Conservative Eulerian numerical methods for geometrical shock dynamics (GSD) and detonation shock dynamics (DSD)
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Experiments in weak-shock dynamics were conducted using a 17-in. diameter shock tube. Weak shocks were generated in air by a compressed nitrogen driver gas; the incident shock waves were brought to a focus by reflecting them from concave cylindrical reflectors at the endwall of the tube. It was found that the behavior of a shock discontinuity at a focus is determined by nonlinear gasdynamic processes. Consideration is also given to nonlinear resonance phenomena, i.e., phenomena associated with oscillatory motion in ducts, with amplitude so large that weak shocks occur. Attention is given to nonlinear resonance in open and closed tubes and to thermal and relaxation effects.
The principal aim of this project was to determine whether x ray emission from instability-generated shocks in dynamical models of highly unstable hot-star winds could explain the x ray flux spectrum observed from such hot stars by Einstein and other x ray satellites. Our initial efforts focused on extending the earlier isothermal simulations of wind instabilities to include an explicit treatment of the energy balance between shock heating and simplified radiative cooling. It was found, however, that direct resolution of cooling regions behind shocks is often impractical, and thus additional, indirect methods for determining this shock x ray emission were also developed. The results indicate that the reverse shocks that dominate simple 1-D instability models typically have too little material undergoing a strong shock to produce the observed x ray emission. Other models with more strongly driven variability from the wind base sometimes show high-speed collisions between relatively dense clumps, and in these instances the computed x ray flux spectrum matches the observed spectrum quite well. This suggests that collisions between relatively large scale wind streams of different speeds may be more suited to producing the observed x rays than the reverse shocks arising from small-scale instabilities.
Detonation shock dynamics is a powerful method to model the behaviour of High Explosives (HE). However in order to use this method, the underlying relationship between the local radius of curvature and the detonation speed must be known. Previous work has developed methods to calculate this effect using simple, single-step Arrhenius and polytropic gas, models for the chemical reaction and the equation of state, respectively. In recent years, more complex models for both reaction rates and equations of state have been developed which show better agreement with experimental data than these simple models, especially when considering condensed phase explosives.. This work presents the governing equations for solving these problems in a way that is generalised to use arbitrary equations of state as well as reaction models which may have more than a single step and multiple product species. This implementation is verified against exact solutions, demonstrating that the equations were implemented properly. The verified algorithm is then validated against experimental data and high fidelity simulations, showing that it is able to make accurate predictions in a regime where the underlying assumptions of the governing equations are valid. Importantly, this approach has many applications: from creating equivalent detonation shock dynamics models for existing reactive burn calibrations for HE; to developing new functional forms and calibrations of reactive burn models for condensed phase high explosives.
Magnetized collisionless shocks are common in astrophysical systems, and scaled versions can be created in laboratory experiments by utilizing laser-driven piston plasmas to create these shocks in a magnetized background plasma. A key parameter for these experiments is the angle θB between the shock propagation direction and the background magnetic field. We performed quasi-1D piston-driven shock simulations to explore shock formation, evolution, and key observables relevant to laboratory experiments for a range of shock angles between θB=90° to θB=30°. Our results show that the spatial and temporal scales of shock formation for all angles considered are similar when expressed in terms of the perpendicular component of the magnetic field. In a steady state, ion and electron temperatures become more isotropic, and the electron-to-ion temperature ratio is higher for smaller θB. At θB=30°, ion heating parallel to the magnetic field becomes dominant, associated with more ions being reflected at one discontinuity and subsequently trapped by the next discontinuity due to shock reformation.
A computational study of the influence of shock motion on flutter and divergence in transonic flow is presented. The numerical scheme models the entire fluid-structure system as a single continuum dynamics problem, by using a mixed Eulerian-Lagrangian formulation. No assumptions of small displacements are made, but the effect of viscosity is neglected. The results from this study indicate that the shock dynamics gives rise to limit cycles and highly nonlinear aeroelastic phenomena, such as weak divergence and flutter-divergence interactions. Although the shocks typically are destabilizing at the linear flutter boundary, they often have a strongly stabilizing effect for moderate-amplitude motions. The shocks are thus capable of quenching an emerging bending-torsion flutter motion and turning it into limit cycle flutter. The usefulness of classical flutter and divergence boundary diagrams is severely limited in transonic flow, because much of the global dynamic stability information is lost in such a presentation.
The present work considers theoretically the problem of radiation losses on the shock layer during hypersonic flight, and in particular, results are presented for the stagnation line shock layer for a wide variety of flight conditions, providing a new overview of radiation-gas dynamic coupling within a shock layer. The present results are based on a previous model (Engel, Farmer, et al., 1973) of a viscous radiating shock layer. An important result is that the radiation-gas dynamic coupling effect on the radiative heating can be related to a single parameter, namely, the radiative cooling parameter, whereas the effect on the shock layer thickness is not a simple function of this parameter.
The interaction between radiation and a shock wave propagating through a stellar atmosphere is investigated. Departures from local thermodynamic equilibrium (LTE) are permitted in the first two levels of a 10-level hydrogen atom; levels 3-10 are in LTE. A piston moving at constant velocity into the bottom of the atmosphere drives a shock wave. This shock produces precursor radiation that diffuses through the gas well ahead of the shock and causes a mild luminosity flash in the emergent Balmer and free-free radiation when it reaches the surface. The precursor wave deposits a large amount of radiative energy in the outer layers of the atmosphere, initiating a radiation-induced pressure wave. The process of energy transfer from the radiation field to the compression wave is similar to the Eddington valve mechanism which drives stellar pulsations. Material is accelerated outward by the radiation-induced wave; eventually it free-falls inward, hits the quasistationary atmosphere, and forms an accretion shock. The piston driven shock is weakened by radiative energy losses. When it reaches the surface, the shock is invisible in the continuum radiation.
In this paper, we present an experiment that explores the plasma dynamics of a 7μm diameter carbon wire after being irradiated with a near-relativistic-intensity short pulse laser. Using an x-ray free electron laser pulse to measure the small angle x-ray scattering signal, we observe that the scattering surface is bent and prone to instability over tens of picoseconds. The dynamics of this process are consistent with the presence of a sharp, propagating shock front inside the wire, moving at a speed close to the hole boring velocity or that expected from a thermal shock at a few tens of Mbar.
The 2010 April 03 solar event was studied using observations from STEREO SECCHI, SOHO LASCO, and Wind kilometric Type II data (kmTII) combined with WSA-Cone-ENLIL model simulations performed at the Community Coordinated Modeling Center (CCMC). In particular, we identified the origin of the coronal mass ejection (CME) using STEREO EUVI and SOHO EIT images. A flux-rope model was fit to the SECCHI A and B, and LASCO images to determine the CMEs direction, size, and actual speed. J-maps from STEREO COR2HI-1HI-2 and simulations fromCCMC were used to study the formation and evolution of the shock in the inner heliosphere. In addition, we also studied the time-distance profile of the shock propagation from kmTII radio burst observations. The J-maps together with in-situ datafrom the Wind spacecraft provided an opportunity to validate the simulation results andthe kmTII prediction. Here we report on a comparison of two methods of predictinginterplanetary shock arrival time: the ENLIL model and the kmTII method; andinvestigate whether or not using the ENLIL model density improves the kmTIIprediction. We found that the ENLIL model predicted the kinematics of shock evolutionwell. The shock arrival times (SAT) and linear-fit shock velocities in the ENLILmodel agreed well with those measurements in the J-maps along both the CME leading edge and the Sun-Earth line. The ENLIL model also reproduced most of the largescale structures of the shock propagation and gave the SAT prediction at Earth with an error of 17 hours. The kmTII method predicted the SAT at Earth with an error of 15 hours when using n0 4.16 cm3, the ENLIL model plasma density near Earth; but itimproved to 2 hours when using n0 6.64 cm3, the model density near the CMEleading edge at 1 AU.
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Dynamics of collisions between shock intersections and wave configurations in gases and condensed explosives
An investigation of the dynamics of shock waves in weakly ionized argon plasmas has been performed using a pressure ruptured shock tube. The velocity of the shock is observed to increase when the shock traverses the plasma. The observed increases cannot be accounted for by thermal effects alone. Possible mechanisms that could explain the anomalous behavior include a vibrational/translational relaxation in the nonequilibrium plasma, electron diffusion across the shock front resulting from high electron mobility, and the propagation of ion-acoustic waves generated at the shock front. Using a turbulence model based on reduced kinetic theory, analysis of the observed results suggest a role for turbulence in anomalous shock dynamics in weakly ionized media and plasma-induced hypersonic drag reduction.