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NASA NTRS1992

A review of transport theory

Ways in which energy change terms arise in the transport equation and how the various terms relate to the modes of energy exchange between the particles and plasma are shown. It is argued that the transport equation cannot be used to describe the initial acceleration of thermal particles by plasma shocks or relativistic shocks where the energetic particle speeds are never much greater than the flow speeds. In most other situations, it describes almost any acceleration process that can be caused by a moving plasma. It describes shock acceleration for both parallel shocks and oblique ones, and stochastic acceleration by the turbulent motion of the scatterers as well as by their motion across the magnetic field.

Jones, Frank C.↗

NASA NTRS1994

Three-dimensional hydrodynamic Bondi-Hoyle accretion. 2: Homogeneous medium at Mach 3 with gamma = 5/3

We investigate the hydrodynamics of three-dimensional classical Bondi-Hoyle accretion. Totally absorbing spheres of varying sizes (from 10 down to 0.01 accretion radii) move at Mach 3 relative to a homogeneous and slightly perturbed medium, which is taken to be an ideal gas (gamma = 5/3). To accommodate the long-range gravitational forces, the extent of the computational volume is 32(exp 3) accretion radii. We examine the influence of numerical procedure on physical behavior. The hydrodynamics is modeled by the 'piecewise parabolic method.' No energy sources (nuclear burning) or sinks (radiation, conduction) are included. The resolution in the vicinity of the accretor is increased by multiply nesting several (5-10) grids around the sphere, each finer grid being a factor of 2 smaller in zone dimension that the next coarser grid. The largest dynamic range (ratio of size of the largest grid to size of the finest zone) is 16,384. This allows us to include a coarse model for the surface of the accretor (vacuum sphere) on the finest grid, while at the same time evolving the gas on the coarser grids. Initially (at time t = 0-10), a shock front is set up, a Mach cone develops, and the accretion column is observable. Eventually the flow becomes unstable, destroying axisymmetry. This happens approximately when the mass accretion rate reaches the values (+/- 10%) predicted by the Bondi-Hoyle accretion formula (factor of 2 included). However, our three-dimensional models do not show the highly dynamic flip-flop flow so prominent in two-dimensional calculations performed by other authors. The flow, and thus the accretion rate of all quantities, shows quasi-periodic (P approximately equals 5) cycles between quiescent and active states. The interpolation formula proposed in an accompanying paper is found to follow the collected numerical data to within approximately 30%. The specific angular momentum accreted is of the same order of magnitude as the values previously found for two-dimensional flows.

Ruffert, Maximilian↗

NASA NTRS2004

Global Dayside Ionospheric Uplift and Enhancement Associated with Interplanetary Electric Fields

The interplanetary shock/electric field event of 5-6 November 2001 is analyzed using ACE interplanetary data. The consequential ionospheric effects are studied using GPS receiver data from the CHAMP and SAC-C satellites and altimeter data from the TOPEX/ Poseidon satellite. Data from ~100 ground-based GPS receivers as well as Brazilian Digisonde and Pacific sector magnetometer data are also used. The dawn-to-dusk interplanetary electric field was initially ~33 mV/m just after the forward shock (IMF BZ = -48 nT) and later reached a peak value of ~54 mV/m 1 hour and 40 min later (BZ = -78 nT). The electric field was ~45 mV/m (BZ = -65 nT) 2 hours after the shock. This electric field generated a magnetic storm of intensity DST = -275 nT. The dayside satellite GPS receiver data plus ground-based GPS data indicate that the entire equatorial and midlatitude (up to +/-50(deg) magnetic latitude (MLAT)) dayside ionosphere was uplifted, significantly increasing the electron content (and densities) at altitudes greater than 430 km (CHAMP orbital altitude). This uplift peaked ~2 1/2 hours after the shock passage. The effect of the uplift on the ionospheric total electron content (TEC) lasted for 4 to 5 hours. Our hypothesis is that the interplanetary electric field ''promptly penetrated'' to the ionosphere, and the dayside plasma was convected (by E x B) to higher altitudes. Plasma upward transport/convergence led to a ~55-60% increase in equatorial ionospheric TEC to values above ~430 km (at 1930 LT). This transport/convergence plus photoionization of atmospheric neutrals at lower altitudes caused a 21% TEC increase in equatorial ionospheric TEC at ~1400 LT (from ground-based measurements). During the intense electric field interval, there was a sharp plasma ''shoulder'' detected at midlatitudes by the GPS receiver and altimeter satellites. This shoulder moves equatorward from -54(deg) to -37(deg) MLAT during the development of the main phase of the magnetic storm. We presume this to be an ionospheric signature of the plasmapause and its motion. The total TEC increase of this shoulder is ~80%. Part of this increase may be due to a "superfountain effect." The dayside ionospheric TEC above ~430 km decreased to values ~45% lower than quiet day values 7 to 9 hours after the beginning of the electric field event. The total equatorial ionospheric TEC decrease was ~16%. This decrease occurred both at midlatitudes and at the equator. We presume that thermospheric winds and neutral composition changes produced by the storm-time Joule heating, disturbance dynamo electric fields, and electric fields at auroral and subauroral latitudes are responsible for these decreases.

ionosphere↗

NASA NTRS1985

Hybrid simulation techniques applied to the earth's bow shock

The application of a hybrid simulation model, in which the ions are treated as discrete particles and the electrons as a massless charge-neutralizing fluid, to the study of the earth's bow shock is discussed. The essentials of the numerical methods are described in detail; movement of the ions, solution of the electromagnetic fields and electron fluid equations, and imposition of appropriate boundary and initial conditions. Examples of results of calculations for perpendicular shocks are presented which demonstrate the need for a kinetic treatment of the ions to reproduce the correct ion dynamics and the corresponding shock structure. Results for oblique shocks are also presented to show how the magnetic field and ion motion differ from the perpendicular case.

Winske, D.↗

DOE OSTI2020

PETN Exploding Bridgewire (EBW) Detonators: A Review

Exploding bridgewire (EBW) detonators have been used in weapon systems since the 1940s but there is huge debate surrounding how energy is transferred throughout the EBW firing system and the mechanism by which the exploding wire leads explosive detonation. This report summarizes the underpinning technologies and physical processes that are currently understood and reviews the various efforts to quantify the mechanism by which the PETN is initiated. The behavior of the firing system is very well understood and predictable. The energy delivered to the wire has been empirically modelled but further investigation is required to understand the role of material heterogeneities and their effect on initiation. The energy delivered by the exploding wire has been quantified in many studies but it is not possible to correlate these to a particular design or firing regime and thus definitive conclusions are impossible. The energy absorbed by the PETN is also not well understood. Therefore, the initiation mechanism within the PETN EBWs has not been determined for EBW detonators. There is strong evidence that a shock-to-detonation (SDT) mechanism is not the sole cause of initiation. There is insufficient understanding of how electrical sparks transmit energy to PETN to make any judgement regarding the role gas ionization plays. Deflagration-to-detonation (DDT) seems like the most likely candidate for initiation but there is still a great lack of evidence for the presence of this mechanism.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

NASA NTRS1976

Table and charts of equilibrium normal-shock and shock-tube properties for pure carbon dioxide with velocities from 1 to 16 km/sec

Equilibrium thermodynamic and flow properties are presented in tabulated and graphical form for moving, standing, and reflected normal shock waves in pure CO2. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular weight ratio, isentropic exponent, velocity, and species mole fractions. Incident (moving) shock velocities are varied from 1 to 16 km/sec for a range of initial pressure of 5 N/sq m to 500 kN/sq m. The present results are applicable to shock tube flows and to freeflight conditions for a blunt body at high velocities. Working charts illustrating idealized shock tube performance with CO2 test gas and heated helium and hydrogen driver gases are also presented.

Miller, C. G., III↗

NASA NTRS1998

Numerical Study of Interaction of a Vortical Density Inhomogeneity with Shock and Expansion Waves

We studied the interaction of a vortical density inhomogeneity (VDI) with shock and expansion waves. We call the VDI the region of concentrated vorticity (vortex) with a density different from that of ambiance. Non-parallel directions of the density gradient normal to the VDI surface and the pressure gradient across a shock wave results in an additional vorticity. The roll-up of the initial round VDI towards a non-symmetrical shape is studied numerically. Numerical modeling of this interaction is performed by a 2-D Euler code. The use of an adaptive unstructured numerical grid makes it possible to obtain high accuracy and capture regions of induced vorticity with a moderate overall number of mesh points. For the validation of the code, the computational results are compared with available experimental results and good agreement is obtained. The interaction of the VDI with a propagating shock wave is studied for a range of initial and induced circulations and obtained flow patterns are presented. The splitting of the VDI develops into the formation of a non-symmetrical vortex pair and not in a set of vortices. A method for the analytical computation of an overall induced circulation Gamma(sub 1) as a result of the interaction of a moving VDI with a number of waves is proposed. Simplified, approximated, expressions for Gamma(sub 1) are derived and their accuracy is discussed. The splitting of the VDI passing through the Prandtl-Meyer expansion wave is studied numerically. The obtained VDI patterns are compared to those for the interaction of the VDI with a propagating shock wave for the same values of initial and induced circulations. These patterns have similar shapes for corresponding time moments.

Povitsky, A.↗

NASA NTRS1974

Tables and charts of equilibrium normal shock and shock-tube solutions for helium-hydrogen mixtures with velocities to 70 km/sec

Equilibrium thermodynamic and flow properties are presented in tabulated and graphical form for moving, standing, and reflected normal shock waves into helium-hydrogen mixtures representative of proposed outer planet atmospheres. The volumetric compositions of these mixtures are 0.35He-0.65H2, 0.20He-0.80H2, and 0.05He-0.95H2. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular-weight ratio, isentropic exponent, velocity, and species mole fractions. Incident (moving) shock velocities are varied from 4 to 70 km/sec for a range of initial pressure of 5 N/sq m to 100 kN/sq m. The present results are applicable to shock-tube flows and to free-flight conditions for a blunt body at high velocities. A working chart illustrating idealized shock-tube performance with a 0.20He-0.80H2 test gas and heated helium driver gas is also presented.

Miller, C. G., III↗

NASA NTRS1988

Hypersonic shock structure with Burnett terms in the viscous stress and heat flux

The continuum Navier-Stokes and Burnett equations are solved for one-dimensional shock structure in various monatomic gases. A new numerical method is employed which utilizes the complete time-dependent continuum equations and obtains the steady-state shock structure by allowing the system to relax from arbitrary initial conditions. Included is discussion of numerical difficulties encountered when solving the Burnett equations. Continuum solutions are compared to those obtained utilizing the Direct Simulation Monte Carlo method. Shock solutions are obtained for a hard sphere gas and for argon from Mach 1.3 to Mach 50. Solutions for a Maxwellian gas are obtained from Mach 1.3 to Mach 3.8. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Shock density thickness, density asymmetry, and density-temperature separation are all more accurately predicted by the Burnett equations than by the Navier-Stokes equations.

Chapman, Dean R.↗

DOE OSTI2022

Proper orthogonal decomposition based reduced-order modeling of flux-Limited gray thermal radiation

Here, in this work, a proper orthogonal decomposition (POD) based reduced-order model (ROM) is developed to solve gray, flux-limited thermal radiation diffusion. We focus on the variable opacity radiation penetration benchmark posed by Olson, Auer, and Hall. The T -3 relationship for opacity in conjunction with high-temperature radiation penetrating an initially cold material produces a strong thermal radiation shock. This class of problems is particularly challenging for standard POD-based reduced-order modeling due to the nonlinearities presented by 1) the T 4 source term, and 2) flux-limited diffusion operator. To address these challenges and develop a cost competitive ROM, we employ a “hyper-reduction” technique through discrete empirical interpolation (DEIM) and allow for adaptive reduced-order projections through principal interval decomposition (PID). Performance of the proposed methodology is quantified by comparing the cost savings and accuracy relative to a full-order computation. Reference solutions and snapshot data are obtained through a full-order calculation performed by the University of Chicago maintained astrophysics code, FLASH. For consistency and potential extensibility, the developed ROM is also implemented in FLASH. We find that in the initialization regime, where the thermal radiation wave is initially created by the warming of the material, this class of problems is highly reducible and suitable for POD-based ROMs. However, the strong convective nature of the wave propagation regime is less reducible and more challenging to create an efficient ROM.

42 ENGINEERING↗

NASA NTRS1994

Scaling craters in carbonates: Electron paramagnetic resonance analysis of shock damage

Carbonate samples from the 8.9-Mt nuclear (near-surface explosion) crater, OAK, and a terrestrial impact crater, Meteor Crater, were analyzed for shock damage using electron paramagnetic resonance (EPR). Samples from below the OAK apparent crater floor were obtained from six boreholes, as well as ejecta recovered from the crater floor. The degree of shock damage in the carbonate material was assessed by comparing the sample spectra to the spectra of Solenhofen and Kaibab limestone, which had been skocked to known pressures. Analysis of the OAK Crater borehole samples has identified a thin zone of allocthonous highly shocked (10-13 GPa) carbonate material underneath the apparent crater floor. This approx. 5- to 15-m-thick zone occurs at a maximum depth of approx. 125 m below current seafloor at the borehole, sited at the initial position of the OAK explosive, and decreases in depth towards the apparent crater edge. Because this zone of allocthonous shocked rock delineates deformed rock below, and a breccia of mobilized sand and collapse debris above, it appears to outline the transient crater. The transient crater volume inferred in this way is found to by 3.2 +/- 0.2 times 10(exp 6)cu m, which is in good agreement with a volume of 5.3 times 10(exp 6)cu m inferred from gravity scaling of laboratory experiments. A layer of highly shocked material is also found near the surface outside the crater. The latter material could represent a fallout ejecta layer. The ejecta boulders recovered from the present crater floor experienced a range of shock pressures from approx. 0 to 15 GPa with the more heavily shocked samples all occurring between radii of 360 and approx. 600 m. Moreover, the fossil content, lithology and Sr isotopic composition all demonstrate that the initial position of the bulk of the heavily shocked rock ejecta sampled was originally near surface rock at initial depths in the 32 to 45-m depth (below sea level) range. The EPR technique is also sensitive to prehistoric shock damage. This is demonstrated by our study of shocked Kaibab limestone from the 49,000-year-old Meteor (Barringer) Crater Arizona.

Polanskey, Carol A.↗

NASA NTRS2004

A General Relativistic Magnetohydrodynamics Simulation of Jet Formation with a State Transition

We have performed the first fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation of jet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity sim 0.3c) is created as shown by previous two-dimensional axisymmetric simulations with mirror symmetry at the equator. The 3-D simulation ran over one hundred light-crossing time units which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted due in part to magnetic pressure from the twisting the initially uniform magnetic field and from gas pressure associated with shock formation. At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface of the thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outwards with a wider angle than the initial jet. The widening of the jet is consistent with the outward moving shock wave. This evolution of jet-disk coupling suggests that the low/hard state of the jet system may switch to the high/soft state with a wind, as the accretion rate diminishes.

Nishikawa, K. I.↗

NASA NTRS1974

Effects of interplanetary shock waves on energetic charged particles

Experimental data on the influence of interplanetary perpendicular and oblique shock waves on the ambient energetic protons are presented along with a theoretical analysis of the acceleration of particles in almost perpendicular shock waves. It was found that low-energy protons can be accelerated in perpendicular shock waves by repeated crossings of the shock front up to a maximum energy given by the product of their initial energy times the ratio of the magnetic fields. High-energy protons need to stay at the shock front for longer times than low-energy protons in order to reach the same relative energy gain. In the theoretical study of proton acceleration at almost perpendicular shock waves, it was found that protons reflected at shock waves with the angle between the upstream magnetic field and the shock normal greater than about 80 deg achieve large energy gains at the shock front. The larger this angle, the higher the energy gain. However, the reflection and energization of protons at these shock waves is not 'instantaneous', neither is it a one-step process: it is performed through repeated crossings of the shock front.

Sarris, E. T.↗

NASA NTRS1986

Observational discrimination between modes of shock propagation in interstellar clouds: Predictions of CH+ and SH+ column densities in diffuse clouds

Considerable effort in recent years has been devoted to the study of shocks in the diffuse interstellar medium. This work has been motivated partly by the observations of rotationally excited states of H2, and partly by the realization that species such as CH(+), OH and H2O might be formed preferentially in hot, post-shock gas. The problem of CH(+) and the difficulties encountered when trying to explain the high column densities, observed along lines of sight to certain hot stars, have been reviewed earlier. The importance of a transverse magnetic field on the structure of an interstellar shock was also demonstrated earlier. Transverse magnetic fields above a critical strength give rise to an acceleration zone or precursor, in which the parameters on the flow vary continuously. Chemical reactions, which change the degree of ionization of the gas, also modify the structure of the shock considerably. Recent work has shown that large column densities of CH(+) can be produced in magnetohydrodynamic shock models. Shock speeds U sub s approx. = 10 km/s and initial magnetic field strengths of a few micro G are sufficient to produce ion-neutral drift velocities which can drive the endothermic C(+)(H2,H)CH(+) reaction. It was also shown that single-fluid hydrodynamic models do not generate sufficiently large column densities of CH(+) unless unacceptably high shock velocities (u sub s approx. 20 km/s) are assumed in the models. Thus, the observed column densities of CH(+) provide a constraint on the mode of shock propagation in diffuse clouds. More precisely, they determine a lower limit to the ion-neutral drift velocity.

Flower, D. R.↗

NASA NTRS1975

Acceleration of charged particles in oblique MHD shocks

The motion of high energy charged particles in ideal oblique MHD shocks has been studied extensively. The orbits of charged particles can be solved exactly from Lorentz force equation. It is found that a charged particle may cross the shock front many times before it leaves the shock and it is energized during crossings. The most energetic particles are those with initial pitch and phase near the boundary between crossing and reflected particles. The reflected particles cross the shock about twice as many times as the passing particles do. The energy gain increases for larger values of shock strength and speed. If reflection occurs, the energy gain is larger for smaller angles between the field and shock surface. The introduction of scattering results in a few more higher energy particles.

Chen, G.↗

NASA NTRS1989

Monte Carlo simulation of particle acceleration at astrophysical shocks

A Monte Carlo code was developed for the simulation of particle acceleration at astrophysical shocks. The code is implemented in Turbo Pascal on a PC. It is modularized and structured in such a way that modification and maintenance are relatively painless. Monte Carlo simulations of particle acceleration at shocks follow the trajectories of individual particles as they scatter repeatedly across the shock front, gaining energy with each crossing. The particles are assumed to scatter from magnetohydrodynamic (MHD) turbulence on both sides of the shock. A scattering law is used which is related to the assumed form of the turbulence, and the particle and shock parameters. High energy cosmic ray spectra derived from Monte Carlo simulations have observed power law behavior just as the spectra derived from analytic calculations based on a diffusion equation. This high energy behavior is not sensitive to the scattering law used. In contrast with Monte Carlo calculations diffusive calculations rely on the initial injection of supra-thermal particles into the shock environment. Monte Carlo simulations are the only known way to describe the extraction of particles directly from the thermal pool. This was the triumph of the Monte Carlo approach. The question of acceleration efficiency is an important one in the shock acceleration game. The efficiency of shock waves efficient to account for the observed flux of high energy galactic cosmic rays was examined. The efficiency of the acceleration process depends on the thermal particle pick-up and hence the low energy scattering in detail. One of the goals is the self-consistent derivation of the accelerated particle spectra and the MHD turbulence spectra. Presumably the upstream turbulence, which scatters the particles so they can be accelerated, is excited by the streaming accelerated particles and the needed downstream turbulence is convected from the upstream region. The present code is to be modified to include a better description of particle scattering (pitch-angle instead of hard-sphere) and as iterative procedure for treating the self-excitation of the MHD turbulence.

Campbell, Roy K.↗

NASA NTRS1993

Analysis of unsteady wave processes in a rotating channel

The impact of passage rotation on the gas dynamic wave processes is analyzed through a numerical simulation of ideal shock-tube flow in a closed rotating-channel. Initial conditions are prescribed by assuming homentropic solid-body rotation. Relevant parameters of the problem such as wheel Mach number, hub-to-tip radius ratio, length-to-tip radius ratio, diaphragm temperature ratio, and diaphragm pressure ratio are varied. The results suggest possible criteria for assessing the consequences of passage rotation on the wave processes, and they may therefore be applicable to pressure-exchange wave rotors. It is shown that for a fixed geometry and initial conditions, the contact interface acquires a distorted three-dimensional time-dependent orientation at non-zero wheel Mach numbers. At a fixed wheel Mach number, the level of distortion depends primarily on the density ratio across the interface as well as the hub-to-tip radius ratio. Rarefaction fronts, shocks, and contact interfaces are observed to propagate faster with increasing wheel Mach number.

Larosiliere, L. M.↗

NASA NTRS1993

Analysis of unsteady wave processes in a rotating channel

Larosiliere, Louis M.↗