Transverse Shock Waves Research Articles

The Evolution Equations of Shock Deformation Problems with Plane Surfaces of Discontinuities in Elastic Inhomogeneous Mediums

For the model of the nonlinear elastic medium with inhomogeneous properties represented by a continuous change of the elastic moduli and density, the motion problems of a plane longitudinal or transverse shock waves are considered. The matched asymptotic expansions method allows to determine the evolution equations reflecting the nonlinearity of the wave processes and the inhomogeneity of the medium. The transition to the limiting inner problem of the small parameter method is dictated by the chain of inner problems, the solutions of which require a changes in all of the independent variables and their scales.

Phase Transition Experimental and Theoretical Study of Micro Power Generator Supplying Source for CMOS Chip Based on Ferroelectric Ceramic Nano-Porous Material.

We demonstrated both experimentally and in theory analysis and calculation that the tin-modified lead zirconate titanate nanoporous ferroelectric generator system can perform as a micro-power supplying source for CMOS chip. The ferroelectric ceramic phase transition under transverse shock wave compression can charge external storage capacitor. The nanoporous microstructure ferro-electric ceramic micro-pulsed-power system is capable of generating low output voltage pulses and supplying CMOS chip with micro power sources. We developed the methodology for theory analysis and experimental operation of the ferroelectric generator. Analysis of the porous ferroelectric ceramic material was carried out by X-ray diffractometry and X-ray photoelectron spectroscopy. Microstructures and surface morphology of porous ferroelectric ceramics samples were examined by using scanning electron microscopy. The planar shock wave experiments were conducted on a compressed-gas gun. The experimental results were in good agreement with the theory analysis. Keywords: PSZT Ferroelectric Ceramic, Shock Wave, Phase Transition, Depolarization, Micro-Power-Generator.

Propagation mechanisms of supersonic combustion waves

The propagation of a supersonic combustion wave in an obstructed channel is investigated using high-speed schlieren photography. Experiments were carried out in a 2.54cm wide by 7.82cm tall channel with equally spaced 1.91cm tall fence-type obstacles mounted on the top and bottom surfaces. Tests were carried out with stoichiometric hydrogen–oxygen mixtures over an initial pressure range of 8–30kPa. The high-speed video shows that combustion wave propagation in the quasi-detonation propagation regime is very complex involving coupled local explosions, not all of which involve detonation initiation. For the most reactive mixtures (d/λ>6.5) a sustained detonation propagates through the channel with some weakening due to diffraction around obstacles. For less reactive mixtures (6.5>d/λ>2) detonation propagation is intermittent, where the detonation fails due to diffraction around the obstacles and then is re-initiated at the channel centerline following the collision of two transverse shock waves. The transverse shock wave originates from a detonation that forms immediately following shock reflection off the top and bottom obstacle faces. Detonation initiation occurs at the corner, where the channel wall and obstacle meet, as a result of shock focusing and propagates into the unburned gas ahead of the flame. For mixtures where d/λ<2, the wave propagation is governed by the outcome of the shock reflection off the obstacle pair (top and bottom). If shock reflection off the obstacle pair initiates an explosion at the obstacle face, the collision of the resulting two transverse shock waves produces a local explosion at the channel centerline after each obstacle resulting in an average lead shock velocity roughly equal to the isobaric speed of sound of the products. If shock reflection does not result in ignition of the gas at the obstacle face, the resulting propagation is in the choked flame regime.

Nano-scale spinning detonation in a condensed phase energetic material

A single-headed spinning detonation wave is observed in molecular dynamics simulations of a condensed phase detonation of an energetic material confined to a round tube. The EM is modeled using a modified AB reactive empirical bond order (REBO) potential. The simulated spinning detonation is similar to those observed in the gas phase. However, in addition to the incident, oblique, and transverse shock waves well known from gas-phase spinning detonations, a contact shock wave generated by a contact discontinuity is uncovered in our MD simulations.

The awakening of BL Lacertae: observations by Fermi, Swift and the GASP-WEBT★

Since the launch of the Fermi satellite, BL Lacertae has been moderately active at gamma-rays and optical frequencies until May 2011, when the source started a series of strong flares. The exceptional optical sampling achieved by the GLAST-AGILE Support Program (GASP) of the Whole Earth Blazar Telescope (WEBT) in collaboration with the Steward Observatory allows us to perform a detailed comparison with the daily gamma-ray observations by Fermi. Discrete correlation analysis between the optical and gamma-ray emission reveals correlation with a time lag of 0 +- 1 d, which suggests cospatiality of the corresponding jet emitting regions. A better definition of the time lag is hindered by the daily gaps in the sampling of the extremely fast flux variations. In general, optical flares present more structure and develop on longer time scales than corresponding gamma-ray flares. Observations at X-rays and at millimetre wavelengths reveal a common trend, which suggests that the region producing the mm and X-ray radiation is located downstream from the optical and gamma-ray-emitting zone in the jet. The mean optical degree of polarisation slightly decreases over the considered period and in general it is higher when the flux is lower. The optical electric vector polarisation angle (EVPA) shows a preferred orientation of about 15 deg, nearly aligned with the radio core EVPA and mean jet direction. Oscillations around it increase during the 2011-2012 outburst. We investigate the effects of a geometrical interpretation of the long-term flux variability on the polarisation. A helical magnetic field model predicts an evolution of the mean polarisation that is in reasonable agreement with the observations. These can be fully explained by introducing slight variations in the compression factor in a transverse shock waves model.

Effect of the medium inhomogeneity on the evolution equation of plane shock waves

Using the method of matched asymptotic expansions, solutions of boundary-value problems of shock deformation of nonlinear elastic weakly inhomogeneous semispaces are obtained. It is shown that nonlinearity of the model and various properties of the inhomogeneity lead to new evolution equations in the frontal areas of longitudinal and transverse shock waves, the transition to which is due to transformations of all independent coordinates of the problem.

Phase Transformation Experimental and Theoretical Study of Micro-power Generator Supplying Source for IC Chip Based on Ferroelectric Ceramic

We demonstrated both experimentally and in theory analysis and calculation that the PSZT ferroelectric ceramic generator system can perform as a micro power supplying source for IC chip. The ceramic phase transition under transverse shock wave compression can charge external storage capacitor. The ferroelectric micro pulsed power system is capable of generating low output voltage pulses with amplitudes 50.3 V and with transferred energy 1.12 mJ, and supplying IC chip with micro power sources. We developed the methodology for theory analysis and experimental operation of the ferroelectric generator. The experimental results were in good agreement with the theory analysis.

The Evolution Equation for Wave Processes of the Shift Deformation

One-dimensional process of formation and the subsequent motion of a plane transverse shock wave is studied on the basis of solutions of the corresponding nonlinear evolutionary equation. This equation defines behaviour of the solution in front area of wave process and follows from inner series of a matched asymptotic expansions method. A comparative analysis of the volume deformation and forming processes will be carried out and their basic differences are specified. In the capacity of model examples solutions of some concrete boundary value problems of a dynamic shear deformation are observed.

Oblique detonation wave stability around a spherical projectile by a high time resolution optical observation

Spherical projectiles were launched into detonable mixtures over a wide range of projectile velocities from near to about 1.8 times the Chapman–Jouguet (C–J) velocity. Oblique detonation waves (ODWs) and shock-induced combustions (SICs) stabilized around the projectiles were visualized with high time and high spatial resolutions using the Schlieren technique and a high-speed camera with a 1-μs frame speed. Unsteady wave structures called Straw Hat type structures consisting of a SIC region followed by a C–J ODW were observed near stabilizing criticalities of a C–J ODW, and they were divided into two propagation types, depending on whether the C–J ODW could be stabilized [11,12,14]. In the present study, we suggested wave structures of the Straw Hat types based on our examination of dozens of continuous images. Triple points were observed at the intersection of a bow shock, a C–J ODW and a transverse detonation or shock wave when projectile velocities were slightly higher than C–J velocities. Onsets of local explosions in the SIC region for stabilizing the ODW in the Straw Hat type structures have been reported [14]. We observed this stabilizing mechanism by visualizing onsets of periodical local explosions and their transition to spherical detonation waves when the projectile velocity was much higher than the C–J velocity. We also determined stabilizing criticalities using a stoichiometric acetylene-oxygen mixture diluted with argon or krypton in 50% or 75% volumetric fractions, respectively. We found that the stabilizing criticalities did not depend only on the ratio of the projectile diameter and the cell size of the mixture.

Note: Miniature 120-kV autonomous generator based on transverse shock-wave depolarization of Pb(Zr0.52Ti0.48)O3 ferroelectrics

The design of autonomous ultrahigh-voltage generators with no moving metallic parts based on transverse explosive shock wave depolarization of Pb(Zr(0.52)Ti(0.48))O(3) (PZT 52∕48) poled ferroelectrics was explored and studied. It follows from experimental results that the output voltage produced by the shock-wave ferroelectric generators (FEGs) is directly proportional to the number of PZT 52/48 elements connected in series. It was demonstrated that miniature FEGs (volume less than 180 cm(3)) were capable of reliably producing output voltage pulses with amplitudes exceeding 120 kV which is the record reported in open literature.

Interaction of a laser-produced copper plasma jet with ambient plastic plasma

This work is aimed at the investigation of mutual interaction of plastic (CH) and copper axially symmetric plasmas, and the dependence on the ratio of their ablated masses. For that purpose we irradiated a plastic target with a Cu cylindrical insert of diameter 400 µm with a laser beam of radius exceeding that of the insert. In such an arrangement we were able to control the volumes and masses of interacting CH and Cu plasmas by varying the laser beam diameter. The experiment was carried out at the Prague Asterix Laser System (PALS) iodine laser. The laser provided a 250 ps pulse with an energy of 130 J at the third harmonic frequency (i.e. a wavelength of λ3 = 0.438 µm). The interaction of the laser-driven plasma jet with ambient plasma was studied by means of a three-frame interferometric system and a four-frame x-ray pinhole camera. For simulation of the experiment we used the two-dimensional hydrodynamic code ATLANT-HE. The reported results demonstrated that there is an optimal ratio of Cu and plastic plasma masses, at which stable extended Cu plasma jets can be created. Even a relatively thin plastic plasma envelope can compress the Cu plasma and control the jet formation. Thicker plastic plasma layers, however, lead to complex hydrodynamic motion accompanied by generation of transverse shock waves, which can completely suppress the jet formation. The pressure of the plastic plasma was found to be 1.35 times higher than that of the copper plasma. A theoretical analysis of the experimental results allows us to conclude that this difference in pressures follows from the essential differences in expansion dynamics of plasmas with low and high atomic numbers.

The criterion of the existence or inexistence of transverse shock wave at wedge supported oblique detonation wave

A simplified theoretic method and numerical simulations were carried out to investigate the characterization of propagation of transverse shock wave at wedge supported oblique detonation wave. After solution validation, a criterion which is associated with the ratio Φ (u 2/u CJ) of existence or inexistence of the transverse shock wave at the region of the primary triple was deduced systematically by 38 cases. It is observed that for abrupt oblique shock wave (OSW)/oblique detonation wave (ODW) transition, a transverse shock wave is generated at the region of the primary triple when Φ < 1, however, such a transverse shock wave does not take place for the smooth OSW/ODW transition when Φ > 1. The parameter Φ can be expressed as the Mach number behind the ODW front for stable CJ detonation. When 0.9 < Φ < 1.0, the reflected shock wave can pass across the contact discontinuity and interact with transverse waves which are originating from the ODW front. When 0.8 < Φ < 0.9, the reflected shock wave can not pass across the contact discontinuity and only reflects at the contact discontinuity. The condition (0.8 < Φ < 0.9) agrees well with the ratio (D ave/D CJ) in the critical detonation.

Micro-power generator supplying source for integrated circuit chip based on Pb(Sn,Zr,Ti)O3 ferroelectric ceramic

We have demonstrated both experimentally and theoretically that a tin-modified and niobium-modified lead zirconate titanate (Pb(Sn,Zr,Ti)O3) ferroelectric generator system can function as a micro-power supplying source for integrated circuit (IC) chip of separate nonelectric impulse input shock tube digital delay detonator. The ferroelectric ceramic phase transition under transverse shock wave compression can charge an external storage capacitor. The ferroelectric ceramic micro-pulsed-power system is capable of generating low output voltage pulses with an amplitude of 54.2 V and with transferred energy of 1.73 mJ, ultimately supplying an IC chip with micro-power. This work presents the methodology for theoretical analysis and experimental operation of the ferroelectric generator. Theoretical calculations are conducted based on circuit analysis law and principles of dynamic high pressure and shock wave physics. The experimental results were in good agreement with the theoretical analysis.

Note: Autonomous pulsed power generator based on transverse shock wave depolarization of ferroelectric ceramics

Autonomous pulsed generators utilizing transverse shock wave depolarization (shock front propagates across the polarization vector P(0)) of Pb(Zr(0.52)Ti(0.48))O(3) poled piezoelectric ceramics were designed, constructed, and experimentally tested. It was demonstrated that generators having total volume of 50 cm(3) were capable of producing the output voltage pulses with amplitude up to 43 kV with pulse duration 4 μs. A comparison of high-voltage operation of transverse and longitudinal shock wave ferroelectric generators is given.

Phase transition study of integrated circuit chip power supplying based on ferroelectric ceramic

We introduce the tin-modified and niobium-modified lead zirconate titanate ferroelectric ceramics as a micropower supplying source for integrated circuit chip. The ferroelectric ceramic phase transition under transverse shock wave compression can release the depolarization energy to the external storage capacitor. The porous microstructure ferroelectric ceramic micropower-generator is capable of generating low output voltage pulses with amplitudes 50.3 V and with transferred energy 1.12 mJ, and supplying integrated circuit chip with micropower sources. Theoretical calculations are conducted based on circuit analysis law, principle of dynamic high pressure, and shock wave physics, and the calculated response matches well with experimental data.

Performance of Pre-Stressed Sandwich Composites Subjected to Shock Wave Loading

The present paper experimentally studies the dynamic behaviour of prestressed sandwich composites under blast loading. The in-plane static compression loadings are implemented on the sandwich composites before they are subjected to the transverse shock wave loading. Three different pre-stress levels are chosen. 3-D realtime deformation data are captured by two high-speed photography systems: a backview Digital Image Correlation (DIC) system and a side-view camera system. The results show that pre-stresses can induce local buckling in the front face-sheet of sandwich composites, consequently reduce the blast resistance of sandwich composites.

Currents produced by explosive driven transverse shock wave ferromagnetic source of primary power in a coaxial single-turn seeding coil of a magnetocumulative generator

Experimental and digital simulation studies of the generation of seed currents by an ultracompact (8.66–8.75 cm3 in volume) ferromagnetic explosive-driven generator of primary power (FMG) loaded on the coaxial single-turn seeding coil of a magnetocumulative generator (MCG) have been performed. The operation of the FMG is based on transverse shock wave demagnetization of Nd2Fe14B high-energy hard ferromagnets. The FMG is capable of producing in the coaxial seeding coil of MCG a seed current with peak amplitude I(t)max=3.0 kA and full width at half maximum of 60 μs. The methodology was developed for digital simulation of the seeding processes in the combined FMG/MCG system.

Completely explosive pulsed power minisystem

It is demonstrated that it is feasible to produce pulsed power using an autonomous completely explosive system that harnesses two physical phenomena successively: the transverse shock wave demagnetization of Nd2Fe14B high-energy hard ferromagnets and magnetic cumulation.

Transverse shock wave demagnetization of Nd2Fe14B high-energy hard ferromagnetics

The action of transverse shock waves (the shock wave propagates across the magnetization vector M) on the magnetic phase state of a Nd2Fe14B high-energy hard ferromagnetic was investigated experimentally. The design of the ferromagnetic sample, which was made as a hollow cylinder, has made it possible to dramatically reduce the amount of the explosive that initiates a transverse shock wave in Nd2Fe14B to 1.0 g (for Nd2Fe14B samples weighing 67.5 g). The results of the experiment have shown that the transverse shock wave propagating through Nd2Fe14B causes “hard ferromagnetic-to-paramagnetic” phase transformation terminating by practically complete demagnetization of Nd2Fe14B. Pulse generators based on the transverse shock wave demagnetization of hollow cylindrical Nd2Fe14B samples with diameter of 25.4 mm and length of 19.1 mm are capable of producing high-voltage pulses [peak voltage of 11.3 kV, full width at half maximum (FWHM) of 4.5 μs] and high-current pulses (peak current of 1.93 kA, FWHM of 100 μs, peak power of 27.0 kW). The effect of transverse shock wave demagnetization of high-energy hard ferromagnetic, Nd2Fe14B, was detected.

TRANSVERSE RESONANT OSCILLATIONS IN ACOUSTIC DUCTS

A theoretical study is made of the flow induced by a piston, performing rotational sinusoidal vibrations in a uniform two-dimensional planar duct. A frequency of the forced vibrations is close to a cut-off frequency. It is shown that exactly at a cut-off frequency the steady-state response represents a transverse periodic shock wave, propagating between duct walls and decaying algebraically in the far field.