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«INTRODUCTION A detonation is the most devastating form of gas explosion. Unlike the deflagration, a detonation does not require confinement or ...»

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Figure 11 shows detonation propagation limits within pipes and channels. We see that a pipe is more supportive of detonation propagation than a channel.

Figure 12 Requirements for successful transmission of a planar detonation into an unconfined threedimensional spherical detonation wave.

Figure 12 shows requirements for a successful planar detonation transmission from a pipe or channel into an unconfined situation (i.e. three-dimensional spherical detonation wave). In order to make a successful transmission, there is a need for more cells than for the planar propagation mode. The information in Figure 12 is useful in evaluating the possibility for transmission of a detonation from a confined area, like a building, ventilation duct, culvert etc. into an unconfined situation.

The requirement for propagation in an unconfined cloud is shown in Figure 13.

Figure 13 Limit for propagation of detonation waves in an unconfined fuel-air cloud.


The above shows that detonations in the open are possible. Initiation is possible from more confined areas such as a culvert or just by flame accelerations in congested areas.

This may have consequences for predicting the consequences of vapour cloud explosions;

i.e. explosions of clouds in landbased petrochemical installations such as refineries.

Methods for blast prediction such as the Multi-Energy method (Van den Berg, 1985) assume that blast is only generated in the congested parts of the cloud. As a result the blast prediction methods use the combustion energy in these congested areas only. In case of a detonation also the unconfined parts of the cloud will contribute to the blast possibly causing it to be much stronger at larger distances. The fact that a vapour cloud detonation can be expected even for the relatively low reactive fuels may make blast prediction methods such as the Multi-Energy method unreliable. On the other hand it should be emphasised that low reactive fuels will be able to reach detonations over a relatively small fuel concentration region only whereas more reactive fuels such as ethylene, ethylene-oxide, acetylene and hydrogen have a more wider explosive area with high reactivity concentrations. This will make it unlikely that low reactive fuel will reach detonations in reality. For the more reactive fuels a detonation may however, be possible also in realistic clouds.


Considering loading due to detonations one has to consider the full pressure-time history and not just the maximum pressures. So far we have discussed the detonation pressure (i.e. CJ-pressure) of a detonation front only. After the detonation front (CJ-plane) the combustion products will expand, i.e. the pressure will fall. How fast this expansion will take place, i.e. how fast the pressure will fall will depend on the boundary conditions.

The expansion of the combustion products forming a detonation wave propagating in a tube (i.e. one-dimensional propagation) is illustrated in Figure 14. The tube is closed at x = 0 and propagates from left to right. When the detonation is at x = L, the tail of the expansion wave will be located at approximately x = L/2 which means that the tail of the expansion wave propagates at half of the detonation velocity for this boundary condition. The expansion process between the wave front (CJ-conditions) and tail of the expansion wave can be approximated as being isentropic.

In this case the pipe is closed at x = 0. The boundary condition at x = 0 is therefore gas velocity equal to zero (u = 0 m/s). For this boundary condition the pressure will expand to P » 0.4 PCJ. Note that this pressure is approximately the same as the constant volume combustion pressure. This pressure will be constant from x = 0 to the tail of the rarefaction wave (i.e. x » L/2).

For other boundary conditions, u ¹ 0 m/s, the pressure will vary with the boundary conditions. The mode of propagation for the detonation, i.e. spherical or planar mode, will influence the expansion slope behind the wave.

Figure 14 Pressure-distance profile for a detonation propagation in a tube with a closed end (i.e. closed at x = 0).


The probability of occurrence of a detonation in fuel-air mixtures depends strongly upon the type of fuel. Very reactive fuels, such as hydrogen, acetylene or ethylene, may detonate in an accident situation. For accident situations involving such fuels, detonations should be regarded as a possible scenario.

Other fuels are less likely to detonate. Generally, however, in large gas clouds with a high degree of confinement and/or with a high density of obstructions, detonations cannot be ruled out.

Presently the most effective way of mitigating the occurrence of a detonation is to avoid situations where the deflagration can accelerate to a condition where transition from deflagration is possible, i.e. high pressure deflagrations.

Propagation and transmission of detonation waves depend mainly on the cell size (i.e.

type of fuel and fuel concentration) and geometrical conditions. By operating with geometrical dimensions (d, w, h) smaller than the limits indicated it is very unlikely that a stable detonation will occur.

The cell size as a measure of detonability is not an exact number. In the literature a variation of a factor of two is often found. When using cell sizes for estimation of limiting conditions for successful propagation or transmission, they should be regarded as approximate values. Hence safety factors should be used.


Acton, M.R., Sutton, P and Wickens, M.J. (1990)

An investigation of mitigation of gas cloud explosions by water sprays, Piper Alpha:

Lessons for Life Cycle Safety Management, Symposium Series No. 122, IChemE, Rugby, UK Al-Hassan, T. and Johnson, D.M. (1998) Gas explosions in large scale offshore module geometries: overpressures, mitigation and repeatability Paper presented during the 17th International confrence on Offshore Mechanics and Arctic Engineering, 6-9 July, Lisbon Bartknecht, W. (1971) "Brenngas- und Staubexplosionen".

Forschungsbericht F45, Bundesinstitut für Arbeidsschutz (Bifa), Dortmund, W.


Berg, A.C. van den (1985) "The multi-energy method. A framework for vapour cloud explosion blast prediction".

Journal of Hazardous Materials 12.

Bjørkhaug, M. and Hjertager, B.H. (1984) "The influence of obstacles on flame propagation and pressure development in a radial vessel of ten metre radius. Final Report".

CMI Report No. 843403-9, Chr. Michelsen Institute, Bergen, Norway.

Engebretsen, T. (1991) "Propagation of gaseous detonations through regions of low reactivity". PhD. Thesis, ITE, NTH, Trondheim, Norway.

Fickett, W. and Davis, W.C. (1979) "Detonation".

University of California Press, Berkeley.

Hjertager, B.H., Fuhre, K., Parker, S. and Bakke, J.R. (1985) "Flame acceleration of propane-air in a large-scale obstructed tube".

Progr. AIAA, Vol. 94, pp.504-522 Lee, J.H. (1984) "Dynamic parameters of gaseous detonations".

Ann. Rev. Fluid Mech., 16.

Moen, I.O., Bjerketvedt, D., Jenssen, A. and Thibault, P.A. (1985) "Transition to detonation in a large fuel-air cloud".

Combustion and Flame 61.

Moen, I.O., Bjerketvedt, D., Engebretsen, T., Jenssen, A., Hjertager, B.H. and Bakke, J.R. (1989) "Transition to detonation in a flame jet".

Combustion and Flame 75.

Shepherd, J.E., Melhem, G.A. and Athens, P. (1991) "Unconfined Vapor Cloud Explosions: A New Perspective", International Conference and Workshop on Modelling and Mitigating the Consequences of Accidental Releases Steen, H. and Schampel, K. (1983) "Experimental investigation of the run-up distance of gaseous detonations in large pipes", 4th International Symposium on Loss Prevention and Safety Promotion in the Process Industries, Pergamon Press, London, UK, pp. E23-E33.

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