Shock Wave Model Research Articles

A Modified Calculation Method for a Centered Water Nozzle Steam–Water Injector

A centered water nozzle steam–water injector is driven by cold water to pump steam at a low pressure and to produce a high outlet water pressure. It can be used as a safety pump in a light water reactor to inject cooling water into the reactor core with no power supply in case of an accident. In this study, a modified calculation method for a centered water nozzle steam–water injector is proposed and verified by experimental data in the literature. The calculation method consists of a water nozzle model, a steam nozzle model, a mixing section model, and a shock wave model. Comparisons between the calculated results and the experimental results under different inlet steam pressures, inlet water pressures, and back pressures are conducted, and the calculated results show good agreement with the experimental results. The calculated results with different back pressures show that no shock wave occurs in the mixing section when the back pressure is small, but with the back pressure increasing, the pressure undergoes a dramatic increase in the throat tube, and the shock wave position moves towards the inlet of the mixing section. Due to the complexity of shock wave characteristics, it is necessary to conduct a more in-depth study of shock wave characteristics in the mixing section to determine more detailed boundary conditions for shock wave generation.

Ecological Driving for Connected and Automated Vehicles at Unsaturated Intersections Considering Queue Effects

In this paper, an ecological driving (eco-driving) algorithm considering queue effects is proposed for connected and automated vehicles (CAVs) at unsaturated intersections in order to reduce fuel consumption and travel time. Firstly, after the traffic flow parameters are obtained using vehicle-to-infrastructure communication technology, the kinematic shockwave model is used to predict the vehicle queue length at the saturated intersections. Secondly, to decrease fuel consumption, a fuel-saving optimization problem is formulated using the estimated queue length, and for real-time control, the formulated optimization problem is decomposed into two subproblems depending on whether the CAV will stop to queue. Then, to reduce fuel consumption and travel time simultaneously, the eco-driving algorithm is designed, where the trajectory re-optimization process is implemented in order not to block the upstream vehicles. Finally, extensive simulations are carried out on VISSIM to demonstrate the control performance of the proposed eco-driving algorithm on CAVs and on the entire traffic flow. Simulation results show that the proposed eco-driving algorithm can significantly decrease the fuel consumption and travel time of both CAVs and the traffic flow, and higher market penetration rate of CAVs can result in better control performance.

Research on the Influence of Impedance-Layer Changes on the Protective Properties of Wave-Impedance Materials under Hypervelocity Impact

The hypervelocity impact of space debris causes damage or destruction to spacecraft. The continuous damage caused by space debris creates greater requirements for protective materials. Wave-impedance gradient-protection material is a new type of space-debris-protection material with high kinetic-energy dissipation. However, the relationship between the distribution characteristics of the impedance layer and the protective performance is still unclear. This study provides guidance for the design of high-performance wave-impedance gradient materials by establishing the quantitative relationship between impedance-layer distribution characteristics and protective performance. Based on the one-dimensional shock-wave theory, this paper analyzes the propagation process of shock waves in wave-impedance gradient materials, establishes a transmission model of shock waves with changes in impedance layers, and quantitatively studies the influence of the change in wave impedance on the impact pressure, internal-energy conversion, and projectile- breaking characteristics by means of a numerical simulation. The results show that, when the surface and back of the wave-impedance gradient material are titanium alloy and nylon, respectively, the total transmission coefficient increases from 0.206 to a maximum of 0.339 with the continuous change in the gradient. The reduction amplitude of the shock wave with time under the three working conditions is Ti-Al-Mg-Ny > Ti-Al-Ny > Ti-Ny. The relationship of the transformed internal energy is Ti Al-Mg-Ny > Ti-Al-Ny > Ti-Ny, and the projectile breaking area is Ti-Al-Mg-Ny > Ti-Al-Ny > Ti-Ny. The analysis shows that the continuous change in wave impedance is beneficial to reduce the attenuation of the amplitude of the shock wave in the hypervelocity projectile, to keep the stress amplitude of the shock wave at a higher level, and to improve the internal-energy conversion and impact-breaking degree of the projectile, thereby enhancing the protection performance of the wave-impedance gradient material.

Experimental investigation of pressure characteristics behind the reflected shock waves in a metrological shock tube

The pressure behind the reflected shock wave (RSW) in real shock tubes deviates from the ideal behavior. This results in lower measurement accuracy and thus affects experiments and interpretations. The deviations depend on several factors, such as the pressure magnitude, shock tube geometry, and working gas. This study investigated it quantitatively and attempted to accurately describe its characteristics via the introduction of two parameters: pressure gain and pressure rise. To improve the accuracy of the pressure gain measurement, a model of the incident shock wave (ISW) attenuation was proposed and the influence of the shock tube geometry was explored. The experimental results showed that the measurement accuracy was significantly improved: in the cases of 0.07, 0.14, 0.25, and 0.30 mm thick aluminum diaphragms, it was improved by approximately 4, 7, 12, and 22 times, respectively. In addition, a model of the pressure rise dependence on the Mach number of the ISW was constructed through a linear fit of the pressure rise data. Further, the effects of the working gas on the RSW were examined: the results demonstrate that by working with the air the pressure behind the RSW exhibited good stability and amplitude.

Further study on the dynamic loading transmission in cellular solids based on one-dimensional mass-spring model

The characteristics of dynamic loading transmission in cellular solids are studied in the present paper using a one-dimensional (1D) deformation-contact mass-spring model. From the perspective of deformation process, the collisions among adjacent cell walls happen due to the shock-induced localized large deformation and the cellular structure of the material. Two springs representing deformation stress and contact stress, respectively, are introduced to the mass-spring model to represent different deformation and loading transmission mechanisms. Combined with shock-wave model, the contact stress in the densification stage is determined. Both quasi-static and dynamic compression of cellular solids can be described by the 1D mass-spring model, in which the critical impact velocity of the compaction shock is used to distinguish two different compression states. Based on the 1D deformation-contact mass-spring model, several important issues in the dynamic loading transmission in cellular solids, i.e. the deformation-contact process, unloading and reversed loading issue, deformation modes under different loading conditions, stress effectiveness and micro-inertia effect, are examined. The present paper clarifies previous concerns on the mass-spring model and demonstrates its enhanced capability to simulate the dynamic loading transmission in cellular solids.

A spectrum improved peridynamic model for shock wave problems

Most previous peridynamics (PD) based shock wave modeling focuses on the field discontinuity problem but neglects the temporal discontinuous feature. Considering it is of vital importance to reproduce the shock jumps, the spectral properties of PD are studied and improved in this paper. A systematic theoretical analysis is firstly conducted and reveals the overly-dispersive behavior of PD model, including the oscillatory dispersion relation and zero energy modes. To suppress the consequent spurious oscillation, the dissipation effect is nonlocally introduced by viscosity as a minimum variation of conventional PD. Rather than applying the existing viscosities directly, the spectral balance is considered for the good control of both the oscillation and shock width, leading to the proposal of polynomial and force-limited viscous force states. The proposed model is then verified by several impact and explosion cases. The quantification of spectral balance is established and is employed for parameter calibration. The results suggest that the model shows good performance in shock wave modeling, with which both the suppression of oscillation and control of shock width near the shock jump are well achieved.

Comparative study on the copper plasma confined with upward and downward conical cavities in laser-induced breakdown spectroscopy

In this study, the confinement effects of upward and downward conical cavities on laser-induced copper plasma were investigated by optical emission spectroscopy and fast imaging technique. It follows from the time-integrated spectra, the time-resolved spectra, and the spatial distributions of spectral intensity that the superior enhancement effects on spectral intensity are obtained in the upward conical cavity. Compared to the plasmas without confinement, plasma temperature and electron number density are increased in the presence of upward conical cavity, while no enhancements are obtained in the downward conical cavity. Reflection model of shockwave in a conical cavity is established to interpret these phenomena. The enhancement of the plasma plume confined in the upward conical cavity results from the compression of the plume towards its central region by the shockwave, as well as the accelerated collisions between the particles therein. No enhancement effect of the plasma in the downward conical cavity is obtained because of the radial expansion of plasma plume and the population reduction of excited species in the plasma primary core due to the pressure of oblique downward shockwave. This shockwave reflection model is further verified by the fast imaging, where the direct observation of the plasma plume agrees well with the enhancement effects of the two cavities on the spectral intensity.

The behavior of the propagating velocity of rotating detonation waves and counter-rotating shock waves in a hollow combustor

The propagating velocity behavior, mathematical model and influencing factors of rotating detonation waves and counter-rotating shock waves in a hollow combustor with Laval nozzle are investigated. We use our in-house solver BYRFoam developed on OpenFOAM platform. The existence of the shock wave propagating in the opposite direction of the detonation wave in the combustor, called the counter-rotating shock wave, is observed for a wide range. The regular pattern of the propagation of the counter-rotating shock wave is studied and verified by experimental data. The propagating velocity behavior of rotating detonation waves and counter-rotating shock waves is discussed, and the mathematical model of the counter-rotating shock wave is proposed and verified. The results show that there is a clear quantitative relationship between the counter-rotating shock wave and the peak periodic undulation phenomenon of the pressure time curve, that is, the wave packet. This mathematical model connects the counter-rotating shock wave phenomenon in the experiment with the wave packet phenomenon in the experiment. The influencing factors of the counter-rotating shock wave are studied. The results show that increasing inlet total pressure and decreasing nozzle shrinkage ratio can significantly weaken the counter-rotating shock wave in a combustor. Based on this, the relevant parameters of rotating detonation engine (RDE) can be optimized to make the rotating detonation propagate more stable and therefore make the RDE operate more stable, which is of great significance to the practical application of RDE.

On the seismic source function of an underwater explosion

SUMMARYThe seismic source function of an underwater explosion (UWE) is studied based on characteristics of the shock wave and the secondary bubble pulses. A mathematic representation for the full pressure history including overpressure and underpressure caused by both shock wave and bubble pulses is presented. Based on the full pressure model, UWEs’ reduced displacement/velocity potentials both in time and frequency domain are obtained. The new seismic source model overcomes the theoretical inconsistency with the UWE seismic source model presented by Savage & Helmberger taking account of the shock wave overpressure only, and the steady-state reduced displacement potential predicted by the full pressure model is much larger than that predicted by the shock wave model by a factor that would exceed 100 for shallow UWEs. Relative seismic effect between underwater and underground explosions is modelled and the result by the full pressure model is consistent with observations that seismic magnitude of an UWE commonly is much larger than magnitude of an underground explosion of the same yield. And to further validate the full pressure model, Pn spectra of a 10 000lbs UWE off the east coast of Florida detonated on 2016 June 10 are modelled for six regional stations, and the results predicted by the full pressure model agree well with corresponding observations.

Numerical Modeling of Shockwaves Driven by High-Energy Particle Beam Radiation in Tungsten-Made Structures

The investigation of wave propagation in solids requires the development of reliable methods for the prediction of such dynamic events in which the involved materials cover wide ranges of different possible states, governed by plasticity, equation of state, and failure. In the present study, the wave propagation in metals generated by the interaction of high-energy proton beams with solids was considered. In this condition, axisymmetric waves were generated, and, depending on the amount of the delivered energy, different regimes (elastic, plastic, or shock) can be reached. Nonlinear numerical analyses were performed to investigate the material response. The starting point was the energy map delivered into the component as the consequence of the beam impact. The evolution of both hydrodynamic and mechanical quantities was followed starting from the impact and the effects induced on the hit component were investigated. The results showed the portion of the component close to the beam experiences pressure and temperature increase during the deposition phase. The remaining part of the component is traversed by the generated shockwave, which induces high values of strain in a short time or even the failure of the component.

Mechanism Analysis of Rock Failure Process under High-Voltage Electropulse: Analytical Solution and Simulation.

This work aims to investigate and analyse the mechanism of rock failure under high-voltage electropulses in order to evaluate and increase the efficiency of high-voltage pulse technology in geological well drilling, tunnel boring, and other geotechnical engineering applications. To this end, this paper discusses the equivalent circuit of electric pulse rock breaking, the model of shock wave in electro channel plasma, and, particularly, the model of rock failure in order to disclose the rock failure process when exposed to high-voltage electropulse. This article uses granite as an example to present an analytical approach for predicting the mechanical behaviour of high-voltage electropulses and to analyse the damage that occurs. A numerical model based on equivalent circuit, shock wave model, and elasto-brittle failure criterion is developed for granite under electropulse to further examine the granite failure process. Under the conditions described in this study, and using granite as an example, the granite is impacted by a discharge device (Marx generator) with an initial voltage U0 that is 10 kV and a capacitance F that is 5 µF before it begins to degrade at about 40 µs after discharge, with the current reaching its peak at approximately 50 µs. The shock wave pressure then attains a peak at about 70 µs. Dense short cracks form around granite and the dominant cracks grow to an average length of about 20 cm at around 200 µs. The crack width dcr is predicted to be approximately 1.6 mm. This study detects dense cracks in a few centimetres surrounding the borehole, while around seven dominant cracks expand outward. The distribution of the length of the dominating cracks can be inhomogeneous because of the spatial heterogeneity of granite’s tensile strength, however the heterogeneity has an insignificant effect on the crack growth rate, total cracked area, or the number of main cracks. The mechanism of rock failure under electropulse can be well supported by the findings of numerical simulations and analytical studies.

Modeling and simulation of laser shock waves in elasto-plastic 1D layered specimens

The aim of this paper is to study the effect of microstructure heterogeneity upon elasto-plastic wave propagation generated during laser shot peening. We consider a simplified elasto-plastic laminate specimen subjected to uniaxial strain. The microstructure is composed of two phases alternating periodically and perfectly bonded together. The associated PDE system is solved using a high-resolution Godunov scheme, allowing to study the wave propagation in the heterogeneous structure. It is found that, even for a small mechanical contrast between the two phases, the considered laminate microstructure has a significant effect on the distribution of plastic strain. In addition, an elasto-plastic homogenization of the laminate has been carried out, and the resulting Homogeneous Equivalent Medium (HEM) has been used to decrease the computation time of the wave propagation. The HEM-based model is able to reproduce accurately the full-field solution in terms of distribution of mean plastic strain within the specimen and its fluctuation between the two phases.

Transient buildup and dissipation of a compressed plasma shockwave in arc-discharge plasma beams

Electric propulsion offers the advantage of a high specific impulse through a large exhaust velocity and has seen significant progress in space flight applications. Recently, we observed a transient plasma shockwave during pulsed plasma thruster operation when the plasma beam impacted a probe surface. However, details regarding the plasma shockwave formation are still unknown. This work is an experimental investigation of the compression-induced plasma shockwave in the presence of a planar obstruction. To study the complete shockwave buildup and dissipation process, an ultra-high-speed imaging system was set up to visualize the time-resolved shockwave morphology at a sub-microsecond level. In addition, the local magnetic field and plasma density were measured using 2D magnetic coils and a triple Langmuir probe, respectively. The successive images of the shockwave give us a comprehensive understanding of the shockwave buildup process. During the 12 μs operational period of the thruster, two shockwaves were formed during the first cycle of the discharge. It is also interesting to note that there is a 1 μs dissipation period between the two shockwaves with the same cloud of plasma compressing against the probe surface. A shockwave model is also developed to predict the appearance of the two shockwaves. The implication is that the local magnetic field strength can be a key indicator for the plasma shockwave buildup and dissipation process.

Lane-based queue length estimation at signalized intersections using single-section license plate recognition data

Due to full record of discharging vehicle headway, License Plate Recognition (LPR) is used as an ideal source in most existing queue length estimation methods through a double-section detection using shock-wave models or input-output models. However, the impacts of heavy vehicles and miss detection by LPR detectors are mostly ignored. Therefore, this paper proposes a lane-based queue length estimation method using single-section LPR detection, considering miss detection and heavy vehicles. The queue length estimation problem is transformed to a change-point identification problem for discharging headways time-series, using E-Divisive with Medians (EDM) method. The maximal queue length is identified as the change-point of the discharging headways with the maximal differences between queued and non-queued vehicles, considering the queuing homogeneity of a lane group and the miss detection rate of LPR. The proposed method is validated using simulation and empirical cases with promising performance and good robustness under various conditions.

A Theoretical Study of the N2 + H2 Reactive Collisions for High Vibrational and Translational Energies

High translational temperatures appear in the air inside the shock waves layers created by relatively large meteorites, reentry space vehicles, and hypersonic missiles. Under these conditions, reactions between molecular nitrogen and hydrogen are energetically permitted. In the present work, a quasiclassical trajectories study of the N2(v′)+H2(v″) reaction for relative translational energies covering the range of translational energy 20.0≤Etr/kcalmol−1≤120.0 is presented. In the calculations, several values of vibrational quantum numbers v′=0,4,6,8,10,12 and v″=4,6,8,10,12 have been considered. To model the interatomic interactions, a six-dimension global potential energy surface for the ground electronic state of N2H2 was used. The specific initial state reaction cross-sections and rate coefficients are reported. The energy effects produced by the reaction that could influence the shock wave modeling are here considered. An analysis of the possible impact of these processes under the atmospheric composition is also presented.

Micromechanical model of nanoparticle compaction and shock waves in metal powders

A micromechanical model of metal powder compaction is developed as a generalization of the previous model proposed by Mayer et al. (2020). The model is applicable for an arbitrary axisymmetric deformed state including the uniaxial compression and the uniform tri-axial one. It describes the stage of compression of initially spherical particles, the percolation transition to the system of isolated pores and the stage of the collapse of pores. At the first stage, the metal particles are approximated by spheres with indented sectors with two independent indentation depths: One along the dedicated axis and another one along the perpendicular directions. The model of porous medium is formulated in finite deformations and the dislocation-driven plasticity model (Krasnikov and Mayer, 2015) is used to describe the pore collapse at the last stage. MD simulations of uniform tri-axial and uniaxial compression of iron, copper and magnesium nanoparticles of 6, 12 and 18 nanometers in diameter are performed for a number of temperatures. Activity of dislocations, which form dense structures, is the main driver of the plastic deformation of nanoparticles during compaction, while the presence of twins is revealed for copper and magnesium. MD data is used for identification of the model parameters and verification of the model. Bayesian algorithm is implemented for parameter identification, which reveals itself as an efficient tool and allows us to fit the model with the same set of parameters to MD data for all investigated temperatures, particle diameters and modes of compression. The developed and parameterized micromechanical model is embedded into the continuum model of shock wave propagation in metal powder as a constitutive model of the substance. Both partial and complete compaction by the shock wave is investigated by an example of iron. The presence of elastic precursor is revealed for the case of nanopowders because of high yield strength of nanoparticle material achieved due to the strain hardening during the preliminary relaxation under the action of surface tension. At the same time, the precursor is negligible for submicro – and microparticles. Velocities of both the precursor and the plastic shock wave are considerably lower than the sound speed of the bulk metal. This is because the average elastic modulus of powder during compaction is much smaller than that for a compact material.

Improved one-dimensional “piston” model of electrohydraulic shock wave based on discharge current interception

Based on the pulsed current interception of underwater discharge, the characteristics of the steepness of electrohydraulic shock waves (EHSWs) and the peak value still increasing slowly with the electrical energy injection after the acceleration expansion phase of the plasma channel are investigated. The one-dimensional “piston” model of the EHSW generation is improved, and the calculation method for the EHSWs based on the “piston” model is modified. The modified model takes the change of starting points and the rising steepness of EHSWs into account, and the rising edge and peak value of EHSWs can be calculated more precisely.

A Constitutive Modeling and Experimental Effect of Shock Wave on the Microstructural Sub-strengthening of Granular Copper

Micro-sized copper powder (99.95%; O≤0.3) has been shock-processed with explosives of high detonation velocities of the order of 7.5km/s to observe the structural and microstructural sub-strengthening. Axisymmetric shock-consolidation technique has been used to obtain conglomerates of granular Cu. The technique involves the cylindrical compaction system wherein the explosive-charge is in direct proximity with the powder whereas the other uses indirect shock pressure with die-plunger geometry. Numeric simulations have been performed on with Eulerian code dynamics. The simulated results show a good agreement with the experimental observation of detonation parameters like detonation velocity, pressure, particle velocity and shock pressure in the reactive media. A pin contactor method has been utilized to calculate the detonation pressure experimentally. Wide angled x-ray diffraction studies reveal that the crystalline structure (FCC) of the shocked specimen matches with the un-shocked specimen. Field emissive scanning electron microscopic examination of the compacted specimens show a good sub-structural strengthening and complement the theoretical considerations. Laser diffraction based particle size analyzer also points towards the reduced particle size of the shock-processed specimen under high detonation velocities. Micro-hardness tests conducted under variable loads of 0.1kg, 0.05kg and 0.025kg force with diamond indenter optical micrographs indicate a high order of micro-hardness of the order of 159Hv. Nitrogen pycnometry used for the density measurement of the compacts shows that a compacted density of the order of 99.3% theoretical mean density has been achieved.

The modeling of weak shock waves in highly porous powder beds and comments on its relevance to exploding bridgewire (EBW) detonators

A computer modeling study is reported about the constant-piston-velocity compaction response of a 50% porous fine particle and air mixture. It is established that for the 10- $$\upmu \hbox {m}$$ average particle diameter powder chosen (sugar), over the piston velocity range 100–1000 $$\hbox {m}\,\hbox {s}^{-1}$$ , a self-similar shock is formed in 12–14 particle diameters of motion ( $${\approx }\,140~\upmu \hbox {m}$$ ). The shock is found to be statistically bounded, but temporally and spatially variable. At the resulting shock velocities identified for this powder, this results in self-similar behavior if the shock is supported for approximately 100 ns. Therefore, the use of the shock jump equations to estimate the post-shock state is valid after this duration. Further, it is found that a linear shock- and particle-velocity relation works well to model the low-pressure compaction of the powder. The intercept of this relation (commonly called the bulk sound speed in solid materials) is very low (50–100 $$\hbox {m}\,\hbox {s}^{-1}$$ ), but positive. The implications of this powder response on the functioning of exploding bridgewire detonators and the porous pentaerythritol-tetranitrate fill commonly used in them are discussed and compared with other literature on the topic.

Effects of Selective Serotonin Reuptake Inhibitors on Depression-Like Behavior in a Laser-Induced Shock Wave Model.

Primary blast injury can result in depression-like behavior in the long-term. However, the effects of the selective serotonin reuptake inhibitor (SSRI) on the depression induced by mild blast traumatic brain injury (bTBI) in the long-term remain unclear. We generated a mouse model of mild bTBI using laser-induced shock wave (LISW) and administered an SSRI to mice by oral gavage for 14 days after LISW exposure. This study aimed to investigate the mechanisms of SSRI-mediated alleviation of depression-like behavior induced by mild bTBI. Animals were divided into three groups: sham, LISW-Vehicle, and LISW-SSRI. LISW was applied to the head of anesthetized mice at 0.5 J/cm2. Twenty-eight days after the LISW, mice in the LISW-SSRI group exhibited reduced depression-like behavior, a significant increase in the number of cells co-stained for 5-bromo-2'-deoxyuridine (Brd-U) and doublecortin (DCX) in the dentate gyrus (DG) as well as increased brain-derived neurotrophic factor (BDNF) and serotonin levels in the hippocampus compared to the sham and LISW-Vehicle groups. Additionally, levels of phosphorylated cAMP response element binding protein (pCREB) in the DG were significantly decreased in the LISW-Vehicle group compared to that in the sham group. Importantly, pCREB levels were not significantly different between LISW-SSRI and sham groups suggesting that SSRI treatment may limit the downregulation of pCREB induced by mild bTBI. In conclusion, recovery from depression-like behavior after mild bTBI may be mediated by hippocampal neurogenesis induced by increased BDNF and serotonin levels as well as the inhibition of pCREB downregulation in the hippocampus.