Planar Shock Research Articles

Experimental and finite element analysis of the generation mechanism of high impulse noise overpressure (caused by a recoilless weapon) at the bottom of the ear

The intense impulse noise may damage the soldiers’ hearing organs during a weapon's firing. It is essential to find out the generation mechanism of the overpressure at the bottom of the ear. The experiments of measuring the overpressure at the bottom of the ear were conducted through a rotating human head model at a recoilless weapon firing platform. The results showed that the overpressure peak at the bottom of the ear decreases with the increasing incident angle. A simulation of the test condition was developed based on the plane shock wave method. The finite element model was verified reasonably compared to the test results. The Friedlander wave propagating to the ear canal was implemented at different incident angles. The generation of the overpressure at the bottom of the ear was analyzed. According to the pressure nephograms, the impulse noise stagnated at the bottom of the ear, so the overpressure was the total pressure of impulse noise. Two parts of impulse noise entered the canal successively due to the influence of the pinna. The overpressure and Mach number at the entrance of the ear canal both decreased with increasing incident angles, resulting in impulse noise superimposed at the bottom of the ear. Investigating the generation of overpressure at the bottom of the ear under varying incident angles may have important reference value for analyzing and preventing auditory organ damage caused by impulse noise.

Stability of perpendicular magnetohydrodynamic shocks in materials with ideal and nonideal equationsof state.

Magnetized target fusion approach to inertial confinement fusion involves the formation of strong shocks that travel along a magnetized plasma. Shocks, which play a dominant role in thermalizing the upstream kinetic energy generated in the implosion stage, are seldom free from perturbations, and they wrinkle in response to upstream or downstream disturbances. In Z-pinch experiments, significant plasma instability mitigation was observed with pre-embedded axial magnetic fields. To isolate effects, in this work we theoretically study the impact of perpendicular magnetic fields on the planar shock dynamics for different equationsof state. For fast magnetosonic shocks in ideal gases, it was found that the magnetic field amplifies the intensity of the perturbations when γ>2 or it weakens them when γ<2. Weak shocks have been found to be stable regardless of the magnetic plasma intensity and gas compressibility; however, for sufficiently strong shocks the magnetic fields can promote a neutral stability/SAE at the shock if the adiabatic index is higher than 1+sqrt[2]. Results have been validated with numerical simulations performed with the FLASH code.

Визуализация тепловых потоков в высокоскоростном течении за ударной волной

The paper presents the thermographic studies of unsteady heat fluxes behind a plane shock wave in the rectangular 24x48 mm shock tube test section. Consecutive panoramic visualization of the heat fluxes plots on streamlined walls after the plane shock wave interaction with a rectangular obstacle fixed on the channel wall are obtained. The duration of the recorded thermal processes is up to 40 milliseconds after the shock wave passage. The heating and cooling of the test chamber walls streamlined by supersonic flow are visualized using the Telops FAST M200 high-speed infrared camera (operating range 1.5 – 5.1 microns) through the quartz windows transparent to infrared radiation. Visualization of the thermal fields were compared with the shadow images and results of 2D numerical simulation of a nonstationary gas dynamic process after the diffraction of a shock wave with Mach numbers M=2.0-4.5.

Linear stability of shock waves in ultrarelativistic anisotropic hydrodynamics

Linear stability of a plane shock waves in ultrarelativistic anisotropic hydrodynamics is investigated. The properties of the amplitudes of perturbations of physical quantities are studied depending on the components of the wave vector of a small harmonic perturbation. Analytical calculations for the longitudinal and transverse propagation of shock wave normal with respect to the anisotropy axis (beam-axis) and numerical calculations for an arbitrary polar angle are carried out.

Specific-heat ratio effects on the interaction between shock wave and heavy-cylindrical bubble: Based on discrete Boltzmann method

Specific-heat ratio effects on the interaction between a planar shock wave and a two-dimensional heavy-cylindrical bubble are studied by the discrete Boltzmann method. Snapshots of schlieren images and evolutions of characteristic scales, being consistent with experiments, are obtained. The specific-heat ratio effects on some relevant dynamic behaviors such as the bubble shape, deformation process, average motion, vortex motion, mixing degree of the fluid system are carefully studied, as well as the related Thermodynamic Non-Equilibriums (TNE) behaviors including the TNE strength, entropy production rate of the system. Specifically, it is found that the influence of specific-heat ratio on the entropy production contributed by non-organized energy flux (NOEF) is more significant than that caused by non-organized momentum flux (NOMF). Effects of specific-heat ratio on entropy production caused by NOMF and NOEF are contrary. The effects of specific-heat ratio on various TNE quantities show interesting differences. These differences consistently show the complexity of TNE flows which is still far from clear understanding.

Atomistic study of the impact response of bicontinuous nanoporous gold as a protection medium: Effect of porous-nonporous interface on failure evolution

Compared to their non-porous counterparts, metallic foams are known to exhibit improved functionality (e.g., damping capacity) when subjected to high-speed impact loading. Here, we report the results of a molecular dynamics study of bicontinuous nanoporous gold (NPG) subjected to impact loading. Additionally, we investigate the effects of a heterogeneous impact zone on the fate of a witness specimen initially protected by an NPG target. A cube-shaped flyer object (L0= 408.6 Å) composed of full-density f.c.c. gold (FDG) strikes with impact speed Uflyer= 1.0 km s−1 an initially stationary equal-sized NPG target, which subsequently transmits a dispersed shock wave into a protected FDG witness specimen located at the downstream end of the target. The NPG target is stochastic, with porosity ϕ= 0.5 and mean ligament diameter D¯L=64±6 Å. A corresponding simulation for an FDG target serves as a baseline case. As anticipated, the sharp, planar shock imparted by the FDG flyer rapidly becomes highly curved and broadened along the shock direction in the NPG target. Intense plastic and convective flows (ejecta and jetting) lead to spatially heterogeneous mass flow and energy localization, which persist across the entire length of the NPG target studied. Whereas the shock transmitted by the FDG target leaves the witness specimen intact and essentially undamaged, the heterogeneous stress and flow fields imparted by the NPG target results in destruction of the witness. Independent simulations for the same cube-shaped NPG target shocked on the three statistically equivalent {100} target faces reveal modest run-to-run variability in the target and witness responses. The difference in the effects of the NPG and FDG targets on the witness response motivates additional study of the failure evolution inside the witness. It appears from the preliminary results that the porous-nonporous interface might induce a failure pattern that, in some aspects, resembles failure waves observed in brittle solids.

Scattering of Ions at a Rippled Shock

In a collisionless shock the energy of the directed flow is converted to heating and acceleration of charged particles, and to magnetic compression. In low-Mach number shocks the downstream ion distribution is made of directly transmitted ions. In higher-Mach number shocks ion reflection is important. With the increase of the Mach number, rippling develops, which is expected to affect ion dynamics. Using ion tracing in a model shock front, downstream distributions of ions are analyzed and compared for a planar stationary shock with an overshoot and a similar shock with ripples propagating along the shock front. It is shown that rippling results in the distributions, which are substantially broader and more diffuse in the phase space. Gyrotropization is sped up. Rippling is able to generate backstreaming ions, which are absent in the planar stationary case.

A gas dynamic perspective on particle lifting in electrostatic discharge-like devices using multiphase particle-in-cell approach

Although particle–laden electrostatic discharges are widely used in laboratories as well as in industrial applications, the mechanism of particle lifting for particles initially at rest in such highly unsteady systems is not well understood. A multiphase gas–particle solver is developed using the multiphase particle-in-cell (MP-PIC) approach to emulate the interaction of a compressible shock-dominated gas phase with the dense particle phase. First, the two-way coupled solver is initially used to study the interaction of a planar traveling shock with a vertical curtain of particulates. The gas and particle phase evolution was found to be in good agreement with a similar experimental study in Ling et al. [Phys. Fluids 24, 113301 (2012)]. Second, the MP-PIC code is used to study the interaction of an expanding blast wave with a thick bed of particles. The simulation considered forces such as quasi-steady drag, pressure-gradient, added-mass, Saffman, and Magnus forces. We observe that the vertical liftoff particles close to the shock impingement point in this configuration are associated with the quasi-steady drag, pressure gradient, and added-mass forces. Also, the Saffman lift and Magnus forces contribute to lifting particles located radially farther away from the shock impingement point. In addition, the study finds a decrease in particle lifting efficiency with decreasing plasma kernel length and shock strength.

Numerical investigation of the interaction between a converging shock wave and an offset cylindrical bubble containing different gases

A numerical study investigating the interaction process between a converging shock wave and a gas bubble placed at an offset location is presented. As a first step, for proofing the reliability of the used numerical scheme, a simulation of relevant available experimental findings of Hosseini and Takayama [“Richtmyer–Meshkov instability induced by cylindrical shock wave loading of cylindrical gaseous inhomogeneities,” AIAA Paper No. 2000-2464, 2000] and Hosseini and Takayama [“Study of a converging shock wave interaction with a gaseous interfaces in an eccentric arrangement,” in Japanese Symposium on Shock Waves, 2000] is conducted; the tested gases were helium (He) and sulfur hexafluoride (SF6). The converging shock wave had a Mach number of 1.18 prior to its impact on the 50 mm diameter gas bubble. Achieving good agreement with the experimental findings ensures the reliability of the applied numerical scheme. After the converging shock wave impacted the gas bubble, different shock waves are created. These shock waves propagate differently than those observed in the case of planar shock wave impacting a cylindrical gas bubble or that of a converging shock wave where the gas bubble is located at the center. Furthermore, once the converging shock wave converged, a diverging shock wave expands and again impacts the remaining gas bubble, thus creating more complex shock wave patterns. The gas contained inside the bubble has an effect on the location of the converging shock wave focus point. In the case of the heavy gas SF6, the focus point is near the center of the converging shock wave, but in the case of light gas He, it is offset from the converging shock wave focus point and outside of the initial location of the He bubble. The new results from the current numerical simulation include more detailed results for both bubbles, which were not reported in Hosseini and Takayama [“Richtmyer–Meshkov instability induced by cylindrical shock wave loading of cylindrical gaseous inhomogeneities,” AIAA Paper No. 2000-2464, 2000] and Hosseini and Takayama [“Study of a converging shock wave interaction with a gaseous interfaces in an eccentric arrangement,” in Japanese Symposium on Shock Waves, 2000]. In addition, a shock wave focusing of the transmitted shock wave inside the SF6 bubble is observed. This later creates a secondary diverging shock wave. Higher pressure is achieved in the SF6 case.

Energy transformations accompanying a shock wave distortion and disappearance during the interaction with thermally stratified plasma

The results of experiments and numerical simulations of the interaction of a plane shock wave with an area of ionization strata formed by a glow gas discharge are presented. For the experimentally obtained phenomena transformations of kinetic and internal energy have been studied numerically using Euler and Navier-Stokes approaches under the assumption that ionization unstable plasma has stratified gas temperature. Energy transfer between a region of layered energy deposition and heated gas zone behind the shock wave was considered. It has been established that a layered energy deposition can provide the distortion and destruction of a shock wave front and in addition, to create a lot of zones with higher internal and kinetic energy beyond it. These phenomena were shown to be connected with generation in many points of the Richtmyer-Meshkov instability resulting from the interaction of thermal strata with a front of the shock wave.

The Entropy Density Behavior across a Plane Shock Wave.

Entropy density behavior poses many problems when we study non-equilibrium situations. In particular, the local equilibrium hypothesis (LEH) has played a very important role and is taken for granted in non-equilibrium problems, no matter how extreme they are. In this paper we would like to calculate the Boltzmann entropy balance equation for a plane shock wave and show its performance for Grad's 13-moment approximation and the Navier-Stokes-Fourier equations. In fact, we calculate the correction for the LEH in Grad's case and discuss its properties.

On the stability of piston-driven planar shocks

We present a theoretical and numerical stability analysis for a piston-driven planar shock against two-dimensional perturbations. The results agree with the well-established theory for isolated planar shocks: in the range of $h_c&lt; h&lt;1+2 {\mathcal {M}}_2$ , where $h$ is the D'yakov–Kontorovich (DK) parameter related to the slope of the Rankine–Hugoniot curve, $h_c$ is its critical value corresponding to the onset of the spontaneous acoustic emission (SAE) and ${\mathcal {M}}_2$ is the downstream Mach number, non-decaying oscillations of shock-front ripples occur. The effect of the piston is manifested in the presence of additional frequencies occurring by the reflection of the sonic waves on the piston surface that can reach the shock. An unstable behaviour of the shock perturbation is found to be possible when there is an external excitation source affecting the shock, whose frequency coincides with the self-induced oscillation frequency in the SAE regime, thereby being limited to the range $h_c&lt; h&lt;1+2 {\mathcal {M}}_2$ . An unstable evolution of the shock is also observed for planar shocks restricted to one-dimensional perturbations within the range $1&lt; h&lt;1+2 {\mathcal {M}}_2$ . Both numerical integration of the Euler equations via the method of characteristics and theoretical analysis via Laplace transform are employed to cross-validate the results.

The colliding planar shocks platform to study warm dense matter at the National Ignition Facility

We have developed an experimental platform at the National Ignition Facility that employs colliding planar shocks to produce warm dense matter with uniform conditions and enable high-precision equation of state measurements. The platform uses simultaneous x-ray Thomson scattering and x-ray radiography to measure the density, electron temperature, and ionization state in warm dense matter. The experimental platform is designed to create a large volume of uniform plasma (approximately 700×700×150μm3) at pressures approaching 100 Mbar and minimize the distribution of plasma conditions in the x-ray scattering volume, significantly improving the precision of the measurements. Here, we present the experimental design of the platform and compare hydrodynamic simulations to x-ray radiography data from initial experiments studying hydrocarbons, producing uniform densities within ±25% of the average probed condition. We show that the platform creates a homogeneous plasma that can be characterized using x-ray Thomson scattering. Thus, the new platform enables accurate measurements of plasma conditions necessary to test models for the equation of state and ionization potential depression in the warm dense matter regime.

How plane are plane shock waves in solids

The notion of plane shock waves is a macroscopic, very fruitful idealization of near discontinuous disturbance propagating at supersonic speed. Such a picture is comparable to the picture of shorelines seen from a very high altitude. When viewed at the grain scale where the structure of solids is inherently heterogeneous and stochastic, features of shock waves are non-laminar and field variables, such as particle velocity and pressure, fluctuate. This paper reviews select aspects of such fluctuating nonequilibrium features of plane shock waves in solids with focus on grain scale phenomena and raises the need for a paradigm change to achieve a deeper understanding of plane shock waves in solids.

Planar Viscous Shocks with Periodic Perturbations for Scalar Multidimensional Viscous Conservation Laws

This paper studies a Cauchy problem for a scalar multidimensional (multi-d) viscous convex conservation law, in which the initial data is a planar viscous shock with a multi-d periodic perturbation. We show that if the wave-strength and perturbation are both small, then the viscous shock is stable in the space with an exponential decay rate. One contribution of the paper is to establish a new framework to study the stability of viscous shocks in multiple dimensions, where the elementary energy method with the antiderivative technique can be used. The idea is to decompose the multi-d perturbation into a one-dimensional function and a multi-d remainder, where the former can well define its antiderivative and the latter satisfies the Poincaré inequality over a periodic domain.

A numerical study on high-temperature effects of exploding shock waves

A planar shock of initial strength MS = 3.0 was focused to a tiny region in space using a spherically converging test section. The shock accelerates inside the test section, collides with the focusing end wall, and gets reflected. Numerical studies show that the flow behind reflected shock behaves like an expanding jet moving through a confined area. It was observed that this expansion caused the formation of a mushroom-shaped structure. Thermodynamic characterization of the mushroom structure was made, and it was found that the gas temperature inside the mushroom structure is higher than that across the reflected shock itself. High-temperature effects, such as temperature-dependent Cp variations and dissociation–recombination reactions of the test gas, were added to the simulations to better understand the effect of temperature on the expanding hot gas. A reduction of 39% in the peak temperature value was obtained at the focusing end wall. Also, the flow inside the mushroom structure was observed to be a reactive mixture of a hot gas slug. It is observed that prominent molecular dissociation and recombination take place inside the mushroom structure, which is absent across the reflected shock.

Piston driven shock waves in non-homogeneous planar media

In this work, we analyze in detail the problem of piston driven shock waves in planar media. Similarity solutions to the compressible hydrodynamics equations are developed, for a strong shock wave, generated by a time dependent pressure piston, propagating in a non-homogeneous planar medium consisting of an ideal gas. Power law temporal and spatial dependency is assumed for the piston pressure and initial medium density, respectively. The similarity solutions are written in both Lagrangian and Eulerian coordinates. It is shown that the solutions take various qualitatively different forms according to the value of the pressure and density exponents. We show that there exist different families of solutions, for which the shock propagates at a constant speed, accelerates, or slows down. Similarly, we show that there exist different types of solutions, for which the density near the piston is either finite, vanishes, or diverges. Finally, we perform a comprehensive comparison between the planar shock solutions and Lagrangian hydrodynamic simulations, by setting proper initial and boundary conditions. A very good agreement is reached, which demonstrates the usefulness of the analytic solutions as a code verification test problem.

On the 3D global dynamics of terrestrial bow-shock rippling in a quasi-perpendicular interaction with steady solar wind

The phenomenon of bow-shock surface rippling has been studied throughout multidimensional simulations of ad hoc planar shock fronts. However, the investigation of global bow-shock behaviour with a 3D curved scenario has been poorly addressed thus far. In this work, we present an analysis of this scenario occurring during a low-β quasiperpendicular interaction with the interplanetary magnetic field by means of kinetic 3D computer simulations. The analysis was carried out with 3D hybrid simulations properly set to reproduce the interaction between solar wind and a realistic near-Earth environment. We have found that the ripples behave as IMF-perpendicular elongated structures extending along the bow-shock meridian plane and propagating parallel to the IMF orientation from the nose towards the flanks with a constant velocity (in the case studied here ∼8 times the upstream Alfvén speed). We have also confirmed that these ripples feature a broad range of wavelengths along the entire travel path, as locally observed with past simulations and observations (in this case ≥8di). Moreover, from a kinetic analysis of the velocity distribution across the bow-shock nose, we have observed global signatures of the occurrence of shock-front reformation. We suggest that, among other kinetic mechanisms, shock-front reformation in the nose region can play an important role in the perturbation of the bow-shock surface, leading to the generation of modulations ultimately propagating along the bow-shock surface as MHD waves.

Drop Interactions with the Conical Shock Structure Generated by a Mach 4.5 Projectile

This work presents measurements of liquid drop deformation and breakup time behind approximately conical shock waves and evaluates the predictive capabilities of low-order models and correlations developed using planar shock experiments. A conical shock was approximated by firing a bullet at Mach 4.5 past a vertical column of water drops with a mean initial diameter of . The time-resolved drop position and maximum transverse dimension were characterized using backlit stereo images taken at 500 kHz. The gas density and velocity fields experienced by the drops were estimated using a Reynolds-averaged Navier–Stokes simulation of the bullet. Classical correlations predict drop breakup times and deformation in error by a factor of 3 or more. The Taylor analogy breakup (TAB) model predicts deformed drop diameters that agree within the confidence bounds of the ensemble-averaged experimental values using a dimensionless constant compared to the accepted value . Results demonstrate existing correlations are inadequate for predicting the drop response to the three-dimensional relaxation of the flowfield downstream of a conical-like shock and suggest the TAB model results represent a path toward improved predictions.

Persistence of the steady planar normal shock structure in 3‐D unsteady potential flows

AbstractThis paper concerns the dynamic stability of the steady three‐dimensional (3‐D) wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free boundary problem of a quasi‐linear hyperbolic equation of second order in a dihedral‐space domain between the shock front and the solid wall. The key difficulty is brought by the edge singularity of the space domain, the intersection curve between the shock front and the solid wall. Different from the two‐dimensional (2‐D) case, for which the singular part of the boundary is only a point, it is a curve for the 3‐D case in this paper. This difference brings new difficulties to the mathematical analysis of the stability problem. A modified partial hodograph transformation is introduced such that the extension technique developed for the 2‐D case can be employed to establish the well‐posed theory for the initial‐boundary value problem of the linearized hyperbolic equation of second order in a dihedral‐space domain. Moreover, the extension technique is improved in this paper such that loss of regularity in the a priori estimates on the shock front does not occur. Thus, the classical nonlinear iteration scheme can be constructed to prove the existence of the solution to the stability problem, which shows the dynamic stability of the steady planar normal shock without applying the Nash–Moser iteration method.