Stress Waves in Solids [Slides]
The outline for SSDDS Lecture 3 includes: stress and strain, stress waves, waves at interfaces and boundaries, formation of shock waves, and problems.
36 MATERIALS SCIENCE↗
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Spacecraft observations of the solar wind composition
Solar wind composition studies by means of plasma analyzers carried on various spacecraft are reviewed. The average ratio of helium to hydrogen over the solar cycle is close to 0.045; values as low as 0.0025 and as high as 0.25 have been observed. High values have been observed following solar flares and interplanetary shock waves when the flare gas driving the shock arrives at the spacecraft. Ions of He-3(+2), O-16(+6), and O-16(+7) have been observed with Vela 3 electrostatic analyzers. Further measurements with Vela 5 analyzers have shown the presence of N-14(+6), Si-28(+7) to Si-28(+9) and Fe-56(+7) to Fe-56(+12) ions. The relative abundance of oxygen, silicon, and iron in the solar wind of July 6, 1969, was 1.00, 0.21, and 0.17, which is very similar to reported values for the corona. The ratio of helium to oxygen is variable; the average value of He/O is close to 100, but values between 30 and 400 have been observed.
Bame, S. J.↗
Discovery of X-ray emission from two southern supernova remnants
Two soft X-ray sources positionally coincident with the supernova remnants PKS 1209-52 and RCW 103 have been discovered by using the A-2 experiment on HEAO 1. Their measured fluxes are, respectively, about 1.4 x 10 to the -10th erg/cm-sec (0.2-1.0 keV) and about 1.8 x 10 to the -10th erg/cm-sec (0.6-2.0 keV). Spectral data are used to derive physical parameters for each remnant. For PKS 1209-52 the parameters are suggestive of the remnant's being in an advanced evolutionary phase, with shock-heated interstellar material producing the soft X-ray emission. RCW 103, in contrast, is known from radio and optical data to be in an earlier evolutionary phase, and the soft X-ray flux is most likely due to emission originating in a reflected shock wave or in plasma evaporated from shock-heated interstellar clouds.
Tuohy, I. R.↗
An upwind parabolized Navier-Stokes code for chemically reacting flows
A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous, chemically reacting flow around two-dimensional or axisymmetric bodies. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roe's flux-difference splitting scheme which has been modified to account for real gas effects. The algorithm solves the gas dynamic and species continuity equations in a 'loosely' coupled manner. The new code has been validated by computing the laminar flow (at free stream Mach number 25) of chemically reacting air over a wedge and a cone. The results of these computations are compared with the results from a centrally-differenced, fully coupled, nonequilibrium PNS code. The agreement is excellent, except in the vicinity of the shock wave where the present code exhibits superior shock capturing capabilities.
Tannehill, John C.↗
Comparison of shock structure solutions using independent continuum and kinetic theory approaches
A vehicle traversing the atmosphere will experience flight regimes at high altitudes in which the thickness of a hypersonic shock wave is not small compared to the shock standoff distance from the hard body. When this occurs, it is essential to compute accurate flow field solutions within the shock structure. In this paper, one-dimensional shock structure is investigated for various monatomic gases from Mach 1.4 to Mach 35. Kinetic theory solutions are computed using the Direct Simulation Monte Carlo method. Steady-state solutions of the Navier-Stokes equations and of a slightly truncated form of the Burnett equations are determined by relaxation to a steady state of the time-dependent continuum equations. Monte Carlo results are in excellent agreement with published experimental data and are used as bases of comparison for continuum solutions. For a Maxwellian gas, the truncated Burnett equations are shown to produce far more accurate solutions of shock structure than the Navier-Stokes equations.
Fiscko, Kurt A.↗
Chromospheric extents predicted by time-dependent acoustic wave models
Theoretical models for chromospheric structures of late-type giant stars are computed, including the time-dependent propagation of acoustic waves. Models with short-period monochromatic shock waves as well as a spectrum of acoustic waves are discussed, and the method is applied to the stars Arcturus, Aldebaran, and Betelgeuse. Chromospheric extent, defined as the monotonic decrease with height of the time-averaged electron densities, are found to be 1.12, 1.13, and 1.22 stellar radii for the three stars, respectively; this corresponds to a time-averaged electron density of 10 to the 7th/cu cm. Predictions of the extended chromospheric obtained using a simple scaling law agree well with those obtained by the time-dependent wave models; thus, the chromospheres of all stars for which the scaling law is valid consist of the same number of pressure scale heights.
Cuntz, Manfred↗
Physics of the outer heliosphere; Proceedings of the 1st COSPAR Colloquium, Warsaw, Poland, Sept. 19-22, 1989
This volume includes chapters on spectroscopic data on the local interstellar medium and the related XUV radiation background; solar UV backscatter on neutral Galactic gases; entry and dynamics of Galactic and anomalous cosmic rays in the heliosphere; distant solar wind plasma, magnetic field, and solar energetic particles; the interaction of solar wind with the interstellar medium; and deep-space missions. Papers are on the characteristics and the velocity structure of the local interstellar medium, the scattering of solar UV on local neutral gases, solar effects on underground muons at 570 hg/sq cm, and cosmic rays and magnetosonic instabilities of solar wind flow near the heliospheric shock wave. Consideration is also given to the shock heating of the solar wind plasma, solar wind vortex flow in the outer heliosphere, the signature of a viscous interaction at the heliopause, the expected beams of energetic neutral atoms in the outer heliosphere, and the Pioneers 10 and 11 deep-space missions.
Grzedzielski, S.↗
A model for the radio brightness of the supernova remnant 1987A
The recently observed rise in radio flux from SN1987A is earlier than predicted in models of the interaction with the observed line-emitting gas. The observed size of the radio source is roughly consistent with the expected position of the SN shock wave and the position of the termination shock of the blue supergiant progenitor wind. The radio increase is attributed to the interaction of the SN shock with this density jump. The required efficiency of electron acceleration and magnetic field amplification is larger than usually occurs in SNe and SNR. Possible reasons for the enhanced radio emission are particle acceleration by the weak reflected shock that travels through the interaction region, and the action of the Richtmyer-Meshkov instability near the initial termination-shock density jump. The action of these mechanisms is time-limited; the prediction of this model is that the radio flux should begin to decline within the next year.
Chevalier, Roger A.↗
High temperature kinetic study of the reactions H + O2 = OH + O and O + H2 = OH + H in H2/O2 system by shock tube-laser absorption spectroscopy
The reactions: (1) H + O2 = OH + O; and (2) O + H2 = OH + H are the most important elementary reactions in gas phase combustion. They are the main chain-branching reaction in the oxidation of H2 and hydrocarbon fuels. In this study, rate coefficients of the reactions and have been measured over a wide range of composition, pressure, density and temperature behind the reflected shock waves. The experiments were performed using the shock tube - laser absorption spectroscopic technique to monitor OH radicals formed in the shock-heated H2/O2/Ar mixtures. The OH radicals were detected using the P(1)(5) line of (0,0) band of the A(exp 2) Sigma(+) from X(exp 2) Pi transition of OH at 310.023 nm (air). The data were analyzed with the aid of computer modeling. In the experiments great care was exercised to obtain high time resolution, linearity and signal-to-noise. The results are well represented by the Arrhenius expressions. The rate coefficient expression for reaction (1) obtained in this study is k(1) = (7.13 +/- 0.31) x 10(exp 13) exp(-6957+/- 30 K/T) cu cm/mol/s (1050 K less than or equal to T less than or equal to 2500 K) and a consensus expression for k(1) from a critical review of the most recent evaluations of k(1) (including our own) is k(1) = 7.82 x 10(exp 13) exp(-7105 K/T) cu cm/mol/s (960 K less than or equal to T less than or equal to 5300 K). The rate coefficient expression of k(2) is given by k(2) = (1.88 +/- 0.07) x 10(exp 14) exp(-6897 +/- 53 K/T) cu cm/mol/s (1424 K less than or equal to T less than or equal to 2427 K). For k(1), the temperature dependent A-factor and the correlation between the values of k(1) and the inverse reactant densities were not found. In the temperature range of this study, non-Arrhenius expression of k(2) which shows the upward curvature was not supported.
Ryu, Si-Ok↗
Numerical Prediction Methods (Reynolds-Averaged Navier-Stokes Simulations of Transonic Separated Flows)
During the past five years, numerous pioneering archival publications have appeared that have presented computer solutions of the mass-weighted, time-averaged Navier-Stokes equations for transonic problems pertinent to the aircraft industry. These solutions have been pathfinders of developments that could evolve into a major new technological capability, namely the computational Navier-Stokes technology, for the aircraft industry. So far these simulations have demonstrated that computational techniques, and computer capabilities have advanced to the point where it is possible to solve forms of the Navier-Stokes equations for transonic research problems. At present there are two major shortcomings of the technology: limited computer speed and memory, and difficulties in turbulence modelling and in computation of complex three-dimensional geometries. These limitations and difficulties are the pacing items of the continuing developments, although the one item that will most likely turn out to be the most crucial to the progress of this technology is turbulence modelling. The objective of this presentation is to discuss the state of the art of this technology and suggest possible future areas of research. We now discuss some of the flow conditions for which the Navier-Stokes equations appear to be required. On an airfoil there are four different types of interaction of a shock wave with a boundary layer: (1) shock-boundary-layer interaction with no separation, (2) shock-induced turbulent separation with immediate reattachment (we refer to this as a shock-induced separation bubble), (3) shock-induced turbulent separation without reattachment, and (4) shock-induced separation bubble with trailing edge separation.
Mehta, Unmeel↗
Astrophysical Constraints on Chondrule Formation Models
Three petrologic constraints, heating and cooling timescales and the frequency of compound chondrules, are applied to the shock wave and lightning models of chondrule formation. Shocks fit the constraints well; lightning requires high gas densities.
Desch, S. J.↗
Vorticity Transport and Wave Emission in the Protoplanetary Nebula
Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler/Energy equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the nebula to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived using the simulation data and compared with analytical dispersion relations from the linearized Euler/Energy equations.
Davis, S. S.↗
Vorticity Transport and Wave Emission In A Protoplanetary Disk
Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the disk to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived from the nonlinear simulation data and correlated with analytical dispersion relations from the linearized Euler and energy equations.
Davis, S. S.↗
Exit of a blast wave from a conical nozzle
The Eulerian computer code DORF was used in the analysis of a two-dimensional, unsteady flow field resulting from semi-confined explosions for propulsive applications. Initially, the ambient gas inside the conical shaped nozzle is set into motion due to the expansion of the explosion product gas, forming a shock wave. When this shock front exits the nozzle, it takes almost a spherical form while a complex interaction between the nozzle and compression and rarefaction waves takes place behind the shock. The results show an excellent agreement with experimental data.
Kim, K.↗
Novel method to control explosive shock sensitivity: Formulations, experiments and modeling
The microstructure of a heterogeneous high explosive (HE) affects its shock initiation sensitivity and detonation performance. Alteration of the void content and/or void structure (i.e., bulk heating or mechanical damage) therefore changes the shock initiation behavior. Controlling and predicting the change in shock sensitivity after an HE has undergone microstructural changes addresses an important and challenging goal for the design and understanding of novel energetic material formulations. In this study, we aimed to develop HE systems to precisely tune shock sensitivity by a thermal treatment prior to use. Specifically, we incorporated a small fraction (1 wt% or less) of thermally expandable microspheres (TEMs) during the formulation process of various plastic-bonded explosives (PBX). TEMs typically consist of a thermoplastic acrylonitrile shell (10-50 µm diameter), which encapsulates an inert low boiling hydrocarbon. Upon heating, the TEMs expand as the shell softens while the hydrocarbon gasifies, increasing the internal pressure and expanding the particle by as much as 120 vol% (irreversibly). Here, we present our progress on shock sensitivity comparisons of HE formulations doped with TEMs after heating and expansion. Experiments, using Composition C-4 thermally cycled to 120°C, showed an increase in shock sensitivity. Additionally, mesoscale modeling revealed that the TEM itself does not act as a hotspot, but instead has a secondary effect on the response of nearby voids. We conclude that TEMs indeed do provide a method to tune shock sensitivity. Further, our results emphasize the non-uniformity of shock waves at the mesoscale, and that upstream defects influence the reactivity of downstream defects.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Shock behavior of materials
The physics governing the response of materials to shock loading has many applications in various fields, ranging from Earth and planetary science to engineering and ballistics. Elucidating the behavior of materials experiencing the passage of shock waves motivates active research worldwide, including experimental developments with in situ and time-resolved measurements, modern computational approaches, and multi-scale simulations.
36 MATERIALS SCIENCE↗
Numerical modeling of plasma assisted deflagration to detonation transition in a microscale channel
Here, this work numerically studies the plasma assisted deflagration to detonation transition (DDT) of H 2 /O 2 mixtures in a microscale channel with detailed chemistry and transport. The results show that the DDT onset time is non-monotonically dependent on the discharge pulse number. The DDT is accelerated with small pulse numbers, whereas retarded with large ones. Two different DDT regimes, respectively at a small and large plasma discharge number, via acoustic choking of the burned gas and plasma-enhanced reactivity gradient without acoustic choking, are observed. Without plasma discharge, pronounced pressure and temperature gradients in front of the flame are generated by acoustic compression after the choking of the burned gas, triggering DDT via autoignition. With small plasma pulse numbers, the plasma-generated species enhance the ignition kinetics and lead to an increased reactivity in the boundary layer. After the choking of the burned gas, the plasma-enhanced reactivity advances the sequence of autoignition near the wall, strengthens ignition-shock wave coupling, and accelerates DDT. However, with a large discharge pulse number, a direct autoignition initiating DDT can occur without the acoustic choking of the burned gas due to the strongly accelerated reactivity and elevated temperature. In this case, DDT onset is retarded because the elevated temperature increases sonic velocity and the increased reactivity accelerates fuel oxidation in front of the flame, decelerating the formation of a leading shock and subsequent pressure buildup ahead of the flame. The present modeling reveals that no matter with or without plasma discharge, DDT is initiated by autoignition in thermal, pressure, and reactivity gradient fields via the Zel'dovich gradient mechanism. The acoustic choking of the burned gas may not be the necessary condition of DDT with strong plasma-enhanced reactivity gradient. This work provides an answer to the experimentally observed non-monotonic DDT onset time by plasma, which provides guidance to control DDT in advanced detonation engines and fire safety of hydrogen-fueled catalytic reactors in microchannels by non-equilibrium plasma discharge.
33 ADVANCED PROPULSION SYSTEMS↗
A Computational Study of the Thermodynamic Conditions Leading to Autoignition in Nanosecond Pulsed Discharges
Nanosecond pulsed discharges have attracted the attention of engine manufacturers due to the possibility of attaining distributed ignition sites that accelerate burn rates while resulting in very little electrode erosion. Multidimensional modeling tools currently capture the electrical structure of such discharges accurately, but resolving the chemical structure remains a challenging problem owing to the disparity of time-scales in streamer propagation (nanoseconds) and ignition phenomena (microseconds). The purpose of this study is to extend multidimensional results toward resolving the chemical structure in the wake of streamers (or the afterglow) by using a batch reactor model (BRM). This can afford the use of very detailed chemical kinetic information. The full nonequilibrium nature of the electrons is taken into account, along with fast gas heating, shock wave propagation, and thermal diffusion. The results shed light on ignition phenomena brought about by such discharges.
42 ENGINEERING↗