Behavior Of Shock Waves Research Articles

Single-shot imaging of surface molecular ionization in nanosystems

Abstract Using single-shot velocity map imaging technique, explosion imaging of different ion species ejected from 50 nm SiO2 nanoparticles are obtained excitedly by strong near-infrared and ultraviolet femtosecond laser fields. Characteristic momentum distributions showing forward emission of the ions at low excitation intensities and shock wave behaviors at high intensities are observed. When the excitation intensity is close to the dissociative ionization threshold of the surface molecules, the resulting ion products can be used to image the instant near-field distributions. The underlying dynamics of shock formation are simulated by using a Coulomb explosion model. Our results allow one to distinguish the ultrafast strong-field response of various molecular species in nanosystems and will open a new way for further exploration of the underlying dynamics of laser-and-nanoparticle interactions.

Propagation of one-dimensional planar and nonplanar shock waves in nonideal radiating gas

The present study seeks to investigate a quasilinear hyperbolic system of partial differential equations which describes the unsteady one-dimensional motion of a shock wave of arbitrary strength propagating through a nonideal radiating gas. We have derived an infinite hierarchy of the transport equation which is based on the kinematics of one-dimensional motion of shock front. By using the truncation approximation method, an infinite hierarchy of transport equations, which governs the shock strength and the induced discontinuities behind it, is derived to study the kinematics of the shock front. The first three transport equations (i.e., first, second, and third-orders) are used to study the growth and decay behavior of shocks in van der Waals radiating gas. The decay laws for weak shock waves in nonradiating gas are entirely recovered in the second-order truncation approximation. The results obtained by the first three approximations for shock waves of arbitrary strength are compared with the results predicted by the characteristic rule. Also, the effect of nonideal parameters and radiation on the evolutionary behavior of shock waves are discussed and depicted pictorially.

Kinematics of spherical shock waves in an interstellar ideal gas clouds with dust particles

In this article, a system of partial differential equations governing the one‐dimensional motion of inviscid, self‐gravitating, spherical dusty gas cloud is considered. The evolutionary behavior of spherical shock waves of arbitrary strength in an interstellar dusty gas cloud is examined. By utilizing the method based on the kinematics of the one‐dimensional motion of shock waves, we derived an infinite set of transport equations governing the strength of shock waves and induced discontinuity behind it. By applying the truncation procedure to the infinite set of transport equations, we get an efficient system of finite number ordinary differential equations describing shock propagation, which can be regarded as a good approximation of the infinite hierarchy of the system. The truncated equations describing the shock strength and the induced discontinuity are used to analyze the growth and decay behavior of shock waves of arbitrary strength in the dusty gas medium. We considered the first two truncation approximations and the obtained results for the exponent from the successive approximation and compared our results with Guderley's exact similarity solution and the characteristic rule.

Shock deformation in zircon grains from the Mien impact structure, Sweden

AbstractRecognition of impact‐induced deformation of minerals is crucial for the identification and confirmation of impact structures as well as for the understanding of shock wave behavior and crater formation. Shock deformed mineral grains from impact structures can also serve as important geochronometers, precisely dating the impact event. We investigated zircon grains from the Mien impact structure in southern Sweden with the aim of characterizing shock deformation. The grains were found in two samples of impact melt rock with varying clast content, and in one sample of suevitic breccia. We report the first documentation of so‐called “FRIGN zircon” (former reidite in granular neoblastic zircon) from Mien (pre‐erosion diameter 9 km), which confirms that this is an important impact signature also in relatively small impact structures. Furthermore, the majority of investigated zircon grains contain other shock‐related microtextures, most notably granular and microporous textures, that occur more frequently in grains found in the impact melt than in the suevitic breccia. Our findings show that zircon grains that are prime candidates for establishing a new and improved age refinement of the Mien impact structure are present in the impact melt.

Super-resolved shear shock focusing in the human head

Shear shocks, which exist in a completely different regime from compressional shocks, were recently observed in the brain. These low phase speed (≈ 2 m/s) high Mach number (≈ 1) waves could be the primary mechanism behind diffuse axonal injury due to a very high local acceleration at the shock front. The extreme nonlinearity of these waves results in unique behaviors that are different from more commonly studied nonlinear compressional waves. Here we show the first observation of super-resolved shear shock wave focusing. Shear shock wave imaging and numerical simulations in a human head phantom over a range of frequencies/amplitudes shows the super-resolution of shock waves in the low strain and high strain-rate regime. These results suggest that even for mild accelerations injuries as small as a grain of rice on the scale of mm2 can be easily created deep inside the brain. Statement of SignificanceThe relationship between brain motion and traumatic brain injury remains poorly understood despite many decades of investigation. We have developed high frame-rate ultrasound imaging techniques combined with motion tracking sequences that can capture a previously unobtainable high strain and high strain-rate regime. This quantitative imaging method has led to the discovery that shear waves can develop into shear shocks. To the best of our knowledge, we are the only group in the world that has observed these shear shocks in soft tissue. In this manuscript we demonstrate that shear waves are focused into destructive shocks deep inside the human head where rate-dependent metrics, such as acceleration and strain-rate, are amplified by an order of magnitude. Furthermore, it is shown that the destructive power of these shear shocks is superresolved into tiny areas about the size of a grain of rice. To achieve these results, we have made technical innovations in the field of ultrasound by designing shock-capturing imaging sequences, and simulations tools that can model shear shocks. There is an overwhelming amount of evidence that shear shock wave physics is a necessary and primary component of brain biomechanics and, we hypothesize, brain injury. Local measurements and simulations of this shock wave behavior, which are absent from current biomechanical models of the brain, may fundamentally change the way we approach the design of protective equipment in transportation, sports, playground safety, falls and our understanding of the extreme biomechanical environment to which our brains can be subjected.

Directional shock diode behavior through the interaction of geometric voids in engineered polymer assemblies

With the advent of additive manufacturing (AM) techniques, a new class of shockwave mitigation and structural supports has been realized through the hierarchical assembly of polymer materials. To date, there have been a limited number of studies investigating the role of structure on shockwave localization and whether AM offers a means to tailor shockwave behavior. Of particular interest is whether the mesoscopic structure can be tailored to achieve shockwave properties in one direction of impact vs the other. Here, we illustrate directional response in engineered polymer foams. In situ time-resolved x-ray phase contrast imaging at the Advanced Photon Source was used to characterize these diode-like structures. This work offers a breakthrough in materials technology for the development of protective structures that require augmentation of shock in one direction while diminishing transmission in the opposite direction.

Studying perturbations and wave propagations by lane closures on traffic characteristics based on a dynamic approach

Lane closures cause perturbations and wave propagations on traffic characteristics of freeways and consequently affect traffic flow. To conduct a dynamic analysis regarding the effects of lane closures on traffic characteristics, this study aimed to examine the effects of lane closures as multi-static bottlenecks on the evolution and wave propagation of uniform traffic flow in a four-lane divided freeway based on the field study and macroscopic traffic flow model. One-lane closure is a work zone and two-lane closure occurs when the second lane near the one-lane closure is blocked due to an incident caused by a lane change. In addition, the classical Lighthill–Whitham–Richards (LWR) model was combined with the non-linear Greenshield’s speed–density relation to expand the models for characterizing the behavior of shockwaves under lane closures. Thus, based on numerical procedures regarding the Lax–Friedrichs scheme, the results indicated that wave propagations by two-lane closure have significant effects on the perturbations of traffic flow density which are 1.5 times as much as the wave propagations in one-lane closure. Moreover, one-lane closure reduced the capacity by 21% although the two-lane closure caused a 45% decrease in the capacity. A comparison between expanded LWRρ and LWRu models with the LWR model demonstrated that expanded models under two-lane closure and one-lane closure improved LWR model for the congested condition, and between uncongested and congested traffic condition 15.61% and 39%, respectively. Therefore, expanded models revealed a better performance as a dynamic approach to analyze the behavior of wave propagations in jam traffic conditions compared to LWR model under lane closures.

Interaction of waves in one-dimensional dusty gas flow

Abstract The present study uses the theory of weakly nonlinear geometrical acoustics to derive the high-frequency small amplitude asymptotic solution of the one-dimensional quasilinear hyperbolic system of partial differential equations characterizing compressible, unsteady flow with generalized geometry in ideal gas flow with dust particles. The method of multiple time scales is applied to derive the transport equations for the amplitude of resonantly interacting high-frequency waves in a dusty gas. These transport equations are used for the qualitative analysis of nonlinear wave interaction process and self-interaction of nonlinear waves which exist in the system under study. Further, the evolutionary behavior of weak shock waves propagating in ideal gas flow with dust particles is examined here. The progressive wave nature of nonresonant waves terminating into the shock wave and its location is also studied. Further, we analyze the effect of the small solid particles on the propagation of shock wave.

Supersonic and near-equilibrium gas-driven granular flow

Studies have found the surprising ability of hydrodynamic theory, which is based on the validity of the local thermodynamic equilibrium postulate, to capture the main features of shock waves in supersonic granular gases. However, its underlying mechanism remains unclear. To explore the factors underpinning the relationship between hydrodynamic theory and the behavior of shock waves in granular gases, a discrete particle method was used to systematically study gas-driven granular flow in gas–solid fluidized beds. It was shown that the flow of granular gases is typically supersonic, consistent with the previous understanding of shear granular flow. However, the Knudsen numbers and entropy criterion, which are used to quantify the distance from the local thermodynamic equilibrium state, were generally small. This finding explains why hydrodynamic theory can describe the behavior of supersonic granular flows; that is, shock waves in granular gases are locally near-equilibrium even though they are supersonic. This study also indicates that shock waves in ordinary gases and granular gases are fundamentally different.

On the development of a rotated-hybrid HLL/HLLC approximate Riemann solver for relativistic hydrodynamics

ABSTRACTThis work presents the development of a rotated-hybrid Riemann solver for solving relativistic hydrodynamics (RHD) problems with the hybridization of the HLL and HLLC (or Rusanov and HLLC) approximate Riemann solvers. A standalone application of the HLLC Riemann solver can produce spurious numerical artefacts when it is employed in conjunction with Godunov-type high-order methods in the presence of discontinuities. It has been found that a rotated-hybrid Riemann solver with the proposed HLL/HLLC (Rusanov/HLLC) scheme could overcome the difficulty of the spurious numerical artefacts and presents a robust solution for the Carbuncle problem. The proposed rotated-hybrid Riemann solver provides sufficient numerical dissipation to capture the behaviour of strong shock waves for RHD. Therefore, in this work, we focus on two benchmark test cases (odd–even decoupling and double-Mach reflection problems) and investigate two astrophysical phenomena, the relativistic Richtmyer–Meshkov instability and the propagation of a relativistic jet. In all presented test cases, the Carbuncle problem is shown to be eliminated by employing the proposed rotated-hybrid Riemann solver. This strategy is problem-independent, straightforward to implement and provides a consistent robust numerical solution when combined with Godunov-type high-order schemes for RHD.

A fully coupled thermomechanical dislocation model for explosive crystal (β-HMX) subjected to isentropic compression loading

A fully coupled thermomechanical dislocation model is developed to analyze the thermomechanical responses of explosive crystal β-cyclotetramethylene tetranitramine (β-HMX) subjected to isentropic compression loading. The volumetric thermoelastic deformation is considered by a complete equation of state (logarithmic EoS) and the dislocation-based plasticity includes the automatic transition from the low-rate thermally activated to the high-rate drag limited regime. The proposed model is applied for the first time to simulate isentropic compression experiments (ICE) on oriented HMX single crystals. The calculated results can well capture the isentropic elastic limit, stress relaxation and steeper plastic wave speed of the ICE wave profiles. Nonlinear thermoelasticity by both pressure-dependent elasticity tensor and the complete EoS is shown to be responsible for the obvious steepness in wave profiles. The anisotropic elastoviscoplastic response can be distinctly reflected by detailed dislocation activities on seven slip systems instead of phenomenological model just through empirical determination. Pure isentrope is decoupled from quasi-isentrope by subtracting the contribution from deviatoric strain and thermal effect, providing thermodynamically consistent data for complete EoS. Contributions of anisotropic temperature rises by pressure volume work and dislocation-based plasticity work are influenced by loading history. Results provide insights into understanding the transition from isentropic wave to shock wave and ignition behavior of explosives at the mesoscale under complex thermodynamic scenarios.

Effect of explosion source location on tunnel damage

The experimental study, the results of which are presented in this article, focuses on the shock wave behavior in scale models of tunnel structures and their consequences on the damage of tubes simulating tunnel lining. The source of the explosion is located either on the longitudinal axis of the tunnel or it is located near the bottom of the tunnel. The second case is more akin to reality. This article analyzes the consequences of the location of explosion sources and the influence of their brisance. In order to compare the effects of explosions on the tunnel lining, the effect of the charge deposited on the axis of the tunnel is investigated on a 0.5-m-diameter tube, while the effect of the charge deposited outside the tunnel axis is monitored on a 1-m-diameter tube. Thus, the magnitudes of the brisance may be comparable for both cases. The characteristics of the shock waves are described. The mass of the charges is graded so as not to allow a total collapse of the structure, but to manifest its damage.

Numerical simulations and bifurcation analysis of monotonic and oscillatory magnetosonic shock waves in a spin 1/2 degenerate quantum plasma

Nonlinear propagation of monotonic and oscillatory magnetosonic shock waves in a magnetized degenerate quantum plasma consisting of ions and spin 1/2 nonrelativistic degenerate electrons is examined. The well-known reductive perturbation analysis is applied to obtain a Korteweg–de Vries–Burgers equation (KdVBE). The dissipative system of coupled nonlinear, ordinary, differential equations and the equilibrium points are hereby discussed on the basis of the bifurcation analysis. The nonlinear behaviour of shock wave structures is numerically investigated under the fourth order Runge-Kutta method. Numerical simulations show that the behaviour of monotonic and oscillatory magnetosonic shock waves depends essentially on the effects of quantum statistics and the spin magnetization energy. The present results may be helpful for an in-depth understanding of the nonlinear propagation of magnetosonic waves in magnetized degenerate quantum plasma, which occur in the dense astrophysical objects.

The propagation of weak shock waves in non-ideal gas flow with radiation

In the present paper, the evolutionary behavior of weak shock waves propagating in an unsteady one-dimensional flow in non-ideal radiating gas is analyzed. The effect of thermal radiation under optically thin limit is included in the energy equation of the governing system. The method of asymptotic analysis is used to derive the transport equation describing the propagation of waves under the high-frequency conditions which is also used to determine the time of first wave-breaking conditions. The equation governing the propagation of acceleration waves is also obtained. Furthermore, the movement of disturbance in the shape of saw-tooth profile is discussed. The effect of parameter of non-idealness under the influence of radiative heat transfer, on the decay of sawtooth profile is analyzed.

Evolution of acceleration waves in non-ideal radiative magnetogasdynamics

In the present paper, the evolutionary behavior of weak shock waves propagating in an unsteady one-dimensional flow in non-ideal radiating gas under the effect of transverse magnetic field is examined. For the effect of thermal radiation, the radiative transfer equations are approximated under the optically thin limit. It is observed that a linear solution in the characteristic plane may exhibit a non-linear behavior in the physical plane. The transport equation governing the evolution of weak shock waves is obtained which introduces the conditions for shock formation. The time for the first breaking of the wave is determined. Also, the effect of radiative heat transfer on the growth of compressive waves and decay of expansive waves in ideal and non-ideal magnetogasdynamics regime is discussed.

Visualization of shockwave behavior in water and gelatin

Explosive welding is a popular method that is utilized to bond different types of metals. In particular, with the use of underwater explosive welding technique, the uniform acceleration of a thin plate over a very short flying distance is possible, which makes the technique suitable for the welding of thin plates onto a base plate to modify various properties of the surface of interest for protection against extreme environments. However, the use of water complicates the setup of the assembly, and therefore, in this study, we attempt to use other pressure-transmitting media, such as gelatin, which exhibits shockwave propagation similar to water. The similarity of shockwave propagation of the two materials is confirmed via optical observations utilizing a high-speed camera for two types of explosives. Thus, our findings confirm the viability of the use of gelatin as a pressure-transmitting medium for explosive welding.

Analysis of Aerodynamic Performance of a Microscale Radial Flow Wave-rotor for Gas Turbine Topping Cycle

This paper addresses the aerodynamic design of a radial flow wave-rotor for a microscale gas turbine engine. A, wave-rotor topping gas turbine cycle was described. The wave diagram was used for expressing behaviors of shock and expansion waves in the wave-rotor cells. Finally, geometrical configuration of the wave-rotor was described on the basis of aerodynamic design.

Optical generation and control of spatial Riemann waves.

We extend the concept of Riemann waves (RWs) to the spatial domain and demonstrate for the first time, to the best of our knowledge, Riemann beams with a propagation scenario allowing controllable shock formation in a nonlinear optical system. Similar to their standard counterparts, "shifted" RWs are characterized by a local propagation speed proportional to their local amplitude. Their steepening dynamics can be judiciously controlled by means of an additional phase term. In particular, RWs are generated by properly tailoring the initial phase of an optical beam propagating through a thermal solution of an m-cresol/nylon mixture that exhibits a giant self-defocusing nonlinearity. The experimental results show a controllable steepening and shock wave behavior, in good agreement with the prediction from the simple inviscid Burgers equation.

Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based algorithms with pressure-correction methods as well as fully-coupled pressure-based algorithms have been established as promising alternatives to classical density-based algorithms based on Riemann solvers. The current paper investigates the predictive accuracy of fully-coupled pressure-based algorithms without Riemann solvers in modelling the interaction of shock waves with one-dimensional and two-dimensional bubbles in gas-gas and liquid-gas flows. For a gas bubble suspended in another gas, the mesh resolution and the applied advection schemes are found to only have a minor influence on the bubble shape and position, as well as the behaviour of the dominant shock waves and rarefaction fans. For a gas bubble suspended in a liquid, however, the mesh resolution has a critical influence on the shape, the position and the post-shock evolution of the bubble, as well as the pressure and temperature distribution.

Shock Wave Kinematics in a Relaxing Gas with Dust Particles

Abstract In this article, we considered the evolutionary behaviour of one-dimensional shock waves propagating through a relaxing gas with dust particles in a duct with spatially varying cross section. We adopted the procedure based on the kinematics of a one-dimensional motion to derive an infinite hierarchy of transport equations, which describe the evolutionary behaviour of shock of arbitrary strength propagating through the medium. The first three truncation approximations are considered, and the results are compared with existing results in the absence of relaxation and dust particles. The effects of dust particles and relaxation are studied using numerical computations. The results are depicted for different values of dust and relaxation parameters.