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Deflagration

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Contents
  1. 1Definition
  2. 2Conditions for a deflagration
  3. 3How the flame propagates
  4. 4Pressure in a closed vessel
  5. 5Deflagrations in buildings and fires
  6. 6Protection
  7. 7Limits of simple estimates
  8. 8See also
  9. 9Notes
  10. 10References

A deflagration is the propagation of a flame through a flammable mixture of fuel and air at a speed below the speed of sound in that mixture.[1][2] The mechanism is thermal in nature: heat conducted from the reaction zone raises the temperature of the adjacent unburned gas until it reacts.[1][3] When a gas-air mixture or a dust cloud is ignited inside an unvented enclosure, the result is usually a deflagration.[2] Most accidental explosions are deflagrations.[4]

Because the flame travels well below the speed of sound, the pressure rises almost uniformly throughout the enclosure while the flame spreads.[5] This sets it apart from a detonation, in which a shock wave runs through the mixture at supersonic speed and the pressure rises suddenly and unevenly.[5][6] In a closed vessel, a near-stoichiometric hydrocarbon-air deflagration can reach about 7 to 9 times the initial absolute pressure, enough to rupture a vessel or a room that is not designed for it.[7][2] Protection therefore aims to prevent the flammable mixture, to remove ignition sources, or to limit the pressure by venting, suppression or containment.[8][1]

Definition

NUREG-1805, citing Nolan (2000), defines a deflagration as a thermal mechanism by which an explosion reaction propagates through a flammable gas mixture. The reaction velocity is always less than the speed of sound in the mixture.[1] Even so, a deflagration is capable of causing damage.[1] Zalosh describes it in the same way as flame propagation at subsonic speed away from the ignition site.[2]

The difference from a detonation is usually expressed in speed. In a detonation the combustion wave runs through the reactants at supersonic speed, of the order of 2,000 m/s, led by a shock wave that compresses the reactants.[6] In a deflagration the propagation rate stays below the speed of sound in air at 20 °C, approximately 330 m/s.[6] NUREG-1805 also describes deflagrations as a slow subsonic flame front with a slow but uniform rise in pressure and temperature, and estimates detonation pressures at 2 to 4 times those of a deflagration.[9]

Two tubes of gas mixture: top, a slow flame front with even pressure throughout; bottom, a fast front led by a shock with a sharp pressure jump.
A deflagration (top) moves below the speed of sound and the pressure rises almost evenly; a detonation (bottom) is led by a shock wave and the pressure jumps at the front. Based on Iqbal and Salley (2004), p. 15-3, and Zalosh (2002), p. 3-410.

The flame in a deflagration is a premixed flame: fuel and air are mixed before the flame reaches them.[8] Introduction to Fire Safety Engineering gives a gas burner and a Bunsen burner as everyday examples of a premixed flame.[10] In a deflagration the same kind of flame does not stand still on a burner but moves through a cloud or a filled enclosure.[11] Most fires, by contrast, burn as diffusion flames, in which fuel and air mix in the flame itself.[7][10]

Conditions for a deflagration

NUREG-1805 names three elements that must be present at the same time: a flammable mixture of fuel and oxygen, usually from air; a means of ignition; and an enclosure.[6] The fuel can be a gas, a vapour, a mist or a dust.[12] Zalosh describes the hazard as the premixing of fuel and oxidant in a confined space before an ignition source appears; after ignition, the confinement prevents the free expansion of the combustion products.[8]

A mixture is flammable only between its lower and upper flammability limits.[8] A deflagration becomes possible once the gas concentration rises above the lower flammability limit.[9] At the limits themselves a mixture burns with insignificant flame propagation, and between them there is a concentration at which flame propagation reaches its maximum.[13] The terms "explosive limits" and "flammable limits" are used interchangeably; the word "explosive" refers to the pressure rise that a deflagration produces as it passes through a vessel.[14]

Combustible dusts behave in a similar way. They are an explosion hazard when the particles are smaller than about 100 to 400 μm, depending on the material, and when they are suspended in air between the lower and upper explosive limits.[15] Typical lower explosive limits for fine dusts are 30 to 60 g/m³, roughly the same range as for many flammable gases and vapours expressed in the same units.[15]

How the flame propagates

The basic property of a premixed flame is its burning velocity: the speed with which the flame moves, normal to its surface, into the unburned mixture next to it.[16] Maximum laminar burning velocities at room temperature and atmospheric pressure are 41 cm/s for propane-air, 68 cm/s for ethene-air, 175 cm/s for acetylene-air and 320 cm/s for hydrogen-air.[11] For the alkanes and many other hydrocarbons the values lie between 40 and 47 cm/s.[17]

The flame front moves much faster than its burning velocity suggests. The burned gas expands and pushes the unburned gas away from the ignition point, so an observer sees a flame speed that is significantly larger than the burning velocity.[17] Before compression starts, the flame speed equals the burning velocity multiplied by the ratio of burned to unburned gas temperature.[17] For many hydrocarbons near stoichiometric concentration this gives 350 to 440 cm/s.[17]

Circular vessel with a central ignition point, a spherical flame front, burned gas inside and arrows showing unburned gas pushed outwards.
A spherical flame in a closed vessel: the flame burns into the unburned mixture at the burning velocity, while the expanding burned gas pushes the mixture outwards, so the flame front moves several times faster. Based on Zalosh (2002), pp. 3-407 to 3-408.

Turbulence increases the speed further. It wrinkles the flame front and so enlarges its effective area; with propane, ethene and acetylene, the burning velocity roughly doubles as the Reynolds number of the flow increases to 40,000.[11] Theory suggests an increase by a factor of five at very high turbulence.[11] In a duct, the linear speed of the flame equals the burning velocity times the ratio of flame area to duct cross-section, and the flame area is typically two to three times the cross-section.[7] Higher initial temperature also helps: raising a propane-air mixture from 300 to 480 K doubles its maximum burning velocity.[11]

If the hot products cannot vent, they push the flame and the unburned gas forward with increasing velocity, which creates more turbulence ahead of the flame.[7] In a long enough duct the flame front then acts as an accelerating piston, a shock wave forms, and the flame can become a detonation travelling at 1,500 to 3,000 m/s.[7] This process is the deflagration-to-detonation transition. NUREG-1805 notes that whether it can happen depends on both the mixture and its environment.[18]

Pressure in a closed vessel

If the flame burns through the whole enclosure, the final pressure follows from the ideal gas law applied to the mixture before and after burning, since both fill the same volume.[2] In words: the pressure ratio equals the ratio of the number of moles of gas times the absolute temperature, after and before the deflagration.[2] More moles of gas or a hotter gas in the same volume both mean a higher pressure.

PmP0=nbTbn0T0

Symbol Description Unit
Pm pressure at the end of a closed vessel deflagration (absolute) Pa or bar
P0 initial pressure in the enclosure (absolute) Pa or bar
nb number of moles of burned gas at the end of the deflagration mol
n0 number of moles of gas-air mixture initially in the enclosure mol
Tb temperature of the burned gas at the end of the deflagration K
T0 initial temperature of the gas-air mixture K

The relation applies to gas and to dust deflagrations, because only the temperature and composition of the gas set the pressure.[2] It assumes that the flame has burned through the whole enclosure and that no gas escapes.[2] Using the adiabatic flame temperature at constant volume gives a conservative estimate, because real vessels lose heat to their walls.[2][7]

Worked example. Complete combustion of one mole of methane uses two moles of oxygen and forms one mole of carbon dioxide and two moles of water.[19] The nitrogen from the air does not react, so for a stoichiometric methane-air mixture the number of moles stays the same and nb/n0 = 1.[19][20] Simmons gives an initial temperature of 300 K and an adiabatic flame temperature of about 2,200 K for a stoichiometric hydrocarbon-air mixture.[7] With an initial pressure of 1.013 bar:

Pm=1.013 bar×1×2200 K300 K≈7.5 bar (absolute)

This is about 6.5 bar above atmospheric pressure (values rounded up, since they are loads).[7] Simmons states that the pressure can reach a little over 7 bar under adiabatic conditions, and that it will rupture a vessel explosively unless the vessel was designed for it.[7] At constant volume the flame temperature is 200 to 400 °C higher than at constant pressure, about 2,600 K for stoichiometric methane in the calculations shown by Zalosh.[2] With that value the same relation gives about 8.8 bar absolute, close to the calculated value of about 9 atm in the handbook.[2] The measured maximum for methane in Zalosh's table is 7.1 bar gauge, about 8.1 bar absolute.[21]

The measured maximum pressures of twelve gases and vapours lie between 6.8 and 8.1 bar gauge, with two exceptions: acetylene at 10.6 bar gauge and ammonia at 5.4 bar gauge.[21] For twenty dusts the range is 6.7 to 11.2 bar gauge, about the same as for gases.[21] The highest pressures occur in slightly rich mixtures, at equivalence ratios of 1.1 to 1.2. Near the flammability limits, measured pressures are much lower than theory because the combustion is incomplete and heat is lost to the walls.[2][21]

Horizontal bar chart of maximum deflagration pressure for twelve gases; most bars lie between 6.8 and 8.1 bar, acetylene 10.6, ammonia 5.4.
Measured maximum closed-vessel deflagration pressures of twelve flammable gases and vapours in air. Based on Zalosh (2002), p. 3-407, Table 3-16.3.

The pressure does not rise evenly in time. Zalosh gives a calculated example for a vessel of 7.15 m radius. The pressure was only about 2 psig (14 kPa) when the flame had reached half the vessel radius and 16 psig (110 kPa) at 80 % of the radius. The final pressure was 93 psig (641 kPa).[17] Most of the pressure rise therefore occurs when the flame is close to the walls.[17] The time needed to reach the maximum depends on the size of the enclosure and the fuel, and can extend to a few hundred milliseconds.[6]

A mixture that fills only part of an enclosure still produces a pressure rise, roughly in proportion to the fraction of the total gas mass that burns.[17] In an example by Zalosh, 200 g of n-butane leaks into a filling room of 4 × 4 × 3 m and mixes stoichiometrically with part of the air.[5] Filling the whole room would take 3.52 kg of butane, so about 5.7 % of the mass burns and the pressure rises by about 0.46 bar.[5] This exceeds the strength of rooms in industrial facilities, even though 200 g spread evenly through the room would be too little to form a flammable mixture at all.[5]

Deflagrations in buildings and fires

Explosions in open air are fundamentally different from confined explosions in vessels, pipework or buildings, and they require different countermeasures.[22] In a confined explosion the overpressure comes from the expansion of the hot gases.[22] When gases escape through an explosion vent, which may simply be a door or a window, the resulting turbulence can produce a second pressure peak.[22]

Fires can create the premixed mixture themselves. A backdraft occurs when fresh air reaches the fuel-rich smoke of an oxygen-starved fire, and it has the characteristics of a premixed fuel-air deflagration.[13] A smouldering fire can produce enough unburned fuel and carbon monoxide to form a premixed atmosphere; if the mixture reaches its autoignition temperature, the smoke cloud deflagrates in a smoke explosion.[13] Such explosions have been observed in smouldering fires involving polyurethane foam.[13]

Introduction to Fire Safety Engineering describes the smoke gas explosion in the same terms. Flammable gases from decomposition or incomplete combustion are premixed with air and lie between the lower and upper explosion limits.[23] They can be ignited by autoignition or by an ignition source such as a spark from electrical equipment or glowing particles from the fire.[23]

In industry, dust deflagrations can cause severe secondary explosions. A deflagration inside process equipment can make the equipment fail and send a blast wave through the building, which raises settled dust from walls and floors.[24] The flame emerging from the equipment often ignites this dust cloud, even if the cloud fills only a small part of the building.[24] NUREG-1805 lists possible secondary explosions among the hazards of a deflagration, together with failure of equipment, ejection of flame and unburned product, and personal injury.[6]

Protection

Explosion protection interrupts the sequence of events at one of three points. It prevents the formation of a fuel-air mixture, for example by ventilation or inerting, or removes ignition sources, for example by grounding equipment. The third option is to limit the pressure build-up.[8] Inerting lowers the oxygen concentration below the limiting oxidant concentration. The NFPA 69 guideline quoted by Zalosh keeps the oxygen at least 2 volume per cent below that value when it is monitored continuously.[15]

Explosion venting discharges combustion gases during a deflagration so that the pressure stays below the damage threshold of the enclosure, which may be a room, a building or a piece of equipment.[12] The vent opening is usually covered by blow-off panels, rupture discs or other engineered vent devices.[12] The most effective vents open early, are as large as possible and let the combustion gases escape without restriction.[12] Normal process openings are usually too small to prevent destructive pressures.[6]

Explosion suppression detects an incipient explosion and discharges an extinguishing agent from pressurised containers before the pressure reaches the damage threshold.[25] Unlike venting, it releases no flame or fuel, so it suits indoor equipment and equipment holding toxic materials.[25] A third option is deflagration pressure containment: the vessel and its connections are designed to withstand the maximum pressure of an internal deflagration.[1]

Venting and suppression both rely on the relatively slow, uniform pressure rise of a deflagration. Because vents open only after the explosion has started, they cannot cope with a detonation, whose peak pressure arrives instantly with the shock front.[12] The sudden, non-uniform pressure rise of a detonation also rules out explosion suppression.[26]

Limits of simple estimates

The closed vessel relation gives an upper bound for an ideal case. Real vessels lose heat to their walls, so measured pressures are somewhat lower, especially for mixtures near the flammability limits.[7][21] The rate of pressure rise depends strongly on turbulence, which varies among gases in a way that cannot be predicted in advance.[24] Measured rates of pressure rise, expressed as the KG value for gases and the KST value for dusts, are therefore used in practice.[24] The vent area needed depends on the size of the enclosure and on this rate of pressure rise.[12]

Connected vessels raise the pressure further. Burning in one vessel raises the pressure in a connected vessel; if the flame then enters the second vessel, it starts from a higher pressure and produces a higher final pressure.[7] Long ducts can accelerate the flame towards a detonation, which the simple relation does not cover.[7]

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 Iqbal and Salley (2004), p. F-20.
  2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 Zalosh (2002), p. 3-406.
  3. ↑ Simmons (2002), p. 1-148.
  4. ↑ Zalosh (2002), p. 3-413.
  5. ↑ 5.0 5.1 5.2 5.3 5.4 Zalosh (2002), p. 3-410.
  6. ↑ 6.0 6.1 6.2 6.3 6.4 6.5 6.6 Iqbal and Salley (2004), p. 15-3.
  7. ↑ 7.00 7.01 7.02 7.03 7.04 7.05 7.06 7.07 7.08 7.09 7.10 7.11 Simmons (2002), p. 1-147.
  8. ↑ 8.0 8.1 8.2 8.3 8.4 Zalosh (2002), p. 3-402.
  9. ↑ 9.0 9.1 Iqbal and Salley (2004), p. 16-8.
  10. ↑ 10.0 10.1 Van Rossum (2027), §4.3.
  11. ↑ 11.0 11.1 11.2 11.3 11.4 Simmons (2002), p. 1-146.
  12. ↑ 12.0 12.1 12.2 12.3 12.4 12.5 Zalosh (2002), p. 3-414.
  13. ↑ 13.0 13.1 13.2 13.3 Iqbal and Salley (2004), p. 15-4.
  14. ↑ Iqbal and Salley (2004), p. B-25.
  15. ↑ 15.0 15.1 15.2 Zalosh (2002), p. 3-403.
  16. ↑ Simmons (2002), p. 1-144.
  17. ↑ 17.0 17.1 17.2 17.3 17.4 17.5 17.6 Zalosh (2002), p. 3-408.
  18. ↑ Iqbal and Salley (2004), p. B-26.
  19. ↑ 19.0 19.1 Van Rossum (2027), §3.3.
  20. ↑ Van Rossum (2027), §4.2.
  21. ↑ 21.0 21.1 21.2 21.3 21.4 Zalosh (2002), p. 3-407.
  22. ↑ 22.0 22.1 22.2 Iqbal and Salley (2004), p. 15-5.
  23. ↑ 23.0 23.1 Van Rossum (2027), §4.10.
  24. ↑ 24.0 24.1 24.2 24.3 Zalosh (2002), p. 3-409.
  25. ↑ 25.0 25.1 Zalosh (2002), p. 3-417.
  26. ↑ Zalosh (2002), p. 3-411.

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.
  • Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
  • 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.
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