Shock Wave Propagation Research Articles

Obliquely Propagating Self-Gravitational Shock Waves in Non-Relativistic Degenerate Quantum Plasmas

A rigorous theoretical investigation has been carried out on the propagation of non-linear self-gravitational shock waves (SGSHWs) in a magnetized super dense degenerate quantum plasma system (DQPS) composed of inertia-less non-relativistic degenerate electrons and inertial non-degenerate extremely heavy nuclei/element. The nonlinear propagation of these SGSHWs in the plasma system under consideration is studied by the standard reductive perturbation technique, which is valid for a small finite amplitude limit. The nonlinear dynamics of the SGSHWs are found to be governed by the Burgers equation. The Burgers equation is derived analytically and solved numerically. It has been found that the considered plasma model supports positive potential shock waves only. The fundamental properties (amplitude, steepness, etc.) of these SGSHWs are significantly modified by the variation of kinematic viscosity, obliqueness and number density of the plasma species. The results of our present investigation can be applied to astrophysical compact objects like neutron stars. Journal of Engineering Science 15(1), 2024, 21-29

VELOCITY AND EVOLUTION OF SHOCK WAVES IN SAND WITH INCREASING WATER CONTENT

Interest in the problems of shock wave propagation in saturated porous media is associated with studying seismic exploration issues, modeling the hummer effect during hydraulic fracturing, studying the water-gas impact on formations for the purpose of efficient oil production, etc. Experimental work on waves in bulk media is usually carried out in shock tubes. Traditionally, shock tubes are used to study the characteristics of the propagation of shock waves in various media, to analyze the wave properties of these media based on the speed of the shock waves and the change in the shape of the pulse along the passage of the first – main pulse. In a shock tube equipped with a section of bulk media, the wave is repeatedly reflected from the surface of the porous medium under study and the upper end of the tube. Re-reflected waves can be used to study changes in the environment that occurred under the influence of a shock wave, i.e. as probing pulses. In this article, sounding is understood as identifying acoustic properties (changing the shape of shock pulse diagrams and their velocities). This paper presents the results of experimental studies of the propagation of shock waves of small amplitude in sand with a volumetric content of liquid in the pore space from 0 to 40 %, and illustrates the influence of the presence of liquid in the pores on the shape of the main and probing pulses. The research was carried out using the Shock Tube installation, in the Laboratory of Experimental Hydrodynamics of the Mavlyutov Institute of Mechanics of Ufa Branch RAS. An increase in the speed of wave propagation was established with increasing water saturation of sand in the range from 0 to 40 %. An increase in the amplitude of reflected waves when passing through sand, the formation of peaks and stretching of pulses were discovered. The research results can be used in processing geophysical data to interpret seismograms of sandy deposits saturated with gas-liquid systems.

Self-similar flow behind a shock wave in a gas under the effect of viscosity, heat conduction, and variable ambient density

Self-similar solutions have been investigated to describe the propagation of planar shock waves in a non-ideal gas generated by a piston under viscous stress and heat flux. The equation of state for non-ideal gas incorporates the correction in pressure and volume of the gas. The piston position and ambient density vary exponentially with time. Newton’s law of viscosity is used for the viscous stress and Fourier’s law of heat conduction is taken for heat flux. The viscosity coefficient is taken as constant whereas the thermal conductivity coefficient varies with temperature and density following the power law. The shock jump conditions have been derived for the viscous non-ideal gas using integral form of conservation laws. The shock Reynolds number Re s has been introduced to study the effect of viscosity on shock propagation in non-ideal gas. It is found that similarity solution exists only in an ideal gas under the condition that the ambient density exponent is equal to twice the shock position exponent. This study shows that shock Reynolds number Re s and heat conduction parameter Γ c can be used to control the variation of the flow variables and piston position significantly. The shock strength decreases with increase in the value of shock Reynolds number Re s but is independent of the heat conduction parameter Γ c . The pressure, density, and adiabatic compressibility have significant deviations from high to low viscous flow of ideal gas but the velocity and heat flux undergo negligible change. The results do not support the claim of negligible effect of viscosity in earlier studies and establish the impact of viscosity and heat flux on shock propagation in an ideal gas.

Ultraviolet laser-induced fragmentation of hydrocarbon fuel droplets

The present study aims to understand droplet fragmentation due to instabilities from the radiative heating process. We focus on the plasma-induced breakup mechanism of iso-octane and n-hexane droplets from the nucleation of holes through sheets and instabilities. The plasma generation inside the droplets leads to an intense explosion followed by fragmentation of the droplets. A droplet is suspended in the air using an acoustic levitator and exposed to ultraviolet nanosecond laser pulses. The droplet sizes used are in the range of 0.5–2 mm in diameter, and laser energies are 10–20 mJ per pulse. Initially, plasma formation followed by shock wave emission is observed during the impact of the laser pulse. Afterward, the droplet opens at one side and is stretched vertically to form a liquid sheet. The hole formation and its rapid growth result in the breaking of the thin liquid sheet. Small droplets and ligaments emerge from the circular edge of the sheet, which follows the well-known ligament distribution. This study reveals the detailed analysis of expansion dynamics, evolution of single and multiple holes, and instabilities associated with the liquid sheet. The results observed are categorized into four different mechanisms: (1) plasma formation followed by shock wave propagation, (2) droplet deformation, (3) sheet breakup through nucleation of holes followed by rapid growth, and (4) complete atomization.

Comprehensive analysis of normal shock wave propagation in turbulent non-ideal gas flows with analytical and neural network methods

Shock wave propagation in gases through turbulent flow has wide-reaching implications for both theoretical research and practical applications, including aerospace engineering, propulsion systems, and industrial gas processes. The study of normal shock propagation in turbulent flow over non-ideal gas investigates the changes in pressure, density, and flow velocity across the shock wave. The Mach number is derived for the system and explored across various gas molecule quantities and turbulence intensities. This study analytically investigated the normal shock wave propagation in turbulent flow of adiabatic gases with modified Rankine–Hugoniot conditions. Artificial neural network (ANN) techniques are used to estimate the solutions for shock strength and Mach number training validation phases of back-propagated neural networks with the Levenberg–Marquardt algorithm. The results reveal that pressure ratio with density ratio increase for higher values of increase in the turbulence level as well as intermolecular forces. A reverse trend is observed in velocity coefficient after shock in the presence of adiabatic gas. The regression coefficient values obtained using the network model ranged from 0.999 99 to 1, indicating an almost perfect correlation. These findings demonstrate that the ANN can predict the Mach number with high accuracy.

Stimulation characteristics of natural reservoir system under high-voltage electropulse-assisted fluid injection

This study elucidates the findings of a computational investigation into the stimulation characteristics of natural reservoir systems enhanced by high-voltage electropulse-assisted fluid injection. The presented methodology delineates the comprehensive rock-fracturing process induced by electropulse and subsequent fluid injection, encompassing the discharge circuit, plasma channel formation, shockwave propagation, and hydro-mechanical response. A hydromechanical model incorporating an anisotropic plastic damage constitutive law, discrete fracture networks, and heterogeneous distribution is developed to represent the natural reservoir system. The results demonstrate that high-voltage electropulse effectively generates intricate fracture networks, significantly enhances the hydraulic properties of reservoir systems, and mitigates the adverse impact of ground stress on fracturing. The stimulation-enhancing effect of electropulse is observed to intensify with increasing discharge voltage, with enhancements of 118.0%, 139.5%, and 169.0% corresponding to discharge voltages of 20 kV, 40 kV, and 60 kV, respectively. Additionally, a high-voltage electropulse with an initial voltage of U0 = 80 kV and capacitance C = 5 μF has been shown to augment the efficiency of injection activation to approximately 201.1% compared to scenarios without electropulse. Under the influence of high-voltage electropulse, the fluid pressure distribution diverges from the conventional single direction of maximum stress, extending over larger areas. These innovative methods and findings hold potential implications for optimizing reservoir stimulation in geo-energy engineering.

New insights on cavitating flows over a microscale backward-facing step

This study introduces the first experimental analysis of shear cavitation in a microscale backward-facing step (BFS) configuration. It explores shear layer cavitation under various flow conditions in a microfluidic device with a depth of 60 μm and a step height of 400 μm. The BFS configuration, with its unique characteristics of upstream turbulence and post-reattachment pressure recovery, provides a controlled environment for studying shear-induced cavitation without the complexities of other microfluidic geometries. Experiments were conducted across four flow patterns: inception, developing, shedding, and intense shedding, by varying upstream pressure and the Reynolds number. The study highlights key differences between microscale and macroscale shear cavitation, such as the dominant role of surface forces on nuclei distribution, vapor formation, and distinct timescales for phenomena like shedding and shockwave propagation. It is hypothesized that vortex strength in the shear layer plays a significant role in cavity shedding during upstream shockwave propagation. Results indicate that increased pressure notably elevates the mean thickness, length, and intensity within the shear layer. Instantaneous data analysis identified two vortex modes (shedding and wake modes) at the reattachment zone, which significantly affect cavitation shedding frequency and downstream penetration. The wake mode, characterized by stronger and lower-frequency vortices, transports cavities deeper into the channel compared to the shedding mode. Additionally, vortex strength, proportional to the Reynolds number, affects condensation caused by shockwaves. The study confirms that nuclei concentration peaks in the latter half of the shear layer during cavitation inception, aligning with the peak void fraction region.

Space–time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation

The space–time adaptive ADER–DG finite element method with LST–DG predictor and a posteriori sub–cell ADER–WENO finite–volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical method does not use any ideas of splitting or fractional time steps methods. The modification of the LST–DG predictor has been developed, based on a local partition of the time step in cells in which strong reactivity of the medium is observed. This approach made it possible to obtain solutions to classical problems of flows with detonation waves and strong stiffness, without significantly decreasing the time step. The results obtained show the very high applicability and efficiency of using the ADER–DG–PN method with a posteriori sub–cell limiting for simulating reactive flows with detonation waves. The numerical solution shows the correct formation and propagation of ZND detonation waves. The structure of detonation waves is resolved by this numerical method with subcell resolution even on coarse spatial meshes. The smooth components of the numerical solution are correctly and very accurately reproduced by the numerical method. Non–physical artifacts of the numerical solution, typical for problems with detonation waves, such as the propagation of non–physical shock waves and weak detonation fronts ahead of the main detonation front, did not arise in the results obtained. The results of simulating rather complex problems associated with the propagation of detonation waves in significantly inhomogeneous domains are presented, which show that all the main features of detonation flows are correctly reproduced by this numerical method. It can be concluded that the space–time adaptive ADER–DG–PN method with LST–DG predictor and a posteriori sub–cell ADER–WENO finite–volume limiting is perfectly applicable to simulating fairly complex reacting flows with detonation waves.

Insight into profiled CNT/polymer interphase: A molecular dynamic simulation study of load transfer and shock response

In this paper, by utilising molecular dynamic simulations, profiled carbon nanotubes (CNT), represented by CNT containing bead and spiral structure, were built from warping graphene layers with carefully introduced defects. The tensile behaviour of profiled CNTs, pulling and shock response of profiled CNTs within the polyamide matrix were investigated and compared to the corresponding conventional CNT. The result indicates that as mechanically interlocked with the matrix, profiled CNT could effectively relieve the stress concentration during load transfer by distributing the stress into a larger part of the matrix. In this case, a more efficient load transfer could be achieved, thus contributing to the mechanical performance of the composite without modification of the chemical structure. However, the profiling geometry, which is shaped by defects, will introduce stress concentration within the profile CNTs when subject to a tensile load. The stress concentration may not only deteriorate the tensile performance of CNTs, such as ultimate load at break and modulus but also result in an earlier deformation. In this case, care should be taken during the design phase of the profiled CNT. For shocking responses, profiled CNTs were capable of constraining the local chain move thus contributing to the integrity of the composite system during shockwave propagation.

Numerical Modeling of the Interaction of a Monodisperse Gas Suspension with a Shock Wave Moving at an Angle to the Separation Boundary of a Homogeneous Gas and a Gas Suspension

The work is devoted to the study of the influence of the dispersed phase on the dynamics of gas suspensions during numerical modeling of the dynamics of gas suspensions. In this study, based on the continuum technique of dynamics of inhomogeneous media, the interaction of a shock wave propagating from a homogeneous gas with a gas suspension was numerically simulated. For each of the components of the mixture, a complete hydrodynamic system of equations of motion was solved, which included the equations of conservation of density, the equations of conservation of the spatial components of the momentum of the mixture components, and the equations of conservation of energy of the components. The carrier medium was described as a viscous, compressible heat-conducting gas. The mathematical model took into account interfacial heat transfer. The mathematical model also took into account the interphase exchange of momentum, which included the force of aerodynamic drag, the dynamic force of Archimedes and the force of added masses. The system of equations of the mathematical model was integrated using the finite difference method. To suppress numerical oscillations, a nonlinear correction scheme was used. Large volumetric contents of the dispersed phase were considered. The influence of interfacial interaction on the process of shock wave propagation has been studied.

Lie symmetry approach for shock wave propagation in a self-gravitating non-ideal gas under the influence of monochromatic radiation and magnetic field in rotating medium

Lie symmetry approach for shock wave propagation in a self-gravitating non-ideal gas under the influence of monochromatic radiation and magnetic field in rotating medium

Large Scale Simulation of 3D Fault Rupture Subjected to Far‐Field Loading With PDS‐FEM: Application to the 2018 Palu Earthquake

AbstractSimulating dynamic rupture of fault systems can be computationally demanding, as it requires reproducing complex fault geometry and accurately capturing waves propagating away from the rupture front. It is in particular challenging to predict an initial stress state consistent with fault geometries, heterogeneous distribution of surrounding materials, and far‐field tectonic loading. While standard techniques such as contact analysis and Lagrangian multipliers can be used to model the fault, it can lead to significant computational overhead in FEM. We extended Particle Discretization Scheme‐FEM, which provides numerically efficient crack treatment, without requiring contact analysis, to simulate dynamic fault rupture as a frictional crack propagating along a pre‐existing shear crack surface. Initial stress, which is consistent with initial frictional forces, material distribution and fault geometry, is derived using Coulomb friction and far‐field boundary conditions. The study first demonstrates the ability of the numerical method to reproduce a 2D ideal supershear scenario, and the underlying Burridge‐Andrew rupture mechanism. The methodology is then applied to the large scale simulation of the 2018 Palu earthquake on the Palu‐Koro fault. The simulation successfully reproduces the early and sustained supershear rupture which was observed for the Palu earthquake. Also, it indicates that the presence of an off‐fault damage zone can contribute to the low rupture velocity measured during the earthquake. Unlike sub‐Rayleigh earthquakes, the shockwave propagation was observed to lead to significant amplitudes of the ground motion even far from the fault.

Effects of Particle Migration on the Relaxation of Shock Wave Collisions.

The non-equilibrium characteristics during the shock relaxation process hold a foundational position in various fields. In contrast to the propagation of a single shock wave, the collision process of two shock waves exhibits distinct non-equilibrium features. Employing non-equilibrium molecular dynamics, we simulated the collision of ultra-strong shock waves in a classical gas system, investigating the relationship between equilibrium relaxation time and shock intensity. Tracking the spatial migration of microscopic particles in the shock collision region during the relaxation process, we observed a significant contribution of particle migration to the average energy changes during relaxation. The discussion on particle migration provides a valuable new perspective for understanding the microscopic mechanisms of the relaxation process.

Fracture toughness and cavitation erosion behavior of Fe-based amorphous composite coatings with Ni-coated Al2O3 addition

Fe-based amorphous composite coatings were prepared on 304 stainless steel substrates using atmosphere plasma spraying (APS), aiming to investigate the effect of Ni-coated Al2O3 particles addition on fracture toughness and cavitation erosion behavior of Fe-based composite coatings. The microstructure, phase composition, elastic modulus, microhardness and fracture toughness of the coating were characterized using scanning electron microscopy with energy dispersive spectroscopy (EDS), X-ray diffraction (XRD), microhardness tester and nanoindentation. The cavitation erosion behavior of Fe-based coatings was investigated by ultrasonic vibration cavitation method. Fe-based amorphous composite coatings exhibit a characteristic lamellar microstructure and reveal the presence of amorphous phases along with α-(Fe, Cr), NiO, Ni and Al2O3 crystalline phases. When the content of Ni-coated Al2O3 in coating increases from 0 wt% to 3 wt%, there is slight deterioration in porosity from 3.64 % to 4.75 % and fracture toughness from 2.579 MPa·m1/2 to 2.392 MPa·m1/2, yet an increase in microhardness from 925.4 HV0.5 to 1090.3 HV0.5. The composite coating with 3 wt% Ni-coated Al2O3 demonstrates the peak cavitation resistance and its cumulative mass loss is significantly reduced by 36.4 % compared to the pure Fe-based coating. The cavitation erosion failure of Fe-based amorphous composite coatings is predominantly characterized by the brittle fracture mechanism. The fundamental process driving cavitation erosion damage involves the material peeling and coating delamination instigated by intense micro-jet impact and shock wave propagation. The proposed Fe-based amorphous composite coatings can be applied to improve the anti-cavitation performance of components in contact with high-speed fluids, such as ship propellers and centrifugal pump blades.

Simulations of the optical diffraction patterns produced by the pressure field of a clinical shock wave source

Today, shock waves are used to treat a wide variety of ailments. Consequently, there is a need to develop efficient methodologies for comparing and evaluating the pressure fields generated by different equipment. Hydrophones are commonly utilized for accurate pressure measurements although they can be damaged by pitting due to acoustic cavitation. Furthermore, the range of measurement is limited by the position of the device. Optical methods have also been proposed since the presence of a disturbing device in the wave propagation medium is not necessary, and they provide a broader registering field. Nevertheless, these methods do not provide accurate measurements compared with those obtained with polyvinylidene difluoride or fiber-optic hydrophones. Herein, an optical method for shock wave characterization based on diffraction analysis, that can lead to more precise results, is proposed. The phase fluctuations of a light wave produced when it traverses the shock wave pressure field are calculated. The diffraction patterns produced by this perturbed wave at an observation plane at different propagation distances are presented. Considering the state of the art of high-speed cameras, we conclude that an experimental setup, based on the results reported here, can contribute to the evaluation and comparison of shock wave generators for medical applications.

Repetitive shock waves generated by a single long pulse underwater arc discharge

The electrohydraulic effect induced by underwater arc discharge is an efficient way to generate controllable, high-intensity shock waves. However, the development process of underwater arc discharge involves the complex coupling of plasma arc, gas bubble, and liquid medium, of which the evolution mechanism is not well understood. In this paper, the underwater arc discharge process at a millisecond pulse (>50 ms) was investigated by high-speed shadow imaging and colorimetric temperature measurement, and a simulation model of bubble pulsation was proposed to quantitatively estimate the state variation and energy transfer of the gas bubble. The results indicate that the whole arc discharge process can be categorized into three successive stages: short-period oscillation, long-period oscillation, and quasi-steady state. The vapor inside the bubble can reach a supercritical state (827 K and 140 MPa) at the minimum bubble radius. The simulation shows that the light radiation absorption and the heat conduct loss through metal electrodes are the two dominant factors influencing the pulsation of the bubble, and further analysis indicates that the dynamic evolution of the arc determines the bubble pulsation mode. Our findings demonstrate why and how repetitive electrohydraulic shock waves can be generated by a single long pulse underwater arc discharge, providing a low-cost way of shock wave generator based on an AC/DC high-voltage power source.

Propagation of nonclassical shock waves in Hall-magnetohydrodynamics model of non-ideal fluids

Propagation of nonclassical shock waves in Hall-magnetohydrodynamics model of non-ideal fluids

Exact solutions, conservation laws, and shock wave propagation of two-lanes traffic flow model via Lie symmetry

In this study, we consider a hyperbolic system of quasi-linear partial differential equations, governed by the traffic flow model on two lanes. We employ symmetry analysis and establish one-dimensional optimal subalgebras. Subsequently, we reduce the model into a system of ordinary differential equations for each optimal subalgebra and construct some new exact solutions; some of them are presented graphically. Further, by imposing the traveling wave transformation, we derive solutions including peakon-type solitons and upward parabola solitons. Furthermore, we demonstrate the existence of the nonlinear self-adjointness property of the model and formulate conservation laws. Finally, we discussed the evolutionary behavior of C1-waves, characteristic shock, and their interactions through one of the obtained exact solutions.

Predicting Wall Pressure in Shock Wave/Boundary Layer Interactions with Convolutional Neural Networks

Within the dynamic realm of variable-geometry shock wave/boundary layer interactions, the wall parameters of the flow field undergo real-time fluctuations. The conventional approach to sensing these changes in wall pressure through sensor measurements is encumbered by a cumbersome process, leading to diminished efficiency and an inability to provide swift predictions of wall parameters. This paper introduces a data-driven methodology that leverages non-contact schlieren imaging to predict wall pressure within the flow field, a technique that holds promise for informing the optimized design of variable-geometry systems. A sophisticated deep learning framework, predicated on Convolutional Neural Networks (CNN), has been engineered to anticipate alterations in wall pressure stemming from high-speed shock wave/boundary layer interactions. Utilizing an impulsive wind tunnel with a Mach number of 6, we have procured a sequence of schlieren images and corresponding wall pressure measurements, capturing the continuous variations induced by an attack angle from a shock wave generator. These data have been instrumental in compiling a comprehensive dataset for the training and evaluation of the CNN. The CNN model, once trained, has adeptly deduced the distribution of wall pressure from the schlieren imagery. Notwithstanding, it was observed that the CNN’s predictive prowess is marginally diminished in regions where pressure variations are most pronounced. To assess the model’s generalization capabilities, we have segmented the dataset according to different temporal intervals for network training. Our findings indicate that while the generalization of all models crafted was less than optimal, Model 4 demonstrated superior generalization. It is thus suggested that augmenting the training set with additional samples and refining the network architecture will be a worthwhile endeavor in subsequent research initiatives.

Experimental and Numerical Simulation of Ejecta Size and Velocity of Hypervelocity Impact Rubble-Pile Asteroid

Rubble-pile asteroids may be the type of near-Earth object most likely to threaten Earth in a future collision event. Small-scale impact experiments and numerical simulations for large-scale impacts were conducted to clarify the size ratio of the boulder/projectile diameter effects on ejecta size–velocity distribution. A series of small-scale impact cratering experiments were performed on porous gypsum–basalt targets at velocities of 2.3 to 5.5 km·s−1. Three successive ejection processes were observed by high-speed and ultra-high-speed cameras. The momentum transfer coefficient and cratering size were measured. A three-dimensional numerical model reflecting the random distribution of the interior boulders of the rubble-pile structure asteroid is established. The size ratio (length to diameter) of the boulder size inside the asteroid to the projectile diameter changed from 0.25 to 1.7. We conducted a smoothed particle hydrodynamics numerical simulation in the AUTODYN software to study the boulder size effect on the ejecta size–velocity distribution. Simulation results suggest that the microscopic porosity on regolith affects the propagation of shock waves and reduces the velocity of ejecta. Experiments and numerical simulation results suggest that both excavation flow and spalling ejection mechanism can eject boulders (0.12–0.72 m) out of the rubble-pile asteroid. These experiments and simulation results help us select the potential impact site in a planetary defense scenario and reduce deflection risk. are comprised primarily of boulders of a range of sizes.