wavenumber (k), azimuthal mode number (m), liner aspect ratio, and equilibrium quantities in each region. For small k, a positive g (inward radial acceleration in the lab frame) tends to stabilize the sausage mode, but destabilize the kink mode. For large k, a positive g destabilizes both the kink and sausage mode. Using the 1D-HYDRA simulation results for an equilibrium model that includes a pre-existing axial magnetic field and a preheated fuel, we identify several stages of MRT-sausage-kink mode evolution. We find that the m = 1 kink-MRT mode has a higher growth rate at the initial stage and stagnation stage of the implosion, and that the m = 0 sausage-MRT mode dominates at the main part of implosion. This analysis also sheds light on a puzzling feature in Harris' classic paper of MRT [E. G. Harris, Phys. Fluids 5, 1057 (1962)]. An attempt is made to interpret the persistence of the observed helical structures [Awe et al., Phys. Rev. Lett. 111, 235005 (2013)] in terms of non-axisymmetric eigenmode
Measurements of Magneto-Rayleigh-Taylor instability growth in solid liners on the 20 MA Z facility.
Bigman, Verle; Vesey, Roger Alan; Shores, Jonathon; Herrmann, Mark C.; Stamm, Robert (General Atomics, San Diego, CA); Killebrew, Korbie (General Atomics, San Diego, CA); Holt, Randy (General Atomics, San Diego, CA); Blue, Brent (General Atomics, San Diego, CA); Nakhleh, Charlie; McBride, Ryan D.; Leifeste, Gordon T.; Smith, Ian Craig; Stygar, William A.; Porter, John Larry, Jr.; Cuneo, Michael Edward; Bennett, Guy R.; Schroen, Diana Grace (General Atomics, San Diego, CA); Sinars, Daniel Brian; Lopez, Mike R.; Slutz, Stephen A.; Atherton, Briggs W.; Tomlinson, Kurt; Edens, Aaron D.; Savage, Mark Edward; Peterson, Kyle J.
2010-07-01
The magneto-Rayleigh-Taylor (MRT) instability is the most important instability for determining whether a cylindrical liner can be compressed to its axis in a relatively intact form, a requirement for achieving the high pressures needed for inertial confinement fusion (ICF) and other high energy-density physics applications. While there are many published RT studies, there are a handful of well-characterized MRT experiments at time scales >1 {micro}s and none for 100 ns z-pinch implosions. Experiments used solid Al liners with outer radii of 3.16 mm and thicknesses of 292 {micro}m, dimensions similar to magnetically-driven ICF target designs [1]. In most tests the MRT instability was seeded with sinusoidal perturbations ({lambda} = 200, 400 {micro}m, peak-to-valley amplitudes of 10, 20 {micro}m, respectively), wavelengths similar to those predicted to dominate near stagnation. Radiographs show the evolution of the MRT instability and the effects of current-induced ablation of mass from the liner surface. Additional Al liner tests used 25-200 {micro}m wavelengths and flat surfaces. Codes being used to design magnetized liner ICF loads [1] match the features seen except at the smallest scales (<50 {micro}m). Recent experiments used Be liners to enable penetrating radiography using the same 6.151 keV diagnostics and provide an in-flight measurement of the liner density profile.
Measurements of Magneto-Rayleigh-Taylor instability growth in solid liners on the 20 MA Z facility
The magneto-Rayleigh-Taylor (MRT) instability is the most important instability for determining whether a cylindrical liner can be compressed to its axis in a relatively intact form, a requirement for achieving the high pressures needed for inertial confinement fusion (ICF) and other high energy-density physics applications. While there are many published RT studies, there are a handful of well-characterized MRT experiments at time scales >1 (micro)s and none for 100 ns z-pinch implosions. Experiments used solid Al liners with outer radii of 3.16 mm and thicknesses of 292 (micro)m, dimensions similar to magnetically-driven ICF target designs (1). In most tests the MRT instability was seeded with sinusoidal perturbations (λ = 200, 400 (micro)m, peak-to-valley amplitudes of 10, 20 (micro)m, respectively), wavelengths similar to those predicted to dominate near stagnation. Radiographs show the evolution of the MRT instability and the effects of current-induced ablation of mass from the liner surface. Additional Al liner tests used 25-200 (micro)m wavelengths and flat surfaces. Codes being used to design magnetized liner ICF loads (1) match the features seen except at the smallest scales (<50 (micro)m). Recent experiments used Be liners to enable penetrating radiography using the same 6.151 keV diagnostics and provide an in-flight measurement of the liner density profile.
A review of the ablative stabilization of the Rayleigh-Taylor instability in regimes relevant to ICF
It has been recognized for many years that the most significant limitation of ICF is the Rayleigh-Taylor (R-T) instability. It limits the distance an ablatively driven shell can be moved to several times its initial thickness. Fortunately material flow through the unstable region at velocity vA reduces the growth rate to √1+kL/kg -βkvA with β from 2-3. In recent years experiments using both x-ray drive and smoothed laser drive to accelerate foils have confirmed our understanding of the R-T instability. The growth of small initial modulations on the foils is measured for growth factors up to 60 for direct drive and 80 for indirect drive. For x-ray drive large stabilization is evident After some growth, the instability enters the non-linear phase when mode coupling and saturation are also seen and compare well with modeling. Normalized growth rates for direct drive are measured to be higher, but strategies for reduction by raising the isentrope are being investigated. For direct drive, high spatial frequencies are imprinted from the laser beam and amplified by the R-T instability. Modeling shows an understanding of this ''laser imprinting.''
It has been recognized for many year's that the most significant limitation of ICF is the Rayleigh-Taylor (R-T) instability. It limits the distance an ablatively driven shell can be moved to several times its initial thickness. Fortunately material flow through the unstable region at velocity vA reduces the growth rate to √1+kL/kg -βkvA with β from 2-3. In recent years experiments using both x-ray drive and smoothed laser drive to accelerate foils have confirmed our understanding of the ablative R-T instability in planar geometry. The growth of small initial modulations on the foils is measured for growth factors up to 60 for direct drive and 80 for indirect drive. For x-ray drive large stabilization is evident. After some growth, the instability enters the non-linear phase when mode coupling and saturation are also seen and compare well with modeling. Normalized growth rates for direct drive are measured to be higher, but strategies for reduction by raising the isentrope are being investigated. For direct drive, high spatial frequencies are imprinted from the laser beam and amplified by the R-T instability. Modeling shows an understanding of this ''laser imprinting.''
Guo, L.-J.; Huang, Y.-M.; Bhattacharjee, A. [Space Science Center, University of New Hampshire, Durham, NH 03824 (United States); Innes, D. E., E-mail: yiminh@princeton.edu, E-mail: amitava@princeton.edu, E-mail: guol@mps.mpg.de, E-mail: innes@mps.mpg.de [Max Planck/Princeton Center for Plasma Physics, Princeton, NJ 08540 (United States)
2014-12-01
Supra-arcade downflows (hereafter referred to as SADs) are low-emission, elongated, finger-like features observed in active region coronae above post-eruption flare arcades. Observations exhibit downward moving SADs intertwined with bright upward growing spikes. Whereas SADs are dark voids, spikes are brighter, denser structures. Although SADs have been observed for more than a decade, the mechanism of the formation of SADs remains an open issue. Using three-dimensional resistive magnetohydrodynamic simulations, we demonstrate that Rayleigh-Taylor-type instabilities develop in the downstream region of a reconnecting current sheet. The instabilities result in the formation of low-density coherent structures that resemble SADs, and high-density structures that appear to be spike-like. Comparison between the simulation results and observations suggests that Rayleigh-Taylor-type instabilities in the exhaust of reconnecting current sheets provide a plausible mechanism for observed SADs.
Analytic theory of the Rayleigh-Taylor instability in a uniform density plasma-filled ion diode
The J-vector x B-vector forces associated with the surface current of a plasma-filled ion diode will accelerate this plasma fill toward the anode surface. It is well known that such a configuration with a high I is susceptible to the hydromagnetic Rayleigh-Taylor instability in certain geometries. A number of ion diode plasma sources have been proposed, most of which have a falling density going away from the wall. A somewhat more unstable case, however, is that of uniform density. In this report we attempt to establish an upper limit on this effect with a simple analytic model in which a uniform-density plasma is accelerated by the magnetic field anticipated in a PBFA-II diode. We estimate the number of linear e-foldings experienced by an unstable surface as well as the most damaging wavelength initial perturbation. This model, which accounts approximately for stabilization due to field diffusion, suggests that even with a uniform fill, densities in excess of a few 1015 are probably not damaged by the instability. In addition, even lower densities might be tolerated if perturbations near the most damaging wavelength can be kept very small
Hall and gyro-viscosity effects on the Rayleigh-Taylor instability in a 2D rectangular slab
Effects of the Hall term and the gyro-viscosity on the Rayleigh-Taylor instability in a 2D rectangular slab are studied numerically. Nonlinear magneto-hydrodynamic (MHD) simulations with these effects reveal that the combination of the Hall term and the gyro-viscosity causes the lower growth rates and the lower saturation level of unstable modes relative those in the single-fluid MHD case, while neither the gyro-viscosity nor the Hall term shows a strong stabilization effect only by itself. It is also shown that the mixing width of the density field can grow as large as that in the single-fluid MHD case, even though the saturation level of the kinetic energy is lowered and the detailed density profile becomes sharper. These numerical results suggest that the extension of the MHD equations can bring about a growth of unstable modes in a lower level, although it does not necessarily mean a weaker impact of the instability to the equilibrium. (author)
M. Agoor. Bothaina
2014-01-01
Full Text Available The Rayleigh-Taylor instability (RIT at the interface of two superposed Couple-stress Casson fluids flowing in porous medium and in the presence of a uniform normal magnetic field is studied. The fluids have different densities. For mathematical simplicity, the stability analysis based on fully developed approximations is used. The maximum wave numbers and the corresponding maximum frequency are obtained. The Growth rate of Rayleigh-Taylor instability in the case of non-Newtonian Casson fluid with couple-stress through porous medium is discussed. The effects of physical parameters of the problem such as the permeability parameter, magnetic parameter, non-Newtonian Parameter and couple-stress parameter on the regions of stability are discussed numerically and illustrated graphically through a set of figures.
Wu, Dong; Zhou, C T; Yan, X Q; Yu, M Y; He, X T
2012-01-01
It is shown that the transverse Rayleigh Taylor like instability can be well stabilized by using elliptically polarized laser in the hole boring radiation pressure acceleration regime. The $\\bm{J}\\times\\bm{B}$ effect of the laser will thermalize the local electrons and support a transverse diffusion mechanism of the ions, resulting in the stabilization of the short wavelength perturbations, which is quite similar to the ablative Rayleigh Taylor instability in the initial confinement fusion research. The proper range of polarization ratio is obtained from a theoretical model for the given laser intensity and plasma density. The stabilization mechanism is well confirmed by two dimensional Particle-in-Cell simulations, and the ion beam driven by the elliptically polarized laser is more concentrated and intense compared with that of the circularly polarized laser.
Four types of Rayleigh-Taylor instability analyses have been applied to thin gas films. In particular, the Dispersion relation including phase change was derived based on the lubrication approximation. The evaporation effect was shown to be negligible to find the most dangerous wavelength and the most rapid growth rate. As a result, it was shown that λd = 2π√2σ/Δρg should be used for the most dangerous wavelength for thin vapor films. This value was used to modify the existing critical heat flux for saturated pool boiling on horizontal surfaces. The modified correlations showed good predictions in the wide rate of pressure. Moreover, the thin vapor film analysis correctly led to the expression for the vapor film thickness at minimum film boiling, which is consistent with the well-known existing correlation. The question raised in introduction is now answered. If the viscosity effect is neglected for thin gas films, the most dangerous wavelength and the most rapid growth rate are incorrectly predicted. Therefore, the viscous flow analysis must be performed than the inviscid flow analysis
Velikovich, A. L.; Schmit, P. F.
2015-11-01
Bell-Plesset effects accounting for the time dependence of the radius, velocity and acceleration of the Rayleigh-Taylor-unstable surface are ubiquitous in the instability of spherical laser targets and magnetically driven cylindrical liners. We present an analytical model that, for an ideal incompressible fluid and small perturbation amplitudes, exactly accounts for the Bell-Plesset effects in finite-thickness targets and liners through acceleration and deceleration phases. We derive the time-dependent dispersion equations determining the ``instantaneous growth rate'' and demonstrate that by integrating this growth rate over time (the WKB approximation) we accurately evaluate the number of perturbation e-foldings during the acceleration phase. In the limit of the small target/liner thickness, we obtain the exact thin-shell perturbation equations and approximate thin-shell dispersion relations, generalizing the earlier results of Harris (1962), Ott (1972) and Bud'ko et al. (1989). This research was supported by the US DOE/NNSA (A.L.V.), and in part by appointment to the Sandia National Laboratories Truman Fellowship in National Security Science and Engineering (P.F.S.), which is part of the Laboratory Directed Research and Development (LDRD) Program, Project No. 165746, and sponsored by Sandia Corporation (a wholly owned subsidiary of Lockheed Martin Corporation) as Operator of Sandia National Laboratories under its U.S. Department of Energy Contract No. DE-AC04-94AL85000.
Yager-Elorriaga, D. A.; Steiner, A. M.; Patel, S. G.; Jordan, N. M.; Gilgenbach, R. M.; Lau, Y. Y.; Weis, M. R.; Zhang, P.
2015-11-01
At the Michigan Accelerator for Inductive Z-Pinch Experiments (MAIZE) facility, a 1-MA Linear Transformer Driver (LTD) is being used to deliver 500-600 kA to cylindrical liners in order to study the magneto Rayleigh-Taylor (MRT), sausage, and kink instabilities in imploding and exploding Al plasmas. The liners studied in this experiment had thicknesses of 400 nm to 30 μm, heights of 1-2 cm, and diameters of 1-6 mm. The plasmas were imaged using 4-time-frame, laser shadowgraphy and shearing-interferometry at 532 nm. For imploding liners, the measured acceleration was found to be less than predicted from the current pulse, indicating significant diffusion of the azimuthal magnetic field. A simple experimental configuration is presented for ``end-on'' laser probing in the r- θ plane in order to study the interior of the liner. Finally, the effects of axial magnetic fields are determined by modifying the return current posts and incorporating external coils. Experimental growth rates are determined and discussed. This work was supported by DOE award DE-SC0012328. S.G. Patel supported by Sandia National Labs. D.A. Yager was supported by NSF fellowship grant DGE 1256260.
Livescu, D
2013-11-28
A tentative review is presented of various approaches for numerical simulations of two-fluid gaseous mixtures at high density ratios, as they have been applied to the Rayleigh-Taylor instability (RTI). Systems exhibiting such RTI behaviour extend from atomistic sizes to scales where the continuum approximation becomes valid. Each level of description can fit into a hierarchy of theoretical models and the governing equations appropriate for each model, with their assumptions, are presented. In particular, because the compressible to incompressible limit of the Navier-Stokes equations is not unique and understanding compressibility effects in the RTI critically depends on having the appropriate basis for comparison, two relevant incompressible limits are presented. One of these limits has not been considered before. Recent results from RTI simulations, spanning the levels of description presented, are reviewed in connection to the material mixing problem. Owing to the computational limitations, most in-depth RTI results have been obtained for the incompressible case. Two such results, concerning the asymmetry of the mixing and small-scale anisotropy anomaly, as well as the possibility of a mixing transition in the RTI, are surveyed. New lines for further investigation are suggested and it is hoped that bringing together such diverse levels of description may provide new ideas and increased motivation for studying such flows. PMID:24146007
In this research, competitions between Rayleigh-Taylor instability (RTI) and Kelvin-Helmholtz instability (KHI) in two-dimensional incompressible fluids within a linear growth regime are investigated analytically. Normalized linear growth rate formulas for both the RTI, suitable for arbitrary density ratio with continuous density profile, and the KHI, suitable for arbitrary density ratio with continuous density and velocity profiles, are obtained. The linear growth rates of pure RTI (γRT), pure KHI (γKH), and combined RTI and KHI (γtotal) are investigated, respectively. In the pure RTI, it is found that the effect of the finite thickness of the density transition layer (Lρ) reduces the linear growth of the RTI (stabilizes the RTI). In the pure KHI, it is found that conversely, the effect of the finite thickness of the density transition layer increases the linear growth of the KHI (destabilizes the KHI). It is found that the effect of the finite thickness of the density transition layer decreases the ''effective'' or ''local'' Atwood number (A) for both the RTI and the KHI. However, based on the properties of γRT∝√(A) and γKH∝√(1-A2), the effect of the finite thickness of the density transition layer therefore has a completely opposite role on the RTI and the KHI noted above. In addition, it is found that the effect of the finite thickness of the velocity shear layer (Lu) stabilizes the KHI, and for the most cases, the combined effects of the finite thickness of the density transition layer and the velocity shear layer (Lρ=Lu) also stabilize the KHI. Regarding the combined RTI and KHI, it is found that there is a competition between the RTI and the KHI because of the completely opposite effect of the finite thickness of the density transition layer on these two kinds of instability. It is found that the competitions between the RTI and the KHI depend, respectively, on the Froude number, the density ratio of the light fluid to the heavy one, and the
Effects of magnetic field, sheared flow and ablative velocity on the Rayleigh-Taylor instability
It is found that magnetic field has a stabilization effect whereas the sheared flow has a destabilization effect on the RT instability in the presence of sharp interface. RT instability only occurs in the long wave region and can be completely suppressed if the stabilizing effect of magnetic field dominates. The RT instability increases with wave number and flow shear, and acts much like a Kelvin-Helmholtz instability when destabilizing effect of sheared flow dominates. It is shown that both of ablation velocity and magnetic filed have stabilization effect on RT instability in the presence of continued interface. The stabilization effect of magnetic field takes place for whole waveband and becomes more significant for the short wavelength. The RT instability can be completely suppressed by the cooperated effect of magnetic field and ablation velocity so that the ICF target shell may be unnecessary to be accelerated to very high speed. The growth rate decreases as the density scale length increases. The stabilization effect of magnetic field is more significant for the short density scale length. (author)
Egly, H
2007-10-15
This thesis deals with the dynamics of accelerated ablative front spreading in Inertial Confinement Fusion experiments. ICF is designed for the implosion of a deuterium-tritium spherical target. The outer shell, the ablator, is irradiated providing a high level pressure inside the target. During this first stage, the ablation front propagating inwards is perturbed by hydrodynamics instabilities, which can prevent the fusion reaction in the decelerated stage. We propose here a study on Rayleigh-Taylor instabilities during ablation process, in the two dimensional case. In order to obtain a numerical solution, we perform an asymptotic analysis in the limit of a high temperature ratio, between the remaining cold ablator and the hot ablated plasma. This study is divided in two steps. First, the thermo-diffusive part of the set of equations is approximated by a Hele-Shaw model, which is then perturbed by the hydrodynamics part. Using a vortex method, we have to solve the advection of a vortical sheet moving with the ablation front. We compute the numerical solution on an Eulerian mesh coupled with a marker method. The thermal part is computed by implementing the Fat Boundary Method, recently developed. The hydrodynamic part is obtained from a Finite Volume scheme. (author)
Rayleigh-Taylor mixing in supernova experiments
Swisher, N. C.; Abarzhi, S. I., E-mail: snezhana.abarzhi@gmail.com [Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Kuranz, C. C. [University of Michigan, Ann Arbor, Michigan 48109 (United States); Arnett, D. [University of Arizona, Tucson, Arizona 85721 (United States); Hurricane, O.; Remington, B. A.; Robey, H. F. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)
2015-10-15
We report a scrupulous analysis of data in supernova experiments that are conducted at high power laser facilities in order to study core-collapse supernova SN1987A. Parameters of the experimental system are properly scaled to investigate the interaction of a blast-wave with helium-hydrogen interface, and the induced Rayleigh-Taylor instability and Rayleigh-Taylor mixing of the denser and lighter fluids with time-dependent acceleration. We analyze all available experimental images of the Rayleigh-Taylor flow in supernova experiments and measure delicate features of the interfacial dynamics. A new scaling is identified for calibration of experimental data to enable their accurate analysis and comparisons. By properly accounting for the imprint of the experimental conditions, the data set size and statistics are substantially increased. New theoretical solutions are reported to describe asymptotic dynamics of Rayleigh-Taylor flow with time-dependent acceleration by applying theoretical analysis that considers symmetries and momentum transport. Good qualitative and quantitative agreement is achieved of the experimental data with the theory and simulations. Our study indicates that in supernova experiments Rayleigh-Taylor flow is in the mixing regime, the interface amplitude contributes substantially to the characteristic length scale for energy dissipation; Rayleigh-Taylor mixing keeps order.
Nonlinear theory of laser imprint, Richtmyer-Meshkov and Rayleigh-Taylor instabilities
Implosion process in laser fusion can be divided into three phases: start-up, acceleration and stagnation phases and various hydrodynamic instabilities appear in each phase. Analytical models are developed to study nonlinear evolutions of the hydrodynamic instabilities in these phases, and compared with multi-dimensional simulations. We mainly discuss the formation of double spiral structures caused by the singularity of vorticity in the RM spikes, the effect of the ablative stabilization in nonlinear growth of the RT instability with a finite bandwidth and the effect of the radiation cooling on the stability in the stagnation phase. Various smoothing effect, such as radiation smoothing and hydrodynamic smoothing, are also studied in the start-up phase. (author)
Simulating Rayleigh-Taylor (RT) instability using PPM hydrodynamics @scale on Roadrunner (u)
Woodward, Paul R [Los Alamos National Laboratory; Dimonte, Guy [Los Alamos National Laboratory; Rockefeller, Gabriel M [Los Alamos National Laboratory; Fryer, Christopher L [Los Alamos National Laboratory; Dimonte, Guy [Los Alamos National Laboratory; Dai, W [Los Alamos National Laboratory; Kares, R. J. [Los Alamos National Laboratory
2011-01-05
The effect of initial conditions on the self-similar growth of the RT instability is investigated using a hydrodynamics code based on the piecewise-parabolic-method (PPM). The PPM code was converted to the hybrid architecture of Roadrunner in order to perform the simulations at extremely high speed and spatial resolution. This paper describes the code conversion to the Cell processor, the scaling studies to 12 CU's on Roadrunner and results on the dependence of the RT growth rate on initial conditions. The relevance of the Roadrunner implementation of this PPM code to other existing and anticipated computer architectures is also discussed.
Wu, Dong; Qiao, B; Zhou, C T; Yan, X Q; Yu, M Y; He, X T
2014-01-01
It is shown that the transverse Rayleigh-Taylor-like (RT) instability in the hole boring radiation pressure acceleration can be suppressed by using elliptically polarized (EP) laser. A moderate ${J}\\times{B}$ heating of the EP laser will thermalize the local electrons, which leads to the transverse diffusion of ions, suppressing the short wavelength perturbations of RT instability. A proper condition of polarization ratio is obtained analytically for the given laser intensity and plasma density. The idea is confirmed by two dimensional Particle-in-Cell simulations, showing that the ion beam driven by the EP laser is more concentrated and intense compared with that of the circularly polarized laser.
Gupta, M R; Roy, Sourav; Banerjee, Rahul; Khan, Manoranjan
2010-01-01
The nonlinear evolution of two fluid interfacial structures like bubbles and spikes arising due to the combined action of Rayleigh-Taylor and Kelvin-Helmholtz instability or due to that of Richtmyer-Meshkov and Kelvin-Helmholtz instability resulting from oblique shock is investigated. Using Layzer's model analytic expressions for the asymptotic value of the combined growth rate are obtained in both cases for spikes and bubbles. However, if the overlying fluid is of lower density the interface perturbation behaves in different ways. Depending on the magnitude of the velocity shear associated with Kelvin-Helmholtz instability both the bubble and spike amplitude may simultaneously grow monotonically (instability) or oscillate with time or it may so happen that while this spike steepens the bubble tends to undulate. In case of an oblique shock which causes combined action of Richtmyer-Meshkov instability arising due to the normal component of the shock and Kelvin Helmholtz instability through creation of velocity...
Konovalov, V. V.; Lyubimov, D. V.; Lyubimova, T. P.
2016-06-01
The linear instability of a vapor film formed at the surface of a flat horizontal heater surrounded by an externally cooled liquid is investigated in the presence of a gravitational field. Consideration is given to the case when the stationary base state is characterized by the heat fluxes balanced at the interface between the two media. The critical value of the heat flux required for the complete suppression of the Rayleigh-Taylor instability by the phase transition has been evaluated mainly in the absence of the natural convection in the liquid layer and is found to be different from the known data obtained by approximate approaches. The case of the instability suppression in the system when long-wave disturbances have the longest lifetime is described. It has been shown that the media pressure influence on the phase transition, revealed in thin vapor films, can markedly increase the growth rate of long-wave disturbances and prevent their suppression.
Reactive Rayleigh-Taylor Turbulence
Chertkov, M; Vladimirova, N
2008-01-01
The Rayleigh-Taylor (RT) instability develops and leads to turbulence when a heavy fluid falls under the action of gravity through a light one. We consider this phenomenon accompanied by a reactive transformation between the fluids, and study with Direct Numerical Simulations (DNS) how the reaction (flame) affects the turbulent mixing in the Boussinesq approximation. We discuss "slow" reactions where the characteristic reaction time exceeds the temporal scale of the RT instability. In the early turbulent stage, effects of the flame are distributed over a maturing mixing zone, whose development is weakly influenced by the reaction. At later times, the fully mixed zone transforms into a conglomerate of pure-fluid patches of sizes proportional to the mixing zone width. In this "stirred flame'' regime, temperature fluctuations are consumed by reactions in the regions separating the pure-fluid patches. This DNS-based qualitative description is followed by a phenomenology suggesting that thin turbulent flame is of ...
Modica, Frank; Zhiglo, Andrey
2013-01-01
(abridged) There exists a substantial disagreement between computer simulation results and high-energy density laboratory experiments of the Rayleigh-Taylor instability Kuranz et al. (2010). We adopt the Braginskii formulation for transport in hot, dense plasma, implement and verify the additional physics modules, and conduct a computational study of a single-mode RTI in two dimensions with various combinations of the newly implemented modules. We find that magnetic fields reach levels on the order of 11 MG in the absence of thermal conduction. We observe denting of the RT spike tip and generation of additional higher order modes as a result of these fields. Contrary to interpretation presented in earlier work Nishiguchi (2002), the additional mode is not generated due to modified anisotropic heat transport effects but due to dynamical effect of self-generated magnetic fields. The main effects of thermal conduction are a reduction of the RT instability growth rate (by about 20% for conditions considered here)...
Complete text of publication follows. Using ground-based measurements we investigate the simultaneous occurrence of dark band structures in the OI 630 nm nightglow emission all-sky images associated with the Rayleigh-Taylor instability (RTI) and Perkins instability. This is the first reported observation related to the quasi north-south aligned intensity depletion bands (plasma bubble) simultaneously with the presence of medium scale traveling ionospheric disturbances (MSTIDs) in the tropical region using OI 630 nm nightglow emission all-sky images. On February 27-28, 2006, the OI 630 nm emission all-sky images obtained at Cachoeira Paulista (22.7 deg S, 45.0 deg W), Brazil, were used to map the spatial and temporal locations of plasma bubble and MSTIDs in the bottomside of the F-region. The ionospheric plasma bubble zonal drift measured by the all-sky imaging showed that it moved to eastward with average speed of 50 m/s, whereas MSTIDs moved from southeast to northwest with average speed of about 40 m/s. Also, digisonde observations registered abrupt increases in both the F-layer peak height (hmF2) and base height (h'F) when the MSTIDs passed over Cachoeira Paulista. It should be pointed out that these thermospheric/ionospheric events are not related to geomagnetic disturbed conditions. In this work, we present and discuss the dynamics of these kind airglow structures and their effects in the thermosphere/ionosphere dynamics.
A two-dimensional computational methodology has been developed which uses a phenomenological representation of initial perturbations to model the evolution of magnetically driven Rayleigh-Taylor instabilities in a hollow z-pinch. The drive current waveform and x-ray output obtained from the perturbed two-dimensional models differ qualitatively from the results of one-dimensional (unperturbed) models. The results form the perturbed model reproduce the principle features of z-inch experiments conducted on the Los Alamos Pegasus 2 facility. The authors discuss the computational approach used in this study and present comparisons between simulations and experimental measurements of current waveforms, visible framing camera pictures, spectra, XRD and bolometry data
Nonideal Rayleigh-Taylor mixing
Sharp, David Howland [Los Alamos National Laboratory; Lin, Hyun K [STONY BROOK UNIV.; Iwerks, Justin G [Los Alamos National Laboratory; Gliman, James G [Los Alamos National Laboratory; [NON LANL
2009-01-01
Rayleigh-Taylor mixing is a classical hydrodynamic Instability, which occurs when a light fluid pushes against a heavy fluid. The two main sources of nonideal behavior in Rayleigh-Taylor (RT) mixing are regularizations (physical and numerical) which produce deviations from a pure Euler equation, scale Invariant formulation, and non Ideal (i.e. experimental) initial conditions. The Kolmogorov theory of turbulence predicts stirring at all length scales for the Euler fluid equations without regularization. We Interpret mathematical theories of existence and non-uniqueness in this context, and we provide numerical evidence for dependence of the RT mixing rate on nonideal regularizations, in other words indeterminacy when modeled by Euler equations. Operationally, indeterminacy shows up as non unique solutions for RT mixing, parametrized by Schmidt and Prandtl numbers, In the large Reynolds number (Euler equation) limit. Verification and validation evidence is presented for the large eddy simulation algorithm used here. Mesh convergence depends on breaking the nonuniqueness with explicit use of the laminar Schmidt and PrandtJ numbers and their turbulent counterparts, defined in terms of subgrid scale models. The dependence of the mixing rate on the Schmidt and Prandtl numbers and other physical parameters will be illustrated. We demonstrate numerically the influence of initial conditions on the mixing rate. Both the dominant short wavelength Initial conditions and long wavelength perturbations are observed to playa role. By examination of two classes of experiments, we observe the absence of a single universal explanation, with long and short wavelength initial conditions, and the various physical and numerical regularizations contributing In different proportions In these two different contexts.
邱孝明; 黄林; 简广德
2002-01-01
A magnetohydrodynamic (MHD) formulation is derived to investigate and compare the mitigation effects of both the sheared axial flow and finite Larmor radius (FLR) on the Rayleigh-Taylor (RT) instability in Z-pinch implosions. The sheared axial flow is introduced into MHD equations in a conventional way and the FLR effect into the equations via а/аt → -i(ω + ik2⊥ρi2Ωi), as proposed in our previous paper [Chin. Phys. Lett. 2002, 19:217] , where k2⊥ρ2i is referred to FLR effect from the general kinetic theory of magnetized plasma. Therefore the linearized continuity and momentum equations for the perturbed massdensity and velocity include both the sheared axial flow and the FLR effect. It is found that the effect of sheared axial flow with a lower peak velocity can mitigate RT instability in the whole wavenumber region and the effect of sheared axial flow with a higher one can mitigate RT instability only in the large wavenumber region (for normalized wavenumber κ＞ 2.4); The effect of FLR can mitigate RT instability in the whole wavenumber region and the mitigation effect is stronger than that of the sheared axial flow with a lower peak velocity in the almost whole wavenumber region.
Casner, A.; Masse, L.; Liberatore, S.; Loiseau, P.; Masson-Laborde, P. E.; Jacquet, L.; Martinez, D.; Moore, A. S.; Seugling, R.; Felker, S.; Haan, S. W.; Remington, B. A.; Smalyuk, V. A.; Farrell, M.; Giraldez, E.; Nikroo, A.
2015-05-01
Academic tests in physical regimes not encountered in Inertial Confinement Fusion will help to build a better understanding of hydrodynamic instabilities and constitute the scientifically grounded validation complementary to fully integrated experiments. Under the National Ignition Facility (NIF) Discovery Science program, recent indirect drive experiments have been carried out to study the ablative Rayleigh-Taylor Instability (RTI) in transition from weakly nonlinear to highly nonlinear regime [A. Casner et al., Phys. Plasmas 19, 082708 (2012)]. In these experiments, a modulated package is accelerated by a 175 eV radiative temperature plateau created by a room temperature gas-filled platform irradiated by 60 NIF laser beams. The unique capabilities of the NIF are harnessed to accelerate this planar sample over much larger distances ( ≃1.4 mm) and longer time periods ( ≃12 ns) than previously achieved. This extended acceleration could eventually allow entering into a turbulent-like regime not precluded by the theory for the RTI at the ablation front. Simultaneous measurements of the foil trajectory and the subsequent RTI growth are performed and compared with radiative hydrodynamics simulations. We present RTI growth measurements for two-dimensional single-mode and broadband multimode modulations. The dependence of RTI growth on initial conditions and ablative stabilization is emphasized, and we demonstrate for the first time in indirect-drive a bubble-competition, bubble-merger regime for the RTI at ablation front.
Perturbations on an interface driven by a strong blast wave grow in time due to a combination of Rayleigh-Taylor, Richtmyer-Meshkov, and decompression effects. In this paper, the results from a computational study of such a system under drive conditions to be attainable on the National Ignition Facility [E. M. Campbell, Laser Part. Beams 9, 209 (1991)] are presented. Using the multiphysics, adaptive mesh refinement, higher order Godunov Eulerian hydrocode, Raptor [L. H. Howell and J. A. Greenough, J. Comput. Phys. 184, 53 (2003)], the late nonlinear instability evolution for multiple amplitude and phase realizations of a variety of multimode spectral types is considered. Compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions by allowing for memory of the initial conditions to be retained in the mix-width at all times. The loss of transverse spectral information is demonstrated, however, along with the existence of a quasi-self-similar regime over short time intervals. Certain aspects of the initial conditions, including the rms amplitude, are shown to have a strong effect on the time to transition to the quasi-self-similar regime
The Rayleigh-Taylor (RT) instability of an accelerating fluid interface is examined considering the effects of compression and geometrical convergence on incompressible perturbations of an interface separating two homogeneous compressible fluid layers of different mass densities. These effects occur in the implosion of inertial confinement fusion capsules. A complete description of Bell-Plesset effects is presented in terms of a simple model formulated in terms of the mass amplitude of perturbations of planar, cylindrical, and spherical interfaces. This formulation makes a clear distinction between perturbation growth driven by buoyant force - the RT instability - and modifications of perturbation behavior by compression and geometrical convergence - the Bell-Plesset (BP) effects [G. I. Bell, Los Alamos National Laboratory, Report LA-1321 (1951); M. S. Plesset, J. Appl. Phys. 25, 96 (1954)]. BP effects modify RT growth rates and may affect RT stability criteria, but they are not a distinct instability. These effects vary widely in their nature and importance from application to application, depending on the relative rates of RT growth, radial convergence, and uniform compression. Limiting cases are compared and contrasted. BP effects are generally different for each component of the perturbation solution pair. BP effects on perturbation growth in cylindrical implosion experiments have been analyzed successfully [e.g., W. W. Hsing et al., Phys. Plasmas 4, 1832 (1997)], in terms of an incomplete single-component solution that is indistinguishable from unperturbed flow, indicating that the component exhibiting true ongoing perturbed motion is largely absent. This static mass perturbation solution is often treated as the one and only BP effect, even though it occurs as one of a pair of solutions and only in the limit of a vanishing RT effect
Dutta, Urmi; Baruah, Amiya; Mandal, Nibir
2016-07-01
In many geological systems inversion of density stratification sets in Rayleigh-Taylor (RT) instabilities, leading to an ascent of relatively low-density materials through the high-density overburden in the form of diapirs. These diapirs often originate from dipping low-density layers. This study aims to show how the initial tilt of such source layers can control the ascent behavior of diapirs initiated by RT instabilities. Using two-layer viscous models we produced RT instabilities in physical experiments, and investigated the effects of source-layer tilts (β). Our experiments suggest that these diapirs ascend with contrasting lateral spreading rates in the up and down slope directions, resulting in their axi-asymmetric geometry. However, their heads retain a circular outline on the horizontal top surface, where the upwelling axis is located away from their geometric centre in the up-slope direction. In this paper we present a series of experimental models to demonstrate the spectrum of axi-symmetric to -asymmetric geometrical transitions with increasing β. Our experiments also reveal that, when β is large (> 4o) the diapirs become unstable, resulting in a continuous migration of their stems in the upslope direction. Using the volume of fluid (VOF) method we ran computational fluid dynamic (CFD) simulations to study the underlying hydrodynamics of axi-asymmetric diapiric growth. The CFD simulations show that β > 0o conditions develop stronger flow vortices on the down-slope side of an ascending diapir, leading to a pressure difference between the up- and down-slope flanks. Such a differential pressure causes the diapir head to spread at a faster rate in the tilt direction. An estimate of the asymmetric spreading rates is given as a function of β. Our present study provides a fundamental understanding of the hydrodynamic flow structure responsible for the asymmetric growth of RT instabilities on tilted source layers, as applicable to a wide range of large
Rayleigh-Taylor Unstable Flames -- Fast or Faster?
Hicks, E P
2015-01-01
Rayleigh-Taylor (RT) unstable flames play a key role in the explosions of Type Ia supernovae. However, the dynamics of these flames is still not well-understood. RT unstable flames are affected by both the RT instability of the flame front and by RT-generated turbulence. The coexistence of these factors complicates the choice of flame speed subgrid models for full-star Type Ia simulations. Both processes can stretch and wrinkle the flame surface, increasing its area and, therefore, the burning rate. In past research, subgrid models have been based on either the RT instability or turbulence setting the flame speed. We evaluate both models, checking their assumptions and their ability to correctly predict the turbulent flame speed. Specifically, we analyze a large parameter study of 3D direct numerical simulations of RT unstable model flames. This study varies both the simulation domain width and the gravity in order to probe a wide range of flame behaviors. We show that RT unstable flames are different from tr...
Rayleigh-Taylor Unstable Flames -- Fast or Faster?
Hicks, E. P.
2015-04-01
Rayleigh-Taylor (RT) unstable flames play a key role in the explosions of supernovae Ia. However, the dynamics of these flames are still not well understood. RT unstable flames are affected by both the RT instability of the flame front and by RT-generated turbulence. The coexistence of these factors complicates the choice of flame speed subgrid models for full-star Type Ia simulations. Both processes can stretch and wrinkle the flame surface, increasing its area and, therefore, the burning rate. In past research, subgrid models have been based on either the RT instability or turbulence setting the flame speed. We evaluate both models, checking their assumptions and their ability to correctly predict the turbulent flame speed. Specifically, we analyze a large parameter study of 3D direct numerical simulations of RT unstable model flames. This study varies both the simulation domain width and the gravity in order to probe a wide range of flame behaviors. We show that RT unstable flames are different from traditional turbulent flames: they are thinner rather than thicker when turbulence is stronger. We also show that none of the several different types of turbulent flame speed models accurately predicts measured flame speeds. In addition, we find that the RT flame speed model only correctly predicts the measured flame speed in a certain parameter regime. Finally, we propose that the formation of cusps may be the factor causing the flame to propagate more quickly than predicted by the RT model.
林其文
2001-01-01
推导并计算了不可压圆筒结构的扰动增长方程及具有弹性的运动方程，讨论了氧气-乙炔混合气体聚爆明胶圆筒的耦合扰动增长规律，研究结果为会聚结构的瑞利-泰勒不稳定性实验提供了很好的理论依据。%Feedthrough perturbation growth equations in an incompressiblecylinder geometry and motion equations in elastic cylinder were derived.Feedthrough perturbation growth in cylindrical gelatine driven by explosions in oxygen-acetylene gas mixture are discussed and analysed.Calculatal results are in good agreement with S. T.Weir et al′s reports.The results are useful for studying Rayleigh-Taylor instability experimentally.
Kumar, M S N
2013-01-01
The formation of the highest mass stars are thought to be dominated by instabilities resulting from gravitation and radiation. Instabilities due to gravitation are commonly demonstrated by observations of fragmentation, but those due to effects of radiation are thus far not found. Here I report on the NACO adaptive optics and mid-infrared diffraction limited VISIR imaging data of an extemely luminous ultra-compact HII region G333.6-0.2. Two infrared sources, one bright in the near-infrared (appearing point-like) and another in the mid-infrared (resolved with an elliptical shape) are uncovered through this data, located at the heart of this region. These infrared sources appear to be embedded in the waist of a bipolar shaped nebula and UCHII region, the lobes of which are separated by a dark patch. It represents an outflow bubble originating from a large toroid viewed in its edge-on configuration. Filamentary features with finger/hook morphology are found connected to the two bright infrared sources which are ...
Multimode Rayleigh-Taylor growth at strongly convergent spherical interfaces
Recently, attention has focused on the effects of spherical convergence on the nonlinear phase of Rayleigh-Taylor growth. In particular, for instability growth on spherically converging interfaces, modifications to the predictions of the Layzer model for the secular growth of a single, nonlinear mode have been reported. On the other hand, applications of interest involve surface perturbations which include the superposition of many unstable modes growing simultaneously. Such weakly nonlinear, multimode growth has previously been studied in the context of the well-known Haan model. Here, we combine the most recent results for enhanced nonlinear single mode growth on spherical interfaces with the Haan model formulation for multimode growth. Remarkably, the multimode results are found not to be substantially modified by including the effects of convergence
Modeling Solid Rayleigh-Taylor Growth
Kaul, Ann M [Los Alamos National Laboratory
2010-09-20
Intense impulses applied to solid materials result in high strain rates, strong plastic strains and significant temperature increments. Data in such regimes would allow confidence in extending material strength models to strain rates of 10{sup 6}-10{sup 7} s{sup -1}. High explosives can be used to accelerate a plate with a perturbation on the side facing the HE, resulting in a Rayleigh-Taylor-like perturbation growth that depends on amplitude and wavelength of the initial surface perturbation, strength of the material, time dependence of the driving pressure force, and temperature of the material. Such experiments have been conducted on perturbed copper plates at LANL, using the LANSCE proton radiography beam to obtain multiple frames of data for each experiment. The results of numerical simulations of these experiments using a 2-D ALE code are presented.
Analytical models are derived for stabilization of the Rayleigh--Taylor instability of an ablatively accelerated slab. The procedure is to conserve mass, momentum, and energy flux across a perturbed interface through which plasma flows. In various regimes, the stabilization mechanism can be described as vortex shedding, compressibility, thermal conduction, and ablation. Comparisons are made with recent fluid simulations, and simple laws relevant to laser-driven ablative acceleration are derived
Stability of Rayleigh-Taylor Vortices in Dusty Plasma
MA Jun; CHEN Yin-Hua; GAN Bao-Xia; WANG Fei-Hu; WANG Dong
2006-01-01
@@ The evolution of Rayleigh-Taylor mode in dusty plasma with vortex-flow is investigated. Based on fluid theory and Bayly's method, we derive the coupling equations describing the Rayleigh-Taylor mode in the core of vortex,and research the evolution characteristics of the perturbation amplitude with time numerically. It is shown that the eccentric of vortex and the content of dust have considerable effects on the amplitude evolutions.
Limits of the potential flow approach to the single-mode Rayleigh-Taylor problem.
Ramaprabhu, P; Dimonte, Guy; Young, Yuan-Nan; Calder, A C; Fryxell, B
2006-12-01
We report on the behavior of a single-wavelength Rayleigh-Taylor flow at late times. The calculations were performed in a long square duct (lambda x lambda x 8lambda), using four different numerical simulations. In contradiction with potential flow theories that predict a constant terminal velocity, the single-wavelength Rayleigh-Taylor problem exhibits late-time acceleration. The onset of acceleration occurs as the bubble penetration depth exceeds the diameter of bubbles, and is observed for low and moderate density differences. Based on our simulations, we provide a phenomenological description of the observed acceleration, and ascribe this behavior to the formation of Kelvin-Helmholtz vortices on the bubble-spike interface that diminish the friction drag, while the associated induced flow propels the bubbles forward. For large density ratios, the formation of secondary instabilities is suppressed, and the bubbles remain terminal consistent with potential flow models. PMID:17280149
Rayleigh-Taylor unstable, premixed flames: the transition to turbulence
Hicks, Elizabeth; Rosner, Robert
2010-11-01
A premixed flame moving against a sufficiently strong gravitational field becomes deformed and creates vorticity. If gravity is strong enough, this vorticity is shed and deposited behind the flame front. We present two-dimensional direct numerical simulations of this vortex shedding process and its effect on the flame front for various values of the gravitational force. The flame and its shed vortices go through the following stages as gravity is increased: no vorticity and a flat flame front; long vortices attached to a cusped flame front; instability of the attached vortices and vortex shedding (Hopf bifurcation); disruption of the flame front by the shed vortices, causing the flame to pulsate; loss of left/right symmetry (period doubling); dominance of Rayleigh-Taylor instability over burning (torus bifurcation); and, finally, complex interactions between the flame front and the vortices. We measure the subsequent wrinkling of the flame front by computing its fractal dimension and also measure mixing behind the flame front by computing the finite-time Lyapunov exponents.
Rayleigh-Taylor unstable flames: The competition between burning, gravity and self-generated flow
Hicks, Elizabeth Peele
A Type Ia supernova explosion may occur if a subsonic nuclear flame in a white dwarf star is wrinkled by turbulence produced by the Rayleigh-Taylor instability and becomes supersonic. Our research investigates the plausibility of this theory by simulating a very simple case- a model flame in 2D. We performed a parameter study in which we changed only the non-dimensional gravitational force, G. The overarching goal of the thesis was to figure out how changing the strength of the Rayleigh-Taylor instability affects the flame surface and therefore the flame speed. At low values of G, this is a transition-to-turbulence type problem and we approached it from the dynamical systems point of view. Specifically, we measured various observables in our simulations and used them to search for simple bifurcation models of the flame behavior. For instance, the initial vortex shedding instability in the wake behind the flame front can be described by a Hopf bifurcation. Overall, simple temporal bifurcations are sufficient to describe the flame for low G. For high values of G, the simple dynamical systems approach breaks down. The area just behind the flame becomes fully turbulent and this turbulence wrinkles the flame front. Because the wrinkling takes place on all scales between the integral scale and the viscous scale, the flame assumes a fractal shape. We measured the fractal dimension of the flame front to assess the importance of this effect. For very high G, it turns out that large-scale Rayleigh-Taylor stretching is responsible for creating a larger part of flame surface than the turbulent wrinkling. This suggests that the flame speed is mostly determined by large-scale stretching driven by the Rayleigh-Taylor instability, not by the secondary interaction of turbulence with the flame front. The flame speed predicted for this situation is much too small for the flame to become supersonic, casting some doubt on the Rayleigh-Taylor wrinkling mechanism for Type Ia explosions.
Gravitationally Unstable Flames: Rayleigh-Taylor Stretching versus Turbulent Wrinkling
Hicks, E. P.; Rosner, R.
2013-07-01
In this paper, we provide support for the Rayleigh-Taylor-(RT)-based subgrid model used in full-star simulations of deflagrations in Type Ia supernovae explosions. We use the results of a parameter study of two-dimensional direct numerical simulations of an RT unstable model flame to distinguish between the two main types of subgrid models (RT or turbulence dominated) in the flamelet regime. First, we give scalings for the turbulent flame speed, the Reynolds number, the viscous scale, and the size of the burning region as the non-dimensional gravity (G) is varied. The flame speed is well predicted by an RT-based flame speed model. Next, the above scalings are used to calculate the Karlovitz number (Ka) and to discuss appropriate combustion regimes. No transition to thin reaction zones is seen at Ka = 1, although such a transition is expected by turbulence-dominated subgrid models. Finally, we confirm a basic physical premise of the RT subgrid model, namely, that the flame is fractal, and thus self-similar. By modeling the turbulent flame speed, we demonstrate that it is affected more by large-scale RT stretching than by small-scale turbulent wrinkling. In this way, the RT instability controls the flame directly from the large scales. Overall, these results support the RT subgrid model.
GRAVITATIONALLY UNSTABLE FLAMES: RAYLEIGH-TAYLOR STRETCHING VERSUS TURBULENT WRINKLING
In this paper, we provide support for the Rayleigh-Taylor-(RT)-based subgrid model used in full-star simulations of deflagrations in Type Ia supernovae explosions. We use the results of a parameter study of two-dimensional direct numerical simulations of an RT unstable model flame to distinguish between the two main types of subgrid models (RT or turbulence dominated) in the flamelet regime. First, we give scalings for the turbulent flame speed, the Reynolds number, the viscous scale, and the size of the burning region as the non-dimensional gravity (G) is varied. The flame speed is well predicted by an RT-based flame speed model. Next, the above scalings are used to calculate the Karlovitz number (Ka) and to discuss appropriate combustion regimes. No transition to thin reaction zones is seen at Ka = 1, although such a transition is expected by turbulence-dominated subgrid models. Finally, we confirm a basic physical premise of the RT subgrid model, namely, that the flame is fractal, and thus self-similar. By modeling the turbulent flame speed, we demonstrate that it is affected more by large-scale RT stretching than by small-scale turbulent wrinkling. In this way, the RT instability controls the flame directly from the large scales. Overall, these results support the RT subgrid model.
GRAVITATIONALLY UNSTABLE FLAMES: RAYLEIGH-TAYLOR STRETCHING VERSUS TURBULENT WRINKLING
Hicks, E. P. [Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and the Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208 (United States); Rosner, R., E-mail: eph2001@columbia.edu [Computation Institute, University of Chicago, 5735 S. Ellis Ave., Chicago, IL 60637 (United States)
2013-07-10
In this paper, we provide support for the Rayleigh-Taylor-(RT)-based subgrid model used in full-star simulations of deflagrations in Type Ia supernovae explosions. We use the results of a parameter study of two-dimensional direct numerical simulations of an RT unstable model flame to distinguish between the two main types of subgrid models (RT or turbulence dominated) in the flamelet regime. First, we give scalings for the turbulent flame speed, the Reynolds number, the viscous scale, and the size of the burning region as the non-dimensional gravity (G) is varied. The flame speed is well predicted by an RT-based flame speed model. Next, the above scalings are used to calculate the Karlovitz number (Ka) and to discuss appropriate combustion regimes. No transition to thin reaction zones is seen at Ka = 1, although such a transition is expected by turbulence-dominated subgrid models. Finally, we confirm a basic physical premise of the RT subgrid model, namely, that the flame is fractal, and thus self-similar. By modeling the turbulent flame speed, we demonstrate that it is affected more by large-scale RT stretching than by small-scale turbulent wrinkling. In this way, the RT instability controls the flame directly from the large scales. Overall, these results support the RT subgrid model.
Multimode Rayleigh-Taylor growth at strongly convergent spherical interfaces
Recently, attention has focused on the effects of spherical convergence on the nonlinear phase of Rayleigh-Taylor growth. In particular, for instability growth on spherically converging interfaces, modifications to the predictions of the Layzer model for the secular growth of a single, nonlinear mode have been reported. On the other hand, applications of interest involve surface perturbations which include the superposition of many unstable modes growing simultaneously. Such weakly nonlinear, multimode growth has previously been studied in the context of the well-known Haan model. Here, we combine the most recent results for enhanced nonlinear single mode growth on spherical interfaces with the Haan model formulation for multimode growth. Remarkably, the multimode results are found not to be substantially modified by including the effects of convergence. This is due to the particular form chosen by Haan in constructing his multimode model. Indeed, in the limit of large mode numbers, explicitly including convergence for the nonlinear regime leads only to logarithmic corrections to Haan's original result
The Transition to Turbulence of Rayleigh-Taylor Unstable Flames
Hicks, Elizabeth P.; Rosner, R.
2011-01-01
Part of the uncertainty surrounding the explosion mechanism of Type 1A supernovae is the extent to which the turbulence created by the flame front can speed the flame up. A premixed flame moving against a sufficiently strong gravitational field becomes deformed and creates vorticity. If gravity is strong enough, this vorticity is shed and deposited behind the flame front. We have completed some two-dimensional direct numerical simulations of this shedding process for various values of the gravitational force. If gravity is weak enough, the flame front remains flat and no vorticity is created. If gravity is slightly stronger, the flame front becomes cusped and creates vorticity; long vortices attach to the flame front and extend behind it. For even larger values of gravity, the far end of these vortices becomes unstable and sheds more vortices. For simulations with increased gravity, the position of the shedding instability moves closer to the flame front. Next, the vortex shedding disturbs the flame front, causing the flame to pulsate. These pulsations lose their left/right symmetry and the period of oscillation doubles. For even higher values of gravity, an additional frequency is introduced into the system as the Rayleigh-Taylor instability begins to dominate over burning. Eventually, the pulsations of the flame become quite complex and the interaction between the flame front and the vortices can't be simply described. We have measured the subsequent wrinkling of the flame front by computing its fractal dimension and the energy spectra behind the flame front. Measurements of the fractal dimension suggest that it saturates, implying that any additional speed up of the flame must be due to large-scale stretching or disruption of the flame front. Our simulations were performed at NERSC which is supported by the Department of Energy.
Stability of target compression in the laser thermonuclear synthesis is discussed. The process is determined by developing the Rayleigh-Taylor instability (RNI). A program unit for description of the RNI evolution by its initial distributions is developed. The results of statistical analysis of the RT mixing calculations are given. The analysis is carried out by means of learning base system and is substantiated on the generalization of great number of data, fulfilled by means of the neural network methods
Reactive Rayleigh-Taylor systems: flame propagation and non-stationarity
Scagliarini, A; Mantovani, F; Sbragaglia, M; Toschi, F; Tripiccione, R
2011-01-01
Reactive Rayleigh-Taylor systems are characterized by the competition between the growth of the instability and the rate of reaction between cold (heavy) and hot (light) phases. We present results from state-of-the-art numerical simulations performed at high resolution in 2d by means of a self-consistent lattice Boltzmann method which evolves the coupled momentum and thermal equations and includes a reactive term. We tune the parameters affecting flame properties, in order to address the competition between turbulent mixing and reaction, ranging from slow to fast-reaction rates. We also study the mutual feedback between turbulence evolution driven by the Rayleigh-Taylor instability and front propagation against gravitational acceleration. We quantify both the enhancement of flame propagation due to turbulent mixing for the case of slow reaction-rate as well as the slowing down of turbulence growth for the fast reaction case, when the flame quickly burns the gravitationally unstable phase. An increase of inter...
Dynamics of bubble growth for Rayleigh--Taylor unstable interfaces
A statistical model is analyzed for the growth of bubbles in a Rayleigh--Taylor unstable interface. The model is compared to solutions of the full Euler equations for compressible two phase flow, using numerical solutions based on the method of front tracking. The front tracking method has the distinguishing feature of being a predominantly Eulerian method in which sharp interfaces are preserved with zero numerical diffusion. Various regimes in the statistical model exhibiting qualitatively distinct behavior are explored
Direct numerical simulation of single mode three-dimensional Rayleigh-Taylor experiments
Hutchinson, Maxwell
2015-01-01
The single-mode Rayleigh-Taylor instability (smRTI) is This study reproduces three low-Atwood single mode Rayleigh-Taylor experimental runs [1] in a specialized version of the Nek5000 [2] spectral element code. The simulations use the initial amplitude, wavelength, acceleration, Atwood number, and viscosity from the three specific experiments and impose no-slip and no-flux boundaries on the velocity and scalar, respectively. The simulations are shown to reproduce the linear, saturation, stagnation, and re-acceleration phases of the smRTI seen in the experiments. Additionally, access to the full velocity and scalar fields demonstrates three different finite size effects: wall drag, wall lift, and a long wavelength mode along the diagonal. One of the simulations is extended by a factor of two in the vertical direction and the resulting late-time dynamics reach Froude numbers around 1.8, higher than previously reported. Finally, inspection of the span-wise flow reveals secondary flows of the first kind that tran...
2D HYDRA Calculations of Magneto-Rayleigh-Taylor Growth and Feedthrough in Cylindrical Liners
Weis, Matthew; Zhang, Peng; Lau, Y. Y.; Gilgenbach, Ronald; Peterson, Kyle; Hess, Mark
2014-10-01
Cylindrical liner implosions are susceptible to the magneto-Rayleigh-Taylor instability (MRT), along with the azimuthal current-carrying modes (sausage, kink, etc). ``Feedthrough'' of these instabilities has a strong influence on the integrity of the liner/fuel interface in the magnetized liner inertial fusion concept (MagLIF). The linearized ideal MHD equations can be solved to quantify these effects, including the presence of an effective gravity and an axial magnetic field. We investigate the potential of this field to mitigate feedthrough, due to MRT growth from various initial surface finishes (seeded, rough), throughout the implosion using our analytic results and the LLNL code, HYDRA. We will present both low and high convergence cases. Lastly, we illustrate the effect shock compression can have on feedthrough in seeded liners for various fill gases (cold and pre-heated) and magnetic field configurations. M. R. Weis was supported by the Sandia National Laboratories.
Rayleigh-Taylor mixing with time-dependent acceleration
Abarzhi, Snezhana
2015-11-01
We extend the momentum model to describe Rayleigh-Taylor (RT) mixing driven by a time-dependent acceleration. The acceleration is a power-law function of time, similarly to astrophysical and plasma fusion applications. In RT flow the dynamics of a fluid parcel is driven by a balance per unit mass of the rates of momentum gain and loss. We find analytical solutions in the cases of balanced and imbalanced gains and losses, and identify their dependence on the acceleration exponent. The existence is shown of two typical regimes of self-similar RT mixing -acceleration-driven Rayleigh-Taylor-type and dissipation-driven Richtymer-Meshkov-type with the latter being in general non-universal. Possible scenarios are proposed for transitions from the balanced dynamics to the imbalanced self-similar dynamics. Scaling and correlations properties of RT mixing are studied on the basis of dimensional analysis. Departures are outlined of RT dynamics with time-dependent acceleration from canonical cases of homogeneous turbulence as well as blast waves with first and second kind self-similarity. Support of National Science Foundation is warmy appreciated.
Validation of Nek5000 against low-Atwood, single-mode Rayleigh Taylor experiments
Hutchinson, Maxwell
2015-11-01
Experiments by Wilkinson and Jacobs demonstrate the stagnation and reacceleration phases of the low-Atwood, single-mode Rayleigh Taylor instability between two water mixtures. We reproduce the experimental conditions of three runs in direct numerical simulations using the spectral element code Nek5000. The simulations required 17 billion grid points on 512 thousand cores of the Mira supercomputer to reach Rayleigh numbers up to 90 million. We extend the vertical dimension to reach higher bubble aspect ratios and demonstrate the limits of wall-bounded single-mode studies. Finally, exploration of the full-field results reveals spanwise secondary flows that enhance mixing at low to moderate Reynolds number. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357.
Acceleration- and deceleration-phase nonlinear Rayleigh-Taylor growth at spherical interfaces
The Layzer model for the nonlinear evolution of bubbles in the Rayleigh-Taylor instability has recently been generalized to the case of spherically imploding interfaces [D. S. Clark and M. Tabak, Phys. Rev. E 71, 055302(R) (2005)]. The spherical case is more relevant to, e.g., inertial confinement fusion or various astrophysical phenomena when the convergence is strong or the perturbation wavelength is comparable to the interface curvature. Here, the model is further extended to the case of bubble growth during the deceleration (stagnation) phase of a spherical implosion and to the growth of spikes during both the acceleration and deceleration phases. Differences in the nonlinear growth rates for both bubbles and spikes are found when compared with planar results. The model predictions are verified by comparison with numerical hydrodynamics simulations
Acceleration and deceleration phase nonlinear Rayleigh-Taylor growth at spherical interfaces
The Layzer model for the nonlinear evolution of bubbles in the Rayleigh-Taylor instability has recently been generalized to the case of spherically imploding interfaces [D. S. Clark and M. Tabak, to appear, PRE (2005).]. The spherical case is more relevant to, e.g., inertial confinement fusion or various astrophysical phenomena when the convergence is strong or the perturbation wavelength is comparable to the interface curvature. Here, the model is further extended to the case of bubble growth during the deceleration (stagnation) phase of a spherical implosion and to the growth of spikes during both the acceleration and deceleration phases. Differences in the nonlinear growth rates for both bubbles and spikes are found when compared with planar results. The model predictions are verified by comparison with numerical hydrodynamics simulations
Self-generated magnetic fields in blast-wave driven Rayleigh-Taylor experiments
Flaig, Markus; Plewa, Tomasz
2015-12-01
We study the effect of self-generated magnetic fields in two-dimensional computer models of blast-wave driven high-energy density Rayleigh-Taylor instability (RTI) experiments. Previous works [1,2] suggested that such fields have the potential to influence the RTI morphology and mixing. When neglecting the friction force between electrons and ions, we do indeed find that dynamically important (β≲103) magnetic fields are generated. However, in the more realistic case where the friction force is accounted for, the resulting fields are much weaker, β≳105 , and can no longer influence the dynamics of the system. Although we find no evidence for dynamically important magnetic fields being created in the two-dimensional case studied here, the situation might be different in a three-dimensional setup, which will be addressed in a future study.
Measurements of Molecular Mixing in a High Schmidt Number Rayleigh-Taylor Mixing Layer
Mueschke, N J; Schilling, O; Youngs, D L; Andrews, M
2007-12-03
Rayleigh?Taylor instability-induced mixing are discussed.
Qualitative and quantitative features of Rayleigh-Taylor mixing dynamics
Ramaprabhu, Praveen; Karkhanis, Varad; Lawrie, Andrew; Bhowmick, Aklant; Abarzhi, Snezhana; RTI Collaboration
2015-11-01
We consider dynamics of Rayleigh-Taylor (RT) flow in a large aspect ratio three-dimensional domain with square symmetry in the plane for fluids with contrasting densities. In order to quantify the interface evolution from a small amplitude single-mode initial perturbation to advanced stage of RT mixing, we apply numerical simulations using the MOBILE code, theoretical analyses, including group theory and momentum model, as well as parameters describing the interplay between acceleration and turbulence. We find: In RT flow, the fluid motion is intense near the interface and is negligible far from the interface. At late times the growth rates of RT bubbles and spikes may increase without a corresponding increase of length-scales in the direction normal to acceleration. The parameters describing the interplay between acceleration and turbulence in RT mixing are shown to scale well with the flow Reynolds number and Froude number.
Nonlinear Rayleigh-Taylor growth in convergine geometry
The early nonlinear phase of Rayleigh-Taylor growth is typically described in terms of the classic Layzer model in which bubbles of light fluid rise into the heavy fluid at a constant rate determined by the bubble radius and the gravitational acceleration. However, this model is strictly valid only for planar interfaces and hence ignores any effects which might be introduced by the spherically converging interfaces of interest in inertial confinement fusion. Here a generalization of the Layzer nonlinear bubble rise rate is given for a self-similar spherically converging flow of the type studied by Kidder. A simple formula for the bubble amplitude is found showing that, while the bubble initially rises with a constant velocity similar to the Layzer result, during the late phase of the implosion, an acceleration of the bubble rise rate occurs. The bubble rise rate is verified by comparison with numerical hydrodynamics simulations
Mueschke, N J; Andrews, M J; Schilling, O
2005-09-26
The initial multi-mode interfacial velocity and density perturbations present at the onset of a small Atwood number, incompressible, miscible, Rayleigh-Taylor instability-driven mixing layer have been quantified using a combination of experimental techniques. The streamwise interfacial and spanwise interfacial perturbations were measured using high-resolution thermocouples and planar laser-induced fluorescence (PLIF), respectively. The initial multi-mode streamwise velocity perturbations at the two-fluid density interface were measured using particle-image velocimetry (PIV). It was found that the measured initial conditions describe an initially anisotropic state, in which the perturbations in the streamwise and spanwise directions are independent of one another. The evolution of various fluctuating velocity and density statistics, together with velocity and density variance spectra, were measured using PIV and high-resolution thermocouple data. The evolution of the velocity and density statistics is used to investigate the early-time evolution and the onset of strongly-nonlinear, transitional dynamics within the mixing layer. The early-time evolution of the density and vertical velocity variance spectra indicate that velocity fluctuations are the dominant mechanism driving the instability development. The implications of the present experimental measurements on the initialization of Reynolds-averaged turbulent transport and mixing models and of direct and large-eddy simulations of Rayleigh-Taylor instability-induced turbulence are discussed.
Mueschke, N J; Andrews, M J; Schilling, O
2006-03-24
The initial multi-mode interfacial velocity and density perturbations present at the onset of a small Atwood number, incompressible, miscible, Rayleigh-Taylor instability-driven mixing layer have been quantified using a combination of experimental techniques. The streamwise interfacial and spanwise interfacial perturbations were measured using high-resolution thermocouples and planar laser-induced fluorescence (PLIF), respectively. The initial multi-mode streamwise velocity perturbations at the two-fluid density interface were measured using particle-image velocimetry (PIV). It was found that the measured initial conditions describe an initially anisotropic state, in which the perturbations in the streamwise and spanwise directions are independent of one another. The evolution of various fluctuating velocity and density statistics, together with velocity and density variance spectra, were measured using PIV and high-resolution thermocouple data. The evolution of the velocity and density statistics is used to investigate the early-time evolution and the onset of strongly-nonlinear, transitional dynamics within the mixing layer. The early-time evolution of the density and vertical velocity variance spectra indicate that velocity fluctuations are the dominant mechanism driving the instability development. The implications of the present experimental measurements on the initialization of Reynolds-averaged turbulent transport and mixing models and of direct and large-eddy simulations of Rayleigh-Taylor instability-induced turbulence are discussed.
Casner, A.; Huser, G.; Vandenboomgaerde, M.; Liberatore, S.; Masse, L.; Galmiche, D.
2008-11-01
Mitigation of Rayleigh-Taylor instabilities growth is a key issue on the road toward ignition. The graded doped ablator is a common concept for NIF [1] and LMJ [2] point designs. A complementary stabilization mechanism based on anisotropic thermal diffusion was theoretically underlined [3] for the ablative Rayleigh-Taylor instability. We will present the first ever experimental tests of these mechanisms. Indirect drive experiments were performed on the OMEGA laser facility with a long-pulse platform. We used in fact gas-filled halfraums and stack 15 drive beams along 2 cones to create a 7 ns long radiation drive. Halfraum energetics with E-IDI-300 phase plates was validated by dedicated shots along P5/P8 and is fairly reproduced by the simulations. These drive measurements allowed also to determine the graded doped planar emulator whose layers thicknesses and composition should be carefully optimized . Side-on and face-on data acquired with germanium-doped plastic samples (modulations wavelength 35 and 50 microns) will be presented and compared with FCI2 hydrocodes simulations. [1] S.W. Haan et al., Phys. Plasmas 12, 056316 (2005). [2] C C-Cl'erouin et al 2008 J. Phys.: Conf. Ser. 112 022023 [3] L. Masse., Phys. Rev. Lett. 98, 245001 (2007).
Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
Castro, Ángel; Córdoba, Diego; Fefferman, Charles; Gancedo, Francisco; López-Fernández, Mar\\'ia
2012-01-01
The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.
Ripesi, P; Schifano, S F; Tripiccione, R
2014-01-01
We study the turbulent evolution originated from a system subjected to a Rayleigh-Taylor instability with a double density at high resolution in a 2 dimensional geometry using a highly optimized thermal Lattice Boltzmann code for GPUs. The novelty of our investigation stems from the initial condition, given by the superposition of three layers with three different densities, leading to the development of two Rayleigh-Taylor fronts that expand upward and downward and collide in the middle of the cell. By using high resolution numerical data we highlight the effects induced by the collision of the two turbulent fronts in the long time asymptotic regime. We also provide details on the optimized Lattice-Boltzmann code that we have run on a cluster of GPUs
Planar and cylindrical Rayleigh-Taylor experiments on Nova (HEP2)
Remington, B.A.; Weber, S.V.; Marinak, M.M. [and others
1996-06-01
A high-density fluid on top of a low-density fluid is Rayleigh-Taylor (RT) unstable. Driven by gravity, random perturbations at the interface between the two fluids will grow: fingers ({open_quotes}spikes{close_quotes}) of the heavier fluid will poke through the lighter fluid, and bubbles of the lighter fluid will rise into the heavier fluid. The RT instability and its shock-driven analog, the Richtmyer-Meshkov (RM) instability, have been a focus of research in inertial confinement fusion (ICF) for some time. In ICF, the driver - laser light, x rays, or ions - heats the outer layer of the capsule wall, causing it to ionize and expand rapidly. The result is a low-density ablated plasma accelerating the high-density capsule wall ({open_quotes}Pusher{close_quotes}). The ablation front is RT unstable, and outer-surface imperfections grow. This growth can seed perturbations at the pusher inner wall, which in turn become RT unstable during deceleration and stagnation. Ultimately, pusher material can mix into the fuel, degrading performance.
Rayleigh Taylor turbulence: self-similar analysis and direct numerical simulations
Ristorcelli, J. R.; Clark, T. T.
2004-05-01
Direct numerical simulations and a self-similar analysis of the single-fluid Boussinesq Rayleigh Taylor instability and transition to turbulence are used to investigate Rayleigh Taylor turbulence. The Schmidt, Atwood and bulk Reynolds numbers are Sc {=} 1, A {=} 0.01, Re {≤} 3000. High-Reynolds-number moment self-similarity, consistent with the the energy cascade interpretation of dissipation, is used to analyse the DNS results. The mixing layer width obeys a differential equation with solution h(t;C_o,h_0) {=} fourth C_o Agt(2+) sqrt{AgC_o}h(1/2) _0 t+h_0; the result for h(t;C_o,h_0) is a rigorous consequence of only one ansatz, self-similarity. It indicates an intermediate time regime in which the growth is linear and the importance of a virtual origin. At long time the well-known h ˜ fourth C_o Agt(2) scaling dominates. The self-similar analysis indicates that the asymptotic growth rate is not universal. The scalings of the second-order moments, their dissipations, and production dissipation ratios, are obtained and compared to the DNS. The flow is not self-similar in a conventional sense there is no single length scale that scales the flow. The moment similarity method produces three different scalings for the turbulence energy-containing length scale, ℓ, the Taylor microscale, la, and the Kolmogorov dissipation scale, eta. The DNS and the self-similar analysis are in accord showing ℓ {˜} Agt(2) , ⪉ {˜} t(1/2) and eta {˜} (({A(2g^2}/{nu^3})t)(-1/4)) achieving self-similar behaviour within three initial eddy turnovers of the inception of the turbulence growth phase at bulk Reynolds numbers in the range of Re = 800 1000 depending on initial conditions. A picture of a turbulence in which the largest scales grow, asymptotically, as t(2) and the smallest scales decrease as t(-1/4) , emerges. As a consequence the bandwidth of the turbulence spectrum grows as t(9/4) and is consistent with the R_t(3/4) Kolmogorov scaling law of fully developed stationary
Three-dimensional Numerical Simulations of Rayleigh-Taylor Unstable Flames in Type Ia Supernovae
Zingale, M A; Rendleman, C A; Day, M S; Bell, J B
2005-01-01
Flame instabilities play a dominant role in accelerating the burning front to a large fraction of the speed of sound in a Type Ia supernova. We present a three-dimensional numerical simulation of a Rayleigh-Taylor unstable carbon flame, following its evolution through the transition to turbulence. A low Mach number hydrodynamics method is used, freeing us from the harsh timestep restrictions imposed by sound waves. We fully resolve the thermal structure of the flame and its reaction zone, eliminating the need for a flame model. A single density is considered, $1.5\\times 10^7 \\gcc$, and half carbon\\slash half oxygen fuel--conditions under which the flame propagated in the flamelet regime in our related two-dimensional study. We compare to a corresponding two-dimensional simulation, and show that while fire-polishing keeps the small features suppressed in two dimensions, turbulence wrinkles the flame on far smaller scales in the three-dimensional case, suggesting that the transition to the distributed burning r...
Huntington, C. M.; Belof, J. L.; Blobaum, K. J. M.; Cavallo, R. M.; Kostinski, N.; Maddox, B. R.; May, M. J.; Plechaty, C.; Prisbrey, S. T.; Remington, B. A.; Rudd, R. E.; Swift, D. W.; Wallace, R. J.; Wilson, M. J.
2015-06-01
A solid-solid phase transition between the bcc (α) and hcp (ɛ) lattice structures in iron is known to occur as the material is compressed. When kept below its melting point, an effective increase in the macroscopic strength of the material accompanies this phase transition. Understanding the strength of iron throughout the deformation process is important for improving models of planetary structure, including interpretation of seismic measurements on Earth. To explore iron strength at high pressures and strain rates, we have performed experiments at the OMEGA laser. The laser drive produces a pressure near 1 Mbar on a thin Fe disk with a sinusoidal ripple pattern imposed on its face. The ripples seed the Rayleigh-Taylor (RT) instability, the growth of which is suppressed by the material strength of the sample. The ripple amplitude is diagnosed with x-ray radiography, and their growth is compared to values from simulations using different material strength models. This work will be compared to previous, similar experiments at 0.1 - 0.3 Mbar pressures. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore Na- tional Laboratory under Contract DE-AC52-07NA27344.
Magneto-Rayleigh-Taylor experiments on a MegaAmpere linear transformer driver
Zier, J. C.; Gilgenbach, R. M.; Chalenski, D. A.; Lau, Y. Y.; French, D. M.; Gomez, M. R.; Patel, S. G.; Rittersdorf, I. M.; Steiner, A. M.; Weis, M.; Zhang, P.; Mazarakis, M.; Cuneo, M. E.; Lopez, M.
2012-03-01
Experiments have been performed on a nominal 100 ns rise time, MegaAmpere (MA)-class linear transformer driver to explore the magneto-Rayleigh-Taylor (MRT) instability in planar geometry. Plasma loads consisted of ablated 400 nm-thick, 1 cm-wide aluminum foils located between two parallel-plate return-current electrodes. Plasma acceleration was adjusted by offsetting the position of the foil (cathode) between the anode plates. Diagnostics included double-pulse, sub-ns laser shadowgraphy, and machine current B-dot loops. Experimental growth rates for MRT on both sides of the ablated aluminum plasma slab were comparable for centered-foils. The MRT growth rate was fastest (98 ns e-folding time) for the foil-offset case where there was a larger magnetic field to accelerate the plasma. Other cases showed slower growth rates with e-folding times of about ˜106 ns. An interpretation of the experimental data in terms of an analytic MRT model is attempted.
Rayleigh-Taylor instabilities (RTI) in inertial confinement fusion (ICF) implosions are expected to generate magnetic fields at the gas-ice interface and at the ice-ablator interface. The focus here is on the gas-ice interface where the temperature gradient is the largest. A Hall-MHD model is used to study the magnetic field generation and growth for 2-D single-mode and multimode RTI in a stratified two-fluid plasma, the two fluids being ions and electrons. Self-generated magnetic fields are observed and these fields grow as the RTI progresses via the ∇ne×∇Te term in the generalized Ohm’s law. Srinivasan et al.[Phys. Rev. Lett. 108, 165002 (2012)] present results of the magnetic field generation and growth, and some scaling studies in 2-dimensions. The results presented here study the mechanism behind the magnetic field generation and growth, which is related to fluid vorticity generation by RTI. The magnetic field wraps around the bubbles and spikes and concentrates in flux bundles at the perturbed gas-ice interface where fluid vorticity is large. Additionally, the results of Srinivasan et al.[Phys. Rev. Lett. 108, 165002 (2012)] are described in greater detail. Additional scaling studies are performed to determine the growth of the self-generated magnetic field as a function of density, acceleration, perturbation wavelength, Atwood number, and ion mass.
Single-mode Rayleigh-Taylor growth-rate measurements with the OMEGA laser system
The results from a series of single-mode Rayleigh-Taylor (RT) instability growth experiments performed on the OMEGA laser system using planar targets are reported. Planar targets with imposed mass perturbations were accelerated using five to six 351-nm laser beams overlapped with total intensities up to 2.5x1014W/cm2. Experiments were performed with both 3-ns ramp and 3-ns flat-topped temporal pulse shapes. The use of distributed phase plates and smoothing by spectral dispersion resulted in a laser-irradiation nonuniformity of 4%endash 7% over a 600-μm-diam region defined by the 90% intensity contour. The temporal growth of the modulation in optical depth was measured using through-foil radiography and was detected with an x-ray framing camera for CH targets with and without a foam buffer. The growth of both 31-μm and 60-μm wavelength perturbations was found to be in good agreement with ORCHID simulations when the experimental details, including noise, were included. The addition of a 30-mg/cc, 100-μm-thick polystyrene foam buffer layer resulted in reduced growth of the 31-μm perturbation and essentially unchanged growth for the 60-μm case when compared to targets without foam. copyright 1997 American Institute of Physics
Linear and nonlinear Rayleigh-Taylor growth at strongly convergent spherical interfaces
Recent attention has focused on the effect of spherical convergence on the nonlinear phase of Rayleigh-Taylor growth. For instability growth on spherically converging interfaces, modifications to the predictions of the Layzer model for the secular growth of a single, nonlinear mode have been reported [D. S. Clark and M. Tabak, Phys. Rev. E 72, 0056308 (2005).]. However, this model is limited in assuming a self-similar background implosion history as well as only addressing growth from a perturbation of already nonlinearly large amplitude. Additionally, only the case of single-mode growth was considered and not the multimode growth of interest in applications. Here, these deficiencies are remedied. First, the connection of the recent nonlinear results including convergence to the well-known results for the linear regime of growth is demonstrated. Second, the applicability of the model to more general implosion histories (i.e., not self-similar) is shown. Finally, to address the case of multimode growth with convergence, the recent nonlinear single mode results are combined with the Haan model formulation for weakly nonlinear multimode growth. Remarkably, convergence in the nonlinear regime is found not to modify substantially the multimode predictions of Haan's original model
Rayleigh-Taylor (RT) instabilities at interfaces of disparate mass densities have long been known to generate magnetic fields during inertial confinement fusion implosions. An externally applied magnetic field can also be efficiently amplified by RT instabilities. The focus here is on magnetic field generation and amplification at the gas-ice interface which is RT unstable during the deceleration phase of the implosion. RT instabilities lead to undesirable mix of hot and cold plasmas which enhances thermal energy loss and tends to produce a more massive warm-spot instead of a hot-spot. Two mechanisms are shown here to mitigate the thermal energy loss from the hot-spot. The first mechanism is the reduction of electron thermal conductivity with interface-aligned magnetic fields. This can occur through self-generated magnetic fields via the Biermann battery effect as well as through externally applied magnetic fields that undergo an exponential growth via the stretch-and-fold magnetohydrodynamic dynamo. Self-generated magnetic fields during RT evolution can result in a factor of 2−10 decrease in the electron thermal conductivity at the gas-ice interface, while externally applied magnetic fields that are compressed to 6–1000 T at the onset of deceleration (corresponding to pre-implosion external fields of 0.06–10 T) could result in a factor of 2–500 reduction in electron thermal conductivity at the gas-ice interface. The second mechanism to mitigate thermal energy loss from the hot-spot is to decrease the interface mixing area between the hot and cold plasmas. This is achieved through large external magnetic fields of 1000 T at the onset of deceleration which damp short-wavelength RT modes and long-wavelength Kelvin-Helmholtz modes thus significantly slowing the RT growth and reducing mix
Three-dimensional Numerical Simulations of Rayleigh-Taylor Unstable Flames in Type Ia Supernovae
Zingale, M.; Woosley, S. E.; Rendleman, C. A.; Day, M. S.; Bell, J. B.
2005-10-01
Flame instabilities play a dominant role in accelerating the burning front to a large fraction of the speed of sound in a Type Ia supernova. We present a three-dimensional numerical simulation of a Rayleigh-Taylor unstable carbon flame, following its evolution through the transition to turbulence. A low-Mach number hydrodynamics method is used, freeing us from the harsh time step restrictions imposed by sound waves. We fully resolve the thermal structure of the flame and its reaction zone, eliminating the need for a flame model. A single density is considered, 1.5×107 g cm-3, and half-carbon, half-oxygen fuel: conditions under which the flame propagated in the flamelet regime in our related two-dimensional study. We compare to a corresponding two-dimensional simulation and show that while fire polishing keeps the small features suppressed in two dimensions, turbulence wrinkles the flame on far smaller scales in the three-dimensional case, suggesting that the transition to the distributed burning regime occurs at higher densities in three dimensions. Detailed turbulence diagnostics are provided. We show that the turbulence follows a Kolmogorov spectrum and is highly anisotropic on the large scales, with a much larger integral scale in the direction of gravity. Furthermore, we demonstrate that it becomes more isotropic as it cascades down to small scales. On the basis of the turbulent statistics and the flame properties of our simulation, we compute the Gibson scale. We show the progress of the turbulent flame through a classic combustion regime diagram, indicating that the flame just enters the distributed burning regime near the end of our simulation.
Single-mode, Rayleigh-Taylor growth-rate measurements on the OMEGA laser system
The results from a series of single-mode, Rayleigh-Taylor (RT) instability growth experiments performed on the OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] using planar targets are reported. Planar targets with imposed mass perturbations were accelerated using five or six 351 nm laser beams overlapped with total intensities up to 2.5x1014 W/cm2. Experiments were performed with both 3 ns ramp and 3 ns flat-topped temporal pulse shapes. The use of distributed phase plates and smoothing by spectral dispersion resulted in a laser-irradiation nonuniformity of 4%-7% over a 600 μm diam region defined by the 90% intensity contour. The temporal growth of the modulation in optical depth was measured using throughfoil radiography and was detected with an x-ray framing camera for CH targets. Two-dimensional (2-D) hydrodynamic simulations (ORCHID) [R. L. McCrory and C. P. Verdon, in Inertial Confinement Fusion (Editrice Compositori, Bologna, 1989), pp. 83-124] of the growth of 20, 31, and 60 μm wavelength perturbations were in good agreement with the experimental data when the experimental details, including noise, were included. The amplitude of the simulation optical depth is in good agreement with the experimental optical depth; therefore, great care must be taken when the growth rates are compared to dispersion formulas. Since the foil's initial condition just before it is accelerated is not that of a uniformly compressed foil, the optical density measurement does not accurately reflect the amplitude of the ablation surface but is affected by the initial nonuniform density profile. (c) 2000 American Institute of Physics
Simulating coronal condensation dynamics in 3D
Moschou, S P; Xia, C; Fang, X
2015-01-01
We present numerical simulations in 3D settings where coronal rain phenomena take place in a magnetic configuration of a quadrupolar arcade system. Our simulation is a magnetohydrodynamic simulation including anisotropic thermal conduction, optically thin radiative losses, and parametrised heating as main thermodynamical features to construct a realistic arcade configuration from chromospheric to coronal heights. The plasma evaporation from chromospheric and transition region heights eventually causes localised runaway condensation events and we witness the formation of plasma blobs due to thermal instability, that evolve dynamically in the heated arcade part and move gradually downwards due to interchange type dynamics. Unlike earlier 2.5D simulations, in this case there is no large scale prominence formation observed, but a continuous coronal rain develops which shows clear indications of Rayleigh-Taylor or interchange instability, that causes the denser plasma located above the transition region to fall do...
3D dynamics of hydrous thermal-chemical plumes in subduction zones
Zhu, G.; Gerya, T.; Yuen, D.; Connolly, J. A. D.
2009-04-01
Mantle wedges are identified as sites of intense thermal convection and thermal-chemical Rayleigh-Taylor instabilities ("cold plumes") controlling distribution and intensity of magmatic activity in subduction zones. To investigate 3D hydrous partially molten cold plumes forming in the mantle wedge in response to slab dehydration, we perform 3D petrological-thermomechanical numerical simulations of the intraoceanic one-sided subduction with spontaneously bending retreating slab characterized by weak hydrated upper interface. I3ELVIS code is used which is developed based on multigrid approach combined with marker-in-cell method with conservative finite-difference schemes. We investigated regional 800 km wide and 200 km deep 3D subduction models with variable 200 to 800 km lateral dimension along the trench using uniform numerical staggered grid with 405x101x101 nodal points and up to 50 million markers. Our results show three patterns (roll(sheet)-, zig-zag- and finger-like) of Rayleigh-Taylor instabilities can develop above the subducting slab, which are controlled by effective viscosity of partially molten rocks. Spatial and temporal periodicity of plumes correlate well with that of volcanic activity in natural intraoceanic arcs such as Japan. High laterally variable surface heat flow predicted in the arc region in response to thermal-chemical plumes activity is also consistent with natural observations.
One-dimensional-turbulence simulations of reactive Rayleigh-Taylor turbulence
Gonzalez, Esteban; Kerstein, Alan; Lignell, David
2011-11-01
We consider the problem of reactive Rayleigh-Taylor turbulence in the Boussinesq framework, and model combustion with a reaction-progress-variable method, and a KPP reaction. The interesting feature of this problem is that the interface (flame) between heavy/cold reactants and light/hot products moves against gravity. Such problem is challenging because of the delicate interplay between turbulence, buoyancy, and reactions, and the wide separation between large and small scales. One model that has the capabilities to deal with these challenges is the one-dimensional-turbulence (ODT) model. In this talk, we discuss ODT results for non-reactive and reactive Rayleigh-Taylor turbulence, and compare them with those from direct numerical simulations (DNS). Here, the key advantage of ODT over DNS is that it can be used to explore larger parameter spaces. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.
Turbulent Rayleigh-Taylor flow driven by time-varying accelerations
Ramaprabhu, Praveen; Lawrie, Andrew; Muthuraman, Karthik; UNC-LMFA Collaboration
2011-11-01
We report on numerical simulations of turbulent Rayleigh-Taylor flow subject to variable acceleration histories. The acceleration profiles were inspired by experiments and theoretical studies, and include an impulsive acceleration, accel-decel profiles, as well as a constant drive as the baseline case. The simulations were performed using the MOBILE software, a variable-density, incompressible fluid flow code. The advection algorithm employs a 3rd-order, monotonicity-preserving upwind scheme, allowing the definition of sharp interfaces in the flow, while pressure convergence is accelerated by the use of a multi-grid scheme. The simulations are initialized with two classes of perturbations: narrow-band, short-wavelength modes and broadband with long-wavelength modes. The effect of initial amplitudes on the perturbations is investigated under the variable drive conditions. The acceleration profiles are capable of producing stages of ``demixing,'' useful in validating turbulence models of RTI.
Two-fluid and the finite Larmor effects on linear and nonlinear growth of the Rayleigh-Taylor instability in a two-dimensional slab are studied numerically with special attention to high-wave-number dynamics and nonlinear structure formation at a low β-value. The two effects stabilize the unstable high wave number modes for a certain range of the β-value. In nonlinear simulations, the absence of the high wave number modes in the linear stage leads to the formation of the density field structure much larger than that in the single-fluid magnetohydrodynamic simulation, together with a sharp density gradient as well as a large velocity difference. The formation of the sharp velocity difference leads to a subsequent Kelvin-Helmholtz-type instability only when both the two-fluid and finite Larmor radius terms are incorporated, whereas it is not observed otherwise. It is shown that the emergence of the secondary instability can modify the outline of the turbulent structures associated with the primary Rayleigh-Taylor instability
Test Problem: Tilted Rayleigh-Taylor for 2-D Mixing Studies
Andrews, Malcolm J. [Los Alamos National Laboratory; Livescu, Daniel [Los Alamos National Laboratory; Youngs, David L. [AWE
2012-08-14
The 'tilted-rig' test problem originates from a series of experiments (Smeeton & Youngs, 1987, Youngs, 1989) performed at AWE in the late 1980's, that followed from the 'rocket-rig' experiments (Burrows et al., 1984; Read & Youngs, 1983), and exploratory experiments performed at Imperial College (Andrews, 1986; Andrews and Spalding, 1990). A schematic of the experiment is shown in Figure 1, and comprises a tank filled with light fluid above heavy, and then 'tilted' on one side of the apparatus, thus causing an 'angled interface' to the acceleration history due to rockets. Details of the configuration given in the next chapter include: fluids, dimensions, and other necessary details to simulate the experiment. Figure 2 shows results from two experiments, Case 110 (which is the source for this test problem) that has an Atwood number of 0.5, and Case 115 (a secondary source described in Appendix B), with Atwood of 0.9 Inspection of the photograph in Figure 2 (the main experimental diagnostic) for Case 110. reveals two main areas for mix development; 1) a large-scale overturning motion that produces a rising plume (spike) on the left, and falling plume (bubble) on the right, that are almost symmetric; and 2) a Rayleigh-Taylor driven mixing central mixing region that has a large-scale rotation associated with the rising and falling plumes, and also experiences lateral strain due to stretching of the interface by the plumes, and shear across the interface due to upper fluid moving downward and to the right, and lower fluid moving upward and to the left. Case 115 is similar but differs by a much larger Atwood of 0.9 that drives a strong asymmetry between a left side heavy spike penetration and a right side light bubble penetration. Case 110 is chosen as the source for the present test problem as the fluids have low surface tension (unlike Case 115) due the addition of a surfactant, the asymmetry small (no need to have fine
Hydrodynamic instability of compressible fluid in porous medium
The hydrodynamic Rayleigh -Taylor instability of two superposed compressible fluids in porous medium has been studied. The dispersion relation is derived for such a medium by using normal mode analysis. The RT instability is discussed for various simplified configuration. The effect of porosity and dynamic viscosity has been analyzed and it is observed that porosity and dynamic viscosity have stabilizing effect on the Rayleigh- Taylor instability of compressible fluids.
Belof, J L; Cavallo, R M; Olson, R T; King, R S; Gray, G T; Holtkamp, D B; Chen, S R; Rudd, R E; Barton, N R; Arsenlis, A; Remington, B A; Park, H; Prisbrey, S T; Vitello, P A; Bazan, G; Mikaelian, K O; Comley, A J; Maddox, B R; May, M J
2011-08-10
We present here the first dynamic Rayleigh-Taylor (RT) strength measurement of a material undergoing solid-solid phase transition. Iron is quasi-isentropically driven across the pressure-induced bcc ({alpha}-Fe) {yields} hcp ({var_epsilon}-Fe) phase transition and the dynamic strength of the {alpha}, {var_epsilon} and reverted {alpha}{prime} phases have been determined via proton radiography of the resulting Rayleigh-Taylor unstable interface between the iron target and high-explosive products. Simultaneous velocimetry measurements of the iron free surface yield the phase transition dynamics and, in conjunction with detailed hydrodynamic simulations, allow for determination of the strength of the distinct phases of iron. Forward analysis of the experiment via hydrodynamic simulations reveals significant strength enhancement of the dynamically-generated {var_epsilon}-Fe and reverted {alpha}{prime}-Fe, comparable in magnitude to the strength of austenitic stainless steels.
Rayleigh Taylor Growth At An Embedded Interface Driven By A Radiative Shock
Huntington, C. M.; Park, H.-S.; Raman, K. S.; Miles, A. R.; MacLaren, S. A.; Kalantar, D. H.; Robey, H. F.; Remington, B. A.; Doss, F. W.; Kline, J. L.; Flippo, K. A.; Kuranz, C. C.; Wan, W.; Drake, R. P.
2015-11-01
Radiative shocks are those where the radiation generated by the shock influences the hydrodynamics of the matter in the system. Radiative shocks occur during supernovae, as well as during the rebound phase of inertial confinement fusion (ICF) capsules. In the presence of a radiative shock, Rayleigh-Taylor (RT) growth at an unstable interface may be reduced relative to the growth from a purely hydrodynamic system. Using a 325 eV hohlraum on the National Ignition Facility (NIF), we are able to, for the first time, generate a radiative shock that traverses an RT-unstable interface. Because the generation of radiation at the shock front is a strong function of shock velocity (~v8), the RT growth in the presence of fast and slow shocks were directly compared. We observe reduced RT spike development when the driving shock is expected to be radiative. The amplitude of the unstable embedded feature was in good agreement with 2D models for both the low-drive (225 eV) and high drive (325 eV) cases. This result has important implications for our understanding of astrophysical radiative shocks, as well as the dynamics of ICF capsules. This work was performed under the auspices of the Lawrence Livermore National Security, LLC, (LLNS) under Contract No. DE-AC52-07NA27344.
Rayleigh-Taylor growth and imprint reduction using foam buffer layers on the Omega Laser
Watt, R. G.; Duke, J. R.; Elliot, N. E.; Gobby, P. L.; Hollis, R. V.; Kopp, R. A.; Mason, R. J.; Pollak, G.; Wilson, D. C.; Willi, O.; Kalantar, D. H.; Boehly, T. R.; Knauer, J. P.; Meyerhofer, D. D.; Smalyuk, V. A.; Verdon, C. P.
1997-11-01
A serious concern for directly driven ICF implosions is the asymmetry imparted to the capsule by laser drive nonuniformities. A distributed phase plate (DPP) with speckle pattern averaged over several coherence times by smoothing with spectral dispersion (SSD) still retains an ``early time imprint''. A supersonically preheated foam, with Au preheat layer, may reduce this imprint, by creating a low density, high temperature thermal plasma between the absorption and ablation surfaces. We report on experiments using machined polystyrene (PS) foams at 30 mg/cc on the Omega laser at 351 nm. The Rayleigh-Taylor growth of intentional solid substrate mass modulations was measured. Similar observed growth with and without foam suggests at most minor isentrope changes in the solid due to the presence of the foam. Significant reduction in the imprint from the OMEGA beams with DPP and distributed polarization rotators (DPR) but without smoothing by spectral dispersion (SSD) is observed when a foam buffer is employed. Recent experimental results will be shown and compared to simulations.
An Investigation of the Influence of Initial Conditions on Rayleigh-Taylor Mixing
Mueschke, N J; Schilling, O
2004-10-04
Experiments and direct numerical simulations (DNS) have been performed to examine the effects of initial conditions on the dynamics of a Rayleigh-Taylor unstable mixing layer. Experiments were performed on a water channel facility to measure the interfacial and velocity perturbations initially present at the two-fluid interface in a small Atwood number mixing layer. The experimental measurements have been parameterized for use in numerical simulations of the experiment. Two- and three-dimensional DNS of the experiment have been performed using the parameterized initial conditions. It is shown that simulations implemented with initial velocity and density perturbations, rather than density perturbations alone, are required to match experimentally-measured statistics and spectra. Data acquired from both the experiment and numerical simulations are used to examine the role of initial conditions on the evolution of integral-scale, turbulence, and mixing statistics. Early-time turbulence and mixing statistics are shown to be strongly-dependent upon the early-time transition of the initial perturbation from a weakly-nonlinear to a strongly-nonlinear flow.
Cherniavski, V. M.; Shtemler, Yu. M.
2013-01-01
The potential flow of an incompressible inviscid heavy fluid over a light one is considered. The integral version of the method of matched asymptotic expansion is applied to the construction of the solution over long intervals of time. The asymptotic solution describes the flow in which a bubble rises with constant speed and the "tongue" is in free fall. The outer expansion is stationary, but the inner one depends on time. It is shown that the solution exists within the same range of Froude n...
Rayleigh-Taylor and Richtmyer-Meshkov Instabilities and Mixing in Stratified Cylindrical Shells
Mikaelian, K O
2004-04-15
We study the linear stability of an arbitrary number N of cylindrical concentric shells undergoing a radial implosion or explosion.We derive the evolution equation for the perturbation {eta}{sub i} at interface i; it is coupled to the two adjacent interfaces via {eta}{sub i{+-}1}. For N=2, where there is only one interface, we verify Bell's conjecture as to the form of the evolution equation for arbitrary {rho}{sub 1} and {rho}{sub 2}, the fluid densities on either side of the interface. We obtain several analytic solutions for the N=2 and 3 cases. We discuss freeze-out, a phenomenon that can occur in all three geometries (planar, cylindrical, or spherical), and ''critical modes'' that are stable for any implosion or explosion history and occur only in cylindrical or spherical geometries. We present numerical simulations of possible gelatin-ring experiments illustrating perturbation feedthrough from one interface to another. We also develop a simple model for the evolution of turbulent mix in cylindrical geometry and define a geometrical factor G as the ratio h{sub cylindrical}/h{sub planar} between cylindrical and planar mixing layers. We find that G is a decreasing function of R/R{sub o}, implying that in our model h{sub cylindrical} evolves faster (slower) than h{sub planar} during an implosion (explosion).
Cherniavski, V M
2013-01-01
The potential flow of an incompressible inviscid heavy fluid over a light one is considered. The integral version of the method of matched asymptotic expansion is applied to the construction of the solution over long intervals of time. The asymptotic solution describes the flow in which a bubble rises with constant speed and the "tongue" is in free fall. The outer expansion is stationary, but the inner one depends on time. It is shown that the solution exists within the same range of Froude number obtained previously by Vanden-Broeck (1984a,b). The Froude number and the solution depend on the initial energy of the disturbance. At the top of the bubble, the derivative of the free-surface curvature has a discontinuity when the Froude number is not equal to 0.23. This makes it possible to identify the choice of the solution obtained in a number of studies with the presence of an artificial numerical surface tension. The first correction term in the neighborhood of the tongue is obtained when large surface tensio...
Analytical model of the ablative Rayleigh-Taylor instability in the deceleration phase
A sharp boundary model for the deceleration phase of imploding capsules in inertial confinement fusion, in both direct and indirect drive, has been developed. The model includes heat conduction, local α-particle energy deposition, and shell compressibility effects. A differential equation for the temporal evolution of the modal amplitude interface is obtained. It is found that the α-particle energy has a strong influence on the evolution of the low l modes, via the compressibility of the shell. The modes are damped by vorticity convection, fire polishing, and α-particle energy deposition. The existence of a cutoff l number arises from the high blow of velocity into the hot region (rocket effect) if density gradient scale length effects are taken into account at the interface. The differential equation for the modal amplitude is used as a postprocessor to the results of 1D-SARA code [J. J. Honrubia, J. Quant. Spectrosc. Radiat. Transfer. 49, 491 (1993)] in a typical capsule for indirect-drive ignition designed on the National Ignition Facility. It is found that modes with l>180 are completely stabilized. The results are in agreement with two-dimensional simulations
Analytical model of the ablative Rayleigh-Taylor instability in the deceleration phase
Sanz, J.; Betti, R.
2005-04-01
A sharp boundary model for the deceleration phase of imploding capsules in inertial confinement fusion, in both direct and indirect drive, has been developed. The model includes heat conduction, local α-particle energy deposition, and shell compressibility effects. A differential equation for the temporal evolution of the modal amplitude interface is obtained. It is found that the α-particle energy has a strong influence on the evolution of the low l modes, via the compressibility of the shell. The modes are damped by vorticity convection, fire polishing, and α-particle energy deposition. The existence of a cutoff l number arises from the high blow of velocity into the hot region (rocket effect) if density gradient scale length effects are taken into account at the interface. The differential equation for the modal amplitude is used as a postprocessor to the results of 1D-SARA code [J. J. Honrubia, J. Quant. Spectrosc. Radiat. Transfer. 49, 491 (1993)] in a typical capsule for indirect-drive ignition designed on the National Ignition Facility. It is found that modes with l >180 are completely stabilized. The results are in agreement with two-dimensional simulations.
Spike morphology in blast-wave-driven instability experiments
The laboratory experiments described in the present paper observe the blast-wave-driven Rayleigh-Taylor instability with three-dimensional (3D) initial conditions. About 5 kJ of energy from the Omega laser creates conditions similar to those of the He-H interface during the explosion phase of a supernova. The experimental target is a 150 μm thick plastic disk followed by a low-density foam. The plastic piece has an embedded, 3D perturbation. The basic structure of the pattern is two orthogonal sine waves where each sine wave has an amplitude of 2.5 μm and a wavelength of 71 μm. In some experiments, an additional wavelength is added to explore the interaction of modes. In experiments with 3D initial conditions the spike morphology differs from what has been observed in other Rayleigh-Taylor experiments and simulations. Under certain conditions, experimental radiographs show some mass extending from the interface to the shock front. Current simulations show neither the spike morphology nor the spike penetration observed in the experiments. The amount of mass reaching the shock front is analyzed and potential causes for the spike morphology and the spikes reaching the shock are discussed. One such hypothesis is that these phenomena may be caused by magnetic pressure, generated by an azimuthal magnetic field produced by the plasma dynamics.
3D Printing Variable Stiffness Foams Using Viscous Thread Instability.
Lipton, Jeffrey I; Lipson, Hod
2016-01-01
Additive manufacturing of cellular structures has numerous applications ranging from fabrication of biological scaffolds and medical implants, to mechanical weight reduction and control over mechanical properties. Various additive manufacturing processes have been used to produce open regular cellular structures limited only by the resolution of the printer. These efforts have focused on printing explicitly designed cells or explicitly planning offsets between strands. Here we describe a technique for producing cellular structures implicitly by inducing viscous thread instability when extruding material. This process allows us to produce complex cellular structures at a scale that is finer than the native resolution of the printer. We demonstrate tunable effective elastic modulus and density that span two orders of magnitude. Fine grained cellular structures allow for fabrication of foams for use in a wide range of fields ranging from bioengineering, to robotics to food printing. PMID:27503148
3D Printing Variable Stiffness Foams Using Viscous Thread Instability
Lipton, Jeffrey I.; Lipson, Hod
2016-08-01
Additive manufacturing of cellular structures has numerous applications ranging from fabrication of biological scaffolds and medical implants, to mechanical weight reduction and control over mechanical properties. Various additive manufacturing processes have been used to produce open regular cellular structures limited only by the resolution of the printer. These efforts have focused on printing explicitly designed cells or explicitly planning offsets between strands. Here we describe a technique for producing cellular structures implicitly by inducing viscous thread instability when extruding material. This process allows us to produce complex cellular structures at a scale that is finer than the native resolution of the printer. We demonstrate tunable effective elastic modulus and density that span two orders of magnitude. Fine grained cellular structures allow for fabrication of foams for use in a wide range of fields ranging from bioengineering, to robotics to food printing.
Rayleigh-Taylor Gravity Waves and Quasiperiodic Oscillation Phenomenon in X-ray Binaries
Titarchuk, Lev
2002-01-01
Accretion onto compact objects in X-ray binaries (black hole, neutron star (NS), white dwarf) is characterized by non-uniform flow density profiles. Such an effect of heterogeneity in presence of gravitational forces and pressure gradients exhibits Rayleigh-Taylor gravity waves (RTGW). They should be seen as quasiperiodic wave oscillations (QPO) of the accretion flow in the transition (boundary) layer between the Keplerian disk and the central object. In this paper the author shows that the main QPO frequency, which is very close to the Keplerian frequency, is split into separate frequencies (hybrid and low branch) under the influence of the gravitational forces in the rotational frame of reference. The RTGWs must be present and the related QPOs should be detected in any system where the gravity, buoyancy and Coriolis force effects cannot be excluded (even in the Earth and solar environments). The observed low and high QPO frequencies are an intrinsic signature of the RTGW. The author elaborates the conditions for the density profile when the RTGW oscillations are stable. A comparison of the inferred QPO frequencies with QPO observations is presented. The author finds that hectohertz frequencies detected from NS binaries can be identified as the RTGW low branch frequencies. The author also predicts that an observer can see the double NS spin frequency during the NS long (super) burst events when the pressure gradients and buoyant forces are suppressed. The Coriolis force is the only force which acts in the rotational frame of reference and its presence causes perfect coherent pulsations with a frequency twice of the NS spin. The QPO observations of neutron binaries have established that the high QPO frequencies do not go beyond of the certain upper limit. The author explains this observational effect as a result of the density profile inversions. Also the author demonstrates that a particular problem of the gravity waves in the rotational frame of reference in the
How Do Hydrodynamic Instabilities Affect 3D Transport in Geophysical Vortices?
Wang, P.; Ozgokmen, T. M.
2014-12-01
Understanding three-dimensional (3D) transport in ocean eddies is important for processes at a variety of scales, ranging from plankton production to climate variability. It is well known that geophysical vortices are subject to various hydrodynamic instabilities. Yet the influence of these instabilities on 3D material transport in vortex systems is not well investigated. Focusing on barotropic, inertial and 3D instabilities, we analyze these instabilities with normal-mode method, and reproduce their characteristics via highly-resolved numerical simulations using a spectral element Navier-Stokes solver. By comparing the simulation results of stable and unstable vortices, we investigate the joint impacts of instabilities on 3D transport through three major aspects: (i) energy transfer, (ii) overturning transport of the secondary circulation, and (iii) rates of vertical exchange and mixing. It is found that instabilities can enhance local nonlinear interactions and cause the kinetic energy wavenumber spectrum to have slopes between the conventional -5/3 and -3 at inertial ranges. The cascade of a new quantity is proposed to explain these non-conventional slopes. One of our main results is the discovery of material exchange between the central vortex and satellite vortices through 3D pathways, called funnels. These funnels modify the concept of elliptic regions that can trap material when confined to 2D dynamics. Thus, we show that a family of vortices, created by the hydrodynamic instabilities of the initially unstable vortex, can still continue to operate in unity in order to complete the 3D transport in these systems. We also show that flow instabilities can double the magnitude of vertical velocity, increase the rate of vertical exchange by an order of magnitude and enhance mixing rate more than 100%.
Madura, T. I.; Clementel, N.; Gull, T. R.; Kruip, C. J. H.; Paardekooper, J.-P.
2015-06-01
We present the first 3D prints of output from a supercomputer simulation of a complex astrophysical system, the colliding stellar winds in the massive (≳120 M⊙), highly eccentric (e ˜ 0.9) binary star system η Carinae. We demonstrate the methodology used to incorporate 3D interactive figures into a PDF (Portable Document Format) journal publication and the benefits of using 3D visualization and 3D printing as tools to analyse data from multidimensional numerical simulations. Using a consumer-grade 3D printer (MakerBot Replicator 2X), we successfully printed 3D smoothed particle hydrodynamics simulations of η Carinae's inner (r ˜ 110 au) wind-wind collision interface at multiple orbital phases. The 3D prints and visualizations reveal important, previously unknown `finger-like' structures at orbital phases shortly after periastron (φ ˜ 1.045) that protrude radially outwards from the spiral wind-wind collision region. We speculate that these fingers are related to instabilities (e.g. thin-shell, Rayleigh-Taylor) that arise at the interface between the radiatively cooled layer of dense post-shock primary-star wind and the fast (3000 km s-1), adiabatic post-shock companion-star wind. The success of our work and easy identification of previously unrecognized physical features highlight the important role 3D printing and interactive graphics can play in the visualization and understanding of complex 3D time-dependent numerical simulations of astrophysical phenomena.
Madura, Thomas; Gull, Theodore R.; Clementel, Nicola; Paardekooper, Jan-Pieter; Kruip, Chael; Corcoran, Michael F.; Hamaguchi, Kenji; Teodoro, Mairan
2015-01-01
We present the first 3D prints of output from a supercomputer simulation of a complex astrophysical system, the colliding stellar winds in the massive (>120 MSun), highly eccentric (e ~ 0.9) binary Eta Carinae. Using a consumer-grade 3D printer (Makerbot Replicator 2X), we successfully printed 3D smoothed particle hydrodynamics simulations of Eta Carinae's inner (r ~110 AU) wind-wind collision interface at multiple orbital phases. These 3D prints reveal important, previously unknown 'finger-like' structures at orbital phases shortly after periastron (φ ~1.045) that protrude radially outward from the spiral wind-wind collision region. We speculate that these fingers are related to instabilities (e.g. Rayleigh-Taylor) that arise at the interface between the radiatively-cooled layer of dense post-shock primary-star wind and the hot, adiabatic post-shock companion-star wind. The success of our work and easy identification of previously unknown physical features highlight the important role 3D printing can play in the visualization and understanding of complex 3D time-dependent numerical simulations of astrophysical phenomena.
Madura, Thomas I; Gull, Theodore R; Kruip, Chael J H; Paardekooper, Jan-Pieter
2015-01-01
We present the first 3D prints of output from a supercomputer simulation of a complex astrophysical system, the colliding stellar winds in the massive (>120 M_Sun), highly eccentric (e ~ 0.9) binary star system Eta Carinae. We demonstrate the methodology used to incorporate 3D interactive figures into a PDF journal publication and the benefits of using 3D visualization and 3D printing as tools to analyze data from multidimensional numerical simulations. Using a consumer-grade 3D printer (MakerBot Replicator 2X), we successfully printed 3D smoothed particle hydrodynamics (SPH) simulations of Eta Carinae's inner (r ~ 110 au) wind-wind collision interface at multiple orbital phases. The 3D prints and visualizations reveal important, previously unknown 'finger-like' structures at orbital phases shortly after periastron (phi ~ 1.045) that protrude radially outward from the spiral wind-wind collision region. We speculate that these fingers are related to instabilities (e.g. thin-shell, Rayleigh-Taylor) that arise a...
Global gyrokinetic models for energetic particle driven Alfvén instabilities in 3D equilibria
Spong, Don; Holod, Ihor
2015-11-01
The GTC global gyrokinetic PIC model has been adapted to 3D VMEC equilibria and provides a new method for the analysis of Alfvénic instabilities in stellarators, 3D tokamaks, and helical RFP states. The gyrokinetic orderings (k||/k⊥ applicable to a range of energetic particle driven instabilities that have been observed in 3D configurations. Applications of this model to stellarators have indicated that a variety of different Alfvén instabilities can be excited, depending on the toroidal mode number, fast ion average energy and fast ion density profile. Both an LHD discharge where bursting n = 1 Alfvén activity in the TAE gap was observed and a W7-X case have been examined. TAE,/EAE/GAE modes have been found in the simulations, depending on the mode family and fast ion profiles used. The dynamical evolution of the instabilities shows the field period coupling between n and n + Nfp expected for a stellarator. The development of gyrofluid reduced models that can capture relevant physics aspects of the gyrokinetic models will also be discussed. Research sponsored by the U.S. Department of Energy under Contract DE-AC05-00OR22725 with UT-Battelle, LLC and the GSEP SciDAC Center.
Mizuno, Yosuke; Lyubarsky, Yuri; ishikawa, Ken-Ichi; Hardee, Philip E.
2010-01-01
We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the non-linear regime nearly ceases for increasing magnetic pitch.
Mizuno, Yosuke; Nishikawa, Ken-Ichi; Hardee, Philip E
2009-01-01
We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the g...
Relativistic MHD simulations of core-collapse GRB jets: 3D instabilities and magnetic dissipation
Bromberg, Omer
2015-01-01
Relativistic jets naturally occur in astrophysical systems that involve accretion onto compact objects, such as core collapse of massive stars in gamma-ray bursts (GRBs) and accretion onto supermassive black holes in active galactic nuclei (AGN). It is generally accepted that these jets are powered electromagnetically, by the magnetised rotation of a central compact object. However, how they produce the observed emission and survive the propagation for many orders of magnitude in distance without being disrupted by current-driven non-axisymmetric instabilities is the subject of active debate. We carry out time-dependent 3D relativistic magnetohydrodynamic simulations of relativistic, Poynting flux dominated jets. The jets are launched self-consistently by the rotation of a strongly magnetised central compact object. This determines the natural degree of azimuthal magnetic field winding, a crucial factor that controls jet stability. We find that the jets are susceptible to two types of instability: (i) a globa...
A 3D GCL compatible cell-centered Lagrangian scheme for solving gas dynamics equations
Georges, Gabriel; Breil, Jérôme; Maire, Pierre-Henri
2016-01-01
Solving the gas dynamics equations under the Lagrangian formalism enables to simulate complex flows with strong shock waves. This formulation is well suited to the simulation of multi-material compressible fluid flows such as those encountered in the domain of High Energy Density Physics (HEDP). These types of flows are characterized by complex 3D structures such as hydrodynamic instabilities (Richtmyer-Meshkov, Rayleigh-Taylor, etc.). Recently, the 3D extension of different Lagrangian schemes has been proposed and appears to be challenging. More precisely, the definition of the cell geometry in the 3D space through the treatment of its non-planar faces and the limiting of a reconstructed field in 3D in the case of a second-order extension are of great interest. This paper proposes two new methods to solve these problems. A systematic and symmetric geometrical decomposition of polyhedral cells is presented. This method enables to define a discrete divergence operator leading to the respect of the Geometric Conservation Law (GCL). Moreover, a multi-dimensional minmod limiter is proposed. This new limiter constructs, from nodal gradients, a cell gradient which enables to ensure the monotonicity of the numerical solution even in presence of strong discontinuity. These new ingredients are employed into a cell-centered Lagrangian scheme. Robustness and accuracy are assessed against various representative test cases.
Coupling frontal photopolymerization and surface instabilities for a novel 3D patterning technology
Vitale, Alessandra; Hennessy, Matthew; Matar, Omar; Douglas, Jack; Cabral, João
2015-03-01
Patterning of soft matter provides an exceptional route for the generation of micro/nanostructured and functional surfaces. We describe a new 3D fabrication process based on coupling frontal photopolymerization (FPP) with precisely controlled, yet spontaneous, interfacial wrinkling. FPP is a complex spatio-temporal process that can lead to well-defined propagating fronts of network formation, both stable and unstable. We investigate this process focusing on the interfacial monomer-to-polymer conversion profile and its wave propagation. A simple coarse-grained model is found to describe remarkably well the planar frontal logarithmic kinetics, capturing the effects of UV light exposure time (or dose) and temperature, as well as the front position. In defined conditions, surface instabilities are introduced and interfere with wave planarity, resulting in the formation of ``minimal'' surfaces with complex 3D geometries. Building on this understanding on the propagation of wavefronts of network formation during photopolymerization, we demonstrate the design and fabrication of 3D patterned polymer materials with tunable shapes with optical and surface functionality.
Dynamical Instability and Soliton Concept
The problem of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is noted that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Rayleigh-Taylor type) instability, with the dispersion terms in the evolution equations. The spinodal instability and the Rayleigh-Taylor instability may compensate each other and lead to stable quasi-soliton type objects. The simple analytical model is presented to illustrate this physical picture. The time evolution of an initially compressed cold nuclear system is analysed in the framework of the inverse mean-field method. It is demonstrated that the nonlinearity and dispersion terms of the evolution equations can lead to clusterization in the final channel. 8 p
Instabilities at planetary gap edges in 3D self-gravitating disks
Lin Min-Kai
2013-04-01
Full Text Available Numerical simulations are presented to study the stability of gaps opened by giant planets in 3D self-gravitating disks. In weakly self-gravitating disks, a few vortices develop at the gap edge and merge on orbital time-scales. The result is one large but weak vortex with Rossby number -0.01. In moderately self-gravitating disks, more vortices develop and their merging is resisted on dynamical time-scales. Self-gravity can sustain multi-vortex configurations, with Rossby number -0.2 to -0.1, over a time-scale of order 100 orbits. Self-gravity also enhances the vortex vertical density stratification, even in disks with initial Toomre parameter of order 10. However, vortex formation is suppressed in strongly self-gravitating disks and replaced by a global spiral instability associated with the gap edge which develops during gap formation.
Quasi 3D ECE imaging system for study of MHD instabilities in KSTAR.
Yun, G S; Lee, W; Choi, M J; Lee, J; Kim, M; Leem, J; Nam, Y; Choe, G H; Park, H K; Park, H; Woo, D S; Kim, K W; Domier, C W; Luhmann, N C; Ito, N; Mase, A; Lee, S G
2014-11-01
A second electron cyclotron emission imaging (ECEI) system has been installed on the KSTAR tokamak, toroidally separated by 1/16th of the torus from the first ECEI system. For the first time, the dynamical evolutions of MHD instabilities from the plasma core to the edge have been visualized in quasi-3D for a wide range of the KSTAR operation (B0 = 1.7∼3.5 T). This flexible diagnostic capability has been realized by substantial improvements in large-aperture quasi-optical microwave components including the development of broad-band polarization rotators for imaging of the fundamental ordinary ECE as well as the usual 2nd harmonic extraordinary ECE. PMID:25430233
Quasi 3D ECE imaging system for study of MHD instabilities in KSTAR
Yun, G. S., E-mail: gunsu@postech.ac.kr; Choi, M. J.; Lee, J.; Kim, M.; Leem, J.; Nam, Y.; Choe, G. H. [Department of Physics, Pohang University of Science and Technology, Pohang 790-784 (Korea, Republic of); Lee, W.; Park, H. K. [Ulsan National Institute of Science and Technology, Ulsan 689-798 (Korea, Republic of); Park, H.; Woo, D. S.; Kim, K. W. [School of Electrical Engineering, Kyungpook National University, Daegu 702-701 (Korea, Republic of); Domier, C. W.; Luhmann, N. C. [Department of Electrical and Computer Engineering, University of California, Davis, California 95616 (United States); Ito, N. [KASTEC, Kyushu University, Kasuga-shi, Fukuoka 812-8581 (Japan); Mase, A. [Ube National College of Technology, Ube-shi, Yamaguchi 755-8555 (Japan); Lee, S. G. [National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of)
2014-11-15
A second electron cyclotron emission imaging (ECEI) system has been installed on the KSTAR tokamak, toroidally separated by 1/16th of the torus from the first ECEI system. For the first time, the dynamical evolutions of MHD instabilities from the plasma core to the edge have been visualized in quasi-3D for a wide range of the KSTAR operation (B{sub 0} = 1.7∼3.5 T). This flexible diagnostic capability has been realized by substantial improvements in large-aperture quasi-optical microwave components including the development of broad-band polarization rotators for imaging of the fundamental ordinary ECE as well as the usual 2nd harmonic extraordinary ECE.
Thermo/Soluto-capillary instabilities in 3D bi-component liquid pools using DNS
Williams, Adam; Saenz, Pedro; Valluri, Prashant; Sefiane, Khellil
2015-11-01
The behaviour of surface tension dominated flows in the presence of a temperature gradient and phase change is of great importance in designing micro-cooling devices. While evaporating pools and droplets have been investigated numerically and experimentally, these studies have dealt only with pure fluids. For bicomponent liquid mixtures, limited experimental studies have been conducted but a rigorous numerical model is absent. We present a two-phase multicomponent DNS model to simulate thermo/soluto-capillary instabilities in bicomponent liquid layers subject to a horizontal temperature gradient. The strategy fully accounts for a deformable interface using a variant of volume-of-fluid method. The presence of a second component introduces thermophoresis in the liquid phase which then gives rise to solutal Marangoni effects. By combining mixture thermodynamics with multiphase DNS, we investigate thermo/soluto-capillary and interfacial instabilities of a 3D bicomponent liquid pool. An important aspect we quantify is the strength of solutal over thermal Marangoni convection and its effect on stability of resultant interfacial waves and phase-separation in the liquid. The model is robust enough to include phase-change and the advection-diffusion of volatile species in the gas phase. Funded by EPSRC, Grant No. EP/K00963X/1.
Delorme, Barthélémy
2015-01-01
Les différents dimensionnements et expériences de Fusion par Confinement Inertiel (FCI) en attaque directe comme indirecte montrent qu'une des principales limites à l'atteinte de l'ignition est l'instabilité de Rayleigh-Taylor (IRT) qui cause la rupture de la coquille de la cible en vol et potentiellement le mélange du combustible chaud du coeur avec celui, froid, de la coquille. La connaissance, la compréhension et la maîtrise des conditions initiales de ce mécanisme sont donc d'un grand int...
Understanding the structure of the turbulent mixing layer in hydrodynamic instabilities
When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface create a characteristic structure of rising bubbles and falling spikes known as Rayleigh-Taylor instability. Rayleigh-Taylor instabilities have received much attention over the past half-century because of their importance in understanding many natural and man-made phenomena, ranging from the rate of formation of heavy elements in supernovae to the design of capsules for Inertial Confinement Fusion. We present a new approach to analyze Rayleigh-Taylor instabilities in which we extract a hierarchical segmentation of the mixing envelope surface to identify bubbles and analyze analogous segmentations of fields on the original interface plane. We compute meaningful statistical information that reveals the evolution of topological features and corroborates the observations made by scientists
WANG Jing-yi; ZOU Jian-feng; ZHENG Yao; REN An-lu
2011-01-01
A front tracking method based on a marching cubes isosurface extractor,which is related filter generating isosurfaces from a structured point set,is provided to achieve sharp resolution for the simulation of non-diffusive interfacial flow.Compared with the traditional topology processing procedure,the current front tracking method is easier to be implemented and presents high performance in terms of computational resources.The numerical tests for 2-D highly-shearing flows and 3-D bubbles merging process are conducted to numerically examine the performance of the current methodology for tracking interfaces between two immiscible fluids.The Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instability problems are successfully investigated with the present marching cubes based front tracking method.
Andronov, V.A.; Zhidov, I.G.; Meskov, E.E.; Nevmerzhitskii, N.V.; Nikiforov, V.V.; Razin, A.N.; Rogatchev, V.G.; Tolshmyakov, A.I.; Yanilkin, Y.V. [Russian Federal Nuclear Center (Russian Federation)
1994-12-31
The report presents the basic results of some calculations, theoretical and experimental efforts in the study of Rayleigh-Taylor, Kelvin-Helmholtz, Richtmyer-Meshkov instabilities and the turbulent mixing which is caused by their evolution. Since the late forties the VNIIEF has been conducting these investigations. This report is based on the data which were published in different times in Russian and foreign journals. The first part of the report deals with calculations an theoretical techniques for the description of hydrodynamic instabilities applied currently, as well as with the results of several individual problems and their comparison with the experiment. These methods can be divided into two types: direct numerical simulation methods and phenomenological methods. The first type includes the regular 2D and 3D gasdynamical techniques as well as the techniques based on small perturbation approximation and on incompressible liquid approximation. The second type comprises the techniques based on various phenomenological turbulence models. The second part of the report describes the experimental methods and cites the experimental results of Rayleigh-Taylor and Richtmyer-Meskov instability studies as well as of turbulent mixing. The applied methods were based on thin-film gaseous models, on jelly models and liquid layer models. The research was done for plane and cylindrical geometries. As drivers, the shock tubes of different designs were used as well as gaseous explosive mixtures, compressed air and electric wire explosions. The experimental results were applied in calculational-theoretical technique calibrations. The authors did not aim at covering all VNIIEF research done in this field of science. To a great extent the choice of the material depended on the personal contribution of the author in these studies.
Simulation of the Initial 3-D Instability of an Impacting Drop Vortex Ring
Sigurdson, Lorenz; Wiwchar, Justin; Walther, Jens Honore
2013-01-01
Computational vortex particle method simulations of a perturbed vortex ring are performed to recreate and understand the instability seen in impacting water drop experiments. Three fundamentally different initial vorticity distributions are used to attempt to trigger a Widnall instability, a...... Rayleigh centrifugal instability, or a vortex breakdown-type instability. Simulations which simply have a perturbed solitary ring result in an instability similar to that seen experimentally. Waviness of the core which would be expected from a Widnall instability is not visible. Adding an opposite......, though tests are not conclusive. Perhaps the opposite-signed secondary vortex was not strong enough or placed appropriately. Elliptical streamlines , as expected, are visible in the core of the solitary ring at early times. Support from the Canadian Natural Sciences and Engineering Research Council grant...
The effect of small 3D magnetic perturbations on linear micro-instability properties
Hegna, C. C.
2014-10-01
Small externally applied non-axisymmetric magnetic perturbations can significantly alter the edge properties of tokamaks. In this work, we model the effect of the applied 3D fields on the flux surface deformation and show that these can alter key geometric properties of interest to microinstabilities. Shielding physics is assumed to be operative so that flux surface integrity is retained. Local 3D equilibrium theory is employed using a perturbative approach to calculate flux surface deformations consistent with magnetostatic force balance. Prior work has shown applied 3D fields can significantly alter ideal ballooning stability boundaries due to order unity 3D field induced changes to the local shear. The impact of 3D fields on ion temperature gradient and trapped electron mode growth rates are quantified using analytically derived proxy functions. Research supported by U.S. DoE Grant No. DE-FG02-86ER53218.
The purpose of this study is to investigate if magnetic resonance imaging with intra-articular contrast (MR-arthro) is as reliable as three-dimensionally reconstructed computed tomography imaging (3D-CT) in quantifying the glenoid bone loss in patients with anterior shoulder instability. Thirty-five patients were included. Sagittal MR-arthro and 3D-CT images of the glenoid surface were obtained pre-operatively. Two observers measured these images twice with OsiriX software in a randomized and blinded way. The intraclass correlations (ICC) of the intra- and inter-observer reliability within one method and an additional Bland-Altman plot for calculating agreement between the two methods were obtained. The joint estimates of the intra-observer reliability, taking into account the data from both observer A and B, for 3D-CT and MR-arthro were good to excellent. The intra-observer reliability was 0.938 (95 % CI: 0.879, 0.968) for 3D-CT and 0.799 (95 % CI: 0.639, 0.837) for MR-arthro. The inter-observer reliability between the two observers within one method (3D-CT or MR-arthro) was moderate to good. 3D-CT: 0.724 (95 % CI: 0.236, 0.886) and MR-arthro: 0.534 (95 % CI: 0.128, 0.762). Comparing both the 3D-CT and MR-arthro method, a Bland-Altman plot showed satisfying differences with the majority of outcomes (89 %) within 1 SD. Good to excellent intra- and moderate to good inter-observer correlations and a satisfying Bland-Altman plot when compared to 3D-CT show tendencies that MR-arthro is reliable and valid for measuring bony defects of the glenoid. (orig.)
3D simulations of supernova remnants evolution including non-linear particle acceleration
Ferrand, Gilles; Ballet, Jean; Teyssier, Romain; Fraschetti, Federico
2009-01-01
If a sizeable fraction of the energy of supernova remnant shocks is channeled into energetic particles (commonly identified with Galactic cosmic rays), then the morphological evolution of the remnants must be distinctly modified. Evidence of such modifications has been recently obtained with the Chandra and XMM-Newton X-ray satellites. To investigate these effects, we coupled a semi-analytical kinetic model of shock acceleration with a 3D hydrodynamic code (by means of an effective adiabatic index). This enables us to study the time-dependent compression of the region between the forward and reverse shocks due to the back reaction of accelerated particles, concomitantly with the development of the Rayleigh-Taylor hydrodynamic instability at the contact discontinuity. Density profiles depend critically on the injection level eta of particles: for eta up to about 10^-4 modifications are weak and progressive, for eta of the order of 10^-3 modifications are strong and immediate. Nevertheless, the extension of the...
Modeling hydrodynamic instabilities of double ablation fronts in inertial confinement fusion
Yanez C.; Sanz J; Olazabal-Loumé M.; Ibanez L.F.
2013-01-01
A linear Rayleigh-Taylor instability theory of double ablation (DA) fronts is developed for direct-drive inertial confinement fusion. Two approaches are discussed: an analytical discontinuity model for the radiation dominated regime of very steep DA front structure, and a numerical self-consistent model that covers more general hydrodynamic profiles behaviours. Dispersion relation results are compared to 2D simulations.
Modeling hydrodynamic instabilities of double ablation fronts in inertial confinement fusion
A linear Rayleigh-Taylor instability theory of double ablation (DA) fronts is developed for direct-drive inertial confinement fusion. Two approaches are discussed: an analytical discontinuity model for the radiation dominated regime of very steep DA front structure, and a numerical self-consistent model that covers more general hydrodynamic profiles behaviours. Dispersion relation results are compared to 2D simulations. (authors)
Self-organization of a plasma due to 3D evolution of the Weibel instability
The nonlinear evolution of the thermal Weibel instability is studied by using three-dimensional particle-in-cell simulations. After a fast saturation due to a reduction in the temperature anisotropy, the instability evolves to a quasistationary state which includes a single mode long wavelength helical magnetic field and a finite degree of temperature anisotropy. The nonlinear stability of this state is explained by periodic variations of the temperature anisotropy axis. At long time scales the magnetic field, wave number, and temperature anisotropy slowly evolve to the decreasing magnitudes
Effects of a weakly 3-D equilibrium on ideal magnetohydrodynamic instabilities
Hegna, C. C. [Departments of Engineering Physics and Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)
2014-07-15
The effect of a small three-dimensional equilibrium distortion on an otherwise axisymmetric configuration is shown to be destabilizing to ideal magnetohydrodynamic modes. The calculations assume that the 3-D fields are weak and that shielding physics is present so that no islands appear in the resulting equilibrium. An eigenfunction that has coupled harmonics of different toroidal mode number is constructed using a perturbation approach. The theory is applied to the case of tokamak H-modes with shielded resonant magnetic perturbations (RMPs) present indicating RMPs can be destabilizing to intermediate-n peeling-ballooning modes.
In present day devices, the external kink ideal MHD instability establishes hard operational boundaries for both the tokamak and the Reversed Field Pinch (RFP) configurations. An interesting feature of it is that its growth rate critically depends on the device passive boundary characteristics and this can slow it down to time scales accessible to modern real time feedback control systems, normally using external active coils as actuators. 3D passive structures and external fields play a key role in determining physics and control of this instability. This is in particular true for equilibria with multimodal unstable RWM spectra where modes can couple to specific 3D features of passive and active magnetic boundary. In the paper we will present recent data and simulations from RFX-mod, a medium size (R = 2 m, a = 0.459 m) device able to confine RFP and tokamak plasmas with currents up to 2 MA and 120 kA, respectively. Successful quantitative modeling of multimodal RWM control experiments performed using different actuator configurations will be presented and commented. (author)