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Fall 2024 started the PhD process for me. This quarter was comprised of two major portions: developing a schedule for completing a PhD program and reading current literature relevant to laser driven Rayleigh-Taylor instabilities.
In this study, ensembles of experimental data are presented and utilized to compare and validate two models used in the simulation of variable-density (Atwood = 0.22), compressible turbulent mixing. Though models of this kind (Reynolds averaged NavierStokes and large-eddy simulations) have been validated extensively with more canonical flows in previous studies, here the present approach offers novelty in the complexity of the geometry, the ensemble-based validation, and the uniformity of the computational framework on which the models are tested. Moreover, all experimental and computational tasks were completed by the authors which has led to a tightly coupled experimental configuration with its “digital twin.” The experimental divergent-shock-tube facility and its data acquisition methods are described and replicated in simulation space. A 2D Euler model which neglects the turbulent mixing at the interface is optimized to experimental data using a Gaussian process. This model then serves as the basis for both the 2D RANS and 3D LES studies that make comparisons to the mixing-layer data from the experiment. A relatively simple RANS model is shown to produce good agreement with experimental data only at late flow development times. The LES ensembles generally show good agreement with experimental data but display sensitivity to the characterization of initial conditions. Resolution-dependent behavior is also observed for certain higher-order statistics of interest. Overall, the LES model successfully captures the effects of divergent geometry, compressibility, and combined nonlinear instabilities inherent to the problem. The successful prediction of mixing width and its growth rate highlight the existence of three distinct regimes in the development of the instability, each with similarities to previously studied instabilities.
Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the $k−2L−a−\mathscr{C}$ and $k−ϕ−L−a−\mathscr{C}$ models by Morgan. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called “tilted rocket rig” inclined RT experiment and in simulation of a shock-accelerated localized patch of turbulence. Here it is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.
The fluid mixing caused by variable-density instabilities is important in a wide variety of scenarios from ocean mixing and astrophysical phenomena to nuclear fusion techniques and atomic weapons. This thesis explores the mixing resulting from a specific instability known as the Blast Driven Instability (BDI). This work investigates the variable density mixing in an explosively driven environment due to the fluid instabilities at the material interfaces. Specifically, diverging Richtmyer-Meshkov (impulsive-acceleration environment) and Rayleigh-Taylor (variable-acceleration environment) instabilities (present in supernova and inertial confinement fusion) are studied using advanced high-speed diagnostics in carefully designed laboratory experiments. The BDI morphology is presented through a time development of Mie scattering images, and steps through the parameter space (varying density ratio and driver speed), highlighting the development of the structures that form during mixing. A scaling criterion is used to relate the two systems of vastly different spatiotemporal scales. Velocity fields in the BDI have been captured for the first time using the high temporal resolution PIV technique. Subsequent analysis of the dynamics of the instability from the velocity fields illustrates the distribution of kinetic energy, the transition to turbulence, and the characteristic growth of the instability are discussed. This study furthers understanding of how blast-driven instability pertains to supernova and inertial confinement fusion science. The morphology of the BDI has been characterized for the first time. This work steps through the parameter space covered in Mie scattering experiments, and how the different parameters contribute to development of structures and mixing. It also examines a scaling of the Atwood number for expanding predictive capabilities to other experimental conditions and simulations. The first collection of velocity fields acquired for the BDI are recorded, and subsequent analysis evaluating the distribution of kinetic energy throughout space and time for two density ratios from the overall parameter space, as well as the transition to turbulence, estimated from a Reynolds number calculated based on momentum mixing are all presented. This information is useful in advancing the development of models to predict physics of high energy density applications where experiments are not always readily available. This research has successfully demonstrated understanding for the time criteria defining regimes where the shock driven (Richtmyer-Meshkov instability) and the buoyancy driven (Rayleigh-Taylor instability) dominates through a parametric study of density variation (Atwood number) and driver speed (Mach number). All this furthers understanding of how the BDI pertains to SN and ICF.
Rayleigh–Taylor (RT) instabilities are important fluid instabilities that arise in inertial confinement fusion (ICF) capsule implosions, and many other contexts. Multi-mode coupling is observed in experiments and plays a substantial role in material mix from RT instabilities. In this work, we study the evolution of highly multimodal perturbations (power law distribution) that approximate those found at manufactured material interfaces. We use simulations of over 2000 different perturbations in the LANL code xRAGE to identify distinct phases in the processes of bubble growth and bubble merger which can be visualized in a 2D phase portrait with clear regimes of mode growth and decay. Our results show that the dynamic evolution of the instability strongly depends on the mode of the perturbations and mode interactions. The merger process accelerates bubble growth. A non-Markovian region and a transition of the instability from: (1) initial exponential growth to (2) linear growth and to (3) quadratic growth and asymptotic behavior, are clearly captured in the phase space. We have developed a quantitative model of bubble growth that reproduces the dynamic behavior of ensembles of perturbations. Implications for ICF capsules designed for robustness against instabilities are discussed.
Here, cylindrical implosion experiments are used to directly measure instability growth in a convergent geometry, providing a wealth of data for model validation. Double cylinders are a natural extension of the platform and enable measurements at a classically unstable interface, the outer surface of the inner cylinder, which experiences no ablative stabilization from the laser drive. However, the utility of this platform relies upon maintaining adequate axial uniformity of the inner cylinder during the implosion. Although previous smaller-scale double cylinder experiments exhibited acceptable levels of axial uniformity, radiation-hydrodynamics simulations of larger-scale double cylinders predict more axial non-uniformity induced by the impedance mismatch as the shock wraps around the axial ends of the inner cylinder. A mechanism to reduce axial non-uniformity in these larger double cylinder implosions is presented, and preliminary experimental data confirms the efficacy of the selected mitigation approach.
Reynolds-Averaged Navier Stokes (RANS) simulations are a popular method for designing ICF experiments, and accurate mixing models are crucial for these simulations to give good predictions. To this end, the present work seeks to demonstrate the Macroscopic Forcing Method (MFM) as a tool for both improving existing RANS models as well as assessing RANS model forms. First, MFM analysis from Lavacot et al. (Phys. Rev. Fluids, 2025) is used to develop the k–L–F model, an extension of the k–L model of Dimonte and Tipton (Phys. Fluids, 2006) that incorporates nonlocality through addition of a turbulent species flux transport equation. MFM is then applied to the k–L–F model along with the k–L and BHR–4 models to assess their forms and compare the model-implied eddy diffusivity moments to those measured from high-fidelity simulations. Furthermore, the analysis reveals that models incorporating nonlocality (k–L–F and BHR–4) match the high-fidelity simulation data better than purely local models (k–L), both in terms of mean fields and eddy diffusivity moments. However, all of the considered RANS models struggle to match temporal moments at high Atwood numbers, highlighting the importance of temporal nonlocality in these regimes and the need for additional improvement even among models incorporating nonlocality.
Iron (Fe) is a primary constituent of terrestrial planetary cores, yet its rheological properties under extreme conditions remain uncertain. Here we present direct measurements of Fe strength at 310-430 GPa pressures and 3700-5800 K temperatures, obtained using Rayleigh-Taylor (RT) instability experiments at the National Ignition Facility. Single-crystal α-Fe samples with [001] and [111] orientations are shock-ramp compressed past the α-ε transition along paths approaching Earth’s inner core conditions. We find that ε-Fe derived from [001] α-Fe is consistently stronger (11-20 GPa) than that from [111] α-Fe (8-18 GPa), contrary to the trend at ambient conditions. Large-scale molecular dynamics simulations reproduce this atypical strength anisotropy and attribute it to microstructural evolution during the phase transition and subsequent ε-phase plasticity. Ripple growth analysis further constrains viscosities of 100-170 Pa·s under the driven conditions. Our results provide experimental benchmarks for Fe rheology at inner-core conditions, with implications for seismic anisotropy and the geodynamo.
The importance of mitigating the Rayleigh–Taylor instability (RTI) in inertial confinement fusion (ICF) is critical to successfully achieve high gain fusion yield. Consequently, understanding the seed mechanisms of RTI and the potential evolution of RTI in ICF relevant conditions is crucial. Single feature perturbations consistently demonstrate non-linear RTI evolution, for which an experimental platform on OMEGA-EP is developed. Manufacturing defects introduced into the target design require exploration of unanticipated changes to RTI development and an identification of targets that will still render quantifiable physics results. Consequently, it is presented that the inherent 3D nature of experimental targets necessitates 3D modeling for accurate design work and predictive modeling of experimental targets, especially when high resolution imaging diagnostics, like Fresnel Zone Plates, are utilized. A study of the morphology of the RTI evolution due to changing initial conditions and the presence of an externally applied magnetic field are also explored. Experimental data show thin-layer RTI morphology comparable to resistive magneto hydrodynamic 3D results. A discussion on the impacts of an externally applied magnetic field makes the case for continued efforts to observe a magnetic field's impact on RTI morphology.
The dynamic-shell concept for inertial confinement fusion (ICF) uses an initially homogeneous target and a carefully shaped laser pulse to form a shell and implode it. The laser pulse consists of a series of pickets that drive shocks into the target. The first few shocks converge inwards and rebound from the center of the target, creating an expanding, low-density plasma. Subsequent shocks are launched into the expanding plasma and eventually coalesce to form a shell, which is then imploded with a traditional ICF laser pulse. This study describes radiation-hydrodynamic simulations that investigate the sensitivity of dynamic-shell targets to imperfections in the laser drive. A one-dimensional (1D) study looks at mistiming and power variations in the pickets and a two-dimensional (2D) study examines irradiation perturbations imposed by the laser-beam geometry. Simulations show that less than ~2% power imbalance or 200 ps timing variation in the pickets is sufficient to keep the yield above 90% of the maximum. Additionally, the 2D simulations show that 72 or more beams are required to keep irradiation nonuniformities low enough to obtain fusion yields close to that of 1D simulations.
Here, we generalize the “filtering spectrum” to probe scales along different directions by spatial coarse-graining. This multidimensional filtering spectrum quantifies the spectral content of flows that are not necessarily homogeneous. From multidimensional spectral information, we propose a simple metric for shape anisotropy at various scales. The method is applied to simulations of two-dimensional (2D) and 3D Rayleigh-Taylor (RT) turbulence, which is inhomogeneous and anisotropic. We show that 3D RT has clear shape anisotropy at large scales with approximately 4:3 vertical to horizontal aspect ratio but tends toward isotropy at small scales as expected. In sharp contrast, we find that RT in 2D simulations, which are still the main modeling framework for many applications, is isotropic at large scales and its shape anisotropy increases at smaller scales where structures tend to be horizontally elongated. While this may be surprising, it is consistent with recent results that large-scale isotropy in 2D RT is due to the generation of a large-scale overturning circulation via an upscale cascade, while small-scale anisotropy is due to the stable stratification resultant from such overturning and the inefficient mixing in 2D.
The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. [J. Fluid Mech. 985, A47 (2024)], the present work extends the macroscopic forcing method to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers (𝐴 = 0.05, 0.3, 0.5, 0.8). It is found that as 𝐴 increases, (1) the eddy diffusivity moments become asymmetric and (2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher 𝐴. There is a particularly strong temporal nonlocality at higher 𝐴, suggesting stronger history effects. In conclusion, the implications of these findings for closure modeling for finite-Atwood RT are discussed.
This report contains a compilation of key results and findings from the ACT project “Determining Exact RANS Operators with the Macroscopic Forcing Method.” The Macroscopic Forcing Method (MFM), a numerical tool for determining closure operators, is used to measure eddy diffusivity moments in Rayleigh-Taylor (RT) instability. It is first applied to low-Atwood 2D RT instability; that work is then extended to 3D RT at different finite Atwood numbers. It is found that nonlocality is important for modeling the mean scalar transport closure operator in RT mixing. Additionally, work is done to improve the statistical convergence of MFM for chaotic problems like RT mixing.
The classical Richtmyer-Meshkov instability (RMI) is a hydrodynamic instability characterizing the evolution of an interface following shock loading. In contrast to other hydrodynamic instabilities such as Rayleigh-Taylor, it is known for being unconditionally unstable: regardless of the direction of shock passage, any deviations from a flat interface will be amplified. In this article, we show that for negative Atwood numbers, there exist special sequences of shocks which result in a nearly perfectly suppressed instability growth. Here, we demonstrate this principle computationally and experimentally with stepped fliers and phase transition materials. A fascinating immediate corollary is that in specific instances, a phase-transitioning material may self-suppress RMI.
Here, we demonstrate the onset of Rayleigh-Bénard convection (RBC) near the fuel-ablator interface of inertial confinement fusion (ICF) implosion simulations for the scenario in which Rayleigh-Taylor or Richtmyer-Meshkov instabilities are suppressed. This convective heating within the cold fuel can degrade the adiabat and therefore performance of ICF implosions even without mixing of fuel and ablator. Our work suggests additional considerations to realize design adiabats in otherwise ideal ICF implosions: first, via control of the temperature differences between ablator and fuel and, second, control of the fuel acceleration which we show has a complex interplay with the RBC dynamics.
The direct-drive double cylinder experimental platform is a high-energy-density (HED) science platform designed to image an imploding cylindrical target. The target consists of a directly-driven outer cylinder and a shock-and-collision driven inner cylinder. The purpose of this platform is to study hydrodynamic instability growth on the inner cylinder, the outer surface of which is classically Rayleigh-Taylor unstable during the acceleration phase. We present results from recent experiments at the OMEGA laser facility. These experiments were designed as a proof-of-principle for the platform, using the same cylinder exterior dimensions and direct-drive beam configuration as previous single cylinder experiments. In these experiments, three sets of targets were fielded: no machined perturbations (smooth), a sinusoidal mode-10 perturbation on the outer surface of the inner cylinder, and a mode-20 perturbation on the outer surface of the inner cylinder. The primary diagnostic was a gated x-ray framing camera which imaged the backlit inner cylinder on-axis for sixteen frames over a time window of 1 ns for each shot. A second side-lit radiograph captured one image per shot, diagnosing axial uniformity. In this report we include an overview of the results from both the backlighter and the sidelighter diagnostics. We discuss at length the experimental analysis process. Finally, we present the results of the smooth target implosion trajectory and compare them to post-shot simulations. We see favorable agreement between simulation and experiment.
The influence of magnetic fields in high-energy-density (HED) systems is a widely unexplored field of research that can play an important role in magnetized inertial confinement fusion (ICF) and in astrophysical systems. Hydrodynamic instabilities are presently believed to be the dominant degradation mechanism in ICF implosions. Therefore, understanding the influence of an imposed B-field on RT growth is important for future mitigation strategies as well as fundamental physics of ICF implosions that utilize B-fields for enhanced performance. The Crab Nebula, one of the most observed objects in our universe, contains elongated spikes of material created by hydrodynamic instabilities, however these spikes do not break-up and become turbulent as they evolve late in time. One hypothesis for this behavior is that B-fields around these spikes prevent vortex generation typical in these types of systems.
Here, an experiment was performed on the OMEGA EP Laser System to investigate the effects of magnetic fields on laser imprint. A 30 µm thick CH target was driven by a single beam delivering 3.0 kJ of UV energy in a 5 ns square pulse without smoothing by spectral dispersion. The Rayleigh-Taylor amplification of this beam's imprint on the target surface was monitored using face-on gated x-ray radiography from a Gd backlighter. Magnetic fields of up to 45 T were applied normal to the target surface. Analysis of the resulting radiographs shows a 60 ± 13% increase in the spectrally resolved surface perturbation amplitudes, consistent at all times and for all unsaturated frequencies. This consistency indicates that the increase in perturbation amplitudes was due to a change in the initial amplitudes rather than Rayleigh-Taylor growth. This is supported by the trajectory of individual modes and the inferred time-averaged perturbation growth rates. Laser imprint is therefore inferred to have increased due to strong magnetic fields that remain in the conduction zone of the target, suppressing off-axis electron motion and limiting the effects of thermal smoothing.