scholarly journals Three-dimensional simulations and analysis of the nonlinear stage of the Rayleigh-Taylor instability

1995 ◽  
Vol 13 (3) ◽  
pp. 423-440 ◽  
Author(s):  
J. Hecht ◽  
D. Ofer ◽  
U. Alon ◽  
D. Shvarts ◽  
S.A. Orszag ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Spherical Geometry ◽  
Taylor Instability ◽  
Three Dimensions ◽  
Type Model ◽  
Late Time ◽  
Nonlinear Stage ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

The nonlinear stage in the growth of the Rayleigh-Taylor instability in three dimensions (3D) is studied using a 3D multimaterial hydrodynamic code. The growth of a single classical 3D square and rectangular modes is compared to the growth in planar and cylindrical geometries and found to be close to the corresponding cylindrical mode, which is in agreement with a new Layzer-type model for 3D bubble growth. The Atwood number effect on the final shape of the instability is demonstrated. Calculations in spherical geometry of the late deceleration stage of a typical ICF pellet have been performed. The different late time shapes obtained are shown to be a result of the initial conditions and the high Atwood number. Finally, preliminary results of calculations of two-mode coupling and random perturbations growth in 3D are presented.

scholarly journals Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime

2018 ◽  
Vol 838 ◽  
pp. 320-355 ◽  
Author(s):  
R. V. Morgan ◽  
W. H. Cabot ◽  
J. A. Greenough ◽  
J. W. Jacobs
Keyword(s):  
Rarefaction Wave ◽  
Three Dimensional ◽  
Single Mode ◽  
Taylor Instability ◽  
Nonlinear Regime ◽  
Diffuse Interface ◽  
Late Time ◽  
Two Dimensional ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number, $A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$, where $\unicode[STIX]{x1D70C}_{2}$ and $\unicode[STIX]{x1D70C}_{1}$ are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of $A=0.49$, $A=0.63$, $A=0.82$ and $A=0.94$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber, $k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$, experiments and simulations, where $\unicode[STIX]{x1D706}$ is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.

scholarly journals On the “Early-Time” Evolution of Variables Relevant to Turbulence Models for the Rayleigh-Taylor Instability

2010 ◽  
Author(s):  
Bertrand Rollin ◽  
Malcolm J. Andrews
Keyword(s):  
Turbulence Model ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Early Time ◽  
Variable Density ◽  
Taylor Instability ◽  
Turbulent Regime ◽  
Rayleigh Taylor Instability

We present our progress toward setting initial conditions in variable density turbulence models. In particular, we concentrate our efforts on the BHR turbulence model [1] for turbulent Rayleigh-Taylor instability. Our approach is to predict profiles of relevant variables before fully turbulent regime and use them as initial conditions for the turbulence model. We use an idealized model of mixing between two interpenetrating fluids to define the initial profiles for the turbulence model variables. Velocities and volume fractions used in the idealized mixing model are obtained respectively from a set of ordinary differential equations modeling the growth of the Rayleigh-Taylor instability and from an idealization of the density profile in the mixing layer. A comparison between predicted profiles for the turbulence model variables and profiles of the variables obtained from low Atwood number three dimensional simulations show reasonable agreement.

scholarly journals Arbitrary Lagrange–Eulerian code simulations of turbulent Rayleigh–Taylor instability in two and three dimensions

2003 ◽  
Vol 21 (3) ◽  
pp. 455-461 ◽  
Author(s):  
S.V. WEBER ◽  
G. DIMONTE ◽  
M.M. MARINAK
Keyword(s):  
Linear Growth ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Grid Refinement ◽  
Group Code ◽  
Interface Reconstruction ◽  
Intercomparison Project ◽  
Rayleigh Taylor Instability

We have performed simulations of the evolution of the turbulent Rayleigh–Taylor instability with an arbitrary Lagrange–Eulerian code. The problem specification was defined by Dimonteet al.(2003) for the “alpha group” code intercomparison project. Perfect γ = 5/3 gases of densities 1 and 3 g/cm3are accelerated by constant gravity. The nominal problem uses a 2562× 512 mesh with initial random multiwavelength interface perturbations. We have also run three-dimensional problems with smaller meshes and two-dimensional (2D) problems of several mesh sizes. Under-resolution lowered linear growth rates of the seed modes to 5-60% of the analytic values, depending on wavelength and orientation to the mesh. However, the mix extent in the 2D simulations changed little with grid refinement. Simulations without interface reconstruction gave penetration only slightly reduced from the case with interface reconstruction. Energy dissipation differs little between the two cases. The slope of the penetration distance versus time squared, corresponding to the α parameter inh= αAgt2, decreases with increasing time in these simulations. The slope, α, is consistent with the linear electric motor data of Dimonte and Schneider (2000), but the growth is delayed in time.

scholarly journals Three-dimensional simulations of the Rayleigh–Taylor instability during the deceleration phase

1994 ◽  
Vol 12 (2) ◽  
pp. 163-183 ◽  
Author(s):  
R.P.J. Town ◽  
B.J. Jones ◽  
J.D. Findlay ◽  
A.R. Bell
Keyword(s):  
Inertial Confinement Fusion ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Three Dimensions ◽  
Inertial Confinement ◽  
Deceleration Phase ◽  
Confinement Fusion ◽  
Rayleigh Taylor Instability ◽  
Three Dimensional Simulations

The growth of the Rayleigh-Taylor instability in three dimensions is ex amined during the deceleration phase of an inertial confinement fusion implosion. A detailed discussion of the three-dimensional hydrocode, PLATO, is presented. A review of previous calculations is given, concentrating on theshape of the R-T instability in three dimensions. Results of the growth rate during the linear phase, the saturation amplitude, and the nonlinear evolution are presented.

scholarly journals Dependence of Enstrophy Transport and Mixed Mass on Dimensionality and Initial Conditions in the Richtmyer–Meshkov Instability Induced Flows1

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Ye Zhou ◽  
Michael Groom ◽  
Ben Thornber
Keyword(s):  
Inertial Confinement Fusion ◽  
Initial Conditions ◽  
Broad Band ◽  
Initial Perturbation ◽  
Density Ratio ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Late Time ◽  
Production Term

Abstract This paper presents a comparative study of the enstrophy budget and mixed mass between two- and three-dimensional flows induced by Richtmyer–Meshkov instability (RMI). Specifically, the individual contributions to the enstrophy budget due to the production from baroclinicity and from vortex stretching (which vanishes in two-dimensional (2D) flow) are delineated. This is enabled by a set of two- and three-dimensional computations at Atwood 0.5 having both narrow- and broad-band perturbations. A further three-dimensional (3D) computation is conducted at Atwood 0.9 using an identical narrowband perturbation to the Atwood 0.5 case to examine the sensitivity to density ratio. The mixed mass is also considered with the goal to obtain insight on how faithfully a simplified calculation performed in two dimensions can capture the mixed mass for an inertial confinement fusion (ICF) or other practical application. It is shown that the late time power law decay of variable density enstrophy is substantially different in two and three dimensions for the narrowband initial perturbation. The baroclinic production term is negligible in three dimensions (aside from the initial shock interaction), as vortex stretching is larger by two orders of magnitude. The lack of vortex stretching considerably reduces the decay rate in both narrowband and broadband perturbations in two dimensions. In terms of mixed mass, the lack of vortex stretching reduces the mixed mass in two dimensions compared to three in all cases. In the broadband cases, the spectral bandwidth in the 2D case is wider; hence, there is a longer time period of sustained linear growth which reduces the normalized mixed mass further.

Molecular mixing in Rayleigh–Taylor instability

1994 ◽  
Vol 265 ◽  
pp. 97-124 ◽  
Author(s):  
P. F. Linden ◽  
J. M. Redondo ◽  
D. L. Youngs
Keyword(s):  
Laboratory Experiments ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Diagnostic Techniques ◽  
Taylor Instability ◽  
Numerical Techniques ◽  
Molecular Mixing ◽  
Rayleigh Taylor Instability ◽  
The Subject ◽  
Careful Assessment

Mixing produced by Rayleigh–Taylor instability at the interface between two layers is the subject of a comparative study between laboratory and numerical experiments. The laboratory experiments consist of a layer of brine initially at rest on top of a layer of fresh water. When a horizontal barrier separating the two layers is removed, the ensuing motion and the mixing that is produced is studied by a number of diagnostic techniques. This configuration is modelled numerically using a three-dimensional code, which solves the Euler equations on a 1803 grid. A comparison of the numerical results and the experimental results is carried out with the aim of making a careful assessment of the ability of the code to reproduce the experiments. In particular, it is found that the motions are quite sensitive to the presence of large scales produced when the barrier is removed, but the amount and form of the mixing is not very sensitive to the initial conditions. The implications of this comparison for improvements in the experimental and numerical techniques are discussed.

scholarly journals Rayleigh-Taylor Instability: A Status Review of Experimental Designs and Measurement Diagnostics

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Arindam Banerjee
Keyword(s):  
Initial Conditions ◽  
Nonlinear Models ◽  
Imaging Techniques ◽  
Mixing Layer ◽  
Single Mode ◽  
Taylor Instability ◽  
Experimental Designs ◽  
Late Time ◽  
Buoyancy Driven Flows ◽  
Rayleigh Taylor Instability

Abstract The focus of experiments and the sophistication of diagnostics employed in Rayleigh-Taylor instability (RTI) induced mixing studies have evolved considerably over the past seven decades. The first theoretical analysis by Taylor and the two-dimensional experimental results by Lewis on RTI in 1950 examined single-mode RTI using conventional imaging techniques. Over the next 70 years, several experimental designs have been used to creating an RTI unstable interface between two materials of different densities. These early experiments though innovative, were arduous to diagnose and provided little information on the internal, turbulent structure and initial conditions of the RT mixing layer. Coupled with the availability of high-fidelity diagnostics, the experiments designed and developed in the last three decades allow detailed measurements of various turbulence statistics that have allowed broadly to validate and verify late-time nonlinear models and mix-models for buoyancy-driven flows. Besides, they have provided valuable insights to solve several long-standing disagreements in the field. This review serves as an opportunity to discuss the understanding of the RTI problem and highlight valuable insights gained into the RTI driven mixing process with a focus on low to high Atwood number (>0.1) experiments.

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