Shock Wave Speed Research Articles

Numerical simulation of shock attenuation with real gas effects and a turbulent boundary layer in the expansion tube

AbstractThe influence of real gas effects and a turbulent boundary layer on shock wave attenuation in the expansion tube is studied by numerically solving the axisymmetric compressible Navier–Stokes equations with an adaptive mesh refinement technique. Numerical simulation results reveal that the ideal gas assumption is not applicable to the expansion tube, and the turbulent boundary layer plays a major role in decreasing the shock wave speed in the acceleration tube of the expansion tube. Shock wave attenuation is attributed to the turbulent boundary layer decreasing the pressure behind the shock wave. The numerical simulations that include the real gas effects and the development of turbulent boundary layers qualitatively agree with analytical solutions in the shock tube, and they show good agreement with the experimental results, especially for the shock speed in the acceleration tube of the expansion tube. Both effects should be considered in the numerical simulation model aimed to support experiments in expansion tubes.

Research on the dynamics of flame propagation and overpressure evolution in full-scale residential gas deflagration

To determine the effect of ignition height on indoor flame spread behavior and overpressure development, a comprehensive full-scale deflagration testing facility was established. Extensive experimental research was conducted within this facility. The findings indicate that indoor flame reignition and the occurrence of secondary explosions are most pronounced with intermediate ignition. Furthermore, the explosion overpressure generated during the reverse turn of shock wave propagation is greater than that produced by the forward turn. In comparison to the peak overpressure Pext in the master bedroom for top, middle, and bottom ignition, the peak overpressure Pext in the second bedroom increased by approximately 14.48 %, 15.04 %, and 19.20 %, respectively. When comparing middle ignition to top ignition, the propagation speed of shock waves in the kitchen balcony, restroom, second bedroom, and master bedroom was enhanced by 34.21 %, 40.85 %, 40.70 %, and 34.65 %, respectively. Furthermore, when comparing middle ignition to bottom ignition, the propagation speed of shock waves in these areas experienced a significant increase of 126.32 %, 124.39 %, 123.26 %, and 113.86 %, respectively. These research findings provide a theoretical foundation and empirical data to support the investigation and analysis of the causes of indoor gas explosion incidents.

Analysis of the Impact of Multiple Explosion Source Layouts on the Kinetic Characteristics of Gas Explosions in Blind Roadways

To investigate the changes in conditions within a blind roadway when multiple gas explosion sources are simultaneously detonated, the fluid dynamics software Fluent14.0 was used to conduct numerical simulation experiments with different numbers (2 and 3) and varying intervals (5 m, 10 m, and 15 m) of explosion sources. The results revealed that multiple explosion sources in gas explosions generate shock waves that propagate in opposite directions, creating pressure overlap zones within the roadway. The pressure waves and shock waves in these overlap zones continuously couple within the roadway. The number of overlap zones decreases incrementally with each encounter of opposing shock waves in the roadway. Unlike single explosion source models, the pressure at various positions within the roadway in multiple explosion source models oscillates due to the coupling of multiple shock waves, with significant peak pressures occurring at the closed end of the roadway and in the pressure overlap zones. Additionally, the propagation patterns of shock waves and flames within the roadway are not associated with the interval distance between explosion sources, whereas the encounter time, speed, and pressure of shock waves increase with the interval distance.

Physical mechanism for prolonged test duration in shock tubes

The main challenge in the operation of shock tubes is the very short test time. Hence, this work was carried out to optimize the ratio of driver section to driven section length and to investigate its effect on the test time in a shock tube. Three different cases were tested in this paper for driver to driven tube length ratio of 2, 1, and 0.5. The study was conducted numerically using ANSYS Fluent CFD solver and k-epsilon realizable turbulent model. The shock wave strength and speed were monitored at two different locations downstream the driven tube for diaphragm pressure ratio of 10. The numerical model was verified with experimental measurements in a shock tube apparatus at the College of Engineering, Universiti Tenaga Nasional, Malaysia (UNITEN). From the numerical and experimental data, the primary shock strength was very comparable, while using low pressure ratio of 10. Subsequently, higher pressure ratio of 20 and 30 were implemented and the results were compared to select the longest test time. A driver section to driven section ratio of 2 resulted in a longer test time of approximately of 20 ms. In addition, insignificant reduction in the test duration of about 5 % was observed after increasing the driver tube pressure to 30 kPa. In contrast, higher peak pressure was recorded for pressure ratio of 30 for all three cases.

Impact of rupture disk morphology on self-ignition during pressurized hydrogen release: A numerical simulation study

In the study of self-ignition during pressurized hydrogen release, the morphology of the rupture disk alters the flow and mixing processes of the gas jet, as well as the development of shock waves, thereby affecting the occurrence of self-ignition. This study employs the LES method based on the RNG-SGS model, EDC model, and NUIMech1.1 H2 combustion mechanism to investigate the flow mixing, shock wave development, and self-ignition phenomena under three different the rupture disk morphologies. The research findings indicate that as the growth trend of the rupture disk rupture ratio increases, the propagation speed of shock waves within the tube and the compression speed of the air and hydrogen-air mixing region accelerate, resulting in an earlier occurrence of self-ignition. A more complex rupture morphology leads to higher mixing rates between hydrogen and air and increased complexity of shock waves. Self-ignition initially occurs in the fuel-lean region of the boundary layer, followed by ignition at the center of the tube. The characteristic number of rupture disk is proposed to describe its impact on the self-ignition time. The competitive relationship between the two elementary reaction pathways of oxygen influences the development of the flame.

Study on the characteristics and predictive model of autoignition induced by shock wave from high-pressure hydrogen leakage

Faced with climate change and increasing environmental pollution, countries around the world are actively exploring strategies for clean, renewable energy. However, under high-pressure conditions, hydrogen leaks can lead to spontaneous combustion, which significantly raises the safety risk of hydrogen applications. This study employs fluid dynamic simulation methods to investigate the development process of shock waves within tubes. It analyzes the effect of release conditions on the propagation speed and shock wave intensity, revealing the impact of shock wave intensity on the temperature distribution and gas composition variation within the hydrogen-air mixture boundary layer. The results show that the tube length and bends have relatively little impact on the shock waves, while discharge pressure and tube diameter significantly affect the propagation speed and intensity of shock waves. Combined with dimensional analysis and data fitting, a predictive model for autoignition of high-pressure hydrogen leakage is established: (Pr/Pa)((DXrx(H₂)rO₂))/Vs2) = 1505(X/D)−1.329.

An explicit primitive conservative solver for the Euler equations with arbitrary equation of state

This work presents a procedure to solve the Euler equations by explicitly updating, in a conservative manner, a generic thermodynamic variable such as temperature, pressure or entropy instead of the total energy. The presented procedure is valid for any equation of state and spatial discretization. When using complex equations of state such as Span–Wagner, choosing the temperature as the generic thermodynamic variable yields great reductions in the computational costs associated to thermodynamic evaluations. Results computed with a state of the art thermodynamic model are presented, and computational times are analyzed. Particular attention is dedicated to the conservation of total energy, the propagation speed of shock waves and jump conditions. The procedure is thoroughly tested using the Span–Wagner equation of state through the CoolProp thermodynamic library and the Van der Waals equation of state, both in the ideal and non-ideal compressible fluid-dynamics regimes, by comparing it to the standard total energy update and analytical solutions where available.

A time-varying shockwave speed model for reconstructing trajectories on freeways using Lagrangian and Eulerian observations

Inference of detailed vehicle trajectories is crucial for applications such as traffic flow modeling, energy consumption estimation, and traffic flow optimization. Static sensors can provide only aggregated information, posing challenges in reconstructing individual vehicle trajectories. Shockwave theory is used to reproduce oscillations that occur between sensors. However, as the emerging of connected vehicles grows, probe data offers significant opportunities for more precise trajectory reconstruction. Existing methods rely on Eulerian observations (e.g., data from static sensors) and Lagrangian observations (e.g., data from connected vehicles) incorporating shockwave theory and car-following modeling. Despite these advancements, a prevalent issue lies in the static assignment of shockwave speed, which may not be able to reflect the traffic oscillations in a short time period caused by varying response times and vehicle dynamics. Moreover, driver dynamics while reconstructing the trajectories are ignored. In response, this paper proposes a novel framework that integrates Eulerian and Lagrangian observations for trajectory reconstruction on freeways. The approach introduces a calibration algorithm for time-varying shockwave speed. The shockwave speed calibrated by the CV is then utilized for trajectory reconstruction of other non-connected vehicles based on shockwave theory. Additionally, vehicle and driver dynamics are introduced to optimize the trajectory and estimate energy consumption by applying a vehicle movement model. The proposed method is evaluated using real-world datasets, demonstrating superior performance in terms of trajectory accuracy, reproducing traffic oscillations, and estimating energy consumption.

Effects of dust size distribution and non-Maxwellian electrons on shock waves in a dusty plasma

We present a study of dust acoustic shock waves in a non-Maxwellian plasma with dust charge fluctuations, which are seen to cause a dissipation term in fluid model, and consequently shocks are generated. In particular, we focus on dust acoustic waves as affected by various dust size distributions. Two distinct dust size distributions—the polynomial and the power law distributions—have been used. For analytical investigation of nonlinear wave propagation in complex plasmas, a reductive perturbation approach is used to obtain the Burgers equation. A dusty plasma system with non-Maxwellian Kappa distribution is considered and it is shown that the amplitude of a shock wave, for the dust size distribution is larger than that for the mono-sized counterpart, while the shock width manifests an opposite trend. Furthermore, the shock wave speed is also affected by the dust size distributions as well as by the nature of velocity distribution function. To benchmark our findings, we apply the proper limit on the spectral index, i.e., κ→∞, and retrieve the Maxwellian results. The current findings are crucial for comprehending respective shock distributions for a plasma system exhibiting non-thermal characteristics and having dust size distributions.

Finite amplitude wave propagation through bubbly fluids

The existence of only a few bubbles could drastically reduce the acoustic wave speed in a liquid. Wood’s equation models the linear sound speed, while the speed of an ideal shock waves is derived as a function of the pressure ratio across the shock. The common finite amplitude waves lie, however, in between these limits. We show that in a bubbly medium, the high frequency components of finite amplitude waves are attenuated and dissipate quickly, but a low frequency part remains. This wave is then transmitted by the collapse of the bubbles and its speed decreases with increasing void fraction. We demonstrate that the linear and the shock wave regimes can be smoothly connected through a Mach number based on the collapse velocity of the bubbles.

Molecular Modeling of Shockwave-Mediated Blood-Brain Barrier Opening for Targeted Drug Delivery.

Bubble-enhanced shock waves induce the transient opening of the blood-brain barrier (BBB) providing unique advantages for targeted drug delivery of brain tumor therapy, but little is known about the molecular details of this process. Based on our BBB model including 28 000 lipids and 280 tight junction proteins and coarse-grained dynamics simulations, we provided the molecular-level delivery mechanism of three typical drugs for the first time, including the lipophilic paclitaxel, hydrophilic gemcitabine, and siRNA encapsulated in liposome, across the BBB. The results show that the BBB is more difficult to be perforated by shock-induced jets than the human brain plasma membrane (PM), requiring higher shock wave speeds. For the pores formed, the BBB exhibits a greater ability to self-heal than PM. Hydrophobic paclitaxel can cross the BBB and be successfully absorbed, but the amount is only one-third of that of PM; however, the absorption of hydrophilic gemcitabine was almost negligible. Liposome-loaded siRNAs only stayed in the first layer of the BBB. The mechanism analysis shows that increasing the bubble size can promote drug absorption while reducing the risk of higher shock wave overpressure. An exponential function was proposed to describe the relation between bubble and overpressure, which can be extended to the experimental microbubble scale. The calculated overpressure is consistent with the experimental result. These molecular-scale details on shock-assisted BBB opening for targeted drug delivery would guide and assist experimental attempts to promote the application of this strategy in the clinical treatment of brain tumors.

Modeling airbursts by comets, asteroids, and nuclear detonations: shock metamorphism, meltglass, and microspherules

Asteroid and comet impacts can produce a wide range of effects, varying from large crater-forming events to high-altitude, non-destructive airbursts. Numerous studies have used computer hydrocode to model airbursts, primarily focusing on high-altitude events with limited surface effects. Few have modeled so-called “touch-down” events when an airburst occurs at an altitude of less than ∼1000 m, and no known studies have simultaneously modeled changes in airburst pressures, temperatures, shockwave speeds, visible materials, and bulk material failure for such events. This study used the hydrocode software Autodyn-2D to investigate these interrelated variables. Four airburst scenarios are modeled: the Trinity nuclear airburst in New Mexico (1945), an 80-m asteroid, a 100-m comet, and a 140-m comet. Our investigation reveals that touch-down airbursts can demolish buildings and cause extensive ground-surface damage. The modeling also indicates that contrary to prevailing views, low-altitude touch-down airbursts can produce shock metamorphism when the airburst shockwave or fragments strike Earth’s surface at sufficiently high velocities, pressures, and temperatures. These conditions can also produce microspherules, meltglass, and shallow impact craters. Regardless of modeling uncertainties, it is known that bolides can burst just above the Earth’s surface, causing significant damage that is detectable in the geologic record. These results have important implications for using shocked quartz and melted materials to identify past touch-down airbursts in the absence of a typical impact crater. Although relatively rare, touch-down events are more common than large crater-forming events and are potentially more dangerous.

On the transition of failure mechanisms during machining process with varied speeds: A molecular dynamics study

Conventional machining theory states that the machining of a ductile material may create continuous, serrated, and/or fragmented chips with increasing machining speeds. In this study, transitions of failure mode under varied machining speeds in single-crystalline silicon were analyzed based on molecular dynamics (MD) simulations of the ultra-high-speed machining of single-crystalline silicon. The MD simulations employ the periodic boundary conditions along the third direction which can mimic the material failure in cutting plane. The uncut depth reaches 39 nm, which is sufficiently large to accommodate complex atomic evolutions. The simulation results indicate that jetted chips occurred in front of the cutter, when the machining speed is increased to approximately 2.7 × 103 m/s, which is attributed to the shock pressure induced by the chip inertia. Essentially, the Rankine-Hugoniot jump conditions were introduced to explain the influence of the shock pressure. Both the calculations based on Rankine-Hugoniot jump conditions and the MD results imply that the shock wave speed is equal to the machining speed at the steady machining state. In addition, the transition from fragmented-chip to jetted-chip morphology exhibits a stage wherein the two primary adiabatic shear bands are simultaneously activated. The present work sheds light on the underlying mechanism of chip formation at an ultra-high-machining speed beyond 1000 m/s.

A data-driven traffic shockwave speed detection approach based on vehicle trajectories data

Traffic shockwaves demonstrate the formation and spreading of traffic fluctuation on roads. Existing methods mainly detect the shockwaves and their propagation by estimating traffic density and flow, which presents weaknesses in applications when traffic data is only partially or locally collected. This paper proposed a four-step data-driven approach that integrates machine learning with the traffic features to detect shockwaves and estimate their propagation speeds only using partial vehicle trajectory data. Specifically, we first denoise the speed data derived from trajectory data by the Fast Fourier Transform (FFT) to mitigate the effect of spontaneous random speed fluctuation. Next, we identify trajectory curves’ turning points where a vehicle runs into a shockwave and its speed presents a high standard deviation within a short interval. Furthermore, the Density-based Spatial Clustering of Applications with Noise algorithm (DBSCAN) combined with traffic flow features is adopted to split the turning points into different clusters, each corresponding to a shockwave with constant speed. Last, the one-norm distance regression method is used to estimate the propagation speed of detected shockwaves. The proposed framework was applied to the field data collected from the I-80 and US-101 freeway by the Next Generation Simulation (NGSIM) program. The results show that this four-step data-driven method could efficiently detect the shockwaves and their propagation speeds without estimating the traffic densities and flows nearby. It performs well for both homogenous and nonhomogeneous road segments with trajectory data collected from total or partial traffic flow.

Methodology for the Identification of Shock Wave Type and Speed in a Traffic Stream Using Connected Vehicle Data

The concept of traffic shock waves was first theorized by Lighthill and Whitham in 1955. The identification of shock wave type and speed in a traffic stream provides critical information about the queue formation and its dissipation. This information can be utilized by various stakeholders for traffic management, emergency response, etc. Such information can also be integrated into the travel time prediction models and real-time route diversions for navigation. Past efforts at identifying shock waves used simulation or analysis based on location-based sensors such as loop detectors. This paper describes scalable methodologies for measuring shock wave propagation using Connected Vehicle (CV) data. The techniques to identify the six different types of shock waves are illustrated through case studies from Indiana highways that use both CV data and the corresponding surveillance camera images. The shock wave speeds for each event are estimated using the linear regression model, with most shock wave speed estimates having a coefficient of determination (R2) of 0.9 or better. Although shock wave speeds vary by traffic flow rates and geometry, the typical backward forming shock wave speeds ranged from 1.75 to 11.76 mph whereas the backward recovery shock wave speeds were observed to be between 5.78 and 16.54 mph. These techniques can be adapted for real-time use to assist traffic management centers with estimating upstream propagation and recovery time. A case study with a car fire is used to illustrate how this shock wave speed data can be used to frame discussions with first responders regarding how reducing incident clearance time can reduce the risk of secondary crashes.

Spall characteristics of three-dimensional graphene networks with embedded copper: A molecular dynamics study

The phenomenon of shock-induced spallation has garnered significant interest in both scientific and industrial circles. Laminated graphene embedded in graphene-reinforced metal-matrix composites have been shown to improve mechanical properties. This study systematically investigates the dynamic response and spall failure of a three-dimensional graphene network (3DGN) with embedded copper composites (3DGCu) and its dependence on the grain sizes (D). Firstly, increasing the wt% of graphene results in significant increase of shock wave speed due to the intrinsic high modulus of graphene, whilst leading to a reduction in shock pressure. Spallation of 3DGCu at low shock velocity is observed, which is dominated by the bonded interaction at the graphene-metal interface. However, the 3DGCu with higher graphene content (smaller D) exhibits both low density and superior spall resistance. In particular, in the sample with 60 wt% graphene, the complete spallation has never occurred and still maintains a relatively high spall strength within the impact velocity of 3.0 km/s. This is due to the remarkable capacity for 3DGN to absorb the kinetic energy during tension. In addition, during shock loading, the graphene component is responsible to the tension loading, whereas the copper metal matrix undergoes compression, leading to a stable post-shock length. These findings offer a novel approach for tailoring the dynamic properties of advanced graphene-based nano-composites with potential applications in extreme environments.

The perturbed Riemann problem for the Chaplygin pressure Aw–Rascle model with Coulomb-like friction

In this paper, we are concerned with the Riemann problem and the perturbed Riemann problem for the Chaplygin pressure Aw–Rascle model with Coulomb-like friction, which can also be seen as the nonsymmetric Keyfitz–Kranzer system with Chaplygin pressure and Coulomb-like friction. For the Riemann problem, we show that it explicitly exhibits two kinds of different structures and the delta shock wave appears in some certain situations. The generalized Rankine–Hugoniot conditions of the delta shock wave are established and the exact position, propagation speed and strength of the delta shock wave are given explicitly. Unlike the homogeneous case, it is shown that the Coulomb-like friction term makes contact discontinuities and the delta shock wave bend into parabolic shapes and the Riemann solutions are not self-similar anymore. For the perturbed Riemann problem with delta initial data, not only the delta shock wave but also the delta contact discontinuity are found in solutions and the friction term makes them bent. Under the generalized Rankine–Hugoniot conditions and the entropy condition, by taking variable substitution, we constructively obtain the global existence of generalized solutions which explicitly exhibit four kinds of different structures. The results in this paper yield a way of studying the wave interaction involving the delta shock wave for conservation laws with source terms and will give us some insights into the research on the Chaplygin pressure Aw–Rascle model, the pressureless Euler equations and the Chaplygin Euler equations with various kinds of source terms.

Estimating Demand Volume for Signalized Corridors Under Oversaturated Conditions Using Aggregated Probe Vehicle Speed Data

Measuring demand directly with vehicle sensors is not possible when demand is larger than capacity for an extended period, as the queue grows beyond the sensor, and the flow measurements at a given point cannot exceed the capacity of the section. The main objective of this study is to develop methods that could be implemented in practice based on readily available data. To this end, two methods are proposed: an innovative method based on shockwave theory and the volume delay function adapted from the Highway Capacity Manual (7th edition). Both methods primarily rely on probe vehicle speeds (e.g., from INRIX) as the input data and the capacity of the segment or bottleneck being analyzed. Probe vehicle data are used to determine the critical times when the queue reaches the end or beginning of a road segment. From these critical times, the shockwave speed for the boundary between congested (high density) traffic and arriving (low density) traffic is estimated. The proposed methods are tested with simulation data generated in VISSIM and validated based on volume data from the field. The field data are collected from a congested arterial in Virginia Beach, VA, and include the ground truth volumes and INRIX speed data aggregated at one-minute intervals. The results show that both methods are effective for estimating the demand volume and produce less than 4% error when tested with field data.

Experimental investigation on the shock wave and spontaneous ignition of high-pressure hydrogen released into a tube through different narrowness inlets

Due to the high probability of hydrogen leaking from narrow cracks of the vessels, an experimental study is conducted to investigate the spontaneous ignition of high-pressure hydrogen released into a tube through inlets with different narrowness, including circular, square (length-width ratio χ = 1), and two slit shapes of χ = 2 and 3, with the same area. Pressure transducers and photoelectric sensors are used to detect shock wave dynamic variation and ignition occurrence. The results indicate that narrow inlets weaken the shock wave intensity and speed, and the weakening effect increases with narrowness. Moreover, spontaneous ignition is affected. The minimum burst pressure required for spontaneous ignition is higher in the cases with square and slit inlets. Most significantly, when χ is 3, it is 2.5 times that of circular inlet. Meanwhile, for narrow inlets, the ignition flame intensity and speed are enhanced, and the inlet of χ = 2 has the greatest impact.

IDILIM: incident detection included linear management using connected autonomous vehicles

AbstractAutonomous vehicle advancements and communication technologies such as V2V, V2I, and V2X have enabled the development of connected and autonomous vehicles. Because CAVs are directly effective in traffic, their application in traffic management and incident management appears promising. They can immediately begin regulating traffic and acting as sensors due to their connectivity to the infrastructure. This research proposes Incident Detection Included Linear Management (IDILIM), a CAV-based incident management algorithm that regulates CAV and traffic speeds based on dynamic and predicted shockwave speeds. The SUMO simulations are carried out on a 10.4-km-long, three-lane facility with 21 sensors every 500 m. In the scenarios, three traffic demands, eleven CAV penetration rates, and varying incident locations, duration, and lanes are used. A total of 20 simulation seeds are used in each scenario. The proposed algorithm necessitates the use of a reliable traffic prediction model. Convolutional Neural Networks, a deep learning algorithm with high estimation accuracy, are used in the prediction model. IDILIM uses the highly accurate traffic prediction output of the Pix-to-Pix model as input at 3-min intervals. Shockwave speed is calculated using model outputs and fed to CAVs. To compare with IDILIM, variable speed limits (VSL) are also modeled. When compared to uncontrolled base scenarios, IDILIM reduced density values greater than 35 veh/km in the critical region by 89.32%. In the same scenario, VSL management decreased by only 52.43%.