Shock tube experiments of Richtmyer-Meshkov turbulence with reshock
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Pellone, Samuel Louis↗
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Single-mode perturbation growth in an idealized spherical implosion
This paper considers a dense imploding spherical shell, where perturbations on the inner surface grow due to hydrodynamic instabilities, geometric convergence and compression. A low-convergence implosion with a single spherical harmonic mode perturbation with mode numbers in the range from $\ell$ = 5 to $\ell$ = 100 and at three different amplitudes is considered. The linear theory of Epstein [1] is extended to incorporate reshock, making it applicable to the full implosion process (while perturbations are linear). Linear theory is employed to choose modes such that quantified geometric convergence and compression effects contribute significantly to perturbation growth at the lower mode number, while at the higher mode number the contribution from Rayleigh–Taylor instability dominates. Simulation results from four independent simulation codes (FLASH, HYDRA, Miranda and Flamenco) are presented. The simulation predictions are validated against linear theory pre-reshock and employed to validate the extended theory across the reshock. The simulations continue to substantially non-linear perturbation amplitudes, beyond the limits of the analytical approach, and the presented perturbation amplitudes can inform future non-linear modeling. In this work, the simulated perturbation amplitudes agree to within approximately 10% for most cases, with isolated cases having differences of greater than 50% from the simulated ensemble-mean. This occurs in the case of a low mode number perturbation with a very small amplitude, where the growth of secondary small-scale instabilities leads to substantial differences between the codes after re-shock.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Time-resolved particle image velocimetry measurements of the turbulent Richtmyer–Meshkov instability
Experiments are presented on the Richtmyer–Meshkov instability (RMI) with a three-dimensional, multi-mode initial perturbation. The experiments use a vertical shock tube, where a stably stratified interface is formed between air and sulphur hexafluoride (SF 6 ) via counterflow. A perturbation is imposed at the interface by vertical oscillation of the gas column, forming Faraday waves. The interface is accelerated by a Mach 1.17 (in air) shock wave, and the development of the mixing region between the gases is investigated using particle image velocimetry. Following shock acceleration, a reflected shock wave from the bottom of the shock tube interacts with the mixing layer a second time (reshock). The experiment is initialized with both high and low amplitude perturbations to examine the effect of the perturbation amplitude on measured quantities. The instability growth exponent (θ) is determined from the kinetic energy field using the width of the mixing layer and the decay of kinetic energy, which are found to be in agreement when the flow is most strongly excited. A growth exponent of θ ≈ 0.5 is found for all cases except the high-amplitude reshocked regime (where θ ≈ 0.33). High-amplitude experiments exhibit the transitional outer Reynolds number (Re ≡ hh˙/ν >10 4 ) required for mixing transition following the incident shock, and both experiments are elevated well above this threshold following reshock. However, neither set of experiments meet the more stringent requirements proposed by Zhou et al. (Phys. Rev.E, vol. 67, issue 5, 2003) which include the time dependent aspect of the RMI, an observation which is also made when examining the spectra.
42 ENGINEERING↗
Preshot Report for the NIF Discovery Science DDCyl Campaign: D_Hyd_DDCyl_DRT_DDD/EEE/FFF
The first Discovery Science shot day with the NIF DDCyl campaign demonstrated that Rayleigh-Taylor instability growth during the deceleration phase is scale-invariant for targets that varied in radial dimension and implosion time-scale by a factor of three. Smaller cylindrical implosions at the OMEGA laser facility were compared to the larger cylinders fielded in our first NIF outing. Both sets of targets had an initial m = 20 sinusoidal perturbation machined on the inner surface of an embedded aluminum marker layer, with the amplitude larger by the same factor of three for the NIF-scale targets. We observed growth factors of 14 at late time (t=λ = 7:7 ns, where λ = 1 for OMEGA and λ = 3 for NIF). These used a high density (300 mg/cm³) CH foam core, providing a very long period of deceleration before the rebounding shock hit the incoming spike tips, but the final convergence was only CR≈ 2:25. For our second shot day with this campaign, we are attempting to increase the convergence ratio to CR≥ 5 before reshock, while still measuring instability growth during the convergence/deceleration phase. As discussed in previous reports, the best way to increase convergence before reshock is to lower the density of the central foam. The preshot designs called for the use of a 30 mg/cm³ CH foam, though the as-built foams are closer to 40-42 mg/cm³, which is predicted to result in a final CR≈ 5:1 before reshock. Other than the lower foam density, the target design is identical to those used previously.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Effect of the numerical discretization scheme in Shock-Driven turbulent mixing simulations
In this work, we evaluate the effects of distinct numerical strategies in simulations of shock-driven turbulent mixing. An air-SF 6 -air gas curtain subjected to Mach 1.2 shock-waves is computed with Implicit Large-Eddy Simulation based on three numerical schemes: directional-split with Harten-Lax-van Leer (HLL) solver; directional-unsplit using HLL-Contact (HLLC) solver; and directional-unsplit with HLLC solver and a Low Mach number Correction (LMC). The results illustrate the importance of the numerical strategy to the accuracy of the predictions. Whereas both split and unsplit schemes result in a similar spatial development of the initial shock-driven instability, only the unsplit schemes can predict the turbulent mixing transition after reshock observed by the laboratory experiments. Such feature increases the mixing rate of the two fluids, this being particularly pronounced when the LMC is active due to i) the reduced flow Mach number, and ii) the larger effective Reynolds number. Since the selected mixing problem is driven by the deposition of vorticity at the fluids’ interface, the resultant flow physics is analyzed by investigating the contribution of distinct inviscid mechanisms to the production of vorticity: baroclinicity, stretching, and dilatation. As expected, it is observed that the production of vorticity is initially dominated by the baroclinicity mechanism. Yet, the relevance of the remainder mechanisms is enhanced after the reshock and may even surpass the baroclinicity term.
42 ENGINEERING↗
High speed PLIF study of the Richtmyer–Meshkov instability upon re-shock
The Richtmyer–Meshkov instability (RMI) of a twice-shocked gas interface is researched using high-speed planar-laser induced fluorescence (PLIF) 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 M = 1.8, and then accelerated again by the transmitted shock that reflects off the end wall of the tube. An estimate of the light gas mole fraction is extracted from high-speed imaging using an iterative process that accounts for the nonlinear temperature dependence of the acetone’s fluorescence quantum yield (FQY) and absorption cross-section. A vorticity deposition model for the initial growth rate after reshock is compared with the Mikaelian model for re-shock. Previously used in literature, the number of generations is shown to naturally arise from a normalisation of the scalar transport equation. A self-similar analysis is then further performed using the mole fraction data to explore the evolution of the RMI after reshock and the higher order moments of the light gas mole fraction are compared with a proposed model.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Shockwave compression and dissociation of ammonia gas
We performed a series of plate impact experiments on NH 3 gas initially at room temperature and at a pressure of ~100 psi. Shocked states were determined by optical velocimetry and the temperatures by optical pyrometry, yielding compression ratios of ~5–10 and second shock temperatures in excess of 7500 K. A first-principles statistical mechanical (thermochemical) approach that included chemical dissociation yielded reasonable agreement with experimental results on the principal Hugoniot, even with interparticle interactions neglected. Theoretical analysis of reshocked states, which predicts a significant degree of chemical dissociation, showed reasonable agreement with experimental data for higher temperature shots; however, reshock calculations required the use of interaction potentials. Here, we rationalize the very different shock temperatures obtained, relative to previous results for argon, in terms of atomic versus molecular heat capacities.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Polyimide dynamically compressed to decomposition pressures: Two-wave structures captured by velocimetry and modeling
We performed a series of six plate impact experiments on polyimide and modeled them using new reactant and products equations of state combined with an Arrhenius rate model. The first experiment was diagnosed with embedded electromagnetic velocity gauges through which we directly observed attenuation of the lead shock to an approximately constant state over a propagation distance of roughly 4 mm. Simulated gauge profiles were in excellent qualitative agreement with experiment and suggested a sluggish chemical reaction that did not proceed to completion. The remaining five experiments were conducted in a transmission geometry and diagnosed velocimetrically at the sample/window interface. All five of these yielded profiles with a sharp shock followed by a more gradual approach to maximum interface velocity that was “rounded” to varying degree. These profiles proved difficult to interpret unambiguously due to the convolution of the reactive wave upon first shock with reflection of the lead wave and reshock or release by the window. Comparison with thermochemical calculations strongly suggests that the point of maximum interface velocity corresponds to the equilibrium reshock or release locus. We discuss the implications of this point for the practice of impedance matching based on the reflected Hugoniot of reactive materials such as polymers. The reactant and thermochemical products equations of state are developmental SESAME tables 97710 and 97720, respectively.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
H_Hyd_Shktub_Mshock_III, JJJ, KKK (S01,S02,S03) on the National Ignition Facility
These experiments are the first experiments in the Mshock campaign at the National Ignition Facility. The experiment is scheduled to be conducted on Dec. 14, 2017. The goal of the Mshock campaign is to study feedthrough dynamics of the Richtmyer- Meshkov instability in a thin layer. These dynamics will be studied in both a reshock configuration (initially) and then in a multi-shock configuration where it is planned to reshock the RM instability up to 3 times (four shocks total).
42 ENGINEERING↗
Shock-Induced Solid-State Reactions in Powders: An Experimentally-Based Reassessment
We have performed a series of ten planar impact experiments on six different materials, including certain reactive powders and two inert materials, using Sandia's 89 - mm powder gun at the STAR facility. Time - resolved particle - velocity histories were determined during each of the experiments from one or more VISAR measurements. We have analyzed the results of these measurements 1) by using jump conditions to determine shock and first reshock states and 2) by comparing measured particle velocity histories to synthetic histories predicted by one - dimensional computational analyses using the CTH shock physics code with various models for inert and reactive materials . These comparisons are consistent with the conclusion for these particular reactive powders, that for the duration of shock loading either 1) there is insignificant reaction or 2) the products of any reaction are indistinguishable from the reactants under the experimental conditions. Shock and reshock states were extracted for shock pressures between 5 and 40 GPa. Densities were at or greater than the theoretical maximum zero - pressure density of the starting mixture. This result would be expected if there were no reaction or negligible reaction for the first two shock states. Two experiments were performed on one reactive powder in a "ring - down " geometry to look for evidence of vapor production on pressure release. In both cases, the measured velocity continued to increase slowly over a period of microseconds for the du ration of the experiment. This observation suggests that vapor is produced along the release path, but information about the mechanism for vapor production cannot be extracted from these data. While it is possible that vapor is produced by a shock - induced reaction involving more than one of the original constituents, a simpler interpretation is that the vapor is made up of products of shock - induced decomposition reactions and/or simple vaporization of the constituents as would be expected to take place under the conditions of these experiments. Other sources of vapor could be water adsorbed on grain surfaces and air originally in the voids. Thus it is not necessary to invoke significant recombination reactions to explain the data. However, in the absence of ring - down control experiments, the possibility remains open. These conclusions are different from those of previous workers, but reassessment of a subset of the earlier data yields results consistent with the present work, i.e., the shock compression data do not provide evidence for strong exothermic reactions.
36 MATERIALS SCIENCE↗
Shock experiments on maskelynite-bearing anorthosite
A series of shock recovery experiments over 9.9-60.4 GPa have been carried out on naturally shocked anorthosite from the Mistastin impact structure in Labrador consisting primarily of diaplectic plagioclase glass or maskelynite, An(50), and pyroxene. Petrographic observations of the experimental products indicate that the component minerals and diaplectic glasses generally retained their initial character throughout, the only exception being the increase in fracturing which occurred in the 9.9 GPa shot. Reshocking at pressures higher than the initial shock tends to lower the refractive index of maskelynite. The increase in refractive index of maskelynite reshocked to pressures lower than the initial pressure is interpreted as due to shock densification of the diaplectic glass above the Hugoniot elastic limit and below the mixed phase regime. The data suggest that the low-high-low density transition of maskelynite occurs about 8 GPa below that of the crystal of corresponding composition.
Lambert, P.↗
Efficacy of Gadolinium Gallium Garnet (GGG) as a High-Impedance Optical Window for Shock Wave Experiments
We conducted a series of plate impact experiments to examine the efficacy of < 111>-oriented gadolinium gallium garnet (GGG) single crystals as high-impedance optical window for Photonic Doppler velocimetry (PDV) under shock and double-shock loading. At ~ 123 GPa, shocked GGG remains fully transparent to 1550 nm light for at least 250 ns without any signal degradation. Above 135 GPa, PDV data measured through GGG exhibit a gradual loss of fringe contrast following shock entrance, which eventually leads to transparency loss. The duration for which shocked GGG remains transparent decreases with increasing pressure, and at ~ 148 GPa, it becomes opaque within ~ 20–30 ns. This limits the use of GGG as an interferometry window between ~ 110–140 GPa under single shock loading. Within this pressure range, the refractive index of GGG increases linearly with density: n = 1.552 + 0.054ρ. In contrast to single shock loading, where GGG becomes opaque rapidly above ~ 140 GPa, double-shocked GGG remains optically transparent for over 100 ns when it is first shocked to ~ 123 GPa and then reshocked to significantly higher pressures (215–233 GPa). Our findings raise the exciting possibility of GGG being used as a high-impedance optical window in multi-shock and shock-ramp loading experiments.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
On modeling Richtmyer–Meshkov turbulent mixing widths
In this paper, we present several observations concerning the Richtmyer- Meshkov mixing widths after a shock or reshock passes through the interface between two fluids. The mixing evolves with two oppositely-moving fronts: A bubble ( b ) side into the heavier fluid and a spike ( s ) side into the lighter fluid. Our first observation concerns the reference surface used to partition the total mix width, h b+s , into separate h b and h s widths. Next, we point out that if and when h b and h s obey power-laws t $\theta$ with separate $\theta$ b and $\theta$ s , then h b+s cannot be given, except as an approximation, by a single $\theta$ b+s . Finally, we describe a fully continuous model for h i (t) , i = b, s, or b + s , as the solution to the “drag equation” with a time-dependent $\theta$ i (t) .
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Explosive-induced shock damage in copper and recompression of the damaged region
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36 MATERIALS SCIENCE↗
Shock compression experiments on Lithium Deuteride (LiD) single crystals
Shock compression experiments in the few hundred GPa (multi-Mbar) regime were performed on Lithium Deuteride single crystals. This study utilized the high velocity flyer plate capability of the Sandia Z Machine to perform impact experiments at flyer plate velocities in the range of 17–32 km/s. Measurements included pressure, density, and temperature between ~190 and 570 GPa along the Principal Hugoniot—the locus of end states achievable through compression by large amplitude shock waves—as well as pressure and density of reshock states up to ~920 GPa. As a result, the experimental measurements are compared with density functional theory calculations, tabular equation of state models, and legacy nuclear driven results that have been reanalyzed using modern equations of state for the shock wave standards used in the experiments.
36 MATERIALS SCIENCE↗
A modal wave-packet model for the multi-mode Richtmyer–Meshkov instability
In this work, a model for multimode perturbations subject to the Richtmyer–Meshkov (RM) instability is presented and compared with simulations and experiments for conditions relevant to inertial confinement fusion. The model utilizes the single mode response to the RM impulse whereby its amplitude h(k, t) first grows with an initial velocity V 0 ∝ kh(k, 0) that eventually decays in time as 1/kV 0 t. Both the growth and saturation stages are subject to nonlinearities since they depend explicitly on the initial amplitude. However, rather than using the individual mode amplitude h(k, t), nonlinearity is taken to occur when the root-mean-square amplitude h rms (k, t) of a wave-packet within wavenumbers k ± δk becomes comparable to 1/k. This is done because nearby sidebands can act in unison for an auto-correlation distance 1/δk beyond nonlinearity as observed in the beam-plasma instability. Thus, the nonlinear saturation amplitude for each mode is reduced from the usual 1/k by a phase space factor that depends on the physical dimensionality, as in the Haan model for the Rayleigh–Taylor instability. In addition, for RM, the average value of kh rms for the initial spectrum is used to calculate a nonlinear factor F NL that reduces V 0 , as observed for single modes. For broadband perturbations, the model describes self-similar growth ∝t θ as successively longer wavelength modes reach saturation. The growing and saturated modes must be discerned because only the former promote θ and are enhanced by reshock and spherical convergence. All of these flows are described here by the model in good agreement with simulations and experiments.
42 ENGINEERING↗
Impact of Numerical Hydrodynamics in Turbulent Mixing Transition Simulations
Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.
74 ATOMIC AND MOLECULAR PHYSICS↗
Diamond formation in double-shocked epoxy to 150 GPa
We present measurements of diamond formation in doubly shocked Stycast 1266 epoxy (comprising C, H, Cl, N, and O) using in situ x-ray diffraction. Epoxy samples were reshocked against a LiF window to pressures between 80 and 148 GPa in experiments at the Omega Laser Facility. Furthermore, the pressure and temperature conditions were diagnosed in situ using velocimetry and optical pyrometry, respectively. X-ray diffraction patterns of the compressed epoxy are consistent with cubic diamond (Fd3¯m), indicating that diamond can precipitate not only from twice-shocked CH polystyrene [Kraus et al. Nat. Astron. 1, 606 (2017)] at these conditions but also from twice-shocked CH polymers with the addition of oxygen, nitrogen, and chlorine. These results, in combination with previous works on CH, CH 2 , CH 4 , and methane hydrate, support that diamond often, but not always, forms from CH-based compounds at extreme pressures and temperatures, indicating that the chemical composition, thermodynamic compression path, and kinetics play an important role.
36 MATERIALS SCIENCE↗