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DOE OSTI2024

A generalization of the shock invariant relationship

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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1986

Breakdown of the conservative potential equation

The breakdown of the conservative potential approximation occurs for all the airfoils tested. It develops as soon as the shock waves appear in the flow field. Since shock waves are not properly represented by the potential approximation, it is conjectured that the breakdown is due to the isentropic shock jump condition of the potential approximation.

Salas, M. D.↗

NASA NTRS1985

Transonic aerodynamic and aeroelastic characteristics of a variable sweep wing

The flow over the B-1 wing is studied computationally, including the aeroelastic response of the wing. Computed results are compared with results from wind tunnel and flight tests for both low-sweep and high-sweep cases, at 25.0 deg. and 67.5 deg., respectively, for selected transonic Mach numbers. The aerodynamic and aeroelastic computations are made by using the transonic unsteady code ATRAN3S. Steady aerodynamic computations compare well with wind tunnel results for the 25.0 deg. sweep case and also for small angles of attack at the 67.5 deg. sweep case. The aeroelastic response results show that the wing is stable at the low sweep angle for the calculation at the Mach number at which there is a shock wave. In the higher sweep case, for the higher angle of attack at which oscillations were observed in the flight and wind tunnel tests, the calculations do not show any shock waves. Their absence lends support to the hypothesis that the observed oscillations are due to the presence of leading edge separation vortices and are not due to shock wave motion as was previously proposed.

Goorjian, P. M.↗

NASA NTRS1985

Transonic aerodynamic and aeroelastic characteristics of a variable sweep wing

The flow over the B-1 wing is studied computationally, including the aeroelastic response of the wing. Computed results are compared with results from wind tunnel and flight tests for both low-sweep and high-sweep cases, at 25.0 and 67.5 deg., respectively, for selected transonic Mach numbers. The aerodynamic and aeroelastic computations are made by using the transonic unsteady code ATRAN3S. Steady aerodynamic computations compare well with wind tunnel results for the 25.0 deg sweep case and also for small angles of attack at the 67.5 deg sweep case. The aeroelastic response results show that the wing is stable at the low sweep angle for the calculation at the Mach number at which there is a shock wave. In the higher sweep case, for the higher angle of attack at which oscillations were observed in the flight and wind tunnel tests, the calculations do not show any shock waves. Their absence lends support to the hypothesis that the observed oscillations are due to the presence of leading edge separation vortices and are not due to shock wave motion as was previously proposed.

Goorjian, P. M.↗

DOE OSTI2022

On various mechanisms of shear wave generation from underground chemical explosions in hard rocks

Significant shear waves observed during underground explosions can make them look similar to natural earthquakes. In the near field, they can be caused by the source geometry and emplacement conditions, heterogeneous and anisotropic properties of the rock mass, relaxation of a non-uniform in situ stress around the source after the departure of the shock wave as well as by activation of nearby faults. Here, the stress relaxation mechanism is important at depth when the difference in main principal stresses becomes significant. Another mechanism of shear motion generation is due to explosive gas flow from the source cavity into the cracks initiated by the shock wave and joints connected to the cavity. Also, the shock wave from the explosion can cause weakening of the rock either due to permanent damage or shock-induced liquefaction at saturated joints. Numerical modelling of underground chemical explosions in hard rock at various confinement stresses has been conducted to compare various mechanisms of shear wave generation and their seismic characteristics with that of a simple fault rupture process observed during an earthquake.

58 GEOSCIENCES↗

NASA NTRS1986

Transonic aeroelastic analysis of the B-1 wing

The flow over the B-1 wing is studied computationally, including the aeroelastic response of the wing. Computed results are compared with results from wind tunnel and flight tests for both low- and high-sweep cases, at 25.0 and 67.5 deg, respectively, for selected transonic Mach numbers. The aerodynamic and aeroelastic computations are made by using the transonic unsteady code ATRAN3S. Steady aerodynamic computations compare well with wind tunnel results for the 25.0 deg sweep case and also for small angles of attack at 67.5 deg sweep case. The aeroelastic response results show that the wing is stable at the low-sweep angle for the calculation at the Mach number at which there is a shock wave. In the higher-sweep case, for the higher angle of attack at which oscillations were observed in the flight and wind tunnel tests, the calculations do not show any shock waves. Their absence lends support to the hypothesis that the observed oscillations are due to the presence of leading-edge separation vortices and not to shock wave motion, as was previously proposed.

Guruswamy, G. P.↗

NASA NTRS1973

Motion of the sources for type 2 and type 4 radio bursts and flare-associated interplanetary disturbances

Shock waves are indirectly observed as the source of type 2 radio brusts, whereas magnetic bottles are identified as the source of moving metric type 4 radio bursts. The difference between the expansion speeds of these waves bottles is examined during their generation and propagation near the flare regions. It is shown that, although generated in the explosive phase of flares, the behavior of the bottles is quite different from that of the waves and that the speed of the former is generally much lower. It is shown that the transit times of disturbances between the sun and the earth give information about the deceleration of shock waves to their local speeds observed near the earth's orbit. A brief discussion is given on the relationship among magnetic bottles, shock waves near the sun, and flare-associated disturbances in interplanetary space.

Sakurai, K.↗

NASA NTRS1987

Numerical simulation of three-dimensional supersonic inlet flow fields

Supersonic inlet flows with mixed external-internal compressions of an axisymmetric inlet model were computed using a combined implicit-explicit (Beam-Warming-Steger/MacCormack) method for solving the three-dimensional unsteady, compressible Navier-Stokes equations in conservation form. Numerical calculations were made of various flows typically found in supersonic inlets such as shock-wave intersections, flow spillage around the cowl lip, shock-wave/boundary-layer interactions, control of shock-induced flow separation by means of boundary layer bleed, internal normal (terminal) shocks, and the effects of flow incidence. Computed results were compared with available wind tunnel data.

Kawamura, T.↗

NASA NTRS2016

Development of Multi-Physics Dynamics Models for High-Frequency Large-Amplitude Structural Response Simulation

An analytic approach is demonstrated to reveal potential pyroshock-driven dynamic effects causing power losses in the Thermo-Electric (TE) module bars of the Mars Science Laboratory (MSL) Multi-Mission Radioisotope Thermoelectric Generator (MMRTG). This study utilizes high-fidelity finite element analysis with SIERRA/PRESTO codes to estimate wave propagation effects due to large-amplitude suddenly-applied pyro shock loads in the MMRTG. A high fidelity model of the TE module bar was created with approximately 30 million degrees-of-freedom (DOF). First, a quasi-static preload was applied on top of the TE module bar, then transient tri-axial acceleration inputs were simultaneously applied on the preloaded module. The applied input acceleration signals were measured during MMRTG shock qualification tests performed at the Jet Propulsion Laboratory. An explicit finite element solver in the SIERRA/PRESTO computational environment, along with a 3000 processor parallel super -computing framework at NASA AMES, was used for the simulation. The simulation results were investigated both qualitatively and quantitatively. The predicted shock wave propagation results provide detailed structural responses throughout the TE module bar, and key insights into the dynamic response (i.e., loads, displacements, accelerations) of critical internal spring/piston compression systems, TE materials, and internal component interfaces in the MMRTG TE module bar. They also provide confidence on the viability of this high-fidelity modeling scheme to accurately predict shock wave propagation patterns within complex structures. This analytic approach is envisioned for modeling shock sensitive hardware susceptible to intense shock environments positioned near shock separation devices in modern space vehicles and systems.

Shock Waves↗

NASA NTRS2006

Shock Structure Analysis and Aerodynamics in a Weakly Ionized Gas Flow

The structure of a shock wave propagating through a weakly ionized gas is analyzed using an electrofluid dynamics model composed of classical conservation laws and Gauss Law. A viscosity model is included to correctly model the spatial scale of the shock structure, and quasi-neutrality is not assumed. A detailed analysis of the structure of a shock wave propagating in a weakly ionized gas is presented, together with a discussion of the physics underlying the key features of the shock structure. A model for the flow behind a shock wave propagating through a weakly ionized gas is developed and used to analyze the effect of the ionization on the aerodynamics and performance of a two-dimensional hypersonic lifting body.

Saeks, R.↗

NASA NTRS1974

Decameter type IV bursts associated with coronal transients

The characteristics of four moving type IV burst observed with a 65- to 20-MHz swept-frequency interferometer are discussed. All four bursts were associated with depletions in the electron content of the white light corona. Characteristics of the bursts are not unique i.e., they differ in source size, structure, duration, and their association with other radio bursts. Following Smerd and Dulk (1971), it is assumed that a shock wave, moving out from the flare site is responsible for the expansion of a magnetic arch or the ejection of a plasmoid which is observed as the usual type IV burst. Behind the shock wave, the compressed coronal gas moves outward, and as it expands it causes a depletion of electrons in the inner corona. After the passage of the shock wave, sometimes the coronal magnetic field structure is restored to its initial situation, as evidenced by the observation of homologous transients.

Gergely, T. E.↗

DOE OSTI2025

Unraveling the role of temperature on the onset of ejecta formation at atomic scales

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.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A thermodynamic analysis of hypervelocity impacts on metals

Hypervelocity impacts on solid surfaces generate and propagate shock waves and create extreme density, pressure, and temperature conditions. Understanding hypervelocity impacts requires a multi-physics approach at the intersection of fluid dynamics, solid mechanics, and quantum theory, which has the capability of spanning multiple different dominating physics regimes. These strong shock conditions found in hypervelocity impacts are studied in the context of high-speed collisions between spacecraft and meteoroids and debris. We study the problem of hypervelocity impacts on metals with the lens of understanding the processes that lead to the creation of an impact generated plasma. In order to characterize the impacting particle as well as its threat to spacecraft from the subsequent radiating plasma an analysis was performed that highlights how the kinetic energy of the impactor is deposited into a target, how the shock wave and shocked material in the target evolve, and how these effects can lead towards the creation of an impact plasma through heating. The analysis suggests that at low velocities the majority of the energy from a hypervelocity impact is stored in reversible elastic energy and does not contribute to strong heating. At higher impact velocities, nucleus and electron thermal components dominate, increasing the energy available for ionization. Overall, this work provides the complete set of state variable initial conditions for any study of hypervelocity impact plasma expansion and its effects.

42 ENGINEERING↗

DOE OSTI2020

Formation and Diagnostics of Collisionless Shocks in Laser-Produced Plasmas (Final Report)

Collisions of supersonic flows occur frequently in astrophysics, and the resulting shock waves are responsible for the properties of many astrophysical phenomena, such as supernova remnants, Gamma Ray Bursts and jets from Active Galactic Nuclei. Because of the low density of astrophysical plasmas, the mean free path due to Coulomb collisions is typically very large; therefore, most shock waves in astrophysics are “collisionless” and form due to plasma instabilities and self-generated magnetic fields. Laboratory experiments at DOE high energy density (HED) facilities can achieve the conditions necessary for the formation of collisionless shocks and will provide a unique avenue for studying the nonlinear physics of shock waves. This project investigates the parameters and experimental configurations needed for the creation of collisionless shocks in the laboratory experiments. This study is being performed with state of the art 3D kinetic plasma simulations. Recent advances in ab-initio particle-in-cell (PIC) simulations of astrophysical shocks enable us to simulate shock formation on timescales and in geometries relevant to the laboratory experiments. The main goal of the proposal is to ascertain which signatures of shock physics can be extracted from the realistic experiments, accounting for limitations imposed by finite spatial and time scales in the lab. To aid the interpretation of current and future experimental data, PIC simulation data have been analyzed using the same diagnostic techniques as used in the laboratory, such as proton radiography and neutronics, to unambiguously predict the experimental signatures of relevant collisionless shock phenomena.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Optimizing ablator thickness for laser shock experiments

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.

design of experiments↗

NASA NTRS1991

Heat transfer, velocity-temperature correlation, and turbulent shear stress from Navier-Stokes computations of shock wave/turbulent boundary layer interaction flows

The properties of 2-D shock wave/turbulent boundary layer interaction flows were calculated by using a compressible turbulent Navier-Stokes numerical computational code. Interaction flows caused by oblique shock wave impingement on the turbulent boundary layer flow were considered. The oblique shock waves were induced with shock generators at angles of attack less than 10 degs in supersonic flows. The surface temperatures were kept at near-adiabatic (ratio of wall static temperature to free stream total temperature) and cold wall (ratio of wall static temperature to free stream total temperature) conditions. The computational results were studied for the surface heat transfer, velocity temperature correlation, and turbulent shear stress in the interaction flow fields. Comparisons of the computational results with existing measurements indicated that (1) the surface heat transfer rates and surface pressures could be correlated with Holden's relationship, (2) the mean flow streamwise velocity components and static temperatures could be correlated with Crocco's relationship if flow separation did not occur, and (3) the Baldwin-Lomax turbulence model should be modified for turbulent shear stress computations in the interaction flows.

Wang, C. R.↗

NASA NTRS1985

Stochastic particle acceleration in solar flares

It is proposed that particles during the second phase of solar flares are accelerated by stochastic resonant scattering off hydromagnetic waves and first order Fermi acceleration in shock waves generated in the impulsive phase of the flare. Solutions allow arbitrary power law momentum dependences of the momentum diffusion coefficient as well as the momentum diffusion coefficient as well as the momentum loss time. The acceleration time scale to a characteristic energy approximately 100 keV for protons can be as short as 5s. The resulting electron spectra show a characteristic double power law with a transition around 200 keV and are correlated to the proton spectra evaluated under equal boundary conditions, indicating that electrons and protons are accelerated by the same mechanism. The correlation between the different spectral indices in the electron double power law and between electron and proton spectra are governed by the ratio of first to second order acceleration and therefore allow a determination of the Alfven Mach number of the shock wave.

Droege, W.↗

NASA NTRS1988

The structure of shocks with thermal conduction and radiative cooling

A general analysis is presented of the structure of a steady state, plane-parallel shock wave in which both thermal conduction and radiative cooling are important. The fluid is assumed to have a perfect-gas equation of state, with radiative cooling a function only of its temperature and density. Conduction in both diffusive and saturated regimes is treated. For the case of a strong shock, with conductivity and cooling function varying as power laws in temperature, approximate analytic solutions describing the shock wave are derived. For a plasma of solar composition, conduction is found to have a significant effect on the shock temperature and overall thickness of the postshock layer only for shock velocities greater than about 30,000 km/s, corresponding to shock temperatures greater than about 10 to the 10th K, but it affects the local structure of parts of the shock wave at much lower velocities. The effects of conduction are greatly enhanced if the heavy-element abundance is increased.

Lacey, Cedric G.↗