Formation Of Shock Waves Research Articles

RISK ZONES FROM THE FILLING STATIONS MODELLING WITH APPLICATION OF GEOINFORMATION TECHNOLOGY

In this paper the questions of technogenic safety of the city Odesa with a population of over 1 million are considered on the example of the analysis of an emergency situation that may arise at filling stations (FS) of the city. The fire safety of theFSsnetwork becomes very important in the context of urban buildings and traffic flows compaction, a significant increase in the number of cars, as well as in the construction of new potentially hazardous objects (PHO) within the urban territory. To solve the problem ofanalysis ofthe risk zones of FSs, a conceptual digital model ofaFS was created, a numerical simulation of the scenario of an unfavourablesituation development at the FS was carried out according to the approved state methodology (an explosion of a vapour-air fuel mixture with a shock wave formation), as well as the obtained zones were visualized on a map of the city of Odessa using the geographic information system QGIS. The digital model of the FS was created taking into account the requirements for the presentation of attributive and spatial data of the relevant GIS. The components of the developed conceptual model are: universal digital identifier, spatial data in the form of type and coordinates of the object, attributive data, which consist of staticand dynamic features, as well as numerical models of emergency situation development. During the visualizing of the obtained calculated data by means of GIS, OSM Place Search, QuickOSM and Multi Ring Buffer plugins were used, as well as data from the OpenStreetMap server. The presented results of modellingand visualization indicate that, when the most unfavourabledevelopment scenarios are realized, the nature of accidents at FS can go beyond the local scale and move to the borders of the residential zone,as well as to nearby industrial buildings and FSs, which in turn can cause unfavourablesituations on them by the domino effect. In addition, the results of the analysis of the obtained heterogeneous modellingand visualization data to determine technogenic risk indicates the possibility of applying the studied principles to other PHOsand also allows to present the data in a visual and accessible form for decision-makers.

Size effects on the plastic shock formation in steady-state cavity expansion in porous ductile materials

In this paper, we have studied the hypervelocity expansion of a spherical cavity in an infinite medium modeled with the extension of the porous plasticity criterion of Gurson (1977) developed by Chen and Yuan (2002) to account for plastic strain gradient induced size effects. Following the self-similar, steady-state solution derived by Cohen and Durban (2013) for size-independent porous materials, we have computed the critical cavity expansion velocity which leads to the emergence of plastic shock waves for a wide range of initial void volume fractions and different values of the length scale parameter that controls the effect of size. We have shown that size effects hinder the emergence of plastic shock waves, so that as the length scale parameter increases, the expansion velocity required for the plastic shock to be formed increases. In addition, while porosity favors the formation of plastic shocks, as shown by Cohen and Durban (2013), our results indicate that the effect of initial void volume fraction on plastic shock wave formation decreases for size-dependent materials.

Variable speed limit strategy with anticipatory lane changing decisions

This paper develops a novel anticipatory Variable Speed Limit (VSL) control strategy that incorporates driver behavior based on trajectory data from probe vehicles. In particular, the research examines how the speed limit controls can be coordinated and optimized to reduce lane changing and overall braking, thus to achieve greater traffic throughput, safety, and sustainability. Driver behavior, such as acceleration/deceleration and lane changing, as reflected in individual trajectory data from GPS enabled probe vehicles are crucial for early detection of shockwave formation and proactive selection of speed limits; and consequently delay, or even eliminate breakdown formation. The core of this approach is the incorporation of a lane changing model which provides a more robust integrated speed limit selection and shockwave detection framework than the one we have developed in an earlier paper. The control principle is formulated in a generic fashion that finds the optimal speed limit control variables for either separate or simultaneous reduction of travel time, crash rates, and fuel consumption over a prediction horizon. The findings from the paper suggested that the VSL strategy was able to result in fewer lane changing rate (LCR) compared to the No-VSL case. Also, the developed algorithm was able to produce higher frequency of lower acceleration and deceleration rates than the No-VSL case, which indicated a smoother acceleration and deceleration pattern that corresponded to lower emission and fuel consumption. The performance of the algorithm was also examined under different probe penetration rates and congestion levels to identify the % of probe needed to achieve simultaneous mobility, safety, and environmental objectives.

Filamentary surface plasma discharge flow length and time scales

Nanosecond surface dielectric barrier discharges (ns-SDBDs) are a class of plasma actuators that utilize a high-voltage pulse of nanosecond duration between two surface-mounted electrodes to create an electrical breakdown of air, along with rapid heating. These actuators usually produce multiple filaments when operated at high pulse frequencies, and the rapid heating leads to the formation of shock waves and complex flow fields. In this work we replicate a single filament of the ns-SDBDs and characterize the induced flow using velocity measurements from particle image velocimetry and density measurements from background-oriented schlieren. The discharge is produced by a high voltage electrical pulse between two copper electrodes on an acrylic base. A hot gas kernel characterizes the flow field formed close to the electrodes that expands and cools over time and a vortex ring that propagates away from the surface while entraining cold ambient fluid. The gas density deficit inside the kernel displays a power-law decay over time. Based on the observations, we develop a simplified theoretical model based on vortex-driven cooling and perform a scaling analysis to obtain the induced flow length and time scales. The results show that the cooling process’s time scales correspond to a circulation-based time scale of the vortex ring, and the length scale of the kernel corresponds to the vortex ring radius. These findings can guide the choice of optimal filament spacing and pulse frequencies in the design, deployment, and operation of ns-SDBDs for flow control.

Full particle-in-cell simulation of the formation and structure of a collisional plasma shock wave.

The formation and structure of a collisional shock wave in a fully ionized plasma is studied via full particle-in-cell simulations, which allows the complex momentum and energy transfer processes between different charged particles to be treated self-consistently. The kinetic energy of the plasma flow drifting towards a reflecting piston is found to be rapidly converted into thermal motion under the cooperative effects of ion-ion collisions, ion-electron collisions, and electric field charged-particle interactions. The subsequent shock evolution is influenced by the "precursor" ion beam before a quasisteady state is reached. The shock wave structure is then analyzed from a two-fluid transport viewpoint, which is found to be affected by "flux-limiting" electron transport, the nonthermal ions, and the charge separation electric field.

Wave propagation in continuous bimodular media

The paper studies wave propagation in 1 D bimodular media. Four cases are investigated: two cases with an external step load applied to a prestressed bimodular rod and two cases with a sign-alternating pulse applied to an unloaded bimodular rod. Shock wave formation and energy dissipation are observed in two cases. Analytical solutions showing the distortion of a wave profile due to shock wave formation for all cases are derived. A method of suppressing an arbitrary tensile pulse in a bimodular rod by creating a compressive pulse is proposed. Validation by numerical modeling using a Godunov-type explicit difference scheme is performed.

The limiting behavior of the Riemann solution to the isentropic Euler system for logarithmic equation of state with a source term

We investigate the limiting behavior of the Riemann solution to the isentropic Euler equations for logarithmic equation of state with the Coulomb‐like friction term. The formation of vacuum state and delta shock waves are identified and analyzed when the pressure vanishes. Unlike the homogeneous case, the Riemann solution is no longer self‐similar. We prove that the Riemann solution of the isentropic Euler equations for logarithmic equation of state with friction term converges to the Riemann solution of the zero‐pressure gas dynamics system with a body force when the pressure vanishes.

Investigation of the Shock Wave Formation and Intensity in Wave Rotor

Abstract Actual formation and intensity of shock wave generated during gradual opening and closure between each port and passages of wave rotor are studied by means of experiment and computational fluid dynamics simulation. The results show that the intensity of shock wave increases with the distance from high-pressure inlet, and the reason for the variation tendency is the superposition of compression waves. By changing the rotational speed and the expansion ratio, the shock wave intensity can be adjusted, but the position where the intensity reaches maximum stays constant basically and keeps the distance near 300 mm from high-pressure inlet. Comparing with the one-dimensional simplification result, the actual intensity of shock wave is lower. The difference between the fact and simplification increases with the rotational speed and expansion ratio. The internal mechanism has been analyzed from the aspect of intake mass. Then, the maximum shock wave intensity is found approximately linear to the intake mass of each rotor passage in each cycle.

Interaction of delta shock waves for a nonsymmetric Keyfitz–Kranzer system of conservation laws

In this work, the mechanism for the formation of the delta shock wave is analyzed to deal with interaction of delta shock waves and contact discontinuities for a system of Keyfitz–Kranzer type by means of analysis and solutions of Riemann problems. A set of numerical experiments are provided, illustrating the theoretical findings numerically. A brief survey of the Keyfitz–Kranzer systems as a base model of fundamental nonlinear phenomena in applications is provided aiming to shed light on the intricate wave structure for other related models of conservation laws appearing in applied sciences.

Thermo-acoustic instability in the process of flame propagation and transition to detonation

The paper is devoted to the numerical analysis of the reactive mixture explosion during the accidents at a launch site. The particular scenario concerns the explosion in the unconfined volume after accidental fuel release into the atmosphere. It is shown that the development of intrinsic flame instability results in the generation of compression waves, which occur to be intensified via the mechanism of thermo-acoustic instability. In turn, intensification of the compression waves leads to the formation of strong shock waves and even detonation in the case of a highly reactive mixture. The leading role in this process belongs to the transversal waves generated in the folds of the developed flame surface and propagated along the flame surface. It is the localization of the compression wave inside the reaction zone that causes amplification of the compression wave due to energy release.

Experimental Study of a Disk Diaphragm Thickness Influence on a Planar Shock Wave Formation and Position During its Propagation in a Gas Shock Tube

A Shock tube is a piece of equipment in which, by creating a pressure difference between the driver and the driven section via the bursting membrane, it has the ability to generate shock waves with very short rise time. One of the important parameters in the shock tube is the planar shock wave and the distance of its formation along the driven section. In this study, the shock wave pressure was measured at different sections along the shock tube as well as at different radial distances, using three piezoresistive pressure sensors. Experiments were repeated with three different thicknesses of diaphragms 0.1, 0.2, and 0.3 mm. Diaphragms were made of Mylar. The results of the tests were extracted using TRAww software, which is a software for signal processing of the pressure sensors, and the distance of the planar shock wave for different diaphragms was obtained. The results show that by increasing the diaphragm thickness and thus increasing the explosion pressure (pressure of the driver area), the shock wave pressure increased, and the planar shock wave propagates further away in the driven section. The uniform duration of the shock wave using a diaphragm with a thickness of 0.1 mm is smaller than the other two diaphragms, and the planar shock wave is not stable until the end of the shock tube. Also, the pressure drop in the driven section after the failure of the diaphragm increases with increasing diaphragm thickness.

Computational investigation to study the effect of a hybrid hydrogen fuelled scramjet combustor on different inlet boundary conditions

Supersonic Combustion ramjet or Scramjet is one of the revolutionary hypersonic innovations that use atmospheric oxygen to undergo the combustion process. For efficient combustion of the fuel different techniques are implemented in the combustor such as flame holding, fuel injection mechanism. A transverse fuel injection system is considered into which parallel fuel injection system is introduced, named as Hybrid scramjet combustor. In this paper, the influence of inlet Mach number on the performance of the hybrid combustor is analyzed. The current model is validated with an already available experimental study in the literature. Both graphical and qualitative analysis was done in the validation. The simulation results are in good agreement with the experimental study. In this study, static pressure contours shows the formation of oblique shock waves. The recirculation region is developed in the model due to the presence of parallel cavities. The temperature contours indicates the starting of combustion process. Due to the presence of strut in the parallel cavities increase the possibility of H2 injection in the combustion which improves the combustion process. The Mach number contours are studied for the different Mach numbers. The contours show the formation of an additional shock wave due to strut, as the Mach number increases the strength of the shock wave also increases. The recirculation region leads to the interaction of boundary layer and shock wave. The shear layer thickness is maximum for Mach number 3.0 and is minimum for Mach number = 2.25. The variation of static pressure for the different Mach number is covered in this paper. The static pressure values increases from the leading edge with the formation of oblique shock waves. This increase is due to the formation of reflected shock waves.

Sonic Boom: From the Physics of Nonlinear Waves to Acoustic Ecology (a Review)

A history of the topic is presented. First, information is given about the development of supersonic aviation. Then, the history of studying the phenomenon of sonic boom generated by flying bullets and projectiles is briefly described. The results of the renowned aeroacoustic scientists K. Doppler and E. Mach are presented, as well as little-known historical facts found in old foreign sources. The need for correct use of the term “sonic boom” is pointed out, which is not limited to aviation acoustics problems, but is inherent to many natural and technogenic phenomena. A 100-year priority of the acoustic effect over its weaker optical counterpart, Vavilov–Cherenkov radiation, is mentioned. Problems related to calculating the generation of perturbations in the interaction of transonic and supersonic flows with real bodies are described: the need to take into account the details of the shape of the aerodynamic profile, peculiarities in the behavior of the boundary layer, the formation of shock waves, generation of flow turbulence, and the kinetics (relaxation and dissociation) of atmospheric gases. The phenomenon of wave resonance, responsible for the formation of the boom when breaking the sound barrier, is discussed. Nonlinear processes in N-wave formation in the propagation of complexly shaped signal are described. The influence of the main effects distorting the N-shaped profile is explained: diffraction, focusing, and multiple relaxation phenomena broadening the shock front. The theory of N-waves in an inhomogeneous medium is discussed. Examples of ray patterns in a standard atmosphere and in the region behind the turbulent boundary layer are constructed. Calculation methods based on nonlinear geometric acoustics and nonlinear quasioptics approximations are presented. Problems related to the consequences of sonic booms and their harmful effects on the environment, structures, and living organisms are indicated. An extensive bibliography and a list of fundamental reviews in the domestic and foreign literature are presented.

Singularity formation for compressible Euler equations with time-dependent damping

<p style='text-indent:20px;'>In this paper, we consider the compressible Euler equations with time-dependent damping <inline-formula><tex-math id="M1">\begin{document}$ \frac{{\alpha}}{(1+t)^\lambda}u $\end{document}</tex-math></inline-formula> in one space dimension. By constructing "decoupled" Riccati type equations for smooth solutions, we provide some sufficient conditions under which the classical solutions must break down in finite time. As a byproduct, we show that the derivatives blow up, somewhat like the formation of shock wave, if the derivatives of initial data are appropriately large at a point even when the damping coefficient grows with a algebraic rate. We study the case <inline-formula><tex-math id="M2">\begin{document}$ \lambda\neq1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ \lambda = 1 $\end{document}</tex-math></inline-formula> respectively, moreover, our results have no restrictions on the size of solutions and the positivity/monotonicity of the initial Riemann invariants. In addition, for <inline-formula><tex-math id="M4">\begin{document}$ 1&lt;\gamma&lt;3 $\end{document}</tex-math></inline-formula> we provide time-dependent lower bounds on density for arbitrary classical solutions, without any additional assumptions on the initial data.

Plane longitudinal waves in a fluid-saturated porous medium with a nonlinear relationship between deformations and displacements of the liquid phase

A mathematical model is presented to describe the propagation of a plane longitudinal wave in a fluid saturated porous medium, taking into account the geometric nonlinearity of the liquid component of the medium. The nonlinear relationship between deformations and displacements refines the classical Biot’s theory, within the framework of which a fluid saturated porous medium is considered. Evolutionary equations for the displacements of the skeleton of the medium and fluid in the pores are obtained. It is shown that, if the liquid is confined in the pores, then the wave propagation is described by an equation that generalizes the well-known Burgers equation and has a solution in the form of a stationary shock wave resulting from mutual compensation of the effects of nonlinearity and dissipation. The dependence of the width of the shock wave front on the viscosity of the fluid saturating the pores and the shock wave amplitude is determined. As the viscosity coefficient increases, the wave profile becomes steeper, i.e., the wave front width decreases. With an increase in the wave amplitude, the front width can either increase or decrease, depending on the other parameters of the original system. The limiting cases of the obtained generalized Burgers equation are analyzed with respect to the fluid viscosity parameter. If the liquid flows freely in the pores, then the system of evolutionary equations is reduced to a single equation of a simple wave, i.e., the propagation of a plane longitudinal wave in a porous medium can be described by the well-known equation of nonlinear wave dynamics - the Riemann equation. The equation describes the nonlinear waves, which are characterized by a steepening of the leading edge with subsequent overturning resulting from the growth of nonlinear effects in the absence of compensating factors such as dispersion and dissipation.

Shock waves in magnetized plasmas with superthermal trapped electrons.

Formation of ion-acoustic shock waves (IAShWs) and their propagation nature in a magnetized plasma in the presence of superthermal trapped electrons are investigated for the first time via the fluid dynamical approach. A magnetized plasma system, comprising of inertial ions and non-inertial electrons following κ-superthermal trapped distribution, is considered to examine the basic features (amplitude, width, phase speed, etc.) of IAShWs in such a plasma. A diffusion effect (due to the ion kinematic viscosity) is taken into account. The reductive perturbation technique is adopted to derive the modified Korteweg de-Vries Burgers’ (mKdVB) equation and the solution of mKdVB equation (derived by adopting the tangent hyperbolic method) is used to investigate the dynamical and structural characteristics (speed, amplitude, width, etc.) of IAShWs. The influence of relevant plasma (configuration) parameters (e.g., the superthermality index κ, concentration of trapped electrons, external magnetic field, and obliquity angle, etc.) on the nature of IAShWs is examined. The applications of the results in space and laboratory plasma environments, where nonthermal trapped electrons are available, are briefly discussed.

Equation-of-state measurements for polystyrene under high presure driven by HEAVEN-I laser facility

The equation of state (EOS) for CH material used as an ablator layer at high pressure is important in the study of implosion dynamics and target design for inertial confinement fusion (ICF). At present, most of EOS data are on the Hugoniot line under shock compression. The EOS data below Hugoniot line need further studying for low-entropy pre- compression. In the present article, the EOS of polystyrene is established under quasi-isentropic compression driven by HEAVEN-I KrF laser facility with a long rising edge (~20 ns). The shock dynamic behaviors of three kinds of CH targets are simulated, which are 100 μm CH planar target, Al-coated CH planar target (10 μm Al, 50 or 150 μm CH), and flyer-impact target composed of flyer (Al-coated CH), 100 μm vacuum layer, and 100 μm CH layer. The planar targets and flyer-impact targets with different thickness are irradiated by six-focused laser beams with total energy of 50–100J, and the free surface velocity and wave average transit velocity are measured by side-on shadowgraph technique. The simulation results indicate that the initial loading process is quasi-isentropic compression process, and then evolves into a weak shock compression process for the CH planar target in the rising edge stage. Comparing with the CH planar target, the reflected rarefaction waves from the Al-CH interface of Al-coated CH target can suppress the enhancement of compression wave, and delay the formation of shock wave when laser directly irradiates the Al layer. The shock pressure of the CH target layer (the third layer) is significantly higher than those of the former two targets in the flyer-impact target. However, the chasing rarefaction wave can unload the compression state incompletely and reduce the pressure when the CH target layer is much thicker than Al layer. The final pressure is about 15 GPa in the CH planar target, while the final pressure is about 30 GPa in flyer-impact target: both of them are less than the pressure threshold of opacity change for the transparent polystyrene. The quasi-isentropic dynamical process is difficult to measure by the velocity interferometer system for any reflector technique. The experimental results show that the average wave transit velocity is significantly less than the final shock velocity derived from the free surface velocities in the CH and Al-coated CH planar target side-on shadow experiments. They indicate that the compression wave enhancement and quasi-isentropic compression process occur in the propagation of wave front. The shock pressure is about 12 GPa in the CH planar target, and about 34 GPa under shock load in the flyer-impact target. The experimental data and shock dynamic processes are basically consistent with the simulation results.

An engineering application of Prosperetti and Lezzi equation to solve underwater explosion bubbles

The dynamic behaviors of underwater explosion bubbles differ for different explosives. The explosive characteristic parameters will result in a greater impact on the motion characteristics of the bubbles. Based on the bubble dynamics equation established by Prosperetti and Lezzi [“Bubble dynamics in a compressible liquid. Part 1. First-order theory,” J. Fluid Mech. 168, 457âĂŞ-478 (1986); “Bubble dynamics in a compressible liquid. Part 2. Second-order theory,” J. Fluid Mech. 185, 289âĂŞ-321 (1987)], we proposed an initial condition and an equation of state (EOS) form applicable for calculating the underwater explosion bubble dynamics of different explosives. With the assumption of instantaneous detonation and initial shock wave formation at the gas–liquid boundary, we calculated the initial state of the bubble boundary and established the initial condition for calculating explosion bubbles. Using the Jones–Wilkins–Lee EOS for different explosives, we constructed an isentropic EOS with a polytropic exponent that varied with density. We calculated and analyzed the differences in the initial expansions and the subsequent oscillations of underwater explosion bubbles with different explosives as well as the effects of different explosive parameters on the explosion bubble dynamics. This study showed that the proposed initial condition and the EOS form with a polytropic exponent that varied with density yielded good calculation accuracy and achieve close association of the underwater explosion bubbles with the properties of the explosive detonation and the characteristics of the detonation products. In addition, the explosion bubbles differed in the initial expansion, where the bubbles produced by explosives with higher densities and greater detonation velocities expanded more rapidly.

The limit Riemann solutions to nonisentropic Chaplygin Euler equations

Abstract We mainly consider the limit behaviors of the Riemann solutions to Chaplygin Euler equations for nonisentropic fluids. The formation of delta shock wave and the appearance of vacuum state are found as parameter ε \varepsilon tends to a certain value. Different from the isentropic fluids, the weight of delta shock wave is determined by variance density ρ \rho and internal energy H. Meanwhile, involving the entropy inequality, the uniqueness of delta shock wave is obtained.

Statistical analysis of characteristics of classified type II radio bursts and their associated solar energetic particle events

In this paper, we investigate 273 type II radio burst events detected by Wind, STEREO spacecraft from January 2010 to March 2018 during the 24th solar cycle. We classify all events as five groups or sub-types according to their starting and ending frequencies, and then analyze the observed characteristics of each group of type II radio bursts and the correlation between the occurrence of solar energetic particle (SEP) events and the associated coronal mass ejection (CME) or type II radio bursts. What we find is as follows. 1) In each group of type II radio burst events, the CME speed (&lt;i&gt;v&lt;/i&gt;), width (WD), mass (&lt;i&gt;m&lt;/i&gt;), and kinetic energy (&lt;i&gt;E&lt;/i&gt;&lt;sub&gt;k&lt;/sub&gt;) associated with SEP events are generally greater than those with no SEP events, indicating that the generation of SEP events requires a fast and wide energetic CME eruption. 2) Compared with type II radio bursts starting from the DH band, type II radio bursts starting from the metric band have a higher proportion of large SEP events. Multi-band type II radio bursts are more likely to produce SEP events than single-band events, where M-DH-KM type II bursts have the highest proportion of SEP events (73%), and the DH IIs only have the lowest one (19%). 3) In each kind of type II radio bursts, the type IIs with SEP events usually have higher starting frequencies (lower shock forming heights), lower ending frequencies (higher ending heights) and longer durations than those with no SEP events; coronal shock waves that are easy to produce SEP events (especially large SEP events) generally begin to form at a lower height (such as &lt; 3&lt;i&gt;R&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt;, &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt;: solar radius), and are sustained to a much larger height (such as &gt; 30&lt;i&gt;R&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt;). 4) There exists a strong negative correlation between the duration and the ending frequency of type II radio burst (&lt;i&gt;cc&lt;/i&gt; = –0.93). The proportion of SEP events increases with the increase of the duration of type II radio burst, and decreases with the increase of the ending frequency, which largely depends on the CME speed and other properties. The results of this paper further show that the generation of SEP events is greatly related to the sub-types and characteristics of type II radio bursts. The higher the starting frequencies and the lower the ending frequencies of type II radio bursts, such as M-DH-KM type II bursts, of which the CME drives to forming shock waves at a very low height and propagates to a very large height, the longer the duration of the shock, the longer the time it takes to accelerate the particles, and the greater the probability of SEP events (especially large SEP events) is.