Shock Wave Front Research Articles

Universal turbulence scaling law −8/3 at fusion implosion

A new interpretation of the known results of simulation of the turbulent regime at the time before the stagnation stage of fusion implosion is stated. For this aim, the universal turbulence energy spectrum obtained by the authors with a scaling law −8/3, which corresponds to the exact solution of one-dimensional Euler equations for the dynamics of a compressible medium, is used. It is stated that the scaling law −8/3 has more relevance in comparison with the Kolmogorov spectrum of −5/3 in the inertial sub-range of scales for the compressible turbulence at this stage of fusion implosion. A possible mechanism for the occurrence of the anisotropic spectrum −8/3 in turbulence associated with hydrodynamic instability of rotation of the medium behind the shock wave front is considered.

Shock wave diagnostics with an ultra-short optical fiber probe

We report a highly localized, rapid-response pressure measurement of a shock wave front in a solid by utilizing a miniature fiber-optic-based probe. The probe used was a 100 μm-long fiber Bragg grating (FBG) inscribed on a standard silica communication fiber, 125 μm in diameter. The optical fiber was embedded within a ceramic zirconia ferrule and was shocked axially by a polycarbonate impactor fired from a gas gun. In a second ferrule, included in the same experiment, a 1 mm long FBG was embedded for comparison. Both FBGs were positioned at the front face of their respective ferrules, in order to sense the region where the shock wave is pristine, with no release waves, and where the stress conditions were expected to be constant for a few hundreds of nanoseconds. A simulation has been performed using LS-DYNA software describing the temporal dependence of the axial stress operating on the zirconia target and the embedded fiber gratings. The reflected spectra of both fiber grating probes were interrogated by an array of wavelength division demultiplexers and 200 MHz InGaAs detectors. Both probes exhibited a wavelength shift that corresponded to the pressure profile of the shock wave that traveled through the fiber, agreeing quite well with the predictions of the simulation. The wavelength blueshift was about 3.5 nm under a calculated shock pressure in the silica of 320 MPa, induced by a shock pressure of 700 MPa in the host zirconia target. Overall, the 100 μm probe demonstrated superior measurement capabilities to the 1 mm probe, both in time response and localization, as well as better agreement with the simulation. Multiple probes can be applied to provide high resolution mapping of shock phenomena in space and time, thus assisting in establishing the dynamic properties of materials under impact loading.

A discrete method and experimental study for the propagation of shock wave induced by high-speed projectile entering water-filled tanks

To provide a general view of how the shock waves propagate and multi-reflect in a water-filled tank, a discrete method for the propagation of shock waves produced by high-speed projectile water entry was proposed based on the law of reflection in this present study. This method was employed to analyze the composition of shock wave fronts at typical moments, the reflection history of any point on the reflected wave front, and the reflection history of points on the arc of a continuous reflected wave front without inflection. Meanwhile, a shadowgraph visualization system for shock waves induced by high-speed projectile water entry was designed and used to capture the shock wave front propagation in the water-filled tank. So that, the images and the wave fronts obtained by the discrete method were combined to analyze the propagation characteristics of the shock wave produced by projectile water entry. Good agreements were found between the theoretical predictions and experimental results.

Dynamics of Ultrafast Phase Transitions in (001) Si on the Shock-Wave Front.

We demonstrate an ultrafast (<0.1 ps) reversible phase transition in silicon (Si) under ultrafast pressure loading using molecular dynamics. Si changes its structure from cubic diamond to β-Sn on the shock-wave front. The phase transition occurs when the shock-wave pressure exceeds 11 GPa. Atomic volume, centrosymmetry, and the X-ray-diffraction spectrum were revealed as effective indicators of phase-transition dynamics. The latter, being registered in actual experimental conditions, constitutes a breakthrough in the path towards simple X-ray optical cross-correlation and pump-probe experiments.

Molecular dynamics simulation of the shock response of materials: A tutorial

The aim of this Tutorial is to help new researchers understand how to perform molecular dynamics (MD) simulations of the shock response of materials and to provide a brief discussion of how MD can provide important insights into issues in the shock physics of crystalline and amorphous materials. Two distinct approaches for generating shock waves are reviewed. Non-equilibrium MD simulations generate a shock front, usually moving along one axis of the sample, with the processes associated with shock wave propagation monitored throughout the simulation. Equilibrium MD simulations characterize the equilibrated state of a shocked material behind the shock wave front, without explicit consideration of the dynamics of wave propagation. Ultimately, using either method, and by using analysis techniques capable of extracting thermodynamic information and identifying defects, MD simulations can provide a powerful mechanistic understanding of shock that complements shock experiments.

Shock wave analysis: A case-study of Magnezitovaya Mine

The article presents the studies into the impact of shock waves induced by underground blasting. The instrumental measurement of actual pressures at the shock wave front in air in Magnezitovaya Mine during blasting is performed. Using the measurement data, the safe distances of shock wave impact out of possible personnel injury risk are determined. The excess pressure at the shock wave front in mine air is calculated with regard to local pressure losses. The calculated excess pressures are compared with the maximum allowable pressures for personnel, timber cofferdams, ventducts, appliances and power lines.

Numerical investigation on flow and film cooling characteristics of coolant injection in rotating detonation combustor

The film cooling is a possible active thermal protection solution for the rotating detonation engines. As the rotating detonation wave is of high periodic and unsteady features, the film cooling characteristics inside the rotating detonation combustor are very complicated. To illustrate the influence of rotating detonation wave on the flow dynamics of coolant jets and the thermal protection performance of film cooling in the rotating detonation combustor, a numerical investigation is performed in the current study, on the base of a simplified physical model wherein only single row of film cooling holes in the axial direction is concerned. The results show that both the blocking effect and oscillating effect occur in the transverse jet injection, upon the impact of sweeping of detonation wave and oblique shock wave. Due to the occupancy of momentary combusting flow invasion into the film cooling hole during one cycle of wave sweeping, the inward flow from the film cooling hole to the combustor chamber is not the pure ‘coolant jet’ but instead of a ‘mixed’ jet. The blocking effect of sweeping oblique shock wave front on the coolant jet injection is significantly weaker when compared to the detonation wave front. With the use of film cooling, the time-averaged temperature on the outer wall of the combustor chamber is reduced effectively, especially in the middle and rear sections of the rotating detonation combustor. The coolant jet injection does not change propagation speed of the rotating detonation wave but reduces a little the peak pressure and peak temperature of each cycle.

Full-field strain measurement using optimal path search method with error control

Digital image correlation (DIC) is one of the main means of optical measurement of the strain field. However, there has been little discussion on the calculation errors at positions with abrupt change. This study seeks to address how to reduce the full-field strain calculation errors and improve the strain accuracy. An optimal path search method (OPSM) with error control for a full-field strain solution is proposed by optimizing the algorithm of the traditional DIC method, using the material displacement field with abrupt change. The strain calculation considering the calculation zone boundary, hole, and shock wave front is discussed. A comparison of the results using the proposed method with the theoretical results shows that this method can effectively obtain full-field strain information, especially at positions with abrupt change in displacement. The application of OPSM to the cellular structure in a quasi-static compression experiment again verifies the validity. This method not only is comparable with the original method in the noise suppression effect but also ensures the approximation of the results to the true values in the displacement zone with abrupt change.

RADIATIVE CHARACTERISTICS OF SHOCK HEATED OXYGEN

The emission spectra of oxygen behind the front of a strong shock wave have been studied in the shock wave velocity ranges of 5.7—7.4 and 8.1—10.0 km/s at pressures before the wave front of 1.0 and 0.25 Torr. Time-integrated sweeps of radiation in a wide spectral range of 200—675 nm as well as temporal oscillograms&#x0D; of oxygen radiation have been obtained. An analysis of the obtained panoramic spectra shows that at low velocities of the shock wave, the system of Schumann—Runge molecular bands dominates in the emission spectrum. An increase in the shock wave velocity leads to the appearance of intense atomic lines in the emission spectrum. The peculiarities of temporal oscillograms for the most typical spectral lines, such as radiation of molecular oxygen at a wavelength of 213 nm (Schumann—Runge system) and radiation of atomic oxygen at wavelengths of 394 and 645 nm, are highlighted.

Quantitative prediction and ranking of the shock sensitivity of explosives via reactive molecular dynamics simulations

A deep understanding of explosive sensitivities and their factors is important for safe and reliable applications. However, quantitative prediction of the sensitivities is difficult. Here, reactive molecular dynamics simulation models for high-speed piston impacts on explosive supercells were established. Simulations were also performed to investigate shock-induced reactions of various high-energy explosives. The fraction of reacted explosive molecules in an initial supercell changed linearly with the propagation distance of the shock-wave front. The corresponding slope could be used as a reaction rate for a specific shock-loading velocity. Reaction rates that varied with the shock-loading pressure exhibited two-stage linearities with different slopes. The two inflection points corresponded to the initial and accelerated reactions, which respectively correlated to the thresholds of shock-induced ignition and detonation. Therefore, the ignition and detonation critical pressures could be determined. The sensitivity could then be a quantitative prediction of the critical pressure. The accuracies of the quantitative shock sensitivity predictions were verified by comparing the impact and shock sensitivities of common explosives and the characteristics of anisotropic shock-induced reactions. Molecular dynamics simulations quantitatively predict and rank shock sensitivities by using only crystal structures of the explosives. Overall, this method will enable the design and safe use of explosives.

Crystallographic-orientation-dependence plasticity of niobium under shock compressions

Plastic deformation mechanism of metals under shock compressions is one of longstanding interests in compression science and materials related field. In this work, shock responses of Nb under the shock compressions along [001], [110] and [111] directions are investigated using large-scale nonequilibrium molecular dynamics (NEMD) simulations. A new reliable embedded atom method (EAM) potential is specially developed for purposes of studying the deformation twinning under high pressures. Our results indicate that the shock wave front exhibits split two-wave structures in all three shock direction. In contrast to traditional understandings, the overdriven pressure of [110] is smaller than that of [001], which is attributed to their different twinning threshold and growth speed. The deformation twins are considerably more pronounced for the shock along [001] and [110] directions than that along [111] direction, which take place along {112}〈111〉 systems. Twins nucleate at the shock front and rapidly grow accompanied by dislocation nucleation and multiplication between the twins. Different twinning mechanisms for the shock along [001] and [110] directions are identified. For the shock along [001], the deformation twin is formed through successive movements of atoms on the alternative (11¯2) plane along the [11¯0] and [11¯3¯] direction. For the shock along [110], the atoms on each (112¯) plane directly move along the [111] direction layer by layer. Using a lattice model combined with the transition state theory, we find that uniaxial compressions along specific directions play the key role for the twinning mechanism.

БІФУРКАЦІЯ ФРОНТІВ РОЗРИВНИХ ХВИЛЬ В ПРУЖНОМУ ШАРУВАТО НЕОДНОРІДНОМУ СЕРЕДОВИЩІ

The paper considers the problem of the transformation of the fronts of weak shock waves in inhomogeneous elastic media with an almost layered structure. The research object is nonstationary wave with strong discontinuity generated in in inhomogeneous transversely isotropic elastic media The aim of this work is to study the effects of bifurcations of discontinuous waves, in particular, on the tasks of propagation in inhomogeneous rocks of seismic waves provoked by explosions, as well as mountain shocks. The research method is the zeroth approximation of the ray method. The paper considers the issue of restructuring of ray systems and fronts of weak shock waves of elastic media. The heterogeneity of which is caused by the variable characteristics of the medium for the regularity of a continuous function, selected in such a way as to ensure that the medium has acquired the properties of a layered structure, but the properties are described by continuous differentiated functions. The work results can be inculcated in research and projection institutes for design of construction of structures, transport and mine destination with the aim of their seismic protection and their screening from action of discontinuous waves generated by different technical failures. KEYWORDS: SHIELDING, DISCONTINUOUS WAVES, ANISOTROPIC LAYERED MEDIA, ELASTIC MEDIUM, RAY METHOD.

Higher criteria for the regularity of a one-dimensional local field

A coupled problem of gasdynamics, vibrational relaxation, and dissociation in the flow of oxygen behind reflected shock waves is studied. The detailed state-to-state kinetic approach is used, which is based on a coupled solution of the momentum and energy conservation equations with the balance equations for molecular vibrational state populations and concentrations of oxygen atoms. Initial conditions corresponding to recent experiments in shock tubes are considered. For different models of physicochemical processes, a comparison is made with experimental data; varying the model parameters yields satisfactory agreement of all gas-dynamic parameters with the measured ones. The key feature of the proposed approach is the allowance for partial vibrational-chemical relaxation in the time interval between the incident and reflected shock waves. When relaxation between the shocks is not frozen, the reflected shock wave propagates through a vibrationally nonequilibrium gas, which significantly affects kinetics and gas dynamics. Accounting for partial relaxation ensures good agreement between the pressure calculated behind the front of the reflected shock wave and the pressure measured in the experiment. On the other hand, comparison with the vibrational temperature calculated indirectly from spectroscopic experimental data under the assumption of frozen relaxation shows noticeable differences near the shock wave front. We conclude that the technique for extracting gas-dynamic parameters fromspectroscopic data has to be improved by taking into account vibrational excitation before the reflected shock wave.

Modeling of dynamic phenomena in aqueous foams (review)

Analytical review of investigations aimed at studying the aqueous foam behavior under the shock-wave impact is given. The main approaches and theoretical approximations used in the development of aqueous foams models are analyzed. The two-phase gas-drop model of aqueous foam is considered, based on the laws of conservation of mass, momentum, and energy in accordance with one-pressure, two-velocity, two-temperature approximations. The model describes foam dynamics under a high - intensity impact, which destroys the foam structure into microdroplets, and takes into account interfacial heat transfer, interfacial drag and virtual mass forces and the phenomenon of foam syneresis (deposition). The numerical implementation of the model was carried out using new solvers in the OpenFOAM software. The analysis of the numerical solution of the spherical explosion in aqueous foam is given for the conditions of the literature experimental data. The syneresis influence on the intensity and velocity of shock wave propagation is shown. The two-phase model of aqueous foam is considered, which takes into account its elastic- viscous-plastic properties for conditions of weak impact that does not destroy foam structure. The model takes into account the elastic properties of aqueous foam at small deformations and describes it as a non-Newtonian fluid when the foam changes its state from the elastic to viscoplastic. The weak shock wave propagation dynamics in the layer of aqueous foam with the formation of a two-wave structure, consisting of the main wave and the elastic precursor ahead of it, is analyzed. The process of local aqueous foam compaction zone formation, followed by a gaseous region, behind the shock wave front is shown. The reliability of the obtained results of numerical studies is confirmed by their agreement with the literature experimental data.

Shock induced melting of sapphire

The method for calculation the melting curves of crystalline bodies based on the Debye model of heat capacity and the Lindemann melting rule is proposed. Hugoniot shock adiabate, determined in dynamic experiments and thermophysical characteristics of the substance under normal conditions are used as input data. Mathematically, the calculation of the melting curveis reduced to the Cauchy problem for a system of ordinary differential equations. This system is solved numerically by the Runge-Kutta method. Using the proposed method, the melting curves of copper, silver, gold, and sapphire at high pressures are calculated. The results obtained for copper, silver and gold were compared with available calculated and experimental data to validate the method. Experiments on shock compression of transparent sapphire sampleswere performed, using a Mach-type cumulative explosive generators. Investigated pressure range (280-1350 GPa) covered a region of shock-induced melting. The temperature of shock front was registered by fast optical pyrometer together with shock velocity. Particle velocity andpressure were obtained by impedance matching technique. Satisfactory agreement of calculatedand experimental data on temperature of melting behind the shock wave front in sapphire was obtained.

Analysis of Nano Order Structure of Shock Wave Front Generated by HVI and Propagating in &lt;100&gt; Direction of fcc Metal

It is difficult to determine experimentally the nanometer level structure of shockwave propagating in solid materials. In present study, molecular dynamics (MD) simulation is performed to clarify quantitatively the atom level structure of shockwave propagating in fcc crystalline Al or Ni in the <100> direction. Simulated metal to metal collision model is similar to the experimental equipment of the split Hopkinson pressure bar which is used for the high strain rate deformation test. The non-closed pack (100) plane of the fcc crystal is the collision plane.

Orientation-dependent shock compression behavior of non-porous/porous NiTi shape memory alloy: An atomic scale study

Crystal orientation has a strong influence on the mechanical behavior of a material, especially at high-strain-rate impact loading. In this study, the effects of different crystallographic orientations on the non-porous/porous NiTi shape memory alloy (SMA) under high-strain-rate impact loading are studied by using molecular dynamic methods. The structural phase transformation process, energy propagation trajectory, defect dislocation evolution, and shock wavefront changes of the NiTi SMA under shock compression are comparatively analyzed. The simulation results show that for three typical crystal orientations, [100], [110], and [111], the phase transformation structures extend in the form of disordered dots, "X"-shaped meshes, and line segments, respectively. Both phase transformation and phase transformation-induced plasticity are more likely to occur in the [110] NiTi SMA; thus, more energy is dissipated, and the propagation speed of the shock wave is the lowest. In addition, the magnitude of the shock wave propagation velocity in the three crystal orientations is of the following order: [111] crystal orientation > [100] crystal orientation > [110] crystal orientation. Finally, the presence of voids affects the propagation patterns of the wavefront, and the crystal orientation directly affects the shape of the shock wavefront and the steepness of the shock wavefront for porous samples. In terms of the crystal orientation and voids, the [110] crystal orientation and voids uniformly arranged along a straight line can improve the buffer performance of the single-crystal NiTi SMA under high-strain-rate impact loading.

Numerical Simulation of Diffracted U-Shaped Sonic Boom Waveform

U-shaped sonic booms associated with the dive maneuver of a supersonic vehicle are numerically simulated in this paper. Usual prediction tools for ordinary sonic booms are not suitable for such a waveform because of the breakdown of geometrical acoustics near the caustic. In this paper, nonlinear Tricomi equation approach is used near the caustic to take diffraction into account, whereas augmented Burgers equation analysis is applied away from the caustic where geometrical acoustics is applicable. The U-shaped waveforms predicted by this method are in good agreement with measured data. The effects of atmospheric turbulence are also considered by replacing one-dimensional analysis using augmented Burgers equation with multidimensional wave propagation analysis near the ground surface. Results with the atmospheric turbulence effects show better agreement with measured U-shaped waveform than ones without such effects. It is also found that the amplitude of the tail shock wave, which is much larger than the front shock wave, is more sensitive than the front shock to atmospheric turbulence.

FORMATION OF CRUSHING ZONE AT THE LEVEL OF TAMPING IN THE CONDITIONS OF MASS EXPLOSIONS

The purpose of the work is to study the sequence of formation of the fracture zone in the area of the array above the ends of the system of adjacent charges in connection with the technological parameters of their mutual location. The task of works is the analytically substantiate the dependence of the value of the undamaged area of the array at the level of the bottomhole on the parameters of the system of downhole charges, taking into account the phenomenon of the edge effect. &#x0D; Research results. Data on the dimentions of the part of the massif in the lborewhole that does not participate in the mass deformation motion of the rock during the formation of adjacent downhole funnels are obtained. It is assumed that this area between adjacent charges is the source of the oversized fraction. &#x0D; Originality. The process of formation of the destroyed zone in space above the end of the boreholeis considered step by step: generation of the shock wave front, the symmetry of which is close to spherical, formation of the loosenning funnel system in the second stage, which does not adjacent charges of the total front of the stress wave from the explosion of downhole charges detonated from their bottom. Behind him moves the deformation front of a complex structure. It is assumed that this front in the system of two adjacent charges acquires a shape similar to a vertical wedge inverted by the base towards the free surface. The expected result of such a step-by-step deformation process is the desired degree of crushing of the rock mass at the level of the tamping. &#x0D; Conclusions and practical implications. Theoretically and calculatedly obtained and recommended rational parameters of the location of the system of well charges of limited length to reduce the size of the non-destructive region of the rock mass at the level of the tamping, which improves the design of mass explosions in mountain slopes.

Numerical and experimental investigation of laser shock microhydroforming technology for microforming thin-walled LA103Z alloy foil with complex microfeatures

In this work, laser shock microhydroforming technology was further investigated. This technology employs liquid as the laser-induced shock wave transmission medium to microform a thin-walled LA103Z magnesium–lithium (Mg-Li) alloy foil with six bump features. A finite element model established by Hypermesh/LS-DYNA was used to illustrate the dynamic transmission of the liquid shock wave and the dynamic plastic deformation of the workpiece. The mechanism by which the liquid shock wave interacted with the closed liquid chamber to generate a homogenised shock wavefront was revealed. The dynamic loading form of the liquid shock wave and the characteristics of the microfeatures of the workpiece resulting from this dynamic loading form were also analysed mechanically. A comparison of the effects of liquid type and laser energy in this process showed that using castor oil as the liquid medium at threshold laser energy achieved the best plastic forming effect of the workpiece. Analysis of the thickness distribution of the workpiece revealed that the rupture was concentrated in the shear thinning region at the edge of the bump features caused by the transient large stress when the laser energy exceeded the threshold value.