Consequence analysis by means of characteristic curves to determine the damage to buildings from bursting spherical vessels

Since the damage suffered by buildings as a consequence of explosions usually affect the people inside them, it is important to take it into account when performing consequence analysis. The aim of this paper is to provide a methodology to estimate consequences to buildings from pressure waves produced by spherical vessel burst. This is done by combining characteristic overpressure–impulse–distance curves [González Ferradás, E., Diaz Alonso, F., Sanchez Perez, J.F., Miñana Aznar, A., Ruiz Gimeno, J. and Martinez Alonso, J., 2006, Characteristic overpressure–impulse–distance curves for vessel burst, Process Safety Progress, 25(3): 250–254] with PROBIT equations. The main advantage of this methodology is that it allows an overview of all the magnitudes involved, as damage is shown in the same graph as the overpressure, impulse and distance. In this paper diagrams and equations are presented to determine minor damage to buildings (broken windows, displacement of doors and window frames, tile displacement, etc.), major structural damage (cracks in walls, collapse of some walls) and collapse (the damage is so extensive that the building is partially or totally demolished).     

Characteristic overpressure–impulse–distance curves for the detonation of explosives, pyrotechnics or unstable substances

A number of models have been proposed to calculate overpressure and impulse from accidental industrial explosions. When the blast is produced by explosives, pyrotechnics or unstable substances, the TNT equivalent model is widely used. From the curves given by this model, data are fitted to obtain equations showing the relationship between overpressure, impulse and distance. These equations, referred to here as characteristic curves, can be fitted by means of power equations, which depend on the TNT equivalent mass. Characteristic curves allow determination of overpressure and impulse at each distance.     

The application of pressure–impulse curves in a blast exceedance analysis

The magnitude of damage due to a vapor cloud explosion can be estimated in many ways, ranging from look-up tables to quantitative risk analysis. An explosion overpressure analysis is a routine part of compliance with the American Petroleum Institute (API) Recommended Practice (RP) 752 when evaluating occupied buildings in a facility that processes flammable or reactive materials. In many cases, a risk-based approach is useful because consequence modeling studies often indicate major problems for buildings at existing facilities. One of the most common risk-based methods, overpressure exceedance, incorporates a wide range of potential explosion scenarios coupled with the probability of each event to develop the probability of exceeding a given overpressure at specific locations. But this and other methods that only use overpressure may not represent an accurate building response. By combining the risk-based methodology of the exceedance analysis with pressure and impulse data in the form of pressure–impulse (P–I) curves, a better measure of building damage can be generated. P–I curves for blast loading determination have been in use for decades, and allow the user to determine levels of damage based on a predicted overpressure and its corresponding impulse. Curves have been published for entire buildings, individual structural members, window breakage, and even consequences to humans. This paper will explore application of P–I curves for building damage, and will highlight some of the benefits, as well as some of the potential problems, of using P–I curves.     

Propagation and intensity of blast wave from hydrogen pipe rupture due to internal detonation

The coupled fluid-structure-rupture model was developed to study the propagation and intensity of blast wave from hydrogen pipe rupture due to internal detonation. The dynamic rupture of pipe and propagation of blast wave were well coupled together in every timestep during the simulation. The numerical model was validated with experiments in terms of both typical rupture profiles and blast overpressures. Results reveal that crack branching of pipe can dramatically increase the rupture opening rate which controls the intensity and shape of the resultant blast wave. Due to the process of crack initiation and extension, the blast wave out of the pipe first forms and then is strengthened by the subsequent compression waves. This makes the maximum peak overpressure appears at a certain standoff distance above the rupture. Despite consuming some percentages of energy, the dynamic rupture of pipe generally presents positive effects (up to 2–3 times) on the blast wave intensity along the jetting direction due to the convergence effect of rupture opening on the release of internal high-pressure gas. Finally, through defining normalized overpressure and impulse based on the same hydrogen detonation in open spaces, the quantitative influences of pipe rupture on the blast wave intensity in cases of different detonation pressures and standoff distances are clarified.     

Numerical simulations on the attenuation effect of a barrier material on a blast wave

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.     

Experimental study on the feasibility of explosion suppression by vacuum chambers

In view of the invalidity of suppression and isolation apparatus for gas explosion, a closed vacuum chamber structure for explosion suppression with a fragile plane was designed on the base of the suction of vacuum. Using methane as combustible gas, a series of experiments on gas explosion were carried out to check the feasibility of the vacuum chamber suppressing explosion by changing methane concentration and geometric structure of the vacuum chamber. When the vacuum chamber was not connected to the tunnel, detonation would happen in the tunnel at methane volume fraction from 9.3% to 11.5%, with flame propagation velocity exceeding 2000 m/s, maximum peak value overpressure reaching 0.7 MPa, and specific impulse of shock wave running up to 20 kPa s. When the vacuum chamber with 5/34 of the tunnel volume was connected to the flank of the tunnel, gas explosion of the same concentration would greatly weaken with flame propagation velocity declining to about 200 m/s, the quenching distance decreasing to 3/4 of the tunnel length, maximum peak value overpressure running down to 0.1-0.15 MPa and specific impulse of shock wave below 0.9 kPa s. The closer the position accessed to the ignition end, the greater explosion intensity weakened. There was no significant difference between larger section and smaller vacuum chambers in degree of maximum peak value overpressure and specific impulse declining, except that quenching fire effect of the former was superior to the latter. The distance of fire quenching could be improved by increasing the number of the vacuum chambers.     

Gas flame acceleration in long ducts

In many practical situations, a flame may propagate along a pipe, accelerate and perhaps transform into a devastating detonation. This phenomenology has been known, more or less qualitatively, for a long time and mitigation techniques were proposed to try and avoid this occurrence (flame arresters, vents,...). A number of parameters need to be known and in particular the “distance to detonation” and more generally the flame acceleration characteristic scales. Very often, the ratio between the detonation run-up distance and the pipe diameter is used without any strong justification other that using a non-dimensional parameter (L/D). In this paper, novel experimental evidence is presented on the basis of relatively large scale experiments using 10 cm and 25 cm inner diameter duct with a length between 7 and 40 m. Homogeneous C₂H₄-air, CH₄-air, C₃H₈-air and H₂-air mixtures were used and different ignition sources. The interpretation suggests that the self-acceleration mechanism of the flame may be much better represented by flame instabilities than by turbulence build-up. One consequence would be that the maximum flame velocity and, following, the maximum explosion overpressure, would be rather linked with the run-up distance than with the L/D ratio.     

Quantitative assessment in safety reports of the consequences from the detonation of solid explosives

Safety reports are mandatory documents in member states of European Union whenever any threshold limits of amounts of either stored or processed hazardous substances are exceeded. After a short introduction to EU Seveso Directives on major-accident hazards involving dangerous substances and to the transposition and implementation by member states, with a brief comment on last 2012/18/EU Directive (also known as Seveso III directive), the paper focuses on drafting of safety reports for industrial activities involving solid explosives. Specifically, the quantitative assessment of consequences from detonation is tackled respect to the side-on overpressure and the debris production. Both direct and inverse problems are illustrated to determine respectively the overpressure value at a given distance, and the explosive amount that allows respecting the regulations. Their solution is based on either analytic or numerical techniques and being based on recent scientific publications on the matter either evaluates or zeroes nonlinear algebraic equations. The availability of these equations avoids grounding the consequences assessment on diagrams and nomograms that otherwise would lead to interpretation and usage errors besides avoiding the automatic solution of the inverse problem. The paper focuses also on details such as embankment, crater, munitions, rocket propellant, building structure, and wall material that, at different levels, play a role in the assessment of detonation consequences. A discussion on debris formation, the available literature, and the evaluation of the impact probability of fragments on both fixed and moving targets closes the paper.     

Structure and flame speed of dilute and dense layered coal-dust explosions

Multidimensional time-dependent simulations were performed to study the interaction of a stoichiometric methane–air detonation with layers of coal dust. The simulations solved equations representing a Eulerian kinetic-theory-based granular multiphase model applicable to dense and dilute particle volume fractions. These equations were solved using a high-order Godunov-based method for compressible fluid dynamics. Two dust layer concentrations were considered: loose with an initial volume fraction of 1%, and dense with an initial volume fraction of 47%. Each layer was simulated with two types of dust: reactive coal and inert ash. Burning of the coal particles results in a coupled complex consisting of an accelerating shock leading a coal-dust flame. The overall structure of the shock–flame complex resembles that of a premixed fast flame with length scales on the order of several meters. The large length scales are direct results of time needed to lift, mix, heat, and autoignite the particle. The flame speeds are large and much larger than the gas-phase velocity. Large spikes of flame speed are characteristic of the 47% case. These spikes and high flame speed are caused by pockets of coal dust autoigniting ahead of the flame. The flame is choked in the 1% case due to the gas-phase products exceeding the sonic velocity with respect to the flame. The 47% case is choked due to attenuation of pressure waves as they propagate through particles. Inert layers of dust substantially reduce the overpressure, impulse, and speed produced by propagating blast wave. The results also show that loose layers of dust are far more dangerous than dense layers. The shock and flame are more strongly coupled for loose layers, propagate at higher velocity, and produce large overpressures and impulses.     

非典型约束形式下海洋平台波纹板舱室抗爆能力评估

针对非典型约束条件即底部端面梁固定约束、其他各端面梁连接约束的海洋平台关键舱室,其波纹板舱壁在油气爆炸载荷下抗爆能力研究不足,采用数值模拟方法,结合考虑材料应变率效应的实验验证,分析爆炸载荷下舱壁动力响应及破坏模式。由传统位移指标不能准确评估该模型的抗爆能力,提出基于应变的评价指标,以此建立P-I评估曲线。研究表明舱壁与底部端面梁连接部位首先达到最大破裂应变发生破裂,其为超压与冲量共同作用结果;舱室可抵抗超压40 kPa、冲量230 kPa·ms的载荷而不发生塑性变形;舱室可抵抗超压85 kPa、冲量400 kPa·ms的载荷而不发生破裂。提出的以应变为指标的P-I曲线可量化舱壁损伤评估区间,结合爆炸载荷值,准确评估舱壁抗爆能力及损伤大小,为工程人员优化舱壁抗爆能力、确定灾后控制措施提供指导。     

Measurement of gas detonation blast loads in semiconfined geometry

The ignition and explosion of combustible vapor clouds represents a significant hazard across a range of industries. In this work, a new set of gas detonations experiments were performed to provide benchmark blast loading data for non-trivial geometry and explosion cases. The experiments were designed to represent two different accident scenarios: one where ignition of the vapor cloud occurs shortly after release and another where ignition is delayed and a fuel concentration gradient is allowed to develop. The experiments focused on hydrogen-air and methane-oxygen detonations in a semiconfined enclosure with TNT equivalencies ranging from 9 g to 1.81 kg. High-rate pressure transducers were used to record the blast loads imparted on the interior walls of a 1.8 m × 1.8 m × 1.8 m test fixture. Measurements included detonation wave velocity, peak overpressure, impulse, and positive phase duration. A comparison of the pressure and impulse measurements with several VCE models is provided. Results show that even for the most simplified experimental configuration, the simplified VCE models fail to provide predictions of the blast loading on the internal walls of the test fixture. It is shown that the confinement geometry of the experiment resulted in multiple blast wave reflections during the initial positive phase duration portion of the blast loading, and thus, significantly larger blast impulse values were measured than those predicted by analytical models. For the pressure sensors that experienced normally-reflect blast waves for the initial blast impulse, the Baker-Strehlow and TNT equivalency models still struggled to accurately capture the peak overpressure and reflected impulse. The TNO multi-energy model, however, performed better for the case of simple normally-reflected blast waves. The results presented here may be used as validation data for future model or simulation development.     

单层柱面网壳结构强震作用下抗震性能研究

地震是严重危害人类生命财产的自然灾害 ,但目前工程界对于网壳结构强震下的抗震性能尚缺乏透彻了解。笔者通过对单层柱面网壳典型算例进行三维地震作用下的双重非线性时程分析 ;观察其多项特征响应指标随地震动逐渐增强的变化情况 ;研究其塑性发展过程和破坏特征 ;对单层柱壳强震作用下的破坏机理进行了探讨 ;并在此基础上对不同参数柱壳弹塑性地震响应规律和破坏特征进行了分析和总结。研究表明 ,地震作用下单层柱壳破坏前均经历了一定的塑性发展过程 ,其破坏的真正原因是结构塑性发展和位形变化的交互作用 ,矢宽比较大的柱壳倾向于动力失稳破坏。     

Laboratory scale tests for the assessment of solid explosive blast effects. Part I: Free-field test campaign

The definition of blast loads applying on a complex geometry structure is still nowadays a hard task when numerical simulations are used, essentially because of the different scales involved: as a matter of fact, modelling the detonation of a charge and its resulting load on a structure requires to model the charge itself, the structure and air surrounding, which rapidly leads to large size models on which parametrical studies become unaffordable. So, on the basis of the Crank–Hopkinson’s law, an experimental set-up has been developed to support reduced scale structures as well as reduced scale detonating solid charges. As a final objective, the set-up must be used to produce the entry data for numerical assessments of the structure resistance.This set-up is composed of a modular table, sensors and targets and has been designed to conduct non-destructive studies. In the context of security, the general aim is to study the effects of detonation shock waves in the vicinity of facility buildings and to test various shock wave mitigation means that could be implemented for the protection of facilities in sensitive locations. Especially, the set-up offers the possibility to measure the loading in terms of pressure-time curves, even for very complex situations like multiple reflections, combination and diffraction.The present paper summarizes the development of the set-up as well as the first tests performed. The main features of the table, the instrumentation and the pyrotechnics are given. Also the paper summarizes a first qualification tests campaign that has been conducted. In this campaign, free-field blast tests (i.e. blast tests performed without structures) have been conducted. Overpressure maxima, arrival time of the shock wave and impulse are presented as non-dimensional characteristics of the pressure-time history. The results obtained have been found in good agreement with reference curves available from the open literature and numerical model results.     

The acceleration of flames in tube explosions with two obstacles as a function of the obstacle separation distance

The separation distance (or pitch) between two successive obstacles or rows of obstacles is an important parameter in the acceleration of flame propagation and increase in explosion severity. Whilst this is generally recognised, it has received little specific attention by investigators. In this work a vented cylindrical vessel 162 mm in diameter 4.5 m long was used to study the effect of separation distance of two low blockage (30%) obstacles. The set up was demonstrated to produce overpressure through the fast flame speeds generated (i.e. in a similar mechanism to vapour cloud explosions). A worst case separation distance was found to be 1.75 m which produced close to 3 bar overpressure and a flame speed of about 500 m/s. These values were of the order of twice the overpressure and flame speed with a double obstacle separated 2.75 m (83 characteristic obstacle length scales) apart. The profile of effects with separation distance was shown to agree with the cold flow turbulence profile determined in cold flows by other researchers. However, the present results showed that the maximum effect in explosions is experienced further downstream than the position of maximum turbulence determined in the cold flow studies. It is suggested that this may be due to the convection of the turbulence profile by the propagating flame. The present results would suggest that in many previous studies of repeated obstacles the separation distance investigated might not have included the worst case set up, and therefore existing explosion protection guidelines may not be derived from worst case scenarios.     

大长径比管道汽油-空气混合气爆炸与抑制实验研究*

为探究狭长受限空间中油气爆炸失控时的发展状态,探索高效环保的油气爆炸抑制方法,利用长径比155的管道开展92号汽油-空气混合气爆炸发展规律和七氟丙烷主动抑爆技术研究。通过测量不同端部开口条件下油气爆炸超压、火焰传播速度、火焰强度等参数,对比研究空爆和抑爆工况下的油气爆炸变化规律,探讨长直管道中的油气爆炸特性,分析七氟丙烷抑爆效果。结果表明:大长径比管道中,端部开口泄爆对降低油气爆炸破坏能力的作用较小,开口与否对最大超压峰值的出现位置有影响;长直管道空爆时,油气爆炸由爆燃发展成爆轰,管道尾部的爆轰波速可达近2 000 m/s;密闭管道中,爆轰发生前火焰传播呈“已燃区-火焰锋面-待燃区-前驱激波-未燃区”的2波3区结构;主动抑爆方式下七氟丙烷抑爆效果良好,最大超压峰值降低幅度可达90%,火焰传播被及时阻断。     

Numerical investigation and analysis of indoor gas explosion: A case study of “6·13” major gas explosion accident in Hubei Province,China

Taking the ' 6·13 ′ major gas explosion accident in Shiyan, Hubei Province, China as an example, three problems were studied in this work: (1)The determination of the volume of natural gas involved in the explosion; (2)The propagation process of shock wave inside the building and the damage evolution process of the accident-related building; (3)The overpressure and fragment injury to the person outside the building. Through the numerical simulation in ANSYS/LS-DYNA software, the volume of natural gas involved in the explosion is determined to be 10240 × 1400 × 400 cm (length × width × height) from three perspectives: the damage to the building, the distribution of overpressure inside the building, and the TNT equivalent of the explosion energy. The simulation results are in good line with the accident, which verifies the effectiveness of the scheme and the accuracy of the numerical model. Based on the reasonable filling scheme, the propagation process of shock waves inside the building, the damage evolution process of the building, and the injury ranges of overpressure and fragments outside the building are analyzed. It can be found that the propagation of shock waves in confined space is complex and variable. The explosion shock waves are first reflected and superimposed in the watercourse, resulting in pressure rise. At about 8ms, the shock waves rushed into the first-floor space of the building, and the maximum overpressure was about 0.56 MPa. At about 50 ms, the shock waves rushed into the second-floor space, and the maximum overpressure was about 0.139 MPa. The first and second-floor slabs and infilled walls were almost completely destroyed. The interior walls of the infilled walls are mainly collapsed, and the exterior walls are ejection around the building as the center. The peak displacement and peak velocity of the interior walls of each floor are about 15% of the exterior walls. The fragments which cause fragment injury mainly come from the retaining wall above the watercourse, the maximum velocity is about 89 m/s, and the maximum displacement is 8.9 m. The safety distance of fragment injury is about 8.8 m, while the safety distance of overpressure injury is about 4.6 m. The lethal distance of fragment injury is greater than that of overpressure injury. Compared with the distance between different damage levels of overpressure injury, the difference in fragment injury is small. Therefore, the safety assessment at the engineering level only needs to consider the safety distance of fragment injury. This study can provide suggestions for evaluating the damage of natural gas cloud explosions in confined spaces and is helpful for accident investigation and safety protection.     

A quantitative correlation of evaluating the flame speed for the BST method in vapor cloud explosions

In recent decades, vapor cloud explosions (VCEs) have occurred frequently and resulted in numerous personnel injuries and large property losses. As a main concern in the petrochemical industry, it is of great importance to assess the consequence of VCEs. Currently, the TNT equivalency method (TNT EM), the TNO multi-energy method (TNO MEM), and the Baker-Strehlow-Tang (BST) method are widely used to estimate the blast load from VCEs. The TNO MEM and BST method determine the blast load from blast curves based on the class number and the flame speed, respectively. To quantitatively evaluate the flame speed for the BST method, the experimental data is adopted to validate the confinement specific correlation (CSC) for the determination of the class number in the TNO MEM. As a bridge, a quantitative evaluation correlation (QEC) between CSC correlation and the flame speed is established and the blast wave shapes corresponding to different flame speeds are proposed. CFD software FLACS was used to verify the quantitative correlation with the numerical models of three geometrical scales. It is found that the calculated flame speeds by the QEC are in good agreement with the simulated ones. A petrochemical plant is selected as a realistic scenario to analyze the TNT EM, TNO MEM, BST method and FLACS simulations in terms of the positive-phase side-on overpressure and impulse at different distances. Compared with the flame speed table, the predicted overpressure from BST curves determined by the proposed QEC is closer to that from FLACS and more conservative. Furthermore, the predicted results of different methods are compared with each other. It is found that the estimated positive-phase side-on overpressure and impulse by the TNO MEM are the largest, and the estimated impulse by the TNT EM is the smallest. Moreover, the estimated overpressure and impulse are larger in the higher reactivity gas.     

Estimation of pressure distribution for shock wave through the bend of bend laneway

Propagation of the air shock wave caused by explosion via the bend of a bend laneway has obvious nonlinear characteristics, compared with its propagation in a straight laneway. These characteristics are important bases to analyze the accident of gas explosion in underground mines and to estimate the blast resistance of underground structures in mines. In this work, the rule of the shock wave propagation via the laneway bend and the pressure distribution are studied by means of the numerical simulation approach. Theoretical results show that attenuation of the peak overpressure with distance does not obey exponent law when the air shock wave goes through the laneway bend. At some locations within the bend zone, the overpressures are higher than ones around those locations, the front of original plane wave bends in the bend of the laneway and after passing through the bend, it gradually returns to the state of plane wave propagation. There is a span dependent on the cross section dimension of laneway and the bend angle and increasing with the bend angle, in which the peak overpressure of shock wave does not uniformly attenuate with distance. When the bend angle is equal to 135°, this span is about five times as long as the corresponding equivalent diameter of the laneway. Additionally, the impulse of air shock wave attenuates uniformly via the laneway bend. On the end section of the complicated pressure distribution area in the bend, it is 66.65–98.7% of that in the straight laneway at the same scaled distance.     

Effect of ignition position on the run-up distance to DDT for hydrogen-air explosions

The method described in this paper enabled reliable and accurate positioning of an overdriven detonation by calculation of shock wave velocities (detonation and retonation) for hydrogen explosions in a closed 18 m long horizontal DN150 pipe. This enabled an empirical correlation between the ignition position and the run-up distance to DDT to be determined. It was shown that the initial ability of the flame to expand unobstructed and the piston-like effect of burnt gas expanding against the closed end of the tube contributed to initial flame acceleration and hence were able to affect the run-up distance to overdriven detonation. Flame speeds and rates of initial pressure rise were also used to explain how these two competing effects were able to produce a minimum in the run-up distance to DDT. The shortest run-up distance to DDT, relative to the ignition position, for this pipe and gas configuration was found when the ignition position was placed 5.6 pipe diameters (or 0.9 m) from the closed pipe end. The shortest run-up distance to DDT relative to the end of the pipe was recorded when the ignition source was placed 4.4 pipe diameters or 0.7 m from the pipe end.     

An overpressure-time history model of methane-air explosion in tunnel-shape space

This study investigated methane-air explosion in tunnel-shape space and developed an overpressure-time history model based on numerical results. The findings revealed that for the progressively vented gas explosion with movable steel obstacles in a 20 m long tunnel, the inner peak overpressure increased as the activation pressure of the tunnel top cover got higher but remained below 6 bar. However, as the activation pressure increased to 8 bar or higher, the peak inner overpressure remained unchanged. As the segment cover panel became wider, the peak pressure was almost unchanged, but the pressure duration and impulse declined significantly. The peak pressure and impulse increased as the tunnel length vary from 10 to 30 m. With fixed tunnel length, higher blast pressure but lower impulse was observed as the inner obstacles were closer or the activation pressure of obstacles was higher. It is also found that a local enlarged space in the tunnel enhanced the peak pressure significantly. An overpressure time history model for the tunnel with fixed top cover and enlarged end zone was established. The model considered activation pressure of vent cover, area and length of vent opening, methane concentration, number and blockage ratio of fixed obstacles was developed to calculate the overpressure and corresponding time at characteristic points of the pressure-history curve. The cubic Hermite interpolation algorithm and a specially tuned formula consisting of the power and exponential function were used to interpolate pressure values between characteristic points. The proposed model can predict both the peak pressure and the overpressure time history with acceptable accuracy.