Methodology for Evaluating Tamper Equation of State in Tamped Richtmyer-Meshkov Instability (RMI) Experiments
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Padgiotis, Athena [Sandia National Laboratories (S↗
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Results for “Richtmyer-Meshkov instability”
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Effect of a diffuse interface on the Richtmyer-Meshkov instability
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Pellone, Samuel Louis↗
Investigation of the Limiting Case of Richtmyer-Meshkov Instabilities in High-Explosive Driven Experiments
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Materials science↗
Reduced mixing in inertial confinement fusion with early-time interface acceleration
In inertial confinement fusion (ICF) implosions, the interface between the cryogenic DT fuel and the ablator is unstable to shock acceleration (the Richtmyer-Meshkov instability, RM) and constant acceleration (Rayleigh-Taylor instability, RT). Instability growth at this interface can reduce the final compression, limiting fusion burnup. If the constant acceleration is in the direction of the lighter material (negative Atwood number), the RT instability produces oscillatory motion that can stabilize against RM growth. Theory and simulations suggest this scenario occurred at early times in some ICF experiments on the National Ignition Facility, possibly explaining their favorable performance compared to one-dimensional simulations. In conclusion, this characteristic is being included in newer, lower adiabat designs, seeking to improve compression while minimizing ablator mixing into the fuel.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Differentiable lagrangian shock hydrodynamics with application to stable shock acceleration of density interfaces
We develop a gradient based optimization approach for the equations of compressible, Lagrangian hydrodynamics and demonstrate how it can be employed to automatically uncover strategies to control hydrodynamic instabilities arising from shock acceleration of density interfaces. Strategies for controlling the Richtmyer-Meshkov instability (RMI) are of great benefit for inertial confinement fusion (ICF) where shock interactions with many small imperfections in the density interface lead to instabilities which rapidly grow over time. These instabilities lead to mixing which, in the case of laser driven ICF, quenches the runaway fusion process ruining the potential for positive energy return. Here, we demonstrate that control of these instabilities can be achieved by optimization of initial conditions with ( > 100) parameters. Optimizing over a large parameter space like this is not possible with gradient-free optimization strategies. This requires computation of the gradient of the outputs of a numerical solution to the equations of Lagrangian hydrodynamics with respect to the inputs. We show that the efficient computation of these gradients is made possible via a judicious application of (i) adjoint methods, the exact formal representation of sensitivities involving partial differential equations, and (ii) automatic differentiation (AD), the algorithmic calculation of derivatives of functions. Careful regularization of multiple operators including artificial viscosity and timestep control is required. We perform design optimization of > 100 parameter energy field driving the Richtmyer Meshkov instability showing significant suppression while simultaneously enhancing the acceleration of the interface relative to a nominal baseline case.
Hydrophysics↗
Project DarkStar: Vision for LLNL in 2030
DarkStar was a Strategic Initiative (FY2021-FY2024) to investigate applications of Artificial Intelligence (AI) and Machine Learning (ML) to scientific problems of complex hydrodynamics, shockwave physics and energetic materials. The research focused on physics and engineering design as a process that can be tremendously accelerated through merging AI with advanced physics simulation on exascale-class platforms, and to experimentally validate this revolutionary new approach through dynamic materials campaigns. A central thread of scientific inquiry was in the application of AI to enable human understanding of how to control hydrodynamic instability (which has impacts to areas such as inertial confinement fusion) via engineering features and time-dependent sources. Motivated by an unfinished line of research started by Dr. Johnny von Neumann, AI-enabled simulation approaches were developed that allowed DarkStar researchers to uncover several ground-breaking discoveries regarding hydrodynamic instability, including how to completely suppress Richtmyer-Meshkov instability (RMI). These S&T discoveries, along with other advances, have shown the way for an entirely new approach to time-dependent problems known as inverse design – the idea that complex systems can be developed directly from a final state that is to be achieved and resolve the initial design via satisfying several constraints simultaneously via AI/ML. Through experimental campaigns conducted across a wide range of facilities in the NNSA complex (the High Explosive Application Facility at LLNL, the Dynamic Compression Sector/Advanced Photon Source at Argonne National Lab, and Special Technologies Laboratory at MSTS) the radical new AI/ML approach to engineering complex material dynamics was verified, establishing a new field of study within the realm of shock physics. As advanced manufacturing capabilities continue to develop, the great importance of inverse design as a means to apply that technology effectively for NNSA missions will feature prominently over this decade. DarkStar has positioned NNSA as a world-leader in this newly emerging cross-disciplinary area of AI methods for advanced physics simulation and pioneered multiple novel approaches that have enabled the broader scientific community. By allowing us to see past the horizon, to 2030 and beyond, DarkStar has illuminated the vast potential of AI/ML to impact a wide range of new national security missions and, consequently, multiple areas of further research have already emerged across the NNSA and DOD complex.
42 ENGINEERING↗
Dynamic Strength and Equation of State of Epon 828 and Diethanolamine (DEA) Polymer Epoxy Under Shock Loading
Polymers are increasingly utilized in engineering applications that can experience high loading rates, necessitating increased understanding of their response under such conditions. The tamped Richtmyer-Meshkov Instability (RMI) method was used to characterize the equation of state and dynamic strength of the polymer Epon 828 cured with Diethanolamine (DEA). Plate impact experiments that drove a uniaxial shock compression wave across a sinusoidally corrugated metal-polymer interface were performed to generate shock stresses from 4-12 GPa and strain rates of approximately 1/s in the polymer. X-ray phase contrast imaging recorded the shock motion in the polymer and subsequent interface evolution. Analysis of this data yielded the polymer equation of state and, in conjunction with numerical modeling, the dynamic strength. The equation of state was validated against one-dimensional plate impact experiments from existing literature. The dynamic strength was compared to prior data for Epon 828 and related polymers at lower strain rates and found to exhibit significant strain rate and pressure-hardening effects. The strength of the Epon 828 polymer at 10 6 1/s was found to be approximately 1.5 GPa, suggesting that it is comparable to the strength of high strength metals at these dynamic conditions.
Equation of state↗
Density variance dynamics in disparate shock tubes
This report discusses two experiments which investigate thin layer, heavy curtain fragmentation from the perspective of a Reynolds-Averaged mix model, in drastically disparate experimental regimes. The first, the centimeter/millisecond-scale “Horizontal Shock Tube” (HST) is a compressed-gas piston-driven shock tube experiment. The second, the “Multishock thin layer” (Mshock) experiment performed at the National Ignition Facility, is a micrometer/nanosecond-scale laser-driven shock tube experiment. Both are situations in which a heavy plane layer (a ‘curtain’) is initially suspended in a lighter medium. After being shocked from at least one side, the layer translates while its interfaces evolve due to the excitation of the Richtmyer-Meshkov instability at its surfaces. The evolution of density variance, which initially exists only on the surface of the layer, as it comes to encompass the whole layer interior is used as a description of layer fragmentation and dissolution. These experiments have each been simulated in the Los Alamos National Laboratory multi-physics code xRAGE, which includes fundamental hydrodynamics, extended plasma physics and radiation effects which are important to drive the high-energy density experiment, and the Besnard-Harlow-Rauenzahn (BHR) turbulence model. In each, the principal diagnostic for comparison is an experimental metric for the density (co)variance, b, which tracks the moments of the density field at the curtain interfaces and body. Due to experimental constraints in different regimes (i.e. optical diagnostics can be deployed on conventional shock tubes, while the plasma shock tubes must be imaged by x-rays; interfaces can be imposed to specification on laser-driven experiments, which are stored in the solid phase, while conventional experiments have imperfect control of the flow fields which separate the layer, etc.) the experiments are not designed to be perfect scaled cognates of one another. However, despite the separation of six orders of magnitude of scaling in time, and four in space, we are able to demonstrate that the same turbulence model, operating in the same fashion in the same computer code, is able to reproduce results in each experiment, by tracking evolution due to common relevant physics. Additionally, we will present preliminary work toward density variance comparisons in a single-interface Richtmyer-Meshkov configuration, the conventional fluid “Vertical Shock Tube” (VST) experiment, and the Modal Initial Conditions (ModCons) campaign fielded at the OMEGA-EP laser facility.
42 ENGINEERING↗
A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening
A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.
42 ENGINEERING↗
Equation-of-state measured via x-ray phase contrast imaging for Epon 828/DEA epoxy
Epoxies are a broad class of polymer materials often used as adhesive, structural or binding materials. Epon 828 is an epoxy resin that can be polymerized with a variety of curing agents with the choice of curing agent potentially having an effect on the resulting epoxy polymer’s material properties. In this study, the dynamic behavior of Epon 828 epoxy resin cured with diethanolamine (DEA) is investigated through a series of tamped Richtmyer-Meshkov instability (RMI) experiments measured with x-ray phase-contrast imaging. The measured shock and particle velocities are combined with data in the literature to calibrate Mie-Grüneisen equations-of-state (EOS) for portions and combinations of the collective dataset. The calibrated Mie-Grüneisen EOS are validated against particle velocity profiles extracted from published literature using the Eulerian hydrocode CTH. Here, the Mie-Grüneisen EOS fit to only the tamped RMI experimental data presented here most closely follows the particle velocity profile in the published literature.
36 MATERIALS SCIENCE↗
Vanishing dynamic strength measured in a transient high-pressure phase of tin
This work reports two independent experimental estimations of the dynamic strength of the body-centered tetragonal (bct) 𝛾 phase of tin, which occurs at pressures above about 9 GPa and transforms promptly back to the ambient 𝛽 phase upon pressure release. Measuring strength in such a transient high-pressure phase is challenging. One measurement used free-surface Richtmyer-Meshkov instabilities generated with gas gun impact. Another set of measurements used ramp-release loading in a pulsed-power facility. Strength estimations came from comparison to simulations using a comprehensive multiphase modeling framework that includes equation of state, shear moduli, and strength separately for each phase, and treats mixed-phase regions. Both experimental methods found the 𝛾-phase strength to be very low, within experimental uncertainty of zero. The existing literature on other materials, by contrast, almost universally reports higher strength in transient high-pressure phases compared with ambient phases. Recent Molecular-Dynamics simulations on tin in the literature showed almost zero deviatoric strength during a deformation-induced bct → bct transformation in which one of the 𝛾-phase 𝑎 axes “flips” to the 𝑐 axis. This reorientation currently provides the most plausible explanation for the low observed strength in 𝛾-phase tin.
36 MATERIALS SCIENCE↗
Onset of Rayleigh-Bénard convection at fuel-ablator interfaces in inertial confinement fusion simulations
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.
Physics - Plasma physics↗
Half-hard copper PTW model parameters for plastic deformation calibrated to strain rates from 10 −3 -10 7 /s
This document demonstrates a calibration of the Preston-Tonks-Wallace (PTW) model of plastic deformation that fairly accurately reproduces the flow stress of half-hard copper across strain rates varying by a factor of more than ten billion. The experiments included are quasistatic compression at low rates, Split Hopkinson Pressure Bar (SHPB) compression at intermediate rates, and arrested Richtmyer-Meshkov instability (RMI) growth at high strain rates. The temperatures vary from liquid nitrogen (77 K) to around 500 K. The largest true strains obtained are approximately 0.5. It would be interesting to compare the results to copper deformation data at higher pressures and higher strains.
36 MATERIALS SCIENCE↗
A theoretical/computational framework to measure SiO2 and MgO viscosity at high pressure
The convection of the mantle of Earth and super-Earths is important for many terrestrial phenomena, from plate tectonics to outgassing. Rheological properties, such as viscosity, regulate the transport of thermal energy and mass. However, the viscosity of mantle-relevant materials, such as MgO, at relevant pressures (>120 GPa) are not well constrained. The objective of this work was to develop a computational platform to simulate novel experiments aiming to measure the viscosity of MgO at high pressures. Experiments performed by our collaborators at Johns Hopkins University and Lawrence Livermore National Laboratory use the OMEGA EP laser facility to shock a corrugated MgO interface to 170 GPa, with resulting velocity evolution governed by the viscous Richtmyer-Meshkov instability. We used an in-house hydrocode to simulate this process and thus provide a bound on viscosity by comparing our simulations results to these experiments, as well as to examine the physical processes at play. We simulated the experiments with different values of MgO viscosity (from inviscid to 10,000 Pa∙s) while taking into account the unsteady laser pulse, the material's equation of state, and the rate-dependent constitutive relation for MgO, and the materials' equations of state. Our results suggest that MgO at these conditions has a viscosity within an order of magnitude of 5000 Pa∙s.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A model for the radio brightness of the supernova remnant 1987A
The recently observed rise in radio flux from SN1987A is earlier than predicted in models of the interaction with the observed line-emitting gas. The observed size of the radio source is roughly consistent with the expected position of the SN shock wave and the position of the termination shock of the blue supergiant progenitor wind. The radio increase is attributed to the interaction of the SN shock with this density jump. The required efficiency of electron acceleration and magnetic field amplification is larger than usually occurs in SNe and SNR. Possible reasons for the enhanced radio emission are particle acceleration by the weak reflected shock that travels through the interaction region, and the action of the Richtmyer-Meshkov instability near the initial termination-shock density jump. The action of these mechanisms is time-limited; the prediction of this model is that the radio flux should begin to decline within the next year.
Chevalier, Roger A.↗
Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity
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.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Two-Fluid Interface Instability Being Studied
The interface between two fluids of different density can experience instability when gravity acts normal to the surface. The relatively well known Rayleigh-Taylor (RT) instability results when the gravity is constant with a heavy fluid over a light fluid. An impulsive acceleration applied to the fluids results in the Richtmyer-Meshkov (RM) instability. The RM instability occurs regardless of the relative orientation of the heavy and light fluids. In many systems, the passing of a shock wave through the interface provides the impulsive acceleration. Both the RT and RM instabilities result in mixing at the interface. These instabilities arise in a diverse array of circumstances, including supernovas, oceans, supersonic combustion, and inertial confinement fusion (ICF). The area with the greatest current interest in RT and RM instabilities is ICF, which is an attempt to produce fusion energy for nuclear reactors from BB-sized pellets of deuterium and tritium. In the ICF experiments conducted so far, RM and RT instabilities have prevented the generation of net-positive energy. The $4 billion National Ignition Facility at Lawrence Livermore National Laboratory is being constructed to study these instabilities and to attempt to achieve net-positive yield in an ICF experiment.
Niederhaus, Charles E.↗
Simultaneous measurements of kinetic and scalar energy spectrum time evolution in the Richtmyer–Meshkov instability upon reshock
The Richtmyer–Meshkov instability (Richtmyer, Commun. Pure Appl. Maths , vol. 13, issue 2, 1960, pp. 297–319; Meshkov, Fluid Dyn. , vol. 4, issue 5, 1972, pp. 101–104) of a twice-shocked gas interface is studied using both high spatial resolution single-shot (SS) and lower spatial resolution, time-resolved, high-speed (HS) simultaneous planar laser-induced fluorescence and particle image velocimetry in the Wisconsin Shock Tube Laboratory's vertical shock tube. The initial condition (IC) is a shear layer with broadband diffuse perturbations at the interface between a helium–acetone mixture and argon. This IC is accelerated by a shock of nominal strength Mach number $M = 1.75$ , and then accelerated again by the transmitted shock that reflects off the end wall of the tube. An ensemble of experiments is analysed after reshock while the interface mixing width grows linearly with time. The kinetic and scalar energy spectra and the terms of their evolution equation are calculated and compared between SS and HS experiments. The inertial range scaling of the scalar power spectrum is found to follow Gibson's relation (Gibson, Phys. Fluids , vol. 11, issue 11, 1968, pp. 2316–2327) as a function of Schmidt number when the effective turbulent Schmidt number is used in place of the material Schmidt number that controls equilibrium scaling. Further, the spatially integrated scalar flux follows similar behaviour observed for the kinetic energy in large eddy simulation studies by Zeng et al. ( Phys. Fluids , vol. 30, issue 6, 2018, 064106) while the spatially varying scalar flux exhibits back scatter along the centre of the mixing layer and forward energy transfer in the spike and bubble regions.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗