Shock Wave Front Research Articles

Torsional waves in hyperelastic shells: Appearing shock waves and energy dissipation

Nonlinear torsional waves propagating in cylindrical shells made of hyperelastic material obeying Ogden model, are studied by a combined approach comprising theoretical and finite element analysis. It was found, apparently for the first time, that delta-like pulses of torsional waves attenuate with distance due to the appearance of shock wave fronts. Moreover, both strain and kinetic mechanical energy dissipate due to the release of thermal energy.

Dust raising law of gas explosion in a 3D reconstruction real tunnel: Based on ALE-DEM model

A method based on the combination of finite element and discrete element theories is proposed to reveal the dust raising law of gas explosion shockwaves in 3D reconstructed real tunnels. The influence of a real tunnel's wall structure on shock wave overpressure is simulated and explored, the mechanism of action of the gas explosion shock wave on coal dust particles is revealed. Results indicate Peak overpressure of the fluid near the uneven walls exceeds that at the center of the tunnel by up to 165%. The sharp increase in shock wave overpressure causes a rapid rise in coal dust. Simultaneously, coal dust can decrease the overpressure at the shock wave front by 6.3% to 34.6%. During the shock wave attenuation period, the ratio between the maximum rise height of coal dust and the total displacement decreases as the distance between coal dust and the explosion source increases.

Pressure dynamics of an internal shock wave emission inside a water droplet and potential cavitation

Shock reflected by a spherical interface is involved in shock-droplet interaction. Here, we investigate the pressure dynamics of an internal spherical shock wave and the potential cavitation inside a spherical water droplet. We conduct hydrodynamic simulation and employ the linear geometrical acoustics approximation to analyze the negative pressure and the wavefront at different intervals d between the source point of the shock and the droplet surface. Studies indicate that the negative pressure at a very large d is primarily attributed to the focusing effect of the droplet surface, whereas the collision of the reflected waves contributes to negative pressure at a small d. The caustic, which is the locus of the cusps (singular points) on the shock wavefront is determined by the parametric equations. Notably, the caustic also has singular points owing to the off-axis reflection. Finally, we evaluate the cavitation inside the droplet. Cavitation occurs on the opposite side of the droplet and moves away from the surface with d increasing, which agrees with previous experimental results. Additionally, we demonstrate that cavitation can occur with less damage to the droplet compared to a planar shock impact on a water droplet.

Appearing shock waves in Arruda – Boyce incompressible rod

The Arruda – Boyce incompressible hyperelastic potentials are used for analyzing one-dimensional acoustic wave propagation in a semi-infinite nonlinearly elastic rod. It has been found that during the propagation of the delta-like pulses, the following phenomena are observed, (i) the shock wave fronts arise; (ii) the pulses spread out due to physical dispersion; (iii) the mechanical energy of the considered system decreases with time, resulting in a decrease of the pulse magnitudes; and, at the same time (iv) thermal energy arises and increases with time, that is caused by formation and propagation of shock wave fronts. The analysis utilizes a combined method consisting of the explicit time integration technique coupled with the finite element method for spatial discretization.

Numerical study on atmospheric explosive welding based on the 2D structured arbitrary Lagrangian-Eulerian method

Smooth particle hydrodynamics (SPH) is often adopted to simulate the waveform interface, which has a crucial effect on the bonding quality in explosive welding (EXW). However, owing to the nature of the SPH method, it is difficult to evaluate the influence of the air medium and calculate detailed waveform structure. In this study, a Cu-Q235 steel EXW model containing air medium was established using a structured arbitrary Lagrangian-Eulerian (S-ALE) method. A full-size 2D model was first performed to acquire welding parameters, which were set to the initial conditions for the next oblique collision method. Subsequently, the experiment was conducted to verify the accuracy of the simulations. The results show that the S-ALE method can effectively predict the waveform and acquire the detailed process of the EXW. With the addition of an air medium, the calculated velocity and pressure of the shock wavefront were approximately 3300 m·s−1 and 15 MPa, respectively. Despite the limited effect of the gas shockwave on the overall waveform, the influence on the large-scale or thin plates cannot be ignored. Furthermore, the simulation indicates that the participation of the air during the wave formation led to the generation of the pore in the vortex zone. The proposed method could predict the waveform structure and optimize the manufacturing process of composite plates in the atmospheric EXW.

Simulation of Relaxation Processes in Hypersonic Flows with One-Temperature Non-Equilibrium Model

Steady-state one-dimensional flows of five-component air behind a normal shock wave are considered with a one-temperature model. A mathematical model is formulated to describe the relaxation of a five-component air mixture with a one-temperature non-equilibrium approximation. A numerical study of non-equilibrium flows of a reacting five-component air mixture behind shock waves at different heights and velocities of free flow is performed. The contribution of different types of reactions to the overall relaxation of the mixture is discussed, and the distributions of macro-parameters of the flow behind the shock wave front are calculated. The lengths of the relaxation zones behind the shock wave front are compared at different initial conditions. Calculations are performed for the standard model of atmosphere.

Terahertz radiation from shockwave front irradiated with femtosecond optical pulses

AbstractFemtosecond double optical pulse experiments with nanosecond time delay were conducted in air. Terahertz pulses were generated from laser plasmas produced by the irradiation with the main pulses on shockwave excited by the pre‐pulse illumination. Intensity of the terahertz pulses depends on the time difference Δt and relative position Δy between the pre‐ and main pulses. We found a characteristic dependence of the intensity of the terahertz pulses on Δy at a longer time delay, Δt = 14.7 ns, which has two maxima while only one maximum was observed when delay times were at and shorter than 9.7 ns. The results are discussed taking into account air density distribution of the shockwave. The terahertz emission spectroscopy shown here can be a useful technique for investigating density structure and its time variation of shockwave with high temporal resolution.

Non-equilibrium aerodynamics between ionization-wave and shock-wave fronts in millimetre-wave supported detonation

A shock wave driven by discharge plasma propagating in a high-power millimetre-wave beam was investigated both experimentally and numerically. A shadowgraph experiment was used to visualize the shock wave and plasma. The ionization wave front of the plasma preceded the shock wave by 2.0–4.0 mm under conditions of 170 GHz beam frequency, atmospheric pressure, and 1.1 GW m−2 peak power density (power density at the beam axis). Furthermore, a two-dimensional computational fluid dynamics (CFD) simulation considering non-equilibrium temperatures and filamentary plasma structures revealed that an ionization-wave front precedes a shock wave front because the energy relaxation requires a few micro-seconds from vibrational excitation at a plasma front to translational excitation for the shock wave formation. Consequently, the distance between an ionization wave front and shock wave front is 3.8 mm in the two-dimensional CFD simulation, which agreed with the experimental results.

ИССЛЕДОВАНИЕ КУМУЛЯТИВНЫХ И УДАРНО-ВОЛНОВЫХ ПРОЦЕССОВ В ВОЗДУШНОЙ СРЕДЕ В СВАРОЧНОМ ЗАЗОРЕ ПРИ СВАРКЕ ВЗРЫВОМ

A photoelectric method is proposed for determining the velocity of the shock wave front in air in the gap between colliding plates during explosion welding. Using traps placed in the welding gap, dispersed metal particles of cumulative origin were discovered, filling the area of shock-compressed air in the gap and significantly affecting the speed of the shock wave front in the air.

Terahertz Radiation from Shockwave Front Irradiated with Femtosecond Optical Pulses

Terahertz Radiation from Shockwave Front Irradiated with Femtosecond Optical Pulses

Role of alpha particles in penetration of solar wind diamagnetic structures into the magnetosphere

We present the results of studies showing the presence of simultaneous jumps in the density of protons (N2/N1)p and alpha particles (N2/N1)α at the boundaries of diamagnetic structures (DS) of various types both in the quasi-stationary slow solar wind (SW) and in sporadic SW. For DS of quasi-stationary slow SW, associated with streamer belt or chains, in the statistics considered in the paper there is a single linear dependence of (N2/N1)α on (N2/N1)p. This means that these jumps have the same physical nature and are related to diamagnetism at the boundaries of DS of quasi-stationary SW streams of various types.
 At the front of interplanetary shock waves (ISW), the (N2/N1)α jump is approximately twice as large as the (N2/N1)p jump. This reflects the features of the collective collisionless plasma heating at ISW fronts and requires further studies. A maximum excess (almost 3 times) of the increase in the alpha-particle density (N2/N1)α over the increase in the proton density (N2/N1)p is observed in eruptive prominences.
 The magnetospheric response in such phenomena as auroras, proton and alpha particle fluxes, geomagnetic field, and geomagnetic pulsations is similar under the influence of DS of various types and ISW. The detected features of the magnetospheric response to the contact with DS of different types and ISW can be interpreted as impulsive passage of the DS matter (plasmoid) into the magnetosphere.
 The results of studies of the (N2/N1)α jumps can be used as an additional important argument in identifying cases of impulsive penetration of DS into the magnetosphere and in examining the physical nature of these penetrations.

Роль альфа-частиц в проникновении диамагнитных структур солнечного ветра внутрь магнитосферы

We present the results of studies showing the presence of simultaneous jumps in the density of protons (N2/N1)p and alpha particles (N2/N1)α at the boundaries of diamagnetic structures (DS) of various types both in the quasi-stationary slow solar wind (SW) and in sporadic SW. For DS of quasi-stationary slow SW, associated with streamer belt or chains, in the statistics considered in the paper there is a single linear dependence of (N2/N1)α on (N2/N1)p. This means that these jumps have the same physical nature and are related to diamagnetism at the boundaries of DS of quasi-stationary SW streams of various types.
 At the front of interplanetary shock waves (ISW), the (N2/N1)α jump is approximately twice as large as the (N2/N1)p jump. This reflects the features of the collective collisionless plasma heating at ISW fronts and requires further studies. A maximum excess (almost 3 times) of the increase in the alpha-particle density (N2/N1)α over the increase in the proton density (N2/N1)p is observed in eruptive prominences.
 The magnetospheric response in such phenomena as auroras, proton and alpha particle fluxes, geomagnetic field, and geomagnetic pulsations is similar under the influence of DS of various types and ISW. The detected features of the magnetospheric response to the contact with DS of different types and ISW can be interpreted as impulsive passage of the DS matter (plasmoid) into the magnetosphere.
 The results of studies of the (N2/N1)α jumps can be used as an additional important argument in identifying cases of impulsive penetration of DS into the magnetosphere and in examining the physical nature of these penetrations.

Feature-informed data assimilation

We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the estimation of state variables and unknown parameters. The observation operator in FIDA is a set-valued functional that involves a search process over a function of state variables, which is fundamentally different from the observation operators in conventional data assimilation. We present three numerical experiments, in which shocks and expanding waves are observed features. These examples serve to demonstrate FIDA's ability to estimate model parameters from such noisy observations.

Oscillating Nonlinear Acoustic Waves in a Mooney–Rivlin Rod

Harmonic wave excitation in a semi-infinite incompressible hyperelastic 1D rod with the Mooney–Rivlin equation of state reveals the formation and propagation of the shock wave fronts arising between faster and slower moving parts of the initially harmonic wave. The observed shock wave fronts result in the collapse of the slower moving parts being absorbed by the faster parts; hence, to the attenuation of the kinetic and the elastic strain energy with the corresponding heat generation. Both geometrically and physically nonlinear equations of motion are solved by the explicit Lax–Wendroff numerical tine-integration scheme combined with the finite element approach for spatial discretization.

Shock-induced melting and crystallization in titanium irradiated by ultrashort laser pulse

Modification of titanium microstructure after propagation of a melting shock wave (SW) generated by a femtosecond laser pulse is investigated experimentally and analyzed using hydrodynamic and atomistic simulations. Scanning and transmission electron microscopy with analysis of microdiffraction is used to determine the microstructure of modified subsurface layers of titanium. We found that two layers are modified beneath the surface. A top surface polycrystalline layer of nanoscale grains is formed from shock-molten material via rapid crystallization. In a deeper subsurface layer, where the shock-induced melting changes into plastic deformation due to attenuation of SW, the grain structure of solid is considerably affected, which results in a grain size distribution differing from that in the intact titanium. Molecular dynamics simulation of single-crystal titanium reveals that the SW front continues to melt even after its temperature drops below the melting curve Tm(P). The enormous shear stress of ∼12 GPa generated in a narrow SW front leads to free slip of atomic planes, collapse of the crystal lattice, and formation of a supercooled metastable melt. Such melt crystallizes in an unloading tail of SW. The mechanical melting ceases after drop in the shear stress giving rise to the shock-induced plastic deformation. The last process triggers a long-term rearrangement of atomic structures in solid. The overall depth of modified layers is limited by SW attenuation to the Hugoniot elastic limit and can reach several micrometers. The obtained results reveal the basic physical mechanisms of surface hardening of metals by ultrashort laser pulses.

High-Speed Flow Visualization by a Nanosecond Volume Discharge during Shock Wave Diffraction on an Obstacle

We study the spatial structure of nonstationary inhomogeneous supersonic airflows as shock wave diffraction on an obstacle occurs in a shock tube of a rectangular cross section. The Mach numbers of shock waves were 2.7–4.4 at initial air pressures of 10–30 Torr. The supersonic flow in the discharge chamber was visualized by high-speed shadowgraphy and by the registration of radiation of combined volume discharge by photo camera and by ICCD camera. In experiments, a combined volume discharge with a current duration of ~ 500 ns was initiated 40–150 μs after the initial shock wave have passed an obstacle. It has been established that the radiation of the volume phase of discharge lasts 400–700 ns, and the displacement of the flow during this time does not exceed 0.6 mm. A correlation is established between the spatial distribution of discharge radiation and the low-density local areas determined as a result of two-dimensional Navier-Stokes based numerical simulation of the flow. As visualized by the glow of the discharge, the shape of the shock wave front is in good agreement with the results of shadowgraphy at different stages of diffraction and with the numerical simulation results.

ON THE INTEGRAL CONVERGENCE OF NUMERICAL SCHEMES CALCULATING GAS-DYNAMIC SHOCK WAVES

A comparative experimental accuracy study of shock-capturing schemes such as RBM(Rusanov-Burstein-Mirin), CWA(Compact high order Weak Approximation) and A-WENO(Alternative Weighted Essentially Non-Oscillatory) schemes is carried out by numerically solving a Cauchy problem with smooth periodic initial data for the Euler equations of gas dynamics. It is shown that in the presence of shock waves, RBM and CWA schemes(in the construction of which nonlinear flux correction is not used) have a higher order of integral convergence, which provides significantly higher accuracy to these schemes (compared to A-WENO scheme) in the areas of shock waves influence, despite noticeable non-physical oscillations at their fronts. This makes it possible to use RBM and CWA schemes as basic ones when constructing combined schemes that monotonically localize shock wave fronts and at the same time maintain higher order accuracy in their influence areas.

Fluxes and spectral indices of rare and abundant nuclei of cosmic rays according to the data of the NUCLEON satellite experiment

During the processing of the data obtained in the space experiment NUCLEON, results were obtained that were of significant astrophysical importance. Using the GALPROP package, the inverse problem of the propagation of cosmic rays from the source (close Supernovae) to the observer was solved, a component spectrum was calculated at the source. It was shown that a systematic change in the power index (slope of the spectrum) was observed at the source, which can be interpreted as incomplete ionization of cosmic rays now of acceleration at the front of the supernova shock wave. Magnetic rigidity spectra analysis was applied for nitrogen nuclei fluxes and the total spectrum of rare nuclei with odd charges from 9 to 19 (F, Na, Al, P, Cl, K). Ratios of odd and even nuclei fluxes are calculated. It turned out that the spectrum of rare, odd nuclei is more rigid than the spectrum of abundant even nuclei (Z = 10–20) at the magnetic rigidity area 300–10 000 GV.

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.

On the Accuracy of Shock-Capturing Schemes Calculating Gas-Dynamic Shock Waves

A comparative experimental accuracy study of three shock-capturing schemes (the second-order CABARET, third-order Rusanov, and fifth-order in space third-order in time A-WENO schemes) is carried out by numerically solving a Cauchy problem with smooth periodic initial data for the Euler equations of gas dynamics. In the studied example, the solution breaks down and shock waves emerge. It is shown that the CABARET and A-WENO schemes, which are constructed using nonlinear limiters as a stabilization mechanism, have approximately the same accuracy in the areas of shock wave influence, while the nonmonotone Rusanov scheme has significantly higher accuracy in these areas despite producing noticeable nonphysical oscillations in the immediate vicinities of shock waves. At the same time, the combined scheme obtained based on the Rusanov and CABARET schemes localizes shock wave fronts, which are captured in a non-oscillatory manner, and preserves higher accuracy in the areas of the shock influence.