Detonation

A detonation is the propagation of a combustion zone through a flammable mixture at a speed greater than the speed of sound in the unreacted mixture. It is led by a shock wave that is driven and sustained by the energy released in the chemical reaction, and the shock and the reaction zone travel together at roughly 1,500 to 2,000 m/s. The shock compresses the unburned mixture ahead of the reaction, which is why the reaction can propagate so fast.

A detonation differs from a deflagration, the much more common subsonic form of explosion, in the way it loads its surroundings. In a deflagration the pressure rises almost evenly through an enclosure; in a detonation it rises suddenly and unevenly as the shock passes. The peak pressure is about twice that of a closed vessel deflagration, roughly 16 to 20 atmospheres for gas-air mixtures that start at atmospheric pressure. Because the pressure peak arrives with the shock, explosion vents and explosion suppression systems cannot protect against a detonation. Accidental detonations are rare, and in practice they develop from a deflagration that accelerates rather than from direct initiation.

Definition and distinction from deflagration

NUREG-1805 distinguishes detonations and deflagrations mainly by the speed of the combustion wave. In a detonation the wave propagates through the reactants at supersonic speed, of the order of 2,000 m/s. In a deflagration the speed stays below that of sound in air at 20 °C, approximately 330 m/s. Supersonic propagation implies a shock wave, which compresses the reactants and makes them react faster.

The shock front brings an abrupt increase in pressure, temperature and density of the gas, and moves the gas particles forward. Zalosh describes the consequence for an enclosure. In a deflagration the flames move well below the speed of sound, about 340 m/s in air at room temperature, so the pressure rises virtually uniformly throughout the enclosure. In a detonation the pressure rise is highly non-uniform and happens virtually instantaneously as the shock passes through the mixture.

Between the two lies the quasi-detonation. If the flame speed is slightly less than the speed of sound, the pressure rise is non-uniform, but no shock waves occur. Like a detonation, a quasi-detonation rules out the use of explosion venting and explosion suppression.

The definitions in the sources apply to combustion waves in gas mixtures. NUREG-1805 also lists condensed phase explosions of high explosives and propellants as a separate class of chemical explosion. The blast of such explosives is the reference for the TNT equivalence method, which expresses a gas explosion as an equivalent mass of TNT. The method is used because the blast effects of TNT have been studied extensively as a function of charge mass and distance.

Structure of a detonation wave

The idealised theory of the detonation front is the Chapman-Jouguet theory, which combines thermochemical equilibrium with the conservation equations of gas dynamics across the front. It gives the peak pressure and the speed of the wave, and its results can be calculated with chemical equilibrium programs such as STANJAN and CET89. The speed equals the Chapman-Jouguet Mach number times the speed of sound in the unburned mixture.

For stoichiometric gas-air mixtures, the Chapman-Jouguet Mach numbers lie in the narrow range 4.9 to 5.5. The speed of sound in most stoichiometric hydrocarbon-air mixtures is 330 to 350 m/s, and in hydrogen-air it is 403 m/s. With the Mach number of 5.38 for propane-air, the detonation therefore travels at roughly 1,780 to 1,880 m/s. For hydrogen-air, with a Mach number of 4.89, it is close to 2,000 m/s. Simmons gives a typical range of 1,500 to 3,000 m/s for detonations that develop in ducts.

Behind the front, the pressure falls to a plateau of about 0.35 times the Chapman-Jouguet pressure when the wave runs away from the ignition point in both directions in a tube. If the wave meets a rigid closed end, it is reflected with a pressure that is about 2.76 times the Chapman-Jouguet pressure for many gas-air mixtures. If the end is open, the wave is reflected as a rarefaction wave, which lowers the pressure. Simmons quotes up to 20 bar behind a detonation in a gas that starts at atmospheric pressure, and up to 100 bar when the wave is reflected from the end of a duct.

Pressure in a tube during a detonation: a sharp peak at the front, a plateau of about 0.35 times the peak behind it, and about 2.76 times the peak when the wave reflects from a rigid closed end. Based on Zalosh (2002), p. 3-411.

A real detonation front is not flat. It consists of a network of curved shock segments that move across the direction of travel. Where they meet, they trace a diamond or fish-scale pattern on a smoke foil placed on the inner wall of a test tube. The width of one such cell, the detonation cell width, is the length scale that describes how easily a mixture detonates.

Peak pressure

The Chapman-Jouguet calculation needs a chemical equilibrium program. Burgess and co-workers suggested a much simpler approximation, quoted by Zalosh: the detonation pressure is about twice the pressure at the end of a closed vessel deflagration of the same mixture. In words: if the same mixture would reach a certain absolute pressure when it burns slowly in a closed vessel, its detonation reaches about double that pressure at the front.

$$P_{\mathrm{C}\mathrm{J}}\approx 2P_{\mathrm{m}}$$

Symbol	Description	Unit
$P_{\mathrm{C}\mathrm{J}}$	Chapman-Jouguet detonation pressure (absolute)	bar
$P_{\mathrm{m}}$	pressure at the end of a closed vessel deflagration of the same mixture (absolute)	bar

The approximation gives the pressure at the detonation front itself in a gas-air mixture. It does not include reflection, which raises the pressure much further at closed ends and walls. Calculated values for near-stoichiometric mixtures at atmospheric initial pressure lie between 16 and 20 atmospheres.

Worked example. For propane in air, the measured maximum closed vessel deflagration pressure is 7.9 bar gauge. With an atmospheric pressure of 1.013 bar this is about 8.9 bar absolute, so:

$$P_{\mathrm{C}\mathrm{J}}\approx 2\times 8.9\mathrm{b}\mathrm{a}\mathrm{r}\approx 18\mathrm{b}\mathrm{a}\mathrm{r}\mathrm{(}\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{)}$$

The result lies within the range of 16 to 20 atmospheres given for near-stoichiometric mixtures. At a rigid closed end, the reflected pressure would be about 2.76 × 17.8 ≈ 50 bar. Behind a freely running wave the pressure falls to about 0.35 × 17.8 ≈ 6.3 bar (values rounded up, since they are loads). For methane, with a measured deflagration maximum of 7.1 bar gauge, the same approximation gives about 16 bar absolute.

The comparison with other values in the sources shows the scale. NUREG-1805 gives a detonation pressure of up to 20 atmospheres (284 psi) and estimates detonation pressure rises at 2 to 4 times those of a deflagration. It also lists pressure effects on people: about 35 kPa is the limit for eardrum rupture and 180 kPa corresponds to 1 % mortality, far below the pressures inside a detonation.

How a detonation starts

A detonation can start in two ways: by direct initiation with a very strong ignition source, or by acceleration of a deflagration. The minimum energy for direct initiation ranges from about 5 kJ for acetylene and hydrogen in air to an estimated 93,000 kJ for methane. These energies are many orders of magnitude above those of accidental ignition sources, so direct initiation can be ruled out in almost all accident scenarios.

The usual route is the deflagration-to-detonation transition. When the hot products of a flame in a duct cannot vent, they push the flame and the unburned gas forward with increasing speed, which creates turbulence ahead of the flame. In a long duct the flame front then acts as an accelerating piston, a shock wave forms ahead of it, and the flame becomes a detonation. The run-up distance is shorter for more reactive mixtures, rough walls or obstructions, larger diameters, higher initial pressure and temperature, and stronger initial turbulence.

Smooth pipes need long run-up distances. In tests in a smooth 5 cm pipe, alkanes in air did not undergo transition within 120 pipe diameters. Flessner and Bjorkland saw no transition with gasoline-air mixtures in a smooth pipe 15 cm in diameter and 16 m long. When they placed an expanded metal liner at the pipe entrance to simulate a rough wall, transition occurred after 74 pipe diameters. NUREG-1805 adds that the ability for such a transition depends on both the mixture and its environment, and that detonable limits, unlike flammability limits, are also influenced by the environment. In process plants, a flammable mixture in a vessel or pipework may explode either as a deflagration or as a detonation.

Detonability and cell width

A sustained detonation is only possible if the space filled with the mixture is larger than some multiple of the cell width. In a pipe, a detonation will not propagate if the pipe diameter is less than about one third of the cell width. It will not pass from the open end of a pipe into the surrounding mixture if the pipe diameter is less than 13 cell widths.

Critical sizes for a detonation in a pipe, expressed in the cell width Sc of the mixture. Based on Zalosh (2002), p. 3-412.

Measured or calculated cell widths for stoichiometric gas-air mixtures range from about 1 cm for acetylene to about 28 cm for methane. Hydrogen has 1.5 cm, ethylene 2.8 cm and propane 6.9 cm. These values apply at atmospheric pressure and room temperature; higher initial pressure or temperature gives smaller cells, and some fuel-rich mixtures have cells up to 40 % smaller than the tabulated values. A small cell width therefore means a mixture that can detonate in smaller pipes and spaces.

Detonation cell widths of stoichiometric gas-air mixtures at atmospheric pressure and room temperature; a smaller cell means a mixture that can detonate in smaller spaces. Based on Zalosh (2002), p. 3-412, Table 3-16.4.

Zalosh gives an example of how the criterion is used. A process oven is fed by a fuel line 1 cm in diameter and 5 m long that contains a stoichiometric propane-air mixture. With a cell width of 6.9 cm, a detonation needs a pipe of at least 2.3 cm, so it cannot run through the line. With hydrogen-air the limit is 0.50 cm, so a detonation in the line would be possible, but it could only pass into the oven through a pipe wider than about 20 cm. Explosion venting can therefore still protect the oven.

Effects on structures

Detonations load structures in a different way from deflagrations. Their pressure loads have a high peak and a short duration, which calls for special consideration when the structural resistance is evaluated. The load is described by the impulse, the integral of the overpressure over time, which in a pipe grows with the distance from the point of initiation. Pipeline detonations often cause periodic ruptures along the length of the pipe: each break relieves the pressure, and the load builds up again over the next length.

The remains after an explosion can show which kind it was. Detonative loads tend to produce fragmented debris from brittle failure, whereas structural steel loaded by deflagration pressures beyond its yield point bulges and fails in a more ductile way. In the hydrogen fuel-line example, the average pressure on the pipe wall during the passage of the detonation was about 530 kPa, about one third of the Chapman-Jouguet pressure.

Well-documented accidental detonations are rare, since most accidental explosions are deflagrations. One example is a refinery accident described by Jacobs and co-workers. A mixture of 3 % naphtha, 19 % oxygen and 78 % inert gas at 105 psig, about 720 kPa above atmospheric, entered several large items of process equipment. The equipment was connected by more than 1,000 ft (about 300 m) of piping, and pressures of 3,000 to 4,000 psi, about 21 to 28 MPa, developed at some locations.

Detonations in open clouds and assessment

Outside equipment, the related hazard is the vapour cloud explosion: a large cloud of flammable gas or vapour ignited in an obstructed area such as a chemical plant. The strength of its blast depends on the flame speed that develops and on the degree of confinement. NUREG-1805 notes that a premixed gas-air mixture ignited inside a building gives a maximum pressure of about 8 bar. An unconfined vapour cloud explosion gives pressures of the same order, and a detonation even higher pressures. It adds that detonations are very rare.

No exact criteria exist to decide whether a given situation will produce a detonation rather than a deflagration. Sherman and Berman developed a semi-quantitative method that classifies mixtures by cell size and geometries by size, confinement, obstructions and venting, and extrapolates the test data subjectively. The assessment matters because the usual explosion protection for deflagrations does not work: vents open only after the explosion has started, while the peak pressure of a detonation arrives at once with the shock front. Protection against detonation therefore relies on preventing the flammable mixture, on geometries below the critical size, or on structures designed for the detonation loads.

See also

• Explosion venting
• Hydrogen safety
• Inerting
• Deflagration index

References

• Iqbal, N., & Salley, M. H. (2004). Fire Dynamics Tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program (NUREG-1805). U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor Regulation.
• Simmons, R. F. (2002). Premixed burning. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-144–1-154). National Fire Protection Association; Society of Fire Protection Engineers.
• Zalosh, R. (2002). Explosion protection. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-402–3-421). National Fire Protection Association; Society of Fire Protection Engineers.