Spherical Shock Research Articles

On using converging shock waves for pressure amplification in shock tubes

While conventional shock tubes have a distinct advantage in dynamic calibration methods due to their inherent capability to generate pressure pulses of desired amplitude and fast rise time, they are limited to the lower levels of the pressure amplitude realization range (≤7 MPa). With the increasing need for a traceable dynamic calibration standard across wider pressure ranges, a novel technique using converging shock waves is demonstrated in this work that pushes the upper limit of the standard shock tube into the medium-high pressure range. The experiments are conducted in the shock tube facility equipped with a test section that smoothly transforms the incident plane shock into a spherical shock wave that converges, accelerates and thereby amplifies its strength many folds. The experimentally recorded pressure traces are compared with numerical simulations performed by an in-house code. Using this technique, pressure pulses with peak amplitudes in the range of 30–40 MPa, with 3.4% uncertainty based on numerical reference profile, were realized in the test section with nominal usage of resources.

Effect of the dynamic pressure on the similarity solution of cylindrical shock waves in a rarefied polyatomic gas

The similarity solution for a strong cylindrical shock wave in a rarefied polyatomic gas is analyzed on the basis of Rational Extended Thermodynamics with six independent fields; the mass density, the velocity, the pressure and the dynamic pressure. A new ODE system for the similarity solution is derived in a systematic way by using the method based on the Lie group theory proposed in the context of the spherical shock wave in a rarefied monoatomic gas in Donato and Ruggeri (J Math Anal Appl 251:395, 2000). The boundary conditions are also specified from the Rankine–Hugoniot conditions for the sub-shock. The derived similarity solution is characterized by only one dimensionless parameter $$\alpha $$ related to the relaxation time for the dynamic pressure. The numerical analysis of the similarity solution is also performed. The solution agrees with the well-known Sedov–von Neumann–Taylor (SNT) solution when $$\alpha $$ is small. When $$\alpha $$ is larger, due to the presence of the dynamic pressure, the deviation from the SNT solution is evident; the strength of a peak near the shock front becomes smaller and the profile becomes broader.

Experimental investigation of interactions between turbulent cylinder wake and spherical shock wave

Interactions between a spherical shock wave and a turbulent cylinder wake are studied with wind tunnel experiments. The shock wave is generated outside the wake and propagates across the turbulent wake. Instantaneous streamwise velocity is measured on the wake centerline while peak overpressure of the shock wave is measured outside the wake after the shock wave has passed across the wake. The experiments are performed for various conditions of the cylinder wake to investigate the influences of the root-mean-squared (rms) velocity fluctuation and of the length of the turbulent region through which the shock wave propagates. The velocity fluctuation opposite to the shock propagation direction is positively correlated with the peak-overpressure fluctuation. The mean peak overpressure decreases after the shock wave propagates in the wake. These relations between velocity and peak overpressure are explained by the shock-surface deformation, where the peak overpressure is increased and decreased, respectively, for the shock surfaces with concave and convex shapes in relation to the shock propagation direction. The correlation coefficients between the velocity and peak-overpressure fluctuations and the rms peak-overpressure fluctuation increase with the rms velocity fluctuation. The rms peak-overpressure fluctuation becomes independent of the turbulent length on the shock ray once the shock wave has propagated through a sufficiently long turbulent region. The peak-overpressure fluctuation has a probability density function (PDF) close to a Gaussian shape even though the PDF of velocity fluctuations in the wake is negatively skewed.

Influence of aqueous foam syneresis on the shock wave propagation velocity

Numerical simulation of the spherical shock pulse propagation in aqueous foam with volumetric liquid fraction of 0.0083 has been carried out in accordance with the published experimental data on the explosion of HE in aqueous foam. The assumption is used that the foam structure is destroyed by the shock wave, which leads to the transformation of the foam into a monodisperse gas-droplet mixture. The system of equations for the two-phase gas-droplet model of aqueous foam includes the laws of conservation of mass, momentum, energy for each phase and the equation for the dynamics of the volumetric liquid fraction in a single-pressure, two-velocity, two-temperature approximations in a three-dimensional formulation and takes into account the forces of the Schiller-Naumann interfacial drag, the Ranz-Marshall interphase contact heat exchange and the effect of foam syneresis on the initial distribution of its volumetric liquid fraction. Realistic equations of state in the form of Peng-Robinson and Mie-Gruneisen are used to describe the thermodynamic properties of air and water that make up a gas-droplet mixture. Numerical modeling of the processes under consideration was carried out in the open software of computational fluid dynamics OpenFOAM using the finite volume method based on the iterative two-step PIMPLE algorithm. The analysis of the effect of foam syneresis on the dynamics of shock pulse in aqueous foam is given. It was found that the uneven distribution of the liquid fraction in the foam, caused by its sedimentation under the gravity, leads to the increase in the shock pulse velocity in upper layers of the foam. In comparative analysis of numerical solutions and experimental data at sensor locations, the importance of taking into account syneresis phenomena in modeling the dynamics of shock wave in aqueous foam is shown. The reliability of calculations obtained by the proposed model is confirmed by their agreement with experimental data.

Exact Self-similar Solution for Spherical Shock Wave in a Non-ideal Gas with Azimuthal Magnetic Field under Isothermal Flow Condition

Exact Self-similar Solution for Spherical Shock Wave in a Non-ideal Gas with Azimuthal Magnetic Field under Isothermal Flow Condition

Influence of Heat Transfer on Decreasing Intensity of a Spherical Explosion in Aqueous Foam

The two-phase model of aqueous foam behavior under strong spherical shock wave (SW) impact, is developed using equations of mixture conservation of momentum, mass and internal energy for each phase in Lagrange variables, taking into account bulk viscosity and interphase heat transfer. The numerical implementation of the model was carried out by the counting method, using the Neu-mann-Richtmyer viscosity and the Courant stability condition. The spherical explosion was modeled in the form of a SW, which has the same energy of charge of explosives, as used in experiments. A satisfactory agreement was obtained between the numerical solution, received by the proposed model, the analytical self-similar L.I. Sedov’s solution on a point spherical explosion in a gas and a new experimental data on the spherical explosion in aqueous foam. The causes, which lead to a significant decrease in amplitude and SW velocity in the studied media, are investigated in detail.

A boundary condition for Guderley’s converging shock problem

The Guderley model of a self-similar imploding shock based on the group invariance of the flow equations is a powerful tool in understanding the behavior of converging shock waves. Two modifications described here improve the predictions of observable quantities in spherical-shock wave experiments. First, a noninfinite boundary condition is established by the isentropic release of the outer pressure. Second, a two-temperature system of ions and electrons allows description of higher temperatures while conserving energy and without perturbing the overall hydrodynamics of the solution. These modifications of the Guderley model improve the prediction of the observables in laser driven spherical shock experiments in reference to a one dimensional (1-D) hydrodynamics code.

Analysis of BLEVE overpressure using spherical shock theory

The near-field hazards from BLEVE including blast, ground force, drag loading from the rapid liquid phase change and projectiles. There are several correlations available in the literature for the far field blast overpressure from a BLEVE, usually requiring the calculation of the available expansion energy and the application of correction factors. However, there is very little information available for near-field effects and how this is affected by the details of vessel failure.This work presents near-field blast overpressure data and prediction models to fill in this gap. First, experimental measurements of overpressure in the near-field of a small scale cylindrical controlled BLEVE experiments with propane (V=0.6L, d =50mm, L=300mm) were performed. Then, this work establishes a prediction model based solely on the vapour phase properties at failure, using shock tube overpressure prediction and spherical shock propagation models.The model predicts well the strongest tests and is conservative with all the others. Scaling the model up to larger scale experimental data from literature shows that it is transposable, proposing a simple physics-based prediction model for BLEVE overpressure.

Nanosecond shock wave-induced surface acoustic waves and dynamic fracture at fluid-solid boundaries.

We investigate the generation and propagation characteristics of leaky Rayleigh waves (LRWs) caused by a spherical shock wave incident on a water-glass boundary both experimentally and numerically. The maximum tensile stress produced on the solid boundary is attributed to the dynamic interaction between the LRWs and an evanescent wave generated concomitantly along the boundary. The resultant tensile stress field drives the initiation of crack formation from pre-existing surface flaws and their subsequent extension along a circular trajectory, confirmative with the direction of the principal stress on the boundary. We further demonstrate that this unique ringlike fracture pattern, prevalent in damage produced by high-speed impact, can be best described by the Tuler-Butcher criterion for dynamic failure in brittle materials. The orientation of the ring fracture extension into the solid also follows closely with the trajectory of the local maximum tensile stress distribution.

Nanodeformation in enstatite single crystals: Simulation of micrometeoroid impacts by femtosecond pulsed laser experiments

Space weathering by micrometeoroid bombardment is a cosmic phenomenon on atmosphere-free celestial bodies, a process that is expected to particularly overprint planetesimals and cosmic dust in debris discs. We reproduced micrometeoroid impact craters by femtosecond pulsed laser irradiation on oriented enstatite single crystals (En93Fs7) to investigate the deformation behavior and its orientation dependence. All microcraters show typical bowl shaped morphologies, a glass surface layer with splash like ejecta material and subsurface layering. Although we could reproduce melting and vaporization as typical space weathering effects in the enstatite experiments, there is no formation of agglutinate particles or metallic nanoparticles (npFe0). The shock effects in the deformation layer consist of planar structures like microfractures and cleavages, amorphous lamellae, stacking faults and clinoenstatite lamellae. Their activation and/or orientation depends on the shock direction. In special orientations we observe the activation of glide systems along specific low indexed crystallographic planes. Due to the short timescale and the high strain rates, the most prominent effect is the failure of enstatite by microfracturing along non-rational crystallographic planes. Common deformation mechanisms reported in meteorites like the formation of clinoenstatite lamellae via shearing along [001] (100) occur less frequently. Shear is apparently the dominant mechanism in the formation of the above-mentioned effects and causes also their modification by frictional heating. The wide-spread formation of amorphous lamellae is, for example, interpreted to be the result of this shear heating along planar structures. We interpret this unconventional deformation behavior as a consequence of the small spatial and temporal scale of the experiments, resulting in a short-lived spherical shock wave with high deviatoric stresses in contrast to a long pressure pulse and quasi-hydrostatic compression in large scale impacts that produce typical shock features.

Shock-wave experiment with the Chelyabinsk LL5 meteorite: experimental parameters and the texture of the shock-affected material)

The shock experiment with Chelyabinsk LL5 light lithology material was performed as a spherical geometry shock. The material experienced shock and thermal metamorphism from the initial S3–4 up to complete melt stage. Temperature and pressure realized were estimated above 2000°С and 90 GPa. Textural shock effects were studied by the means of optical and electron microscopy. By the only experimental impact, all the range of the shock pressures and temperatures was realized. Four zones were revealed from the petrographic analysis: 1 – melt zone, 2 – melted silicates zone, 3 – black ring zone, 4 – weakly shocked initial material. Several features of the material texture were noted: displacement of the metal and troilite phases from the central melt zone; mixed lithology zone formation (light-colored chondrules within the silicate melt); dark-colored lithology ring formation; generation of radial-oriented shock veins. Thus, at the experimental fragment, four texture zones were formed. These zones correspond to the different lithology types of the Chelyabinsk LL5 meteorite, which could be found in different fragments of the meteoritic shower from UrFU collection. The results obtained prove that the shock wave loading experiment could be used for space shock modeling. Therefore, the processes of the small bodies of the Solar system could be experimentally modeled at the laboratory conditions.

Properties of Eu3+-doped zirconia ceramics synthesized under spherical shock waves and vacuum annealing

The work is dedicated to the study of the phase stability of (Zr, Hf, Y, Eu)Ox ceramics with the calculated formula Zr0.41Hf0.41Y0.09Eu0.09O1.91 synthesized by the co-precipitation method and subjected to detonation in spherical shock waves and vacuum annealing at 1700 °C. The phase composition of the starting precursor and ceramic samples was investigated by X-ray diffraction analysis. To analyze the local structure of samples, the method of rare-earth ion spectroscopy was applied with the use of the local cathodoluminescence technique. It was demonstrated that detonation in spherical shock waves leads to a decrease of residual monoclinic phase in ceramics, and vacuum annealing leads to its complete disappearance. The significant changes in the phase composition of ceramics after the impact of high temperature in vacuum and high pressure under spherical shock waves are not observed. Such materials can be used as stable matrices for actinide immobilization or advanced luminescence materials to be applied under extreme conditions.

Cosmic-ray Spectrum Steepening in Supernova Remnants. I. Loss-free Self-similar Solution

Abstract The direct measurements of cosmic rays (CRs), after correction for the propagation effects in the interstellar medium, indicate that their source spectra are likely to be significantly steeper than the canonical E −2 spectrum predicted by the standard diffusive shock acceleration (DSA) mechanism. The DSA has long been held responsible for the production of galactic CRs in supernova remnant (SNR) shocks. The γ-ray “probes” of the acceleration spectra of CRs on the spot, inside the SNRs, lead to the same conclusion. We show that the steep acceleration spectrum can be attributed to the combination of (i) spherical expansion, (ii) tilting of the magnetic field along the shock surface, and (iii) shock deceleration. Because of (i) and (ii), the DSA is efficient only on two “polar caps” of a spherical shock where the local magnetic field is within ≃45° to its normal. The shock-produced spectrum observed edge-on steepens with the particle energy because the number of freshly accelerated particles with lower energies continually adds up to a growing acceleration region. We demonstrate the steepening effect by obtaining an exact self-similar solution for the particle acceleration at an expanding shock surface with an arbitrary energy dependence of particle diffusivity κ. We show that its increase toward higher energy steepens the spectrum, which deeply contrasts with the standard DSA spectrum where κ cancels out.

Shock-Wave Experiment with the Chelyabinsk LL5 Meteorite: Experimental Parameters and the Texture of the Shock-Affected Material

A spherical geometry shock experiment with the light-colored lithology material of the Chelyabinsk LL5 ordinary chondrite was carried out. The material was affected by shock and thermal metamorphism whose grade ranged from initial stage S3-4 to complete melting. The temperature and pressure were estimated at >2000°С and >90 GPa. The textural shock effects were studied by optical and electron microscopy. A single experimental impact has produced the whole the range of shock pressures and temperatures and, correspondingly, four zones identified by petrographic analysis: (1) a melt zone, (2) a zone of melting silicates, (3) a black ring zone, and (4) a zone of weakly shocked initial material. The following textural features of the material were identified: displacement of the metal and troilite phases from the central melt zone; the development of a zone of mixed lithology (light-colored fragments in silicate melt); the origin of a dark-colored lithology ring; and the generation of radiating shock veinlets. The experimental sample shows four textural zones that correspond to the different lithology types of the Chelyabinsk LL5 meteorite found in fragments of the meteoritic shower in the collection at the Ural Federal University. Our results prove that shock wave loading experiment can be successfully applied in modeling of space shocks and can be used to experimentally model processes at the small bodies of the solar system.

Statistics of overpressure fluctuations behind a weak shock wave interacting with turbulence

The overpressure fluctuations behind a weak shock wave interacting with turbulence are studied by wind tunnel experiments, where a spherical shock wave propagates in grid turbulence. The experiments are conducted for various values of the shock Mach number MS0 of the shock wave and turbulent Mach number MT of the grid turbulence. The experimental results show that the root-mean-squared peak-overpressure fluctuation divided by the averaged peak-overpressure, σΔp/⟨Δp⟩, where the inherent noise caused by the experimental facility is removed, follows a power law of MT2/(MS02−1). The probability density functions of the overpressure fluctuations are close to the Gaussian profile for a wide range of MT2/(MS02−1). A shock deformation model based on the deformation due to nonuniform fluid velocity is proposed for the investigation of the influences of turbulence on the shock wave. The deformation changes the cross-sectional area of the ray tube, which is related to the shock Mach number fluctuation of the area. The model for a weak shock wave yields the relation σΔp/⟨Δp⟩≈(1/3)[MT2/(MS02−1)]1/2, which agrees well with the experimental results. The model also predicts the Gaussianity of the peak-overpressure fluctuations behind the shock wave interacting with Gaussian velocity fluctuations. Good agreements between the model and experiments imply that the change in the shock wave characteristics by the interaction with turbulence is closely related to the shock wave deformation caused by the fluctuating turbulent velocity field.

Acceleration of Solar Wind Particles by Traveling Interplanetary Shocks

Abstract The acceleration of thermal solar wind (SW) protons at spherical interplanetary shocks driven by coronal mass ejections is investigated. The SW velocity distribution is represented using κ-functions, which are transformed in response to simulated shock transitions in the fixed-frame flow speed, plasma number density, and temperature. These heated SW distributions are specified as source spectra at the shock from which particles with sufficient energy can be injected into the diffusive shock acceleration process. It is shown that for shock-accelerated spectra to display the classically expected power-law indices associated with the compression ratio, diffusion length scales must exceed the width of the compression region. The maximum attainable energies of shock-accelerated spectra are found to be limited by the transit times of interplanetary shocks, while spectra may be accelerated to higher energies in the presence of higher levels of magnetic turbulence or at faster-moving shocks. Indeed, simulations suggest that fast-moving shocks are more likely to produce very high energy particles, while strong shocks, associated with harder shock-accelerated spectra, are linked to higher intensities of energetic particles. The prior heating of the SW distribution is found to complement shock acceleration in reproducing the intensities of typical energetic storm particle (ESP) events, especially where injection energies are high. Moreover, simulations of ∼0.2–1 MeV proton intensities are presented that naturally reproduce the observed flat energy spectra prior to shock passages. Energetic particles accelerated from the SW, aided by its prior heating, are shown to contribute substantially to intensities during ESP events.

Exact Similarity Solution for the Propagation of Spherical Shock Wave in a van der Waals Gas with Azimuthal Magnetic Field, Radiation Heat Flux, Radiation Pressure and Radiation Energy Under Gravitational Field

We investigated the exact similarity solutions for shock wave propagation in non-ideal gas with radiation heat flux under gravitational field by taking radiation pressure and radiation energy into account in the presence of azimuthal magnetic field for spherical geometry. The solutions are in terms of analytical expressions. Similarity method is used to transform the basic equation from a system of partial differential equation into a system of ordinary differential equations. The system of ODE yields exact solutions for initial magnetic field distributions as power law. Consideration of isothermal approximations, radiation pressure, radiation energy and adiabatic compressibility in gravitating medium into accounts leads to new insights into explosion problem in contrast to earlier model. Finally, the product solution of progressive wave given by Mc. Vittie is used to obtain the exact similarity solution under the consideration that the radiation pressure is not equal to zero and the energy loss due to radiation escape is significant. The Alfven–Mach number effect, the parameter of gravitational effect, the parameter of non-idealness of the gas, the radiation pressure number and the adiabatic exponent gamma of the gas are discussed in detail.

Similarity solution for a spherical shock wave in a non‐ideal gas under the influence of gravitational field and monochromatic radiation with increasing energy

The propagation of a spherical shock wave in a non‐ideal gas with or without gravitational effects is investigated under the action of monochromatic radiation. Similarity solutions are obtained for adiabatic flow between the shock and the piston. The numerical solutions are obtained using the Runge‐Kutta method of the fourth order. The density of the gas is assumed to be constant. The total energy of the shock wave is non‐constant and varies with time. The effects of change in values of non‐idealness parameter, gravitational parameter, shock Mach number, radiation parameter, and adiabatic exponent of the gas on shock strength and flow variables are worked out in detail. It is investigated that the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and, therefore, the distance between the inner contact surface and the shock surface is reduced. A comparison is also made between the solutions in the cases of the gravitating and the non‐gravitating media. It is manifested that the gravitational parameter and the radiation parameter have in general opposite behaviour on the flow variables and the shock strength.

Three-dimensional reconstruction of CME-driven shock–streamer interaction from radio and EUV observations: a different take on the diagnostics of coronal magnetic fields

On 2014 October 30, a band-splitted type II radio burst associated with a coronal mass ejection (CME) observed by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) occurred over the southeast limb of the Sun. The fast expansion in all directions of the plasma front acted as a piston and drove a spherical fast shock ahead of it, whose outward progression was traced by simultaneous images obtained with the Nançay Radioheliograph (NRH). The geometry of the CME/shock event was recovered through 3D modeling, given the absence of concomitant stereoscopic observations, and assuming that the band-splitted type II burst was emitted at the intersection of the shock surface with two adjacent low-Alfvén speed coronal streamers. From the derived spatiotemporal evolution of the standoff distance between shock and CME leading edge, we were finally able to infer the magnetic field strength B in the inner corona. A simple radial profile of the form B(r) = (12.6 ± 2.5)r−4 nicely fits our results, together with previous estimates, in the range r = 1.1−2.0 R⊙.

Propagation of strong shock waves in a non-ideal gas

We studied the problem of converging cylindrical and spherical strong shock waves collapsing at the axis/center of symmetry for a non-ideal gas with constant density. We have applied the perturbation series technique which provides us a global solution to the implosion shock wave problem yielding the results of Guderley's local self-similar solution, which is valid only in the vicinity of the axis/center of implosion. We analyzed the flow parameters by expanding the solution in powers of time and found the similarity exponents as well as the corresponding amplitudes in the vicinity of the shock-collapse. The flow parameters and the shock trajectory have been drawn in the region extending from the piston to the center of collapse for different values of adiabatic coefficient and the non-ideal parameter.