Plane Shock Wave Research Articles

Effect of particle arrangement and density on aerodynamic interference between twin particles interacting with a plane shock wave

Unsteady drag, unsteady lift, and movement of one or two moving particles caused by the passage of a planar shock wave are investigated using particle-resolved simulations of viscous flows. The particle motion analysis is carried out based on particle-resolved simulations for one or two particles under a shock Mach number of 1.22 and a particle Reynolds number of 49, and the particle migration and fluid forces are investigated. The unsteady drag, unsteady lift, and particle behavior are investigated for different densities and particle configurations. The time evolution of the unsteady drag and lift is changed by interference by the planar shock wave, Mach stem convergence, and the shock wave reflected from the other particle. These two particles become closer after the shock wave passes than in the initial state under most conditions. Two particles placed in an in-line arrangement approach each other very closely due to the passage of a shock wave. On the other hand, two particles placed in a side-by-side arrangement are only slightly closer to each other after the shock wave passes between them. The pressure waves resulting from Mach stem convergence of the upstream particle and the reflected shock waves from the downstream particle are the main factors responsible for the force in the direction that pushes the particles apart. The wide distance between the two particles attenuates these pressure waves, and the particles reduce their motion away from each other.

The heterogeneous response of martian meteorite Allan Hills 84001 to planar shock

Impact-generated shock waves can change the physical properties of meteorites and their constituent minerals. Accounting for these effects is key to recovering information about the early solar system from meteorite observations. ALH 84001 is a rare ancient sample from the Martian crust, providing a unique window into the thermal and metamorphic evolution of Mars. A well-studied meteorite, past geochemical and petrologic investigations have attempted to deduce its thermal and impact history with some contradictory results. By simulating the passage of a planar shock wave through a synthetic analog for samples of ALH 84001 using the iSALE-2D shock physics code we have determined the meteorite’s likely thermodynamic and physical response during an impact. Our simulations show that heterogeneous shear heating, induced by the planar shock wave, can produce strong thermal gradients on the sub-millimeter ‘mesoscale’ throughout the meteorite, even in relatively weak shock waves (<5GPa). We are able to place new constraints on deformation events experienced by the meteorite during its time on the parent body, including the maximum pressure ALH 84001 has experienced since it acquired its remanent magnetization and its subsequent ejection from Mars.

Collision of localized shocks in AdS5 as a series expansion in transverse gradients

We introduce a computational framework to more efficiently calculate the collision of localized shocks in five dimensional asymptotically Anti-de Sitter space. We expand the Einstein equations in transverse gradients and find that our numerical results agree well with exact solutions already at first order in the expansion. Moreover, the Einstein equations at first order in transverse gradients can be decoupled into two sets of differential equations. The bulk fields of one of these sets has only a negligible contribution to boundary observables, such that the computation on each time slice can be simplified to the solution of several planar shockwave equations plus four further differential equations for each transverse plane ‘pixel’. At the cost of errors of ≲ 10% at the hydrodynamization time and for low to mid rapidities, useful numerical solutions can be sped up by roughly one order of magnitude.

Classical physics from amplitudes on curved backgrounds

We generalise the Kosower-Maybee-O’Connell (KMOC) formalism relating classical observables and scattering amplitudes to curved backgrounds. We show how to compute the final semiclassical state for a particle moving in a curved background in terms of scattering amplitudes on that background. Two-point amplitudes in this framework correspond to conservative physics with background-dependent memory effects. As an application, we consider plane wave and shock wave backgrounds both in electromagnetism and general relativity. We determine the final semiclassical state, showing it satisfies a notion of double copy on curved backgrounds. We then conclude by computing the impulse of a particle on such backgrounds, deriving exact results and velocity memory effects.

Effects of obstacles on shock-induced perturbation growth

Effects of obstacles on interface evolution and mixing width induced by Richtmyer–Meshkov instability are investigated experimentally and numerically. In the experiment, the soap film technique is adopted to create an initial interface whose shape is governed by constraint strips protruding into the flow field. By varying the heights of constraint strips protruding into the flow field, effects of obstacles on post-shock flow features are highlighted. First, the interaction of a planar shock with an unperturbed interface is investigated numerically and experimentally. The results show that the obstacles have negligible effects on the transmitted shock velocity, but they greatly increase the reflected shock velocity. The obstacles induce the non-uniform pressure and velocity fields behind the shock, which change the interface evolution and mixing width. Then, experiments of planar shock wave interacting with single-mode interfaces with different initial amplitudes are performed. Induced by the non-uniform post-shock flow, the experimental schlieren images indicate that the spike tip becomes flat, but its size increases in the spanwise direction and the volume of the bubble is reduced. The effects of obstacles are magnified as their heights increase and are more pronounced when the initial interface amplitudes are small. The linear and nonlinear growth rates obtained from experiments show that the obstacles inhibit the perturbation growth, which is partially caused by less kinetic energy the interface obtains from the shock due to the block by the obstacles.

Turbulence generation by shock interaction with a highly nonuniform medium.

An initially planar shock wave propagating into a medium of nonuniform density will be perturbed, leading to the generation of postshock velocity perturbations. Using numerical simulations we study this phenomenon in the case of highly nonuniform density (order-unity normalized variance, σ_{ρ}/ρ[over ¯]∼1) and strong shocks (shock Mach numbers M[over ¯]_{s}≳10). This leads to a highly disrupted shock and a turbulent postshock flow. We simulate this interaction for a range of shock drives and initial density configurations meant to mimic those which might be presently achieved in experiments. Theoretical considerations lead to scaling relations, which are found to reasonably predict the postshock turbulence properties. The turbulent velocity dispersion and turbulent Mach number are found to depend on the preshock density dispersion and shock speed in a manner consistent with the linear Richtymer-Meshkov instability prediction. We also show a dependence of the turbulence generation on the scale of density perturbations. The postshock pressure and density, which can be substantially reduced relative to the unperturbed case, are found to be reasonably predicted by a simplified analysis that treats the extended shock transition region as a single normal shock.

Interaction of a planar shock wave with two heavy/light interfaces

Interaction of a planar shock wave with two heavy/light interfaces

Vibrational response and temperature of shock-compressed Pt: In situ extended x-ray absorption fine structure measurements to 325 GPa

Single-pulse ($\ensuremath{\sim}100$-ps duration) extended x-ray absorption fine structure (EXAFS) measurements were obtained in laser-shocked Pt to examine atomic vibrational properties and to determine temperatures for shock pressures from 72 to 325 GPa. Pt x-ray absorption spectra were recorded while a planar shock wave was propagating through the Pt sample. The absorption spectrum corresponding to the shocked Pt was obtained by subtracting the ambient Pt contribution from the measured absorption spectrum. Fits to the shocked-state EXAFS data provided Pt lattice parameters consistent with the known Pt Hugoniot and the mean-squared relative displacements (MSRDs) for nearest-neighbor Pt atoms. Pt temperatures in the shocked state, estimated from the MSRDs using the correlated Debye model and correlated Einstein models, were consistent with both the Hugoniot temperatures calculated by integration along the Hugoniot and with the Hugoniot temperatures from published first-principles calculations. However, the agreement between the Hugoniot temperatures from EXAFS measurements and the calculated Hugoniot temperatures is not as good above 200 GPa, likely due to anharmonic effects. The present results demonstrate that single-pulse synchrotron EXAFS measurements in laser-shocked solids are useful for quantitative temperature determination and for examination of vibrational properties, including anharmonicity, at extreme pressure-temperature conditions.

Attenuation and inflection of initially planar shock wave generated by femtosecond laser pulse

Evolution of wavefront geometry during propagation and attenuation of initially planar shock waves generated by femtosecond laser pulses in aluminum is studied. We demonstrate that three stages of shock front inflection take place in consistent hydrodynamics and molecular dynamics simulations.During the first stage, the distance traveled by a near-planar wave DSW≲RL is smaller than the radius of heated laser spot RL. Wave attenuation is associated with one-dimensional plane (1D) rarefaction wave coming from the free surface. Such rarefaction wave shapes the shock wave to a 1D triangular pressure profile along direction normal to target surface with a shock front followed by an unloading tail. The second transitional stage starts after propagation of DSW∼RL, at which the unloading lateral waves begin to arrive to a symmetry axis of flow and initiate inflection of the initially planar shock front. Next at the third stage, the wavefront geometry is finally rounded and rapid attenuation of shock pressure begins at DSW≳RL.It is shown that such divergent shock wave cannot generate plastic deformations in aluminum shortly after propagation of DSW∼RL. Thus, we may estimate the maximal peening depth as a radius of focal spot, which sets an upper limit for the laser shock peening.The cessation of plastic deformation is caused by the fall of the shockwave amplitude below the elastic limit. In this case, the elastic-plastic wave transitions to a purely elastic mode of propagation. For large-sized light spots, this transition ends in the 1D mode of propagation.

Pulse volume discharge behind shock wave in channel flow with obstacle

Action of the localized pulse energy input on the supersonic channel flow around and downstream the obstacle was studied. The pulsed volume discharge with preionization via two plasma sheets was initiated in a non-stationary gas-dynamic flow in the channel with an obstacle (ledge). Experiments were in the shock tube 24mm×48mm with a special discharge chamber. The initial plane shock wave M=2.8–3.4 with a uniform flow behind it passed over the ledge in the form of a parallelepiped of 48mm×6.2mm×2mm, placed on the lower wall of the discharge chamber. The discharge was initiated in different moments of a plane shock wave (and gas flow behind it) movement in the channel. The discharge electric current duration was 200−−500ns. High-speed shadow videos of shock waves from discharge localization zones were recorded. The comparison of shadow flow images, the discharge instant glow images and CFD flowfields were matched. The pulse volume discharge energy was redistributed in the inhomogeneous flowfield (plasma self-localization effect). Influence of the localized pulse energy input on the channel supersonic flow was analyzed: dynamics of shock (blast) waves produced by self-localized plasma in separation areas near the ledge and also discontinuities produces as a result of discontinuities breakdown at oblique shock area ionization. Initial flow configuration disturbed by the pulse volume discharge was restored in time interval up to 120μs.

Shock Hugoniot of porous nanosized nickel

The shock compression of porous nickel from nanosized particles nNi was studied at a pressure range of 4–61 GPa. The average size of the nNi particles was 50 nm, and the porosity of the samples was 50%. Plane shock waves in the samples were generated by the impact of aluminum plates accelerated to velocities ranging from 0.8 to 5 km/s. Laser interferometry was used to monitor particle velocity histories at the interface between the samples and water or LiF windows. The data obtained at pressures below 8 GPa showed a complex shock wave profile with the formation of an elastic precursor wave. The shock Hugoniot and data on the expansion isentropes were obtained. The Hugoniot of nanosized nNi coincided within the experimental errors with the Hugoniot of micron-sized nickel. The Hugoniot calculated on the basis of the equation of state for porous nickel was in good agreement with that of experimental data. It has been established that in the middle pressure range (20–35 GPa), the expansion isentropes in the “pressure–particle velocity” coordinates become noticeably flatter with a significant increase in the particle velocity. The reason for this phenomenon is still unclear. An assumption was made about the onset of particle melting upon reaching pressures above 15 GPa.

Numerical study on the interaction between a shock wave and porous foam and the mitigation mechanism of porous foam filling a straight tube on a blast wave

This study validated a two-phase compressible flow model considering elasto-plastic porous foams. The numerical data were compared with the previous experimental results in terms of the interaction between the planar shock wave and the porous foams and the mitigation effect of a porous foam filling a straight tube on a blast wave. The porous foams in the shock tube interacted with a planar shock wave. The drag between the shocked air and the foams reduced the shock wave strength. Moreover, the flexible foam was significantly deformed by the shock wave. The validation results confirmed good agreement and consistency between the numerical and experimental data. The mitigation effect on the blast wave caused by a high explosive, where the main parameter for comparison was the location of a rigid porous foam layer inside the straight tube, was investigated. In the first case, the porous foam plate was placed on the floor, whereas in the second case, the porous foam plates were placed on the floor, sidewalls and ceiling. The total energy transferred between the porous foam and the shocked air was computed to quantitatively understand the mitigation mechanism of the porous foam on the blast wave. The heat transfer was a dominant factor for the energy transfer from the shocked air to the porous foams. The second case further mitigated the blast wave outside, and the increment of the interface area of the air/porous foam greatly affected the blast wave mitigation.

Assessment of Machine Learning Methods for State-to-State Approach in Nonequilibrium Flow Simulations

State-to-state numerical simulations of high-speed reacting flows are the most detailed but also often prohibitively computationally expensive. In this work, we explore the usage of machine learning algorithms to alleviate such a burden. Several tasks have been identified. Firstly, data-driven machine learning regression models were compared for the prediction of the relaxation source terms appearing in the right-hand side of the state-to-state Euler system of equations for a one-dimensional reacting flow of a N2/N binary mixture behind a plane shock wave. Results show that, by appropriately choosing the regressor and opportunely tuning its hyperparameters, it is possible to achieve accurate predictions compared to the full-scale state-to-state simulation in significantly shorter times. Secondly, several strategies to speed-up our in-house state-to-state solver were investigated by coupling it with the best-performing pre-trained machine learning algorithm. The embedding of machine learning algorithms into ordinary differential equations solvers may offer a speed-up of several orders of magnitude. Nevertheless, performances are found to be strongly dependent on the interfaced codes and the set of variables onto which the coupling is realized. Finally, the solution of the state-to-state Euler system of equations was inferred by means of a deep neural network by-passing the use of the solver while relying only on data. Promising results suggest that deep neural networks appear to be a viable technology also for this task.

Plane shock wave propagation in partially saturated soil

Considered that the gas content of partially saturated soil would decrease under a shock load, which would cause volumetric plastic deformation, Lyakhov's constitutive model is improved. The P-α state equation is used to describe the volume compression relationship of partially saturated soil. Numerical and experimental results are compared to validate the material model. The peak stress and duration of shock wave are crucial to study the dynamic response of underground structures. Considered the saturation of partially saturated soils under natural conditions increases with depth and both peak stress and duration change when shock waves propagate in inhomogeneous media, several partially saturated soil models with linearly decreasing air content in the depth direction are developed. The propagation law of shock waves with various peak stresses and durations in partially saturated soils is studied. The results show that the peak stress caused by the incident load in partially saturated soil first decreases and then increases under incident loads with a shorter duration, and it increases monotonically under incident loads with a longer duration. The rate of change in the incident peak stress is proportional to the air content at the top of the partially saturated soil. The peak free-field stress reaches its maximum, which is 2.2 to 5.5 times the peak stress of the incident load, in fully saturated soil. Long-duration incident loads such as nuclear explosions are more threatening to underground structures than short-duration incident loads. Underground structures buried in fully saturated soil or below fully saturated soil with higher air contents above are more at risk than underground structures buried in partially saturated soil with smaller air contents.

Gigabar shock wave driven by laser-accelerated electron stream

Theoretical and computational results for the generation of a powerful shock wave with pressure behind the front exceeding a gigabar level in the half-space of a solid when the boundary layer is heated by a flux of laser-accelerated electrons are presented. The influence of the energy flux density of the heating stream, the characteristic initial energy and the electron spectrum on the characteristics of the shock wave is investigated. The main attention is paid to the generation of an extremely powerful shockwave, which can be applied in experiments to study the equation of state of matter. For this, the requirements for the parameters of a laser pulse that can ensure the propagation of a plane shock wave with a gigabar pressure when a substance is heated by a beam of laser-accelerated fast electrons, taking into account its divergence, are established. It is shown that one of the features of the propagation of a shock wave under the impact of a thermal piston heated by fast electrons consists in the radiation cooling of the peripheral region of the substance covered by the shock wave. An increase in the compression of matter due to radiation cooling leads to a multiple increase in the density of matter in the peripheral region of the shock wave compared to the density at its front. The final result of this work is to substantiate the use of shock waves driven by a beam of laser-accelerated electrons in a laboratory experiment to study the properties of matter, in particular, metals compressed to a density of several tens of g cc−1 under the action of gigabar pressure.

Observations on the deformation of metal microspheres in shock-driven polymer flows

Solid particles can be fragmented by a fast-moving fluid if their velocity difference is great enough, such as during the atmospheric entry of meteoroids or the shock compression of engineered particulate composites. The extent of particle deformation and breakup in such systems is poorly understood because the necessary extreme conditions make observation difficult and data scarce. To meet this need, experiments combining ultrafast synchrotron-based radiography with plate impact loading were performed at the dynamic compression sector at the advanced photon source. Metal microspheres of several densities and strengths (Au, Ta, and W) were placed inside a polymer matrix. A planar shock wave was then produced in the polymer by the impact of a gun-launched flyer plate. X-ray images of the resulting flow were collected at ∼150 ns intervals. These images document the progression of particle deformation across a range of flow conditions and particle materials. They show that the extent of deformation is sensitive to the ratio of drag stress to particle strength. The deforming particle's shape is determined by the initial shock–particle interaction, fluid stagnation pressure, and vorticity, each acting on its own timescale. A set of scaling relationships is presented to capture these observations and enable comparison with prior hydrodynamic data. The result is a framework for predicting the conditions under which strong particles are severely deformed by a shock-driven flow.

The effect of dust particles on the evolution of planar and non-planar shock wave in two-dimensional supersonic flow of van der Waals gas

The effect of dust particles on the evolution of planar and non-planar shock wave in two-dimensional supersonic flow of van der Waals gas

The Motion of Strong Plane Shock Wave in Highly Viscous Medium

Neglecting the effect of overtaking disturbances, the motion of strong plane shock wave in highly viscous medium has been investigated by Chester-Chisnell- Whitham method. The analytical expressions for shock strength decreases as shock advances for low viscous region of a medium to the high viscous region. The dependence of mach number on propagation distance, Pressure and Particle velocity as well as on adiabatic index has also been analyzed for the cases. The results obtained here are also compared Yadav et al. (2008) for a freely propagating shock. The obtained expansions are computed and discussed through table.

Neural network approach in modelling vibrational kinetics of carbon dioxide

The study is devoted to modeling nonequilibrium vibrational kinetics of carbon dioxide taking into account complex mechanisms of relaxation and intermode energy exchanges. The possibilities of using machine learning methods to improve the performance of numerical simulation of non-equilibrium carbon dioxide flows are studied. Various strategies for increasing the efficiency of the hybrid four-temperature model of CO2 kinetics are considered. The neural network approach proposed by the authors to calculate the rate of vibrational relaxation in each mode turned out to be the most promising. For the problem of spatially homogeneous relaxation, estimates of the error and computational costs of the developed algorithm are carried out, and its high accuracy and efficiency are demonstrated. For the first time, the carbon dioxide flow behind a plane shock wave was simulated in a full state-to-state approximation. A comparison with the results obtained in the framework of the hybrid four-temperature approach is carried out, and the equivalence of the approaches is shown. This makes it possible to recommend developed multitemperature approxima tions as the main tool for solving problems of nonequilibrium kinetics and gas dynamics. The hybrid four-temperature approach using the neural network method for calculating relaxation terms showed the acceleration of numerical simulation in time by more than an order of magnitude, while maintaining accuracy. This technique can be recommended for solving complex multidimensional problems of nonequilibrium gas dynamics, including state-to-state chemical reactions.

Effects of underwater plane shock waves on neutrophil propulsion

Effects of underwater plane shock waves on neutrophil propulsion