Richtmyer-Meshkov Instability Experiments Research Articles

Robust implementation of Physical Regime Sensitivity and demonstration on Richtmyer–Meshkov Instability experiments

We present a robust analytic implementation of Physical Regime Sensitivity (PRS), which quantifies sensitivity of an experiment or application to regimes of a material model’s independent variables rather than to model parameters. The new PRS implementation is tested on impact-driven Richtmyer–Meshkov Instability (RMI) strength experiments on tantalum. Sequential PRS hydrocode simulations perturbed strength in local regimes of independent variables like strain rate to quantify the resulting effects on experimentally measured maximum spike velocities in the instabilities. The numeric behavior of the sensitivity calculation is investigated regarding mesh convergence and the parameters controlling the strength perturbation. The sensitivities generally converge with mesh size at least as quickly as the underlying RMI simulations. A wide range of perturbation amplitudes produced similar normalized sensitivities, indicating the perturbation is not changing physical behavior in the simulation. Adjusting the range (width) over which the strength is perturbed allows for resolving fine sensitivity features covering narrow regimes of independent variables or more broad regimes for general interpretation. For interpreting RMI, PRS shows that the maximum spike velocity of the instability is most sensitive to a narrow regime of strain rates near 107/s, which occurs inside the spike as strength effects arrest the instability. The PRS analyses revealed that a modification to the experimental metric used to assess strength would better isolate the strength effects in the regimes of most interest. Using the new metric to generate pressure PRS curves revealed that sensitivities to strength at near-zero pressure were 3.5 times greater than at the high-pressure shock state, supporting the practice of using RMI to isolate strain rate effects when combined with high-pressure experiments. It is also shown that a simple, calibrated constant strength model can reproduce PRS sensitivities of a complex, multivariate Preston–Tonks–Wallace strength model quite well, which supports the robustness of PRS and its utility for experimental design and interpretation prior to the availability of a sophisticated material strength model.

Multiscale Richtmyer-Meshkov instability experiments to isolate the strain rate dependence of strength.

Theoretical analysis of Richtmyer-Meshkov instability (RMI) experiments for solid strength shows that the strain rate for a given shock should be inversely proportional to the length scale of the sine wave perturbations when η_{0}k, the nondimensional amplitude to wavelength ratio, is held fixed. To isolate the effect of strain rate on strength, free-surface RMI specimens of annealed copper were prepared with three perturbation regions with the same η_{0}k but different length scales, characterized by the wavelength λ varying by a factor of 4.9 from 65 to 130 to 320µm. Three such targets with different fixed η_{0}k^{'}s were impacted to a shock pressure of 25 GPa, and the instability evolution was measured with photon Doppler velocimetry. Strengths estimated by comparing hydrocode simulation to the data increased from 700 to 1200 MPa as λ decreased. The different η_{0}k targets exercised increasing amounts of plastic strain yet showed no evidence of strain hardening. Physical regime sensitivity analysis determined that for 320-65µm wavelength perturbations, the effective strain rates increased from 8.7×10^{6} to 3.3×10^{7}s^{-1}, a factor of 3.8. Thus, the predicted strain rate scaling was mostly achieved but slightly suppressed by increased strength at higher rates. The RMI strength estimates were plotted against constitutive testing data on copper from the literature to show striking evidence of the strength upturn at higher strain rates.

A broad study of tantalum strength from ambient to extreme conditions

By combining experiments and modeling from three US national laboratories, we explore compressive strength in a well-characterized material, tantalum, across pressures from zero to over 350 GPa, strain-rates from 10−3/s to 108/s and temperatures from 148 K to 3800 K. Strength values from 40+ experiments are shown to vary by nearly two orders of magnitude, from 0.15 GPa to over 10 GPa. Cross-comparison of these results allows pressure and strain-rate dependencies to be isolated, and strength increases more significantly with pressure than with strain rate over the range studied. Simulations using Preston-Tonks-Wallace, Livermore Multi-Scale, and Kink-Pair strength models test modeling capabilities and provide further insight into strength mechanics. The widely-used assumption in those models of shear-modulus scaling underpredicts strength by a factor of about two at extreme pressures in pulsed-power planar ramp-release experiments, which largely isolate pressure effects. Richtmyer-Meshkov Instability experiments, which largely isolate strain rate effects at ∼107/s, suggest that modeling assumptions about mechanisms at the highest rates need further study. Laser-driven Rayleigh-Taylor instability experiments, which simultaneously probe extreme pressures and strain rates, provide both model and cross-platform experimental validation. The large-scale collaborative nature of this study covers a wide span of experimental conditions and modeling approaches, allowing for extraordinary insight into dynamic strength.

A dislocation-based dynamic strength model for tantalum across a large range of strain rates

We present a dislocation-based strength model for tantalum that captures the plastic deformation at high strain rates above 103s−1. The model has its origins in molecular dynamic simulations and it is implemented in a 3D continuum framework. We calibrate and validate the model using Split Hopkinson Pressure Bar, plate impact, and Richtmyer–Meshkov instability experiments. With the validated model, we can computationally generate stress–strain curves at strain rates of 103−107s−1 for samples with various initial dislocation densities. Based on the results, we show that the dynamic yield strength of annealed tantalum at high strain rates is followed by softening since mobile dislocation densities rapidly increase due to the high shear stress. This strain-softening is evident only at the high strain rate regime and it is much less pronounced in cold-worked Ta.

Tamped Richtmyer–Meshkov Instability Experiments to Probe High-Pressure Material Strength

Dynamic interface instabilities such as Rayleigh–Taylor, Kelvin–Helmholtz, and Richtmyer–Meshkov are important in a number of physical phenomena. Besides meriting study because of their role in natural events and man-made applications, they can also be used to study constitutive properties of materials in extreme conditions. Both RTI and RMI configurations have been used to study the strength of solids at high strain rates, though RMI has largely been limited to zero or ambient pressure. Recently, advances in imaging have allowed tamped RMI experiments to be performed in which the pressure is maintained above ambient. In this study, we examine the tamped RMI for determining material strength. Through simulation, we explore the behavior of the jetting material and examine the sensitivity of jetting to material properties. We identify simple scaling laws that relate the key physical parameters controlling jetting, which are compared to previous results from the literature. We use these scaling law and other considerations to examine issues associated with tamped RMI experiments.

Experimental evaluation of shear modulus scaling of dynamic strength at extreme pressures

Recent progress in the development of dynamic strength experimental platforms is allowing for unprecedented insight into the assumptions used to construct constitutive models operating in extreme conditions. In this work, we make a quantitative assessment of how tantalum strength scales with its shear modulus to pressures of hundreds of gigapascals through a cross-platform examination of three dynamic strength experiments. Specifically, we make use of Split–Hopkinson pressure bar and Richtmyer–Meshkov instability experiments to assess the low-pressure strain and strain rate dependence. Concurrent examination of magnetically driven ramp-release experiments up to pressures of 350GPa allows us to examine the pressure dependence. Using a modern description of the shear modulus, validated against both ab initio theory and experimental measurements, we then assess how the experimentally measured pressure dependence scales with shear modulus. We find that the common assumption of scaling strength linearly with the shear modulus is too soft at high pressures and offer discussion as to how descriptions of slip mediated plasticity could result in an alternative scaling that is consistent with the data.

Tantalum strength at extreme strain rates from impact-driven Richtmyer-Meshkov instabilities.

Recently, Richtmyer-Meshkov instability (RMI) experiments driven by high explosives and fielded with perturbations on a free surface have been used to study strength at extreme strain rates and near zero pressure. The RMI experiments reported here used impact loading, which is experimentally simpler, more accurate to analyze, and which also allows the exploration of a wider range of conditions. Three experiments were performed on tantalum at shock stresses from 20 to 34 GPa, with six different perturbation sizes at each shock level, making this the most comprehensive set of strength-focused RMI experiments reported to date on any material. The resulting estimated average strengths of 1200-1400 MPa at strain rates of 10^{7}/s exceeded, by 40% or more, a common power law extrapolation from data at strain rates below 10^{4}/s. Taken together with other data in the literature that show much higher strength at simultaneous high rates and high pressure, these RMI data isolated effects and indicated that, in the range of conditions examined, the pressure effects are more significant than rate effects.

Progress in experiments of converging Richtmyer-Meshkov instability

When a corrugated interface separating two fluids of different properties is subjected to an impulsive acceleration, such as a shock wave, perturbations initially presented on the interface will grow with time and finally develop into turbulent mixing. This type of hydrodynamic instability is generally referred to as Richtmyer-Meshkov (RM) instability. RM instability is a significant topic in fluid mechanics, and has become increasingly attractive in recent years due to its academic significance in vortex dynamics and compressive turbulence as well as important applications in the fields of inertial confinement fusion, supersonic combustion and supernova explosion. For example in inertial confinement fusion, the implosion of the spherically converging shock wave induces intensive mixing between the outer ablator and the inner fuel, and hence greatly decreases the fusion yield. Over the past decades, the RM instability induced by a planar shock wave has been intensively studied through experiments, simulations and theories. Previous studies show that the initial perturbation on the density inhomogeneity subjected to a planar shock wave experiences successively linear growth, nonlinear growth and turbulent mixing. The pressure disturbance and the baroclinic vorticity are found to be the main factors responsible for the perturbation development. However, in most realities, RM instability occurs in a convergent geometry, and the geometry convergence nature would significantly complicate the instability development. So far, the RM instability triggered by a converging shock has seldom been investigated, and the instability development pattern in convergent geometry as well as the influences of the convergence effects, such as the Bell-Plesset (BP) and Rayleigh- Taylor (RT) effects, on the instability development remains unclear. To perform a converging experiment, one has to overcome two crucial challenges in RM instability experiments: producing a stable converging shock wave and generating a well-controlled initial interface in laboratory conditions, and these are very difficult to realize using the current experimental methods. In this paper, we review the converging RM instability experiments in two types of shock tube facilities, i.e., the coaxial-structure converging shock tube and the conventional converging shock tube. Various interface formation techniques developed based on these shock tube test sections of different structures are also discussed. Special attention is paid to the influences of the typical convergence effects, including the BP effect, the RT effect and the compressibility, on the instability development. Finally, based on the existing studies, we propose the following three issues for future experimental study: (1) RM instability induced by high Mach number shock waves; (2) developments of three-dimensional interfaces subjected to an impulsive impact; (3) interaction of a rippled shock with an unperturbed or a perturbed density interface.

Using growth and arrest of Richtmyer-Meshkov instabilities and Lagrangian simulations to study high-rate material strength

Experiments applying a supported shock through mating surfaces (Atwood number = 1) with geometrical perturbations have been proposed for studying strength at strain rates up to 107/s using Richtmyer-Meshkov (RM) instabilities. Buttler et al. recently reported experimental results for RM instability growth in copper but with an unsupported shock applied by high explosives and the geometrical perturbations on the opposite free surface (Atwood number = −1). This novel configuration allowed detailed experimental observation of the instability growth and arrest. We present results and interpretation from numerical simulations of the Buttler RM instability experiments. Highly-resolved, two-dimensional simulations were performed using a Lagrangian hydrocode and the Preston-Tonks-Wallace (PTW) strength model. The model predictions show good agreement with the data. The numerical simulations are used to examine various assumptions previously made in an analytical model and to estimate the sensitivity of such experiments to material strength.

Use of the Richtmyer-Meshkov Instability to Infer Yield Stress at High-Energy Densities

We use the Richtmyer-Meshkov instability (RMI) at a metal-gas interface to infer the metal's yield stress (Y) under shock loading and release. We first model how Y stabilizes the RMI using hydrodynamics simulations with a perfectly plastic constitutive relation for copper (Cu). The model is then tested with molecular dynamics (MD) of crystalline Cu by comparing the inferred Y from RMI simulations with direct stress-strain calculations, both with MD at the same conditions. Finally, new RMI experiments with solid Cu validate our simulation-based model and infer Y~0.47 GPa for a 36 GPa shock.

Design for a high energy density Kelvin–Helmholtz experiment

While many high energy density physics (HEDP) Rayleigh–Taylor and Richtmyer–Meshkov instability experiments have been fielded as part of basic HEDP and astrophysics studies, not one HEDP Kelvin–Helmholtz (KH) experiment has been successfully performed. Herein, a design for a novel HEDP X-ray driven KH experiment is presented along with supporting radiation-hydrodynamic simulation and theory.

An Experimental Study of the Richtmyer‐Meshkov Instability in Microgravity

Richtmyer-Meshkov (RM) instability occurs when a planar interface separating two fluids of different density is impulsively accelerated in the direction of its normal. It is one of the most fundamental fluid instabilities and is of importance to the fields of astrophysics and inertial confinement fusion. Because RM instability experiments are normally carried out in shock tubes, where the generation of a sharp, well-controlled interface between gases is difficult, there is a scarcity of good experimental results. The experiments presented here use a novel technique that circumvents many of the experimental difficulties that have previously limited the study of RM instability in shock tubes. In these experiments, the instability is generated incompressibly, by bouncing a rectangular tank containing two liquids off of a fixed spring. These experiments, which utilize PLIF flow visualization, yield time-motion image sequences of the nonlinear development and transition to turbulence of the instability that are of a quality unattainable in shock tube experiments. Measurements obtained from these images, therefore, provide benchmark data for the evaluation of nonlinear models for the late-time growth of the instability. Because the run time in these experiments is limited, new experiments in the NASA Glenn 2.2 second drop tower, capable of achieving longer run times, are currently under way.

Mix experiments using a two-dimensional convergent shock-tube

This article reports the first Richtmyer–Meshkov instability experiments using an improved version of the Atomic Weapons Establishment convergent shock tube. These investigate the shock-induced turbulent mixing across the interfaces of an air/dense gas/air region. Multipoint ignition of a detonatable gas mixture produces a cylindrically convergent shock that travels into a test cell containing the dense gas region. The mixing process is imaged with shadowgraphy. Sample results are presented from an unperturbed experiment and one with a notch perturbation imposed on one of the dense gas interfaces. The unperturbed experiment shows the mixing across the dense gas boundaries and the motion of the bulk dense gas region. Imposition of the notch perturbation produces a mushroom-shaped air void penetrating the dense gas region. Three-dimensional simulations performed using the AWE TURMOIL3D code are presented and compared with the sample experimental results. A very good agreement is demonstrated. Conducting these first turbulent mixing experiments has highlighted a number of areas for future development of the convergent shock-tube facility; these are also presented.

Turbulent Richtmyer–Meshkov instability experiments with strong radiatively driven shocks

The Richtmyer–Meshkov instability is investigated in the turbulent regime with strong radiatively driven shocks (Mach >10) on the Nova laser [Phys. Rev. Lett. 70, 1806 (1993)]. The targets are planar with near solid density and Atwood number ∼−0.9. The interfacial perturbations are three dimensional (3-D), random, and nonlinear with a broad scale distribution such that they develop into a turbulent mixing zone (TMZ). The TMZ is diagnosed radiographically using x-ray dopants localized to the center of the target to avoid edge effects. Two different diagnostic configurations yield comparable results. The total width of the TMZ is found to increase in time as H∼tΘ, with Θ∼0.5±0.1. When compared to shock tube data, this result supports the suggestion [Phys. Fluids 8, 614 (1996)] that Θ decreases with Mach number. The data are used to test turbulence models and to determine the effective drag coefficient Cd∼2.6±1.2 for potential flow mix models in the high compression regime.

A membraneless experiment for the study of Richtmyer–Meshkov instability of a shock-accelerated gas interface

Previous Richtmyer–Meshkov instability experiments carried out in shock tubes have been hampered by the need to separate the two gases with a thin plastic membrane. As a result, many of these experiments have had poor agreement with the linear stability theory of Richtmyer [Commun. Pure Appl. Math. 23, 297 (1960)]. This limitation has been removed in the present investigation by the use of a novel technique in which the interface is formed by flowing light (N2) and heavy (SF6) gases from opposite ends of a vertical shock tube. Both gases exit the shock tube through slots in the test section walls leaving behind a flat motionless interface which is then given a sinusoidal initial shape by gently oscillating the shock tube at a prescribed frequency in the horizontal direction. A weak shock wave (Ms=1.10), generated in the shock tube, impacts the interface and produces the instability. Photographs of the interface, which is visualized by seeding the heavy gas with a water droplet fog and illuminating it with a strobe light source, provide particularly clear views of the developing instability far into the nonlinear regime. In addition, amplitude measurements obtained from these photographs are found to be in good agreement with Richtmyer’s theory.