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Chemical explosions

Essential to the consideration of accidental consequences is the estimation of hazards and hazard levels, e.g., overpressures, thermal radiation, and the estimation of the damage level or the vulnerability of the receiving objects. In chemical explosions, which are usually exothermal oxidation reactions, a great portion of the combustion energy is carried by the developing blast wave which is uniformly distributed in all directions. Depending on the various types of combustion processes (slow deflagration or fast turbulent flame or detonation), the pressure history will be different. It is characterized by the peak overpressure and the pressure increase/decay rate. This effect is strongest at ground level (hemispherical) explosions where due to reflection the respective yield ratio can be twice as high as for a spherical explosion.

Deflagration and detonation differ in peak overpressure, in the duration of the impulse (time-integrated pressure), in the steepness of the wave front, and in the decrease of overpressure with propagation distance. Secondary blast wave parameters are the peak reflected pressure, peak dynamic (blast wind) pressure, shock front velocity, and blast wave length. The different pressure transients for the two combustion modes are shown in Fig. 1.


In a deflagration with flame speeds of 1-10 m/s, the volume expansion of the gas acts like a piston displacing the unburnt gas. The deflagration pressure wave in a confined space is characterized by a slow increase of pressure and fluid velocity in the region preceding the flame front. The pressure in the vessel is independent of the location and mainly determined by the fraction of burnt gas. The static pressure loading in slow deflagration processes is described by the “adiabatic, isochoric, complete combustion” (AICC) pressure representing an upper bound in a confined space. A mitigation of the AICC pressure is given by incomplete combustion, venting, radiation/conduction heat losses, or the addition of diluents. Therefore the maximum static pressure will be generally lower than the AICC pressure. On the other hand, initial turbulence increases the degree of combustion and thus the pressure. The peak pressure in a closed vessel for most hydrocarbon mixtures is in the order of 0.8 MPa, sufficient for many buildings to exceed their failure limits. For a hydrocarbon-oxygen mixture, it is even 1.6 MPa. A hydrogen-air mixture, initially at NTP, will reach a pressure of 0.815 MPa; its volume will increase by a factor of 6.89 (BakerWE:1983).

The pressure buildup depends on the flame propagation and the degree of confinement. Particularly hazardous configurations are those, which are heavily confined like tubes, pipes, or channels, where – if long enough – even in insensitive methane-air mixtures, high flame speeds and pressures can be reached. Venting can reduce the pressure.

Inside a spherical vessel, the pressure rise following the ignition of a flammable mixture is proportional to the cube of the burning velocity. In pipes with no obstacles, the transition distance increases with increasing diameter (example: 8 m for propane-air mixture in a 50 mm diameter pipe) (MoenIO:1993). The effective burning velocity must be as high as ~ 100 m/s to produce significant blast overpressures of 10 kPa. Comparing explosion tests in tubes and in spherical vessels, it was observed that pressures are generally lower in a spherical propagation of the gas mixture (unconfined) than in a planar propagation. The pressure behind the flame front is decaying away from the flame, since wave energy dissipates.

The combustion of a hydrogen-air mixture in an unconfined vapor cloud explosion (UVCE) typically liberates only a fraction of 0.1-10 % of its thermal energy content, in most cases less than 1 % (LindCD:1975). Depending on the combustion mode (deflagration/detonation), the explosion is connected with a more or less destructive pressure shock wave.

Fast Deflagration

In the intermediate stage of a fast deflagration with the flame front still traveling at subsonic speed, a preceding shock wave is developing in the still unburnt mixture. The peak overpressure is lower, the pressure drop, however, takes place over a longer period of time. This means that the impulse, i.e., the integral of pressure over time, which is a measure for the load upon a structure, is about the same in both cases. The peak overpressure increases with increasing flame speed. Transient pressures can be locally higher than the AICC pressure. Inhomogeneities can result in local detonations decaying to deflagrations. When the shock wave leaves the cloud, it turns into an expanding decaying wave. In the long-distance range, the pressure wave for both deflagration and detonation exhibits about the same shape decaying with 1/r.

Local explosions like from jet flames result in locally high pressures and can also result in high flame speed in less confined areas and may even trigger a detonation wave.


In contrast, the detonation is a combustion mode with the flame traveling at supersonic speeds in the order of 2000 m/s. The flame front proceeds by shock wave compression of the unburnt gas. It is characterized by a distinct pressure spike and a subsequent almost exponential decrease. The shock wave, which is at the same time the flame front, is followed by the reaction zone, in which a pressure discontinuity is observed where the pressure even drops to values lower than atmospheric pressure (“molecular collapse”) due to the much denser oxidation product (water) upon hydrogen combustion. The essential parameters are peak overpressure and positive/negative phase of the specific impulse depending on the liberated explosion energy. The combustion process is completed without an expansion of the gas cloud. Peak overpressures in the near field are typically in the range of 1.5-2 MPa. The pressure wave gradually decays and eventually turns into an acoustic wave.

In geometries which allow the transition from deflagration to detonation, pressures near the location where detonation takes place, may be much higher than the CJ (Chapman-Jouguet) pressure of a stabilized (and idealized) detonation wave, which is due to a pre-compression effect by the propagating shock wave (VanWingerdenCJM:1999).

In confined spaces, peak pressures can range between “normal” deflagration peak pressure and very high pressures following DDT. Worst case is considered the DDT on a reflected shock wave produced by a fast flame with an estimated peak pressure to be by a factor of 10 higher than the detonation pressure. The transfer of a detonation wave into adjacent mixtures is possible and has been observed for planar clouds, whereas in spherical clouds, fast deflagrations are more likely to occur.

An explosion in a vessel which is connected by a small opening to another vessel creates a peak overpressure and a pressure increase rate much higher than in a single vessel explosion, a phenomenon known as “pressure piling”. A pressure of more than 3.5 MPa was measured in a two-chamber geometry for a stoichiometric hydrocarbon-air mixture, where 0.8 MPa were expected for the explosion in a single vessel. Unlike the length of the interconnecting tube, its diameter is pertinent for the peak overpressure.

Real Gas Cloud

In reality, a gas cloud shows the typically expected features of a non-premixed, inhomogeneous concentration distribution, air entrainment at the boundaries, and stratification if evolving from a pool of liquefied gas. Furthermore in case of an explosion, a real gas cloud is not an “ideal” explosion source due to a larger-than-infinitesimal volume and a lower energy density and energy deposition rate, thus leading to non-ideal blast waves. Deviations from the ideal situation are able to either enhance or to attenuate the pressure buildup. Non-stoichiometry as well as ignition at the cloud edge will certainly have a damping effect on the pressure buildup. The maximum blast impulse, which becomes larger with increasing shock duration, is not near the explosion center, but about 13-15 charge radii. A near-ground flat long-stretched cloud of heavy gases or vaporized cryogens may experience multi-point ignition connected with a sequence of pressure peaks, and more turbulence-generating terrain roughness or obstacles in the flow path, both effects of which lead to an enhancement of the pressure buildup.

Unlike a heavy gas cloud which would be of a pancake form, a hydrogen vapour cloud would soon cover an area, which is larger than that of a hemispherical cloud with the same explosive inventory. Only in case of just vaporized LH2 after a large-scale spill, the cold gas cloud would travel and stretch near ground, until sufficient air has entrained from the outside to make the gas positively buoyant and develop soon to a vertically stretched cloud shape.

The flame spreading in a non-spherical cloud is spherically until it reaches the cloud edge at some point; then it continues in the direction, where still gas can be found. The pressure is decreasing immediately behind the flame front because of the upward expansion of the combustion products.

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Page last modified on February 21, 2009, at 01:30 AM