Session M10: Flow Instability: Rayleigh-Taylor

Analysis of stable plastic regime of Rayleigh-Taylor instability in elastic-plastic solids

Rayleigh - Taylor instability (RTI) occurs between two materials when their density and pressure gradients are in opposite directions. Most of the past studies involving elastic-plastic (EP) materials have focused on estimating the instability threshold where the material yields and begins to flow. The pure elastic to stable plastic phase transition occurs much earlier than the instability, signifies the first point where the mechanical properties start to vary dramatically, and are rarely addressed in the literature. In this work, the EP transition is explored using a rotating wheel experimental apparatus. The test section attached to the wheel is filled with EP material (mayonnaise) and air such that the free surface of the EP material is driven radially outwards by the centrifugal acceleration. The EP threshold acceleration and the maximum elastic strain that can be fully recovered are explored for different 3D single-mode initial perturbation geometries and acceleration rates. Furthermore, the RT growth of the perturbations in the stable plastic regime is studied by holding the driving acceleration constant at EP transition acceleration until irreversible instability is observed. The perturbation growth is measured continuously, and the driving force based on the material mass, amplitude, and centrifugal acceleration is analyzed.   

Compressible Rayleigh-Taylor Instability with Temperature Variations

Variable transport property effects associated with temperature differences can significantly affect the development of a Rayleigh-Taylor mixing layer.  We consider the idealized configuration of a hotter, less dense fluid pushing against a colder, denser fluid.  Towards obtaining fully resolved simulations of the compressible multi-mode RT instability, comprehensive exploration of 2D simulations at various Atwood numbers, temperature ratios and transport property configurations are performed.  We examine the response of the flow to changes in the transport properties, as well as the long-time behavior and onset of self-similarity.  The temperature differences can enhance profile asymmetries about the interface for flow and mixing statistics such as velocity fluctuation intensities and mass fraction PDFs.  We also track the evolution of turbulent kinetic energy, mass flux and density-specific volume correlation, quantities important for turbulence modeling.   

Numerical Investigations of Plasma Rayleigh-Taylor Instability in ICF Coasting Stage

Accurate simulations of Rayleigh-Taylor instability (RTI) with realistic transport phenomena have been conducted under ICF coasting stage conditions by using a high-order two-fluid plasma solver (Li and Livescu, Phys. Plasmas 26, 012109, 2019). The numerical results show that, for any given Atwood number and hot-spot temperature, the RTI development or lack thereof can be characterized by two critical hot-spot number densities, which increase exponentially with hot-spot temperature and decrease with Atwood number. When the hot-spot number density is smaller than the lower threshold value, RTI is completely suppressed by the electron thermal diffusion and viscous dissipation. Instead, fully developed RTI into chaotic stage (single-mode) or turbulence (multimode) is observed only when the hot-spot number density is larger than the upper threshold value. Though a strong magnetic field (B~10³T) is created by the Biermann battery effect, and its magnitude increases with Atwood number, for all simulations conducted in this study, the self-generated magnetic field is not sufficient to affect the flow dynamics or inhibit the electron thermal conduction because of the extremely large plasma beta (β~10⁵) and small product (x~10^-2) of electron cyclotron frequency and collision time.   

Compressibility Effects on the Rayleigh-Taylor Instability

Rayleigh-Taylor instability (RTI) is important in variety of flows including inertial confinement fusion (ICF). During the coasting stage of ICF, RTI develops between the hot spot and colder surrounding plasma, due to the large temperature and density difference. RTI plays a significant role in the loss of compression and target performance in ICF. In previous works of compressible RTI initial thermal equilibrium is assumed, leading to exponential variation in the background density. Consequently, the effect of compressibility is obscured by that of the background stratification. To isolate compressibility effects, we perform direct numerical simulations (DNS) of RTI with uniform density variation on the two sides of the interface. The speed of sound at the interface is varied and simulations using the gas kinetic method (GKM) are performed for static Mach numbers (M) up to M=0.6. With reference to the  thermal equilibrium case, it is shown that compressibility has a destabilizing effect and the instability grows faster with M. This is notably different from shear flows where compressibility inhibits shear layer growth. Compressibility is also shown to increase the bubble-spike asymmetry in RTI flows. The physics underlying these effects is explored by examining the evolution of pressure and dilatational fields and their role on vorticity dynamics.   

Three- and Four-Equation RANS Modeling of a Small Atwood Number, Transitional Rayleigh–Taylor Mixing Experiment

A priori calibrated three- and four-equation mechanical–scalar Reynolds-averaged Navier–Stokes models [O. Schilling and N. J. Mueschke, Physical Review E 96, 063111 (2017)] are applied to a small Atwood number, transitional Rayleigh–Taylor mixing experiment previously performed in a water channel facility and modeled using direct numerical simulation [N. J. Mueschke and O. Schilling, Physics of Fluids 21, 014106 (2009)]. It is shown that the use of time-dependent model coefficients and initial conditions closely corresponding to those in the experiment are needed to accurately capture transition to turbulence. Comparisons of the mixing layer width, molecular mixing parameter, mean and turbulent fields, and other quantities among the model predictions, experimental data, DNS data, and analytic self-similar solutions are presented are discussed.   

Validation of Two Turbulence Models using High Speed Experimental Data from the Combined RM/RT Instability

High speed experimental data (PIV and Mie Scattering) are presented and used to validate two models commonly used in the simulation of variable density, compressible turbulent mixing. Though these models (Reynolds averaged Navier-Stokes and Large-Eddy Simulation) have previously been validated extensively on more canonical RM and RT flows, the present approach offers a new test case. The combined RM/RT instability, or the Blast Dirven Instability offers a compressible, combined instability in a complex geometry. The models are also validated on a notably uniform computational framework, by the same researchers who took the experimental data, leading to a tightly coupled experimental configuration with its model or "digital twin". The experimental setup of this divergent shock tube is shown along with samples of the high temporally resolved experimental data used for validation. For the model validation, first a non-mixing, 2D computational Euler model is optimized using a Gaussian process comparing simulation outputs to experimental data. This model then serves as the basis for both the RANS and the LES studies that make comparisons to the mixing layer data from the experiment. The RANS model is optimized using a similar Gaussian process. The LES model is validated against experimental data on an ensemble basis, using statistically characterized experimental initial conditions to seed random LES initial conditions. The resulting comparisons of experimental and simulation data for interface trajectory, mixing width, and turbulent kinetic energy are shown.   

Linear and nonlinear stability of two fluid columns of different densities and viscosities subject to gravity

We study the stability of a vertical interface separating two miscible fluid columns of different densities and viscosities subject to gravity. This flow possesses a time-dependent laminar one-dimensional base state with the interface thickness growing as the square root of time (by diffusion). First, numerical integration of the linearized initial value problem is carried out as a function of vertical and spanwise wavenumber, initial time, density and viscosity ratios. Adjoint-based optimization is performed to determine the linearly optimal perturbations (LOPs) that lead to maximum growth of total energy disturbances in finite time. Results indicate that the perturbation energy growth rate at small wavenumbers (less affected by viscosity initially) is dominated by two-dimensional modes (no spanwise variation). Substantial transient growth is observed at higher wave modes initially, followed by asymptotic decay of perturbations at large time. Finally, nonlinear direct simulation of the single-mode LOPs are studied in terms of perturbation energy evolutions, energy cascade, and other statistics relevant to the flow.   

Experimental investigation of the multi-layer Rayleigh-Taylor instability

  Statistically stationary experiments are performed to study the effect of complex stratification pattern on the Rayleigh-Taylor instability. Experiments are conducted in a newly built, blow-down 3-layer gas tunnel facility. Mixing between three gas streams are studied, where the top and bottom streams comprise of air, and the middle stream comprises of air-helium mixture, giving Atwood numbers of the order of 0.1 at the unstable interface between the top and middle streams. There is no shear between these streams. Three experimental cases are investigated, with one middle stream thickness (6 cm) and three Atwood numbers (0.05, 0.1 and 0.25). The growth of the middle layer is measured using back-lit visualization and Mie-scattering techniques. The dynamics of the flow is investigated using particle image velocimetry (PIV) for velocity measurements and laser induced fluorescence (LIF) for density measurements. In addition to extracting quantities of statistical importance from our measurements (like density-velocity correlations), we also look at how different forces fundamentally drive variable density mixing process (using nondimensional parameters like Richardson number), and how such a mixing process reaches an asymptotic state (using the concept of mixing efficiency and molecular mixing parameter). These experiments are of immense significance for atmospheric and oceanic sciences, and variable density turbulence modeling.   

Direct Numerical Simulations of Iso-Thermally Stratified 2D Multi-Mode Compressible Rayleigh-Taylor Instability

Rayleigh-Taylor instability (RTI) occurs at the interface separating two fluids with different densities. The instability is observed when the flow is subjected to an acceleration that is in the opposite direction of the density gradient. Most of the previous scientific literature investigated the RTI under the incompressible assumption, while in many high-density-energy engineering applications and astrophysical phenomena such as inertial confinement fusion and supernova formations, the incompressible assumption may no longer be valid. In this study, the effects of the background iso-thermal stratification strength and Reynolds number on multi-mode two-dimensional RTI are explored with fully compressible direct numerical simulations. It is shown that the increase in the flow compressibility through the strength of the background stratification suppresses the RTI growth and eventually, prevents the RTI mixing layer growth. In addition, the effects of Reynolds number on the height of the suppressed RTI mixing layer are explored. We are also presenting the chaotic behavior within both the weakly, moderately, and strongly stratified RTI mixing layers.   

Deconstructing the Notion of Mergers and Inverse Cascades in 3D Rayleigh-Taylor Flows

We identify two main processes for energy transfer across scales in Rayleigh-Taylor (RT) flows: baropycnal work Λ, due to pressure gradients, and deformation work π, due to flow strain. We show how these fluxes exhibit a quadratic-in-time self-similar evolution similar to RT mixing layer. Λ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales where π takes over. In 3D, π continues a persistent cascade to yet smaller scales, whereas in 2D, π re-channels the energy back to larger scales. This gives rise to a positive feedback loop in 2D-RT (absent in 3D) in which mixing layer growth and the associated potential energy release are enhanced relative to 3D, yielding the well-known larger α values in 2D simulations. Despite higher bulk kinetic energy levels in 2D, small scales are weaker than in 3D. We also find that net upscale cascade in 2D tends to isotropize the large-scale flow, in stark contrast to 3D-RT. These fundamental differences pinpoint the misleading physics inherent to 2D-RT simulations in ICF modeling. Our findings also indicate the absence of net upscale energy transfer in 3D-RT as is often claimed; growth of large-scale bubbles and spikes is not due to "mergers" but solely due to baropycnal work Λ.