Parametric Study of Three-Dimensional Turbulent Shock Wave Boundary Layer Interactions on an Axisymmetric Cone
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Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. Here, in this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy Z S , and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.
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The ongoing improvement in laser technology and target fabrication is opening new possibilities for diagnostic development. An example is x-ray phase-contrast imaging (XPCI), which serves as an advanced x-ray imaging diagnostic in laser-driven experiments. In this work, we present the results of the XPCI platform that was developed at the OMEGA EP Laser-Facility to study multi-Mbar single and double shocks produced using a kilojoule laser driver. Two-dimensional radiation-hydrodynamic simulations agree well with the shock progression and the spherical curvature of the shock fronts. It is demonstrated that XPCI is an excellent method to determine with high accuracy the front position of a trailing shock wave propagating through an expanding CH plasma that was heated by a precursor Mbar shock wave. Furthermore, the interaction between the rarefaction wave and the shock wave results in a clear signature in the radiograph that is well reproduced by radiation-hydrodynamic simulations.
Interactions between shock waves and gas bubbles in a liquid can lead to bubble collapse and high-speed liquid jet formation, relevant to biomedical applications such as shock wave lithotripsy and targeted drug delivery. This study reveals a complex interplay between acceleration-induced instabilities that drive jet formation and radial accelerations causing overall bubble collapse under shock wave pressure. Using high-speed synchrotron X-ray phase contrast imaging, the dynamics of micrometre-sized air bubbles interacting with laser-induced underwater shock waves are visualised. These images offer full optical access to phase discontinuities along the X-ray path, including jet formation, its propagation inside the bubble, and penetration through the distal side. Jet formation from laser-induced shock waves is suggested to be an acceleration-driven process. A model predicting jet speed based on the perturbation growth rate of a single-mode Richtmyer–Meshkov instability shows good agreement with experimental data, despite uncertainties in the jet-driving mechanisms. The jet initially follows a linear growth phase, transitioning into a nonlinear regime as it evolves. To capture this transition, a heuristic model bridging the linear and nonlinear growth phases is introduced, also approximating jet shape as a single-mode instability, again matching experimental observations. Upon piercing the distal bubble surface, jets can entrain gas and form a toroidal secondary bubble. Linear scaling laws are identified for the pinch-off time and volume of the ejected bubble relative to the jet’s Weber number, characterising the balance of inertia and surface tension. At low speeds, jets destabilise due to capillary effects, resulting in ligament pinch-off.
The effort to prevent or mitigate the effects of an impact on Earth is known as planetary defense. A significant component of planetary defense research involves risk assessment. Much of our understanding of the risk from near-Earth objects comes from the geologic record in the form of impact craters, but not all asteroid impacts are crater-forming events. Small asteroids explode before reaching the surface, generating an airburst, and most impacts into the ocean do not penetrate the water to form a crater in the sea floor. The risk from these non-crater-forming ocean impacts and airbursts is difficult to quantify and represents a significant uncertainty in our assessment of the overall threat. We are currently working to better understand impact scenarios that can generate dangerous tsunamis. One of the suggested mechanisms for the production of asteroid–generated tsunamis is by direct coupling of the pressure wave to the water, analogous to the means by which a moving weather front can generate a meteotsunami. To test this hypothesis, we ran a series of airburst simulations and provided time-resolved pressure and wind profiles to use as source functions for tsunami models. We used the CTH hydrocode to model the various airburst scenarios to compare to the results of other simulations and provide time dependent boundary conditions as input to shallow-water wave propagation codes. The strongest and most destructive meteotsunamis are generated by atmospheric pressure oscillations with amplitudes of only a few hPa1 (mbar), corresponding to changes in sea level of a few cm. The resulting wave is strongest when there is a resonance between the ocean and the atmospheric forcing. A Proudman resonance takes place when the atmospheric disturbance’s translational speed (U) equals the longwave phase speed $\sqrt{gh}$ of shallow water wave. Coupling is strongest when the Froude number (Fr=U/c) is unity. A weather front propagates much slower than the speed of sound, so meteotsunamis are most common and dangerous in shallow bodies of water such as the Mediterranean Sea or Lake Michigan. By contrast, the blast wave from an airburst or crater-forming impact propagates at a speed faster than a tsunami in the deepest ocean, and a Proudman resonance cannot be achieved even though the overpressures are orders of magnitude greater. However, blast wave profiles are N-waves in which a sharp shock wave leading to overpressure is followed by a more gradual rarefaction to a much longer-duration underpressure phase. Even though the blast outruns the water wave it is forcing, the tsunami should continue to be driven by the out-of-resonance gradient associated with the suction phase, which may depend strongly on the details of the airburst or impact scenario. The open question is whether there are any conditions under which such an airburst-driven tsunami can be dangerous enough to contribute to the overall impact risk. We have also identified other potential mechanisms for airburst-generated tsunamis: 1) reaction force at the surface from the plume ejected into space, which carries significant momentum, 2) expanding toroidal vortices at the surface, which travel more slowly than the shock wave and can generate a Proudman resonance in relatively shallow ocean (such as continental shelf), and 3) steam explosion from seawater ablation by a “Type II” (Libyan Desert Glass-type) airburst in which the hot vapor jet descends to the surface. On January 15, 2022, the Hunga-Tonga Hunga-Ha’apai volcano, located approximately 60 km north of Tongatapu, the main island of Tonga, violently erupted with a powerful explosion, culminating the period of volcanic activity that started in December of 2021. This event and resulting tsunamis provided an existence proof for the air pressure wave coupling mechanism we proposed. It also suggests that it can be stronger and more significant over much greater distances than we contemplated, leading to global tsunamis associated with impact events on land as well as in the water. Large atmospheric explosions generate global Lamb waves with larger amplitudes, longer periods, and slower speeds than the local and regional blast waves we modeled prior to that event. This paper reviews our analysis and modeling of airburst-driven tsunamis prior to the 2022 Hunga-Tonga Hunga-Ha’apai tsunami, which was the subject of two presentations at the 2023 Planetary Defense Conference and is the subject of another paper currently in preparation.
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This study examines outflow boundary conditions (BCs) in computational fluid dynamics (CFD) simulations of a transition duct with and without guide vanes that converts supersonic flow exiting a rotating detonation combustor (RDC) to subsonic flow to drive a turbine. Since the flow exiting the transition duct has swirling shock waves with significant spatial and temporal variations in pressure, temperature, and Mach number, imposing proper BCs poses a challenge. To ensure all swirling shock waves exit the transition duct without creating non-physical reflected waves at its outlet, this study examined three outflow BCs: (1) the average pressure imposed at the duct’s outlet, (2) a nonreflecting BC (NRBC) with a specified average pressure imposed at the duct’s outlet, (3) the average pressure imposed at the outlet of an extension duct made up of a buffer layer and a sponge layer. This study is based on the three-dimensional, unsteady density-weighted-ensemble-averaged continuity, Navier–Stokes, and energy equations for a thermally perfect gas closed by the realizable k–ε model and “enhanced” wall functions. The results obtained show that imposing an average pressure at the transition duct’s outlet produces spurious waves that degrade the physical meaningfulness of the solution. When the NRBC was applied, swirling shock waves exited the duct’s outlet without creating spurious waves. However, its usage requires the gas to be thermally, as well as calorically, perfect, which this study shows could be a concern. By imposing the average pressure at the outlet of an extension duct, the gas does not need to be calorically perfect. The results obtained show the effects of the sponge layer’s length and coarsening ratio on damping nonuniformities in non-physical reflected waves to ensure the flow exiting the transition duct’s outlet can do so as if there are no boundaries present and has the desired average pressure—even though the BC is applied at the extension duct’s outlet.
Shock wave–bubble interactions in water manifest rich dynamics driven by a combination of strong pressure and density mismatches. They have a wide variety of applications, including the injection of pharmaceuticals, and through scaling, enable the exploration of various aspects of high-energy-density systems such as inertial confinement fusion. In this work, the interaction between a micrometric nitrogen bubble and a planar shock wave, characterized by a Mach number of M = 1.24 and a peak pressure of p max = 0.57 , is experimentally recorded using ultra-high-speed x-ray phase contrast imaging. Highly resolved radiographs provide access to all phase discontinuities along the beam path, offering quantities such as the time-varying bubble size, the speed of a jet produced during the bubble collapse, and the time evolution of the shock wave front, which are critical benchmark data for numerical scheme validation. This study addresses the lack of well-characterized, repeatable, and high spatiotemporal resolution experiments at negative Atwood numbers by providing shock–bubble visualization and corresponding numerical simulation.
Shock invariant relationship, which was conceived for inert shock waves to derive the 4th power relationship between shock pressure and maximum strain rate, is generalized for reactive shock waves such as Chapman–Jouget detonation and shock-induced vaporization. The generalization, based on the first-order reaction models, is a power function relationship between overall dissipated energy (Δe dis ) and reaction time Δτ such that Δe dis Δτ 1/α = constant, where the power coefficient α is found to be in the range of 2/3–4. Experimental data, though scarce, are consistent with the generalization. Implication of the generalization for inert shocks is also considered and suggests a broad range of the 4th power coefficient including an inequality equation that constrains the shock and particle velocity relationship.
Shock wave interactions with perturbations on a free surface can lead to the inversion and growth of the perturbation and eventual ejection of a jet of material, referred to as an ejecta microjet, from shocked surfaces. Here, this study carries out large-scale molecular dynamics (MD) simulations using single-crystal Cu and Sn systems with a pre-existing groove to characterize the localized gradients in temperatures and pressures generated that render the microjet formation. MD simulations are carried out for three loading orientations (along the [001], [011], and [111] directions) and shock pressures ranging from 16 GPa to 100 GPa to understand the role of temperatures generated at the groove vertex on the formation of ejecta. The simulations suggest that the interaction of the shock wave with the groove results in a localized increase in temperatures, leading to localized softening at the groove vertex and the generation of an ejecta microjet. For Cu systems, the simulations suggest that the orientation effects on shock wave structures, velocities, and localized softening affect the ejecta formation at low pressures. Jetting is only observed when temperatures at the groove vertex are high enough to induce localized softening (close to melting temperature), and the jet velocity increases with shock pressure. In contrast, the loading orientation is rendered inconsequential for Sn systems due to the melting of the material during shock compression at the pressures chosen. The jet velocities are similar, regardless of crystal orientation in Sn systems.
In laser shock experiments, a well-defined, flat-top shock wave at the ablator/sample interface is important for accurately probing material response under uniaxial strain compression. However, the relationship between the ablator thickness and the resulting shock wave characteristics is insufficiently understood, limiting the ability to design optimal experiments. To address this need, we conducted a systematic experimental study using a 100 J laser to shock-compress polyimide ablators to peak stresses ranging from 20.4 to 111.6 GPa. Laser interferometry diagnostics measured the transmitted wave profiles at the ablator/sample interface, consistently showing a single jump followed by a constant peak state before the arrival of release waves. Here, by analyzing shock transit time, flat-top duration, and stress, our results establish a framework for selecting ablator thickness to maximize the flat-top duration, improving the precision and reproducibility of laser shock experiments.
This study conducted integrated experiments and computational modeling to investigate the speeds of a developing shock within granular salt and analyzed the effect of various impact velocities up to 245 m/s. Experiments were conducted on table salt utilizing a novel setup with a considerable bore length for the sample, enabling visualization of a moving shock wave. Experimental analysis using particle image velocimetry enabled the characterization of shock velocity and particle velocity histories. Mesoscale simulations further enabled advanced analysis of the shock wave’s substructure. In simulations, the shock front’s precursor was shown to have a heterogeneous nature, which is usually modeled as uniform in continuum analyses. The presence of force chains results in a spread out of the shock precursor over a greater ramp distance. With increasing impact velocity, the shock front thickness reduces, and the precursor of the shock front becomes less heterogeneous. Furthermore, mesoscale modeling suggests the formation of force chains behind the shock front, even under the conditions of weak shock. This study presents novel mesoscale simulation results on salt corroborated with data from experiments, thereby characterizing the compaction front speeds in the weak shock regime.
The propagation of Mbar-range shock waves in low-density foam materials is of interest to target design in all approaches to inertial confinement fusion, high energy density physics, and laboratory astrophysics. We report absolute Hugoniot measurements for CH 1.72 N 0.086 O 0.37 plastic foams with 73 and 94 mg/cm 3 densities in the 32–107 km/s shock velocity range. The experiments were performed on the shock compression platform developed on the NIKE KrF laser facility at the U.S. Naval Research Laboratory. NIKE's 4 or 8-ns long flat-top laser pulses drive steady shock waves into foam targets at the ablative pressures of 1–7 Mbar. The propagation of the ablation and shock fronts is tracked continuously in time using streaked side-on monochromatic x-ray imaging radiography. The straight x−t trajectories of the shock and ablation fronts in the recorded streak images confirmed their steadiness. The SESAME tabulated equation of state predictions generally agrees with our Hugoniot data within a 95% confidence band. The experimental uncertainty of the evaluated shock density compression ratios remains large, indicating the need for more experiments and improved theoretical understanding of the strong shock propagation mechanisms in dry foams.
Ejecta physics plays an important role in material interfaces that are impacted by a strong shock wave. When a shock impacts a rough surface of solid material and melts it, the Richtmyer–Meshkov instability grows perturbations on the surface, which can eject particles. After release, the ejecta travel through the post-shock compressible flow. To accurately simulate a large number of ejecta particles, an Euler–Lagrange approach is preferred, which requires modeling the subgrid-scale physics involved with fluid–particle interactions. We generalize the previous work from Hsiao et al. (2023) to consider systems of moving particles subject to any loading shock. The following improvements were made: (1) Particles are allowed to move relative to each other (2) Non-planar shocks are accounted for along with allowing for variable shock speeds. As a result, the generalized algorithm was tested with particle-resolved simulations for canonical test cases. The results of these tests are discussed and analyzed.
The Euler equations are a subset of the magnetohydrodynamic (MHD) equations in the infinitely collisional, unmagnetized limit. MHD modeling is central to many areas of plasma physics, ranging from low-temperature glow discharges to inertial confinement fusion. An important aspect of the Euler equations is their ability to describe states with discontinuities, such as shock waves. A standard benchmark test for numerical implementation of the Euler equations is the Sod shock tube. In this test, the system is initialized at rest with a pressure and density discontinuity, which results in a shock wave traveling into the low-pressure region and a rarefaction wave traveling into the high-pressure region. Starting with the presentation of the Euler equations, a numerical algorithm is presented here to solve these equations in one dimension. This is followed by an overview of the Sod shock tube problem that includes the precise initial setup and the analytic solution. Finally, the analytic solution is compared with results from numerical simulations.