Converging Shock Waves Research Articles

Effect of spherically converging shock waves on phase and structural state of quenched Al-4 wt % Cu alloy

Optical metallography, scanning and transmission electron microscopy, and microhardness measurements have been used to perform a layer-by-layer study of the structure of a quenched Al-4 wt % Cu alloy subjected to loading by spherically converging shock waves. It has been established that, when using this mode of loading, the high-strain-rate plastic deformation of this alloy occurs via intragranular dislocation slip. No bands of localized deformation at the grain boundaries, twins, and adiabatic shear bands are formed. Highstrain-rate plastic deformation leads to the dissolution of Guinier-Preston zones.

Numerical investigations of the porosity effect on the shock focusing process

The effect of cylindrical obstacles and the porosity in between them along the path of a converging cylindrical shock is studied through numerical simulations. An initially cylindrical converging shock wave is perturbed by cylindrical obstacles placed radially in its path. High pressures and temperatures are achieved as the shock wave is focused. Results show that the shape of the shock wave close to the point of convergence as well as the porosity and type of shock wave reflection the converging shock undergoes influence the peak values. Various configurations of the obstacle size and number are considered. The Guderley constant for each case is compared with previous reported experimental values.

On the acceleration of shock waves and concentration of energy

By a series of simple examples related to exact solutions of problems in gas dynamics and magnetohydrodynamics, possible mechanisms of acceleration of shock waves and concentration of energy are elucidated. The acceleration of a shock wave is investigated in the problem of motion of a plane piston at a constant velocity in the case when the initial density of the medium drops in the presence of constant counterpressure. It is shown that in this situation a “blow-up” regime is induced by a shock wave going to infinity in finite time even for limited work of the piston. A simple spherically symmetric solution with a converging shock wave is constructed and shown to lead to the concentration of energy. A general method for solving one-dimensional non-self-similar problems related to matching the equilibrium state to a motion with homogeneous deformation on a shock wave is discussed; this method leads to a solution in quadratures.

Experimental study on a heavy-gas cylinder accelerated by cylindrical converging shock waves

When an initially perturbed interface separating two fluids with different properties is impulsively accelerated by a shock wave, the flow field will exhibit complex fluid dynamic phenomena due to the misalignment of the density and pressure gradients. It is often referred to as the Richtmyer-Meshkov (RM) instability [1, 2] and has been investigated within the past several decades due to its extensive physical applications such as inertial confinement fusion (ICF) [3], turbulent mixing in scram jet [4] and collapse in supernova [5]. Specifically, in most applications the shock waves maintain two-dimensional (e.g. cylindrical) or three-dimensional (e.g. spherical) converging shapes. Taking the ICF experiments, the thermonuclear fuel is contained in a small spherical solid capsule in advance and illuminated evenly by a number of well-designed laser beams. Simultaneously a spherical converging shock wave is generated and traverses the capsule. In the process even a tiny imperfection of the capsule surface can induce the RM instability and may destroy the fusion reaction [3]. It is therefore of fundamental interest and practical significance to explore the fluid dynamics of the flows in the interaction of interfaces with a converging shock wave.

HELIUM-IGNITED VIOLENT MERGERS AS A UNIFIED MODEL FOR NORMAL AND RAPIDLY DECLINING TYPE Ia SUPERNOVAE

The progenitors of Type Ia Supernovae (SNe Ia) are still unknown, despite significant progress during the last years in theory and observations. Violent mergers of two carbon--oxygen (CO) white dwarfs (WDs) are one candidate suggested to be responsible for at least a significant fraction of normal SNe Ia. Here, we simulate the merger of two CO WDs using a moving-mesh code that allows for the inclusion of thin helium (He) shells (0.01\,\msun) on top of the WDs, at an unprecedented numerical resolution. The accretion of He onto the primary WD leads to the formation of a detonation in its He shell. This detonation propagates around the CO WD and sends a converging shock wave into its core, known to robustly trigger a second detonation, as in the well-known double-detonation scenario for He-accreting CO WDs. However, in contrast to that scenario where a massive He shell is required to form a detonation through thermal instability, here the He detonation is ignited dynamically. Accordingly the required He-shell mass is significantly smaller, and hence its burning products are unlikely to affect the optical display of the explosion. We show that this scenario, which works for CO primary WDs with CO- as well as He-WD companions, has the potential to explain the different brightness distributions, delay times and relative rates of normal and fast declining SNe Ia. Finally, we discuss extensions to our unified merger model needed to obtain a comprehensive picture of the full observed diversity of SNe Ia.

Shock dynamics of weak imploding cylindrical and spherical shock waves with non-ideal gas effects

The author (Anand 2012 Astrophys. Space Sci.342 377–88) recently obtained jump relations across a shock front in non-ideal gas flow taking into consideration the equation of state for a non-ideal gas as given by Landau and Lifshitz. In this paper an analytical solution for one-dimensional adiabatic flow behind weak converging shock waves propagating in a non-ideal gas is obtained by using Whitham's (1974 Linear and Nonlinear Waves (New York: Wiley)) geometrical shock dynamics approach. The effects of an increase in (i) the propagation distance from the centre of convergence, (ii) the non-idealness parameter and (iii) the adiabatic index of the gas, on the shock velocity, pressure, density, particle velocity, adiabatic compressibility and the change in entropy across the shock front, are analyzed. The results provided a clear picture of whether and how the non-idealness parameter and the adiabatic index affect the flow field behind the imploding shock front.

Peculiarity of convergence of shock wave generated by underwater electrical explosion of ring-shaped wire

Nanosecond timescale underwater electrical wire explosions of ring-shaped Cu wires were investigated using a pulsed generator with a current amplitude up to 50 kA. It was shown that this type of wire explosion results in the generation of a toroidal shock wave (SW). Time- and space-resolved optical diagnostics were used to determine azimuthal uniformity of the shock wave front and its velocity. It was found that the shock wave preserves its circular front shape in the range of radii 50μm<r<5 mm. At r≤15μm, azimuthal irregularities of the SW front were obtained indicating the appearance of azimuthal instability. A surprising finding is that the shock wave propagates with a constant velocity of vsw=1.2M, where M is the Mach number. The dynamics of the leading part of the shock wave, based on the oblique shock wave theory, is presented, explaining the constant velocity of the shock wave.

Symmetry of Spherically Converging Shock Waves through Reflection, Relating to the Shock Ignition Fusion Energy Scheme

We examine the properties of perturbed spherically imploding shock waves in an ideal fluid through the collapse, bounce, and development into an outgoing shock wave. We find broad conservation of the size and shape of ingoing and outgoing perturbations when viewed at the same radius. The outgoing shock recovers the velocity of the unperturbed shock outside the strongly distorted core. The results are presented in the context of the robustness of the shock ignition approach to inertial fusion energy.

Deformation behavior of copper upon loading by spherically converging shock waves: Low-intensity loading conditions

X-ray diffraction, optical metallography, transmission electron microscopy, and microhardness measurements were used to perform a layer-by-layer study of the structure of a copper sphere 70 mm in diameter after loading by spherically converging shock waves. It has been found that the high-rate plastic deformation of copper proceeds mostly by slipping, rather than twinning under the used loading conditions. Shear bands are observed at the macrolevel, while a homogeneous dislocation structure, microbands, and microtwins are observed at the microlevel.

Phase and structure state of titanium loaded by spherically converging shock waves

The phase and structural states of titanium spheres loaded by spherical converging shock waves of various intensities were studied layer by layer by means of X-ray diffraction, optical, and transmission electron microscopy. It was established that defects of different types (twins, dislocations, and adiabatic shear bands) are produced during high-rate deformation occurring in materials under such method of pulsed loading. The amount and distribution of the defects depend on the loading intensity. The presence of the ω-phase is revealed only in the layers near the external surface of the titanium sphere after low-intensity loading.

E122 収束爆轟駆動の水中衝撃波に及ぼす収束半径の影響と微生物処理への適用(一般講演(6))

It was shown by theoretical and experimental studies that high temperature and high pressure state is provided in the converging center by converging shock wave or imploding detonation. In particular, the imploding detonation can implode more effectively than the case of the shock wave. The authors examined the microorganism treatment technique using ultra-high pressure underwater shock waves in a steel pipe by the gas imploding detonation until now. The authors tried to confirm the effect of underwater shock wave generation by change minimum converging radial distance of imploding detonation. As a result, the maximum pressure increased in a decrease in the minimum converging radial distance. Therefore, there was large percent of mortality rate with an increase in minimum converging radial distance.

Energy concentration by spherical converging shocks generated in a shock tube

Spherical converging shock waves are produced in a conventional shock tube with a circular cross-section. Initially, plane shocks are transformed into the shape of a spherical cap by means of a smoothly convergent cross-section. The wall shape in the transformation section is designed to gradually change the form of the shock wave until it approaches a spherical shape. Thereafter, the shock enters a conical section where it converges towards the apex of the cone. Numerical calculations with the axisymmetric Euler equations show that the spherical form is only slightly dependent on the initial Mach number of the plane shock within the range 1.5 < MS < 5.5, and is preserved to a close vicinity of the focal point. The test gas is heated to very high temperatures as a result of shock convergence and emits a bright light pulse at the tip of the test section. The light radiation is collected by optical fibers mounted at the tip of the convergence chamber and investigated by photometric and spectroscopic measurements. Experiments are performed with argon and nitrogen and with different initial Mach numbers. The radiation of the shock-heated argon closely resembles blackbody radiation. Fits to the experimental data result in apparent blackbody temperatures in argon of up to ∼27 000 K, some 250 ns after the focusing instant. The initial Mach number in these spectrometric runs is MS = 3.9, indicating an efficient amplification of the shock wave strength.

Effects of the localization of deformations and mass transfer in converging shock waves

Effects of shock wave interaction and the related phenomena of the localization of plastic deformation, destruction, and mass transfer in metal ball samples subjected to explosive loading at pressures of 36 to 150 GPa are studied. A correlation between the macro- and microstructural changes and the geometrical conditions of loading according to various schemes is found. It is shown that the mass transfer effects are of hydrodynamic origin. The depth penetration of the material was 3.2 mm in narrow channels and 0.3 mm in solid material.

Compression of matter by hyperspherical shock waves

A novel compression scheme is proposed, in which hollow targets with specifically curved structures initially filled with uniform matter, are driven by converging shock waves. The self-similar dynamics is analyzed for converging and diverging shock waves. The shock-compressed densities and pressures are much higher than those achieved using spherical shocks due to the geometric accumulation. Dynamic behavior is demonstrated using two-dimensional hydrodynamic simulations. The linear stability analysis for the spherical geometry reveals a new dispersion relation with cut-off mode numbers as a function of the specific heat ratio, above which eigenmode perturbations are smeared out in the converging phase.

Effect of spherically converging shock waves on deformation and phase behavior of high-purity iron

Optical metallography, transmission electron microscopy, and microhardness measurements were used to perform a layer-by-layer study of the structure of a high-purity iron sphere 166 mm in diameter after loading by converging spherical shock waves. It has been found that the plastic deformation of ɛ iron under this loading proceeds by slip; in the middle and deep layers, it proceeds via the formation of localized deformation bands.

The propagation of shock waves in a channel of variable cross section containing a dusty gas

An analytic solution is obtained for one-dimensional adiabatic flow behind converging shock waves propagating through a channel of variable cross section containing a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and small solid particles, in which solid particles are continuously distributed. In order to obtain the analytical solutions, the Whitham's geometrical shock dynamics method is employed and the initial density of the ambient medium is assumed to be constant. The effects of the variation of cross-sectional area of channel on the flow variables immediately behind the shock are investigated. The effects of increase in (i) the mass fraction (concentration) of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also discussed in comparison with a non-dusty gas case.

Phase transformations of enstatite in spherical shock waves

The analysis of available theoretical evaluations and experimental data reveals discrepancies and makes it possible to formulate the goals for the comprehensive study of the behavior of enstatite MgSiO3 in shock isentropic waves of various scale and intensity. The paper presents the layout and results of an explosion experiment on the compression of an enstatite sphere with spherical shock waves and the subsequent recovery of the experimental material and its examination in discrete zones (along the sphere radius) that were produced by shock waves in the material. The latter were examined with the application of scanning electron microscopy, Raman spectroscopy, and X-ray diffraction analysis. The comparison of the systematic variations in the texture, chemistry, and phase composition of enstatite along the sphere radius with calculated pressure P(R, t) and temperature T(R, t) values led us to the following conclusions: enstatite starts melting on an isentrope upon pressure relief after shock wave compression at σxx ≈ 80 GPa and melts on the front of the spherically converging shock wave at σxx ≈ 160 GPa and T ≈ 6300 K. Our laboratory experiments with shock waves were the world’s first in which enstatite was loaded with spherical converging shock isentropic waves and which provided evidence that shock wave-loaded MgSiO3 shows certain morphological and mineralogical features never before detected in this mineral loaded with plane shock wave of smaller amplitude and duration. Goals are formulated for the further studying of shock wave-loaded materials, and the necessity is discussed for conducting an explosion experiment with a five to seven times greater spherical system in order to increase the duration of the shock wave loading impulse.

Rock transformations in spherically converging shock waves: Newly obtained experimental results

The paper presents a concise review of results obtained by studying shock metamorphism of polymineralic rocks with the application of spherical hermetically sealed recovery devices. Such experiments are proved to be able to reproduce principally important features of transformations detected in rocks from natural meteoritic craters (astroblemes). The experimental samples show subspherical concentric zones with different rock transformations, which are generally analogous to zones in natural astroblemes (listed in order from the centers of the spherical samples to their margins): fracturing, diaplectic transformations, selective and then complete melting, and finally, evaporation. However, the laboratory scale of the experiments and the absence of younger overprinted processes, which can obliterate impact transformations of rocks in nature, enable the researcher to reveal distinctive compositional, textural, and phase features of transformations induced in the rocks at increasing isentropic shock wave-induced loading. Data on the mobility of major elements in the course of impact metamorphism show that the type and certain features of the crystal structures of minerals are of paramount importance for the amorphization of the minerals or their shock wave-induced thermal decomposition. The crystal chemical control of mineral transformations was proved to be exerted at a number of levels. High-pressure phases identified in experiments with shock wave loading were determined to crystallize from melt or via a phase transition associated with the migration of elements.

Converging shock wave in a dusty gas through nonstandard analysis

A problem of propagation of strong plane and converging shock wave is studied in a mixture of a gas and small solid particles. It is assumed that the solid particles are continuously distributed in the gas. Jump conditions for plane and converging shock waves are derived using the nonstandard analysis. It is also assumed that the shock thickness occurs at infinitesimal interval and jump functions are smooth across this interval. The distribution of flow parameters across the shock wave are presented in terms of Heaviside functions and Dirac Delta measures.

Effect of spherically converging shock waves on the phase and structural states of the artificially aged Al-4 wt % Cu alloy

Optical metallography, scanning and transmission electron microscopy, and microhardness measurements have been used to layer-by-layer study the structure of an artificially aged Al-4 wt % Cu alloy subjected to loading by spherically converging shock waves. It has been established that the high-strain-rate plastic deformation of this alloy, when using this mode of loading, occurs via intragrain dislocation slip and, in the middle and deep layers, also via the formation of localized-deformation bands at grain boundaries. The intragrain slip occurs inhomogeneously, by the formation of shear bands. The temperature distribution in various layers of the sample has been estimated.