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We conducted a series of numerical simulations to understand the effect of the initiation process of cylindrical high explosives on the blast-wave behavior and peak overpressure distribution. The first case involved the explosion of a cylindrical high explosive whose length-to-diameter ratio was equal to 2 and that was vertically placed above the ground surface. The initiation point was at the top of the high explosive. The initiation process induced the detonation momentum directed from top to bottom, and the detonation products forcefully hit the ground surface, resulting in a higher peak overpressure on the ground surface in comparison with the case using an isothermal constant-pressure volume. After the blast wave expanded far from the initiation point, the computed peak overpressures of the two approaches showed good agreement with those from experiments. The second case involved the explosion of a cylindrical high explosive whose length-to-diameter ratio was unity and that was placed in air. The initiation point was the one end side of the high explosive. The blast wave was divided into three regions that originated from the detonation in the high explosive, an oblique shock wave in air, and a bridge wave connected with them, thus causing an azimuthal distribution of peak overpressure. The highest peak overpressure values were computed in the bridge wave region. To understand the propagation behavior of the blast wave, we should thoroughly observe how and when all the waves affecting the blast-wave behavior are generated and how they propagate and interact with each other.

In this work, we studied detonation in condensed-phase explosives of PETN and the oblique shock waves in the surrounding fluid. The surrounding fluid was modeled as an ideal gas equation of state using the specific heat ratio as a parameter. Depending on the specific heat ratio, four types of flow structures were observed behind the oblique shock wave in the ideal gas. We measured the detonation/shock angles and the contact angle between the detonation products and the ideal gas. When the specific heat ratio was greater than the critical value, the oblique shock wave was detached from the detonation front at the PETN/ideal gas interface. When attached, three types of waves are observed, depending on the specific heat ratio: a strong oblique shock wave, strong and weak oblique shock waves which meet at the triple point as well as a weak oblique shock wave. To understand the properties of the flow near the detonation and the oblique shock waves, they were modeled as planar Chapman–Jouguet (CJ) detonation in PETN and as oblique shock waves in ideal gas. They were theoretically estimated as (1) Prandtl–Meyer expansion of the detonation products from the CJ state, and (2) oblique shock waves around a wedge using oblique shock theory or around a cone using the Taylor–Maccoll equation. From the flow models, we obtained a solution for the pressure equilibrium and parallel flows between the detonation products and ideal gas under the assumption that the wedge and cone angles correspond to the contact angle between them. For the attached cases, the solution was consistent with the simulated observations at the PETN/ideal gas interface. From the flow models, the maximum deflection angles for the detonation products and the ideal gas were obtained, and their magnitude correlations used to classify the four types of flow.

We report numerical simulations undertaken to understand the effects of a protective dike near an underground high-explosive storage facility. Our numerical model allowed us to estimate the peak overpressure of a blast wave around an underground magazine with or without a dike. We varied the internal length-to-diameter ratio of the underground magazine to compare the effects of magazine length. We found that the dike prevented the blast wave and detonation products from expanding along the exit direction and mitigated the peak overpressure near the dike. Our simulated results for peak overpressures outside the magazine on the ground agreed well with experimental results. The azimuthal characteristics, how the peak overpressure was reduced by the increment of the azimuth angle, were independent of the internal length-to-diameter ratio of the magazine. The presence of a dike, however, does change the shape of the iso-peak overpressure zone around the magazine exit which would determine the explosive safety quantity–distance. With a dike, the iso-peak overpressure zone is a circle, and it is an ellipse without the dike on the ground. The parameters to describe these shapes can be expressed as a linear function of the radius of the iso-peak overpressure zone of a surface explosion without any models on the ground.

A two-dimensional numerical simulation of the interaction between a shock wave and a particle cloud curtain (PCC) in a shock tube was conducted to develop the numerical method and to understand how the particle layer mitigates the shock wave. In the present study, computational fluid dynamics/the discrete element method in conjunction with drag force and convective heat transfer models were used to separately solve the continuum fluid and particle dynamics. The applicability of the method to the gas flow and particles was validated through comparison with gas–particle shock-tube experiments, in which the PCC was generated by free fall, and particles initially had a gradient of its volume fraction and falling velocity in height. When the incident shock wave interacted with the PCC, it was reflected from and transmitted through the PCC. The transmitted shock wave had a curved front because the initial gradient in the volume fraction of particles locally changed the interaction between the shock wave and the particles. We calculated the effects of the drag force and heat transfer in mitigating the strength of the transmitted shock wave. The propagation of the transmitted and reflected shock waves and the motion of the PCC induced by the gas flow behind the shock wave agreed well with previous experimental data. After the interaction between the gas flow and the PCC, drag force and heat transfer were activated by the gradients in pressure, velocity, and temperature between them, and the gas flow lost momentum and energy, which weakened the transmitted shock wave. At the same time, the PCC gained momentum and energy and was dispersed. The contact forces between two particles affected the local dispersion of the PCC.

Two-dimensional explosion experiments were conducted to discuss the interaction between a blast wave and sand and show the mitigation effect of the sand on the blast wave. The explosive used was a detonating cord 1.0 m in length, which was initiated in a sand hill shaped like a triangular prism and whose cross section was an isosceles triangle with base angles of 30 $$^\circ $$ . Sand-hill heights of 30 and 60 mm were used as parameters to discuss the effect of sand mass upon blast-wave strength. The interaction of the blast wave with the sand/air interface causes multiple peaks in the blast wave, which are induced by successive transmissions at the interface. The increase in the sand mass further mitigates the blast parameters of peak overpressure and positive impulse. The results of this experiment can be utilized to validate the numerical method of solving the problem of interaction between a compressible fluid and a particle layer.

This paper investigates explosions in a straight square tube in order to understand the mitigation effect of water on blast waves that emerge outside. Numerical simulations are used to assess the effect of water that is filled inside the tube. The water reduces the peak overpressure at the tube exit and outside, which agrees well with the experimental data. The increases in the kinetic and internal energies of the water are estimated, and the internal energy transfer at the air/water interface is shown to be an important factor in mitigating the blast wave on the ground in the present numerical method. Two mechanisms of the energy transfer are proposed in the present study. Initially, the strong shock wave reflects off and transmits water. A high-energy transfer into the water from air is promoted by the shock compression of water. Subsequently, as the shock wave propagates along the water surface, the air is adiabatically compressed continuously, and the pressure and temperature differences between the shocked-air and water induce a more gradual transfer of internal energy into the water.

This paper investigates explosions in a straight square tube in order to understand the mitigation effect of water on blast waves that emerge outside. Numerical simulations are used to assess the effect of water that is put inside the tube. The water reduces the peak overpressure outside, which agrees well with the experimental data. The increases in the kinetic and internal energies of the water are estimated, and the internal energy transfer at the air/water interface is shown to be an important factor in mitigating the blast wave in the present numerical method.

The interaction of a shock wave and particles filling the inside of a straight tube was numerically investigated to understand the mitigation mechanism on a blast wave outside the tube. A shock wave propagating along the particle layer inside the straight tube induced differences in the velocity and temperature between the particle layer and shocked air, inducing energy transfer through a drag effect, heat transfer, and nozzling term. Because the particle layer hardly moved inside the straight tube, the drag effect and nozzling term were too small to mitigate the blast wave. On the other hand, the heat transfer from the air to the particle layer absorbed several tens of percent of the energy released by the high explosive and was the dominant factor in mitigating the blast wave. To estimate the effect of the heat transfer between the particle layer and shocked air, we proposed a novel index estimated by the shocked-air properties, using the Rankine–Hugoniot relation. The numerical data for the heat transfer rate were simply and adequately estimated by the novel index, which indicated that the shocked-air properties were responsible for the heat transfer rate used to determine the mitigation of the blast wave.

This paper numerically visualizes explosion phenomena in order to discuss blast wave characteristics with a two-dimensional axisymmetric room model. After the shock wave exits via an opening, the blast wave propagates into open space. In the present study, a parametric study was conducted to determine the blast wave characteristics from the room exit by changing the room shape and the mass of the high explosive. Our results show that the blast wave characteristics can be correctly estimated using a scaling factor proposed in the present paper that includes the above parameters. We conducted normalization of the peak overpressure curve using the shock overpressure at the exit and the length scale of the room volume. In the case where the scaling factor has the same value, the normalized peak overpressure curve does not depend on the calculation conditions, and the scaling factor describes the blast wave characteristics emerging from the current room model.

This paper visualizes explosions in a subsurface magazine model constructed underground to mitigate the effects of blast waves. Numerical simulations discuss the effect of water that is put inside the magazine model. In the case of the explosion inside the magazine with water, the peak overpressure on the ground becomes smaller than that in the case of the explosion on the ground. The peak overpressures on the ground agree with those in the previous experiment. The increases of kinetic and internal energies of water are then estimated, and that the internal energy transfer at the interface of water and air is one of important factors to mitigate the blast wave on the ground in the present numerical method. As high-pressure gas at the exit of the magazine model drives the blast wave, the exit impulse and pressure are calculated and well reduced in the case with water inside the magazine model. Our study confirms that the exit pressure can scale the peak overpressure on the ground.

This study explored the practicality of a two-phase flow model for granular media in elucidating the attenuation mechanism of the blast wave. To validate the model, the numerical data were compared with the results of the previous experiments in terms of the interaction between the planar shock wave and particle layer, dispersal of steel particles saturated with a liquid explosive after the detonation of the explosive, and attenuation effect of the particle layer on the blast wave. Results of the validation confirmed good agreement and consistency between both data. Next, the attenuation effect on the blast wave created by a spherical pentolite by encircling the high explosive with a particle layer of sand was investigated, where the main parameter for comparison was the particle layer thickness. Here, a thicker particle layer further attenuated the blast wave, whereas a thinner one was accelerated to a velocity exceeding the sound speed of air, which generates a secondary shock wave ahead of the particle layer and behind the incident shock wave. When the secondary shock wave was coupled with the incident shock wave, the blast wave strength was locally recovered. To quantitatively comprehend the attenuation mechanism of the particle layer on the blast wave, the total energy transfer between the particle layer and air was computed. Results revealed a strong correlation between the blast wave strength and the amount of energy transferred between the particle layer and air and to the flow structures generated by the particle motion.

This paper numerically modeled previous experimental results and quantitatively revealed the attenuation effect of a barrier material on a blast wave. Four fluids were considered in the present study: the detonation products, water, foamed polystyrene, and air. These fluids were modeled by Jones-Wilkins-Lee (JWL), stiffened gas, and ideal gas equations of state. A mixture of water and foamed polystyrene was used as a barrier to encircle a 0.1 kg mass of spherical pentolite, and the interface problem between the barrier and the blast wave was investigated. The simulation parameters were the radius and the water volume fraction of the barrier. To elucidate the effect of the barrier, we conducted two series of numerical simulations; one without a barrier, and another with a barrier of 50 or 100 mm in outer radius and 0–1 in the water volume fraction. Peak overpressure, positive impulse, and pressure history all agreed well with the previous experimental results. We focused on the energy transfer from high-pressure detonation products to other fluids. The sum of the kinetic energies of the detonation products and the barrier induced by the blast wave could quantitatively estimate the attenuation effect of the blast wave and was minimized when the water volume fraction was 0.5, as was the case in the previous experiment.

This article presents numerical results of detonation in a two-dimensional curved channel in order to discuss its propagation behavior and the stable propagation limit. We simulated the detonation with various channel widths in two types of the ratios of inner and outer radii (Rout/Rin), which are 1.5 and 2. Two propagation modes, named as marginal and stable modes, were observed. In marginal mode, curved detonation propagates with repetition of decay, re-ignition, and propagation. Its velocity varies from underdriven to overdriven in one cycle. In a stable mode, the detonation propagates steadily while keeping a curved shock front structure and a constant detonation velocity in the circumferential direction. The idea of quasi-steady solution to the numerical results is applied for stable detonation limit. We confirmed that the detonation propagates steadily in the case that a shock radius of the detonation front is larger than the critical value of quasi-steady solution.

We numerically investigated high-pressure hydrogen leakage from transportation facilities, focusing on the steady mass flow rate and pressure distribution in a tube during the leakage. We studied steady leakage from a square opening in a square duct as well as leakage from a ruptured cylindrical tube with unsteady closure of a cutoff valve from fully open. A prediction model for the mass flow rate and pressure distribution inside the tube was proposed; such a model would help prevent physical hazards during an accident. We considered changes in the physical quantities according to the fluid dynamics occurring inside the tube. The flow properties were divided into two phases: (i) the unsteady expansion wave propagating inside a tube filled with hydrogen and (ii) the acceleration of hydrogen due to the reduction in the cross-sectional area between the tube and the leakage opening. To close the prediction model, we introduced contraction coefficient models depending on how the hydrogen leakage occurred. The mass flow rate and pressure drop during the leakage estimated by our prediction model showed good agreement with numerical simulation results when the contraction coefficient model was appropriately chosen. This model is considered highly applicable to the construction condition of pressure sensors, the operating conditions of a valve, and the prediction of mass flow rate during an accident.

Spinning detonations propagating in a circular tube were numerically investigated with a two-step reaction model by Korobeinikov et al. The time evolutions of the simulation results were utilized to reveal the propagation behavior of single-headed spinning detonation. Three distinct propagation modes, steady, unstable, and pulsating modes, are observed in a circular tube. The track angles on a wall were numerically reproduced with various initial pressures and diameters, and the simulated track angles of steady and unstable modes showed good agreement with those of the previous reports. In the case of steady mode, transverse detonation always couples with an acoustic wave at the contact surface of burned and unburned gas and maintains stable rotation without changing the detonation front structure. The detonation velocity maintains almost a CJ value. We analyze the effect of acoustic coupling in the radial direction using the acoustic theory and the extent of Mach leg. Acoustic theory states that in the radial direction transverse wave and Mach leg can rotate in the circumferential direction when Mach number of unburned gas behind the incident shock wave in the transverse detonation attached coordinate is larger than 1.841. Unstable mode shows periodical change in the shock front structure and repeats decoupling and coupling with transverse detonation and acoustic wave. Spinning detonation maintains its propagation with periodic generation of sub-transverse detonation (new reaction front at transverse wave). Corresponding to its cycle, whisker is periodically generated, and complex Mach interaction periodically appears at shock front. Its velocity history shows the fluctuation whose behavior agrees well with that of rapid fluctuation mode by Lee et al. In the case of pulsating mode, as acoustic coupling between transverse detonation and acoustic wave is not satisfied, shock structure of spinning detonation is disturbed, which causes failure of spinning detonation.

Pulsating detonations propagating in circular and square tubes were numerically investigated with a two-step reaction model by Korobeinikov et al. The time evolution of the simulation results was utilized to reveal the propagation mechanism of pulsating detonation. Soot track images on the wall and flow features shows cyclic behavior in longitudinal direction including three regions of multi-headed, single-headed, and no detonation. Pulsating detonation shows strong oscillation in the longitudinal direction and periodic behavior as follows. Shock front separates from the reaction front, and the shock wave velocity becomes underdriven. Local explosion occurs near the flame front and develops on inner detonation propagating to the leading shock wave. After penetration of the inner detonation into the leading shock wave, an overdriven multiheaded detonation appears and is gradually transformed into a spinning detonation with diminishing velocity. After a while, the spinning detonation decays, and the shock front finally separates from the reaction front again. Pulsating detonation propagates with repetition of these processes and its velocity varies from underdriven to overdriven in one cycle of pulsation. In order to discuss the one-dimensional features of pulsating detonation, x–t diagrams of cross-sectionally averaged profile are directly compared with x–t diagram of one-dimensional detonation, and the two agree well in terms of periodicity, as observed in the unsteady mechanism of the large-disturbance regime. Characteristic values such as the velocity in the failed regime obtained by the one-dimensional detonation agree with those by the pulsating detonation in circular and square tubes. Therefore, pulsating detonation is essentially a one-dimensional phenomenon and is dominant to longitudinal instability.

This study was a numerical and experimental investigation of low-temperature auto-ignitions behind reflected shock waves in which a shock tube was employed as the experimental system. We used a high-speed video camera and the Schlieren method to visualize the ignition phenomena. Experiments were performed over a temperature range from 549 ± 10 to 1349 ± 11 K and a pressure range from 56 ± 2 to 203 ± 13 kPa, and a non-diluted stoichiometric acetylene–oxygen mixture was chosen as the combustible gas. We introduced a numerical simulation to help us understand the disturbed temperature distribution behind bifurcated shock waves due to interference between reflected shock waves and the boundary layer developed behind incident shock waves. Additionally, we experimentally observed and evaluated quantitatively a tendency for ignition positions to be located farther from the reflecting wall as the temperature decreased behind reflected shock waves. To focus our attention on the ignition positions, we classified the ignition types behind reflected shock waves as near-wall ignition and far-wall ignition by 4.7 mm distance from reflecting wall. The criterion for these ignition types was estimated to be - 1.0 ⩽ ( ∂ t i / ∂ T 5 t ) p 5 t ⩽ - 0.5 . As a main object in this manuscript, we proposed an ignition model in which local ignition is induced at some distance from reflecting wall based on the numerical simulation and results; the local ignitions at a point distant from the reflecting wall are induced by the temperature rise, with the distance from the reflecting wall, immediately behind concave reflected shock waves due to developing of bifurcated shock waves. We confirmed that there is no discrepancy between the proposed model and experimental results.

Spinning detonations propagating in a circular tube were numerically investigated with a one-step irreversible reaction model governed by Arrhenius kinetics. The time evolution of the simulation results was utilized to reveal the propagation mechanism of single-headed spinning detonation. The track angle of soot record on the tube wall was numerically reproduced with various levels of activation energy, and the simulated unique angle was the same as that of the previous reports. The maximum pressure histories of the shock front on the tube wall showed stable and unstable pitch modes for the lower and higher activation energies, respectively. The shock front shapes and the pressure profiles on the tube wall clarified the mechanisms of two modes. The maximum pressure history in the stable pitch remained nearly constant, and the single Mach leg existing on the shock front rotated at a constant speed. The high and low frequency pressure oscillations appeared in the unstable pitch due to the generation and decay of complex Mach interaction on the shock front shape. The high-frequency oscillation was self-induced because the intensity of the transverse wave was changed during propagation in one cycle. The high-frequency behavior was not always the same for each cycle, and therefore the low frequency oscillation was also induced in the pressure history.