A detonation is the most devastating form of gas explosion. Unlike the deflagration, a detonation does not require confinement or obstructions in order to propagate at high velocity. Particularly in an unconfined situation, the behaviour of a detonation is quite different from a deflagration. A detonation is defined as a supersonic combustion wave (i.e. the detonation front propagates into unburned gas at a velocity higher than the speed of sound in front of the wave). The gas ahead of a detonation is therefore undisturbed by the detonation wave. In fuel-air mixtures at atmospheric pressure, the detonation velocity is typically 1500 - 2000 m/s and the peak pressure is 15-20 bar.
Transition to detonation, propagation and transmission of detonation waves, depend strongly on the reactivity of the gas cloud.
The objective of this chapter is:
- To describe the detonation, so that a detonation can be distinguished from a deflagration.
- To describe under which conditions detonation waves are likely to propagate.
- To describe how to calculate detonation velocities and pressures.
6.1 Detonation Waves
Detonation waves were observed experimentally more than 100 years ago. Chapman and Jouguet were the first to present a theory describing this supersonic combustion wave, propagating at a unique velocity. The C-J (Chapman-Jouguet) theory (Fickett and Davis, 1979) treats the detonation wave as a discontinuity with infinite reaction rate. The conservation equations for mass, momentum and energy across the one-dimensional wave gives a unique solution for the detonation velocity (CJ-velocity) and the state of combustion products immediately behind the detonation wave. Based on the CJ-theory it is possible to calculate detonation velocity, detonation pressure etc. if the gas mixture is known. The CJ-theory does not require any information about the chemical reaction rate (i.e. chemical kinetics).
||CJ-pressure and CJ-detonation velocity for some fuel-air mixtures. |
Initial conditions 25°C and 1.013 bar (Baker et al. 1983).
During World War II, Zeldovich, Döring and von Neumann improved the CJ-model by taking the reaction rate into account. As shown in Figure 6.2 the ZND-model describes the detonation wave as a shock wave, immediately followed by a reaction zone (i.e. flame). The thickness of this zone is given by the reaction rate. The ZND-theory gives the same detonation velocities and pressures as the CJ-theory, the only difference between the two models is the thickness of the wave.
||CJ detonation velocity and pressure for ethylene-air.|
An actual detonation is a three-dimensional shock wave followed by a reaction zone. The leading shock consists of curved shock segments. At the detachment lines between these shock segments, the shock wave interacts in a Mach stem configuration. A two-dimensional illustration of the actual structure is given in Figure 6.2.
||ZND structure and pattern of an actual structure of a detonation front. The characteristic length scale of the cell pattern, the cell size, l, is shown in the figure.|
The size of the fish shell pattern generated by the triple point (Mach stem) of the shock wave is a measure of the reactivity of the mixture representing a length scale characterising the overall chemical reaction in the wave (Lee, 1984). This length scale, l, is often the cell size or the cell width. The more reactive the mixture, the smaller the cell size. Figures 6.3 and 6.4 show the detonation cell size versus fuel concentration for several fuel-air mixtures.
||Cell size vs. fuel concentration for acetylene, ethylene and hydrogen in air (25°C and 1 atm) (Shepherd et al., 1991).|
||Cell size vs. fuel concentration for ethylene, propane and methane in air (25°C and 1 atm) (Shepherd et al., 1991).|
The cell size is measured experimentally and there are some variations in the reported results. Variations of a factor of two is not uncommon.
The cell size, l, is a parameter which is of practical importance. The transition from deflagration to detonation, propagation and transmission to detonation, can to some extent be evaluated based on the knowledge of the cell size of the mixture. This will be discussed in the following sections.
6.2 Rarefaction Wave Behind Detonation Front
So far we have discussed the detonation pressure (i.e. CJ-pressure) of a detonation front. After the detonation front (CJ-plane) the combustion products will expand. This expansion will depend on the boundary conditions.
||Pressure-distance profile for a detonation propagation in a tube with a closed end (i.e. closed at x = 0). |
The expansion of the combustion products forming a detonation wave propagating in a tube (i.e. one-dimensional propagation) is illustrated in Figure 6.5. 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.
6.3 Deflagration to Detonation Transition (DDT)
When a deflagration becomes sufficiently strong, a sudden transition from deflagration to detonation can occur. This has been observed in several experiments, especially in those involving very reactive mixtures, such as near-Stoichiometric acetylene-air, hydrogen-air or fuels with oxygen-enriched atmospheres.
There are also some examples of deflagration to detonation transition in fuel-air mixtures with moderate reactivity.
i) In one CMR experiment (Hjertager et al. , 1988) in the 10 m long wedge-shaped vessel with Stoichiometric propane-air, 100% top confinement and circular obstructions, transition to detonation was observed. This experiment shows that a propane-air explosion initiated with a weak ignition source, can accelerate to a detonation in less than 10 m, if sufficient confinement and obstructions are present.
ii) Moen et al. (1985 and 1989) have observed transition to detonation due to jet flames. In one test they reported transition to detonation in a lean mixture of acetylene-air (5% C2H2) in an essentially unconfined situation. The transition to detonation was caused by a jet-flame shooting into the unconfined cloud. These experiments demonstrated that detonations can be induced in an unconfined fuel-air cloud with moderate reaction rates as long as the size of the cloud is large.
iii) British Gas experiments (Acton et al., 1990) in a pipe rack geometry also showed transition to detonation for propane-air. Transition to detonation occurred after 15 m. This experiment showed that in relatively "open" situations, such as a pipe bridge, the geometry can support flame acceleration to detonation.
These experiments show that transition to detonation can be obtained by flame acceleration due to obstacles and confinement or if a jet flame is shot out from an opening in a confined volume into an unconfined cloud.
The mechanism of transition to detonation is not fully understood. Presently there is no theory which can predict conditions for deflagration to detonation transition. We have only a qualitative understanding of the phenomenon; it is likely that local explosions within explosions cause transition to detonation. The size of these localised explosions must be of the order of 10 times the cell size (Moen, private comm.).
From a practical point of view, it is important to recognise that transition to detonation will cause extremely high pressures in the area where the transition takes place.
Figure 6.6 shows a pressure-time profile from an experiment where transition to detonation occurred. The first pressure rise at t = 2510 µsec. is the shock wave which compresses the unburned gas. The pressure continues to rise after the shock wave, and subsequently a transition to detonation occurs. Due to this pre-compression, the detonation pressure in the transition process is much higher than the pressure in a stabilised detonation wave (i.e. CJ-pressure).
||Pressure-time profile from a pressure transducer located close to an area of transition to detonation (Engebretsen, 1991).|
In an accident situation where transition to detonation has occurred, localised damage can be observed. One example is an accidental explosion inside a pipe. At one particular position the pipe was expanded radially, as shown below:
||Transition to detonation in a pipe. A case history.|
In this case the pipe was able to withstand CJ-pressure, but the pressure at the location where the transition to detonation took place represented a force exceeding the strength of the pipe.
6.4 Propagation and Transmission of Detonation Wave
From the CJ-theory, the detonation velocity and pressure can be predicted, not depending on the geometrical conditions. However, the propagation and transmission of a detonation are limited by geometrical conditions. The limited conditions are controlled by the sensitivity of gas mixtures and length scale of the geometry. As discussed in section 6.1, the cell size is a length scale characterising the reactivity of the mixture. By using these two length scales, the conditions for successful propagation and transmission can be evaluated.
||Requirements for successful propagation of a planar detonation in pipes and channels.|
Figure 6.8 shows detonation propagation limits within pipes and channels. We see that a pipe is more supportive of detonation propagation than a channel.
||Requirements for successful transmission of a planar detonation into an unconfined three-dimensional spherical detonation wave.|
Figure 6.9 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 6.9 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 6.10.
||Limit for propagation of detonation waves in an unconfined fuel-air cloud.|
6.5 Estimating Detonation Loads
To estimate the CJ-values for gas mixtures the STANJAN-program can be used. This may be acquired from Prof. W.C. Reynolds at Stanford University (see STANJAN in the References).
6.6 Guidelines on Detonations
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. In particular no data exist on detonations involving pure methane-air. 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.
The CJ-detonation pressure can be calculated by codes like STANJAN. Such data can be used for stable detonation waves. However, in the event of transition from deflagration to detonation, pressure spikes much higher than the CJ-values (see Figure 6.6) appear.
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 in Figures 6.8-6.10, 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.