On the “Early-Time” Evolution of Variables Relevant to Turbulence Models for the 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.

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

An Appropriate Metric to Switch on a Turbulence Model for Rayleigh-Taylor Instability Driven Mixing

10.1115/ajk2011-16017 ◽

2011 ◽

Author(s):

Bertrand Rollin ◽

Malcolm J. Andrews

Keyword(s):

Turbulence Model ◽

Inertial Confinement Fusion ◽

Initial Conditions ◽

Turbulence Models ◽

Variable Density ◽

Taylor Instability ◽

Engineering Applications ◽

Modal Model ◽

Rt Instability

Rayleigh-Taylor (RT) instability occurs at a perturbed interface between fluids of different densities, when the lighter fluid is accelerated into the heavier fluid (∇p · ∇ρ < 0, where p is pressure, and ρ is density). In time, as the two fluids seek to reduce their combined potential energy, the mixing becomes turbulent. This fundamental instability is observed, and plays a key role, in numerous natural phenomena, e.g. supernovae explosions, and in engineering applications, e.g. Inertial Confinement Fusion (ICF). The importance of initial condition (ICs) effects on the growth and mixing of Rayleigh-Taylor instability open an opportunity for “design” of RT turbulence for engineering, and question our current predictive capability. Indeed, commonly used turbulence models used for engineering applications are tuned for fully developed turbulence, whereas RT instability is a dynamic process that evolves toward turbulence under the influence of ICs. Therefore, our efforts aim at defining a procedure for properly accounting for initial conditions in variable density (RT) turbulence models. Our strategy is to have a model for the “early” evolution of the RT instability that will produce the initial conditions for the turbulence model. We already dispose of a modal model to evolve the RT mixing layer starting from almost any initial conditions. The present work is a first look at determining an appropriate metric for switching from the modal model to a variable density turbulence model.

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

Journal of Turbulence ◽

10.1080/14685248.2013.790549 ◽

2013 ◽

Vol 14 (3) ◽

pp. 77-106 ◽

Cited By ~ 16

Author(s):

B. Rollin ◽

M. J. Andrews

Keyword(s):

Turbulent Mixing ◽

Initial Conditions ◽

Turbulence Models ◽

Taylor Instability ◽

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

Compressibility effects in Rayleigh–Taylor instability-induced flows

10.1098/rsta.2009.0139 ◽

2010 ◽

Vol 368 (1916) ◽

pp. 1681-1704 ◽

Cited By ~ 31

Author(s):

S. Gauthier ◽

B. Le Creurer

Keyword(s):

Compressible Flows ◽

Stokes Equations ◽

Initial Conditions ◽

Density Fluctuations ◽

Taylor Instability ◽

Turbulent Regime ◽

Developed Turbulence ◽

Perfect Fluids ◽

Compressibility Effects

We present a tentative review of compressibility effects in Rayleigh–Taylor instability-induced flows. The linear, nonlinear and turbulent regimes are considered. We first make the classical distinction between the static compressibility or stratification, and the dynamic compressibility owing to the finite speed of sound. We then discuss the quasi-incompressible limits of the Navier–Stokes equations (i.e. the low-Mach number, anelastic and Boussinesq approximations). We also review some results about stratified compressible flows for which instability criteria have been derived rigorously. Two types of modes, convective and acoustic, are possible in these flows. Linear stability results for perfect fluids obtained from an analytical approach, as well as viscous fluid results obtained from numerical approaches, are also reviewed. In the turbulent regime, we introduce Chandrasekhar’s observation that the largest structures in the density fluctuations are determined by the initial conditions. The effects of compressibility obtained by numerical simulations in both the nonlinear and turbulent regimes are discussed. The modifications made to statistical models of fully developed turbulence in order to account for compressibility effects are also treated briefly. We also point out the analogy with turbulent compressible Kelvin–Helmholtz mixing layers and we suggest some lines for further investigations.

Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 2. Nonlinear simulations

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.64 ◽

2013 ◽

Vol 721 ◽

pp. 295-323 ◽

Cited By ~ 16

Author(s):

M. O. John ◽

R. M. Oliveira ◽

F. H. C. Heussler ◽

E. Meiburg

Keyword(s):

Oil Recovery ◽

Stokes Equations ◽

Three Dimensional ◽

Viscous Fingering ◽

Variable Density ◽

Taylor Instability ◽

Constant Density ◽

Streamwise Vorticity ◽

Miscible Displacements ◽

AbstractDirect numerical simulations of the variable density and viscosity Navier–Stokes equations are employed, in order to explore three-dimensional effects within miscible displacements in horizontal Hele-Shaw cells. These simulations identify a number of mechanisms concerning the interaction of viscous fingering with a spanwise Rayleigh–Taylor instability. The dominant wavelength of the Rayleigh–Taylor instability along the upper, gravitationally unstable side of the interface generally is shorter than that of the fingering instability. This results in the formation of plumes of the more viscous resident fluid not only in between neighbouring viscous fingers, but also along the centre of fingers, thereby destroying their shoulders and splitting them longitudinally. The streamwise vorticity dipoles forming as a result of the spanwise Rayleigh–Taylor instability place viscous resident fluid in between regions of less viscous, injected fluid, thereby resulting in the formation of gapwise vorticity via the traditional, gap-averaged viscous fingering mechanism. This leads to a strong spatial correlation of both vorticity components. For stronger density contrasts, the streamwise vorticity component increases, while the gapwise component is reduced, thus indicating a transition from viscously dominated to gravitationally dominated displacements. Gap-averaged, time-dependent concentration profiles show that variable density displacement fronts propagate more slowly than their constant density counterparts. This indicates that the gravitational mixing results in a more complete expulsion of the resident fluid from the Hele-Shaw cell. This observation may be of interest in the context of enhanced oil recovery or carbon sequestration applications.

FULLY 3D RAYLEIGH–TAYLOR INSTABILITY IN A BOUSSINESQ FLUID

The ANZIAM Journal ◽

10.1017/s1446181119000087 ◽

2019 ◽

Vol 61 (3) ◽

pp. 286-304 ◽

Cited By ~ 1

Author(s):

S. J. WALTERS ◽

L. K. FORBES

Keyword(s):

Numerical Calculation ◽

Spectral Method ◽

Large Scale ◽

Three Dimensional ◽

Early Time ◽

Taylor Instability ◽

3D Geometry ◽

Linearized Theory ◽

Boussinesq Fluid

Rayleigh–Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present a linearized theory for arbitrary three-dimensional (3D) initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, and compared and contrasted with the early-time linearized theory.

Simulation of the Tilted Rig Experiment

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2012-72320 ◽

2012 ◽

Author(s):

Bertrand Rollin ◽

Malcolm J. Andrews

Keyword(s):

Initial Perturbation ◽

Mixing Layer ◽

Variable Density ◽

Taylor Instability ◽

Two Dimensional ◽

Two Fluids ◽

Eddy Simulation ◽

Type Variable ◽

Variable Density Turbulence

The tilted rig experiment is a derivative of the rocket rig experiment designed to study mixing of fluids by the Rayleigh-Taylor instability. In the latter experiment, a tank containing two fluids of different densities is accelerated downwards between two parallel guide rods by a rocket motor. Misalignment between density and pressure gradients trigger the instability leading turbulence and mixing of the fluids. In the tilted rig experiment, the rocket rig is inclined by few degrees off the vertical before firing, creating a slanted initial perturbation interface. The purpose of the tilted rig experiment was to help with calibration of mixing models, as it is a unique two-dimensional Rayleigh-Taylor instability flow. We reproduce conditions similar to this experiment using a Monotone Integrated Large Eddy Simulation (MILES) technique, and for the first time look at statistics of turbulence quantities that appears in “RANS-type” variable density turbulence model. Our statistics show that for the most part, the turbulence quantities in this two-dimensional Rayleigh-Taylor instability configuration behave in a similar fashion as in the planar Rayleigh-Taylor instability configuration when looking in a direction perpendicular to the mixing layer centerline.

Simulations of the Tilted Rig Experiment Using the xRAGE and FLAG Hydrocodes

Volume 7: Fluids and Heat Transfer, Parts A, B, C, and D ◽

10.1115/imece2012-93094 ◽

2012 ◽

Author(s):

Bertrand Rollin ◽

Nicholas A. Denissen ◽

Jon M. Reisner ◽

Malcolm J. Andrews

Keyword(s):

Turbulence Models ◽

Variable Density ◽

Taylor Instability ◽

Massively Parallel ◽

Mixing Models ◽

Two Dimensional ◽

Arbitrary Lagrangian Eulerian ◽

Two Fluids ◽

Variable Density Turbulence

The tilted rig experiment is a derivative of the rocket rig experiment designed to study mixing of fluids by the Rayleigh–Taylor instability. In this experiment, a tank containing two fluids of different densities is accelerated downwards between two parallel guide rods by a rocket motor. The rocket rig is inclined by a few degrees off the vertical to force a two-dimensional Rayleigh–Taylor instability. Thus, the tilted rig experiment can help calibrate two-dimensional mixing models. Simulations of the tilted rig experiments using two of Los Alamos National Laboratory’s hydrocodes are reported. Both codes, xRAGE and FLAG, are multidimensional, multimaterial, massively parallel, hydrodynamics codes that solve the Euler equations. xRAGE operates in an Eulerian framework, while FLAG operates in an Arbitrary Lagrangian–Eulerian (ALE) framework, with a Lagrange step followed by mesh relaxation and remapping. Direct comparisons between simulations and experimental results are reported, as well as report the behavior of the variable-density turbulence models implemented in the codes.

Molecular mixing in Rayleigh–Taylor instability

Journal of Fluid Mechanics ◽

10.1017/s0022112094000777 ◽

1994 ◽

Vol 265 ◽

pp. 97-124 ◽

Cited By ~ 93

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 ◽

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.

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

Journal of Fluids Engineering ◽

10.1115/1.4048349 ◽

2020 ◽

Vol 142 (12) ◽

Cited By ~ 1

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 ◽

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.