Deflagration

Deflagration (Lat: de + flagrare, "to burn down") is subsonic combustion propagating through heat transfer; hot burning material heats the next layer of cold material and ignites it. Most "fires" found in daily life, from flames to explosions such as that of black powder, are deflagrations. This differs from detonation, which propagates supersonically through shock waves, decomposing a substance extremely quickly.

A log in a fireplace.

Applications

In engineering applications, deflagrations are easier to control than detonations. Consequently, they are better suited when the goal is to move an object (a bullet in a firearm, or a piston in an internal combustion engine) with the force of the expanding gas. Typical examples of deflagrations are the combustion of a gas-air mixture in a gas stove or a fuel-air mixture in an internal combustion engine, and the rapid burning of gunpowder in a firearm or of pyrotechnic mixtures in fireworks. Deflagration systems and products can also be used in mining, demolition and stone quarrying via gas pressure blasting as a beneficial alternative to high explosives.

Oil/wax fire and water

Adding water to a burning hydrocarbon such as oil or wax produces a deflagration. The water boils rapidly and ejects the burning material as a fine spray of droplets. A deflagration then occurs as the fine mist of oil ignites and burns extremely rapidly. These are particularly common in chip pan fires, which are responsible for one in five household fires in Britain.[1]

Flame physics

The underlying flame physics can be understood with the help of an idealized model consisting of a uniform one-dimensional tube of unburnt and burned gaseous fuel, separated by a thin transitional region of width ${\displaystyle \delta \;}$ in which the burning occurs. The burning region is commonly referred to as the flame or flame front. In equilibrium, thermal diffusion across the flame front is balanced by the heat supplied by burning.[2][3][4][5]

Two characteristic timescales are important here. The first is the thermal diffusion timescale ${\displaystyle \tau _{d}\;}$, which is approximately equal to

${\displaystyle \tau _{d}\simeq \delta ^{2}/\kappa }$,

where ${\displaystyle \kappa \;}$ is the thermal diffusivity. The second is the burning timescale ${\displaystyle \tau _{b}}$ that strongly decreases with temperature, typically as

${\displaystyle \tau _{b}\propto \exp[\Delta U/(k_{B}T_{f})]}$,

where ${\displaystyle \Delta U\;}$ is the activation barrier for the burning reaction and ${\displaystyle T_{f}\;}$ is the temperature developed as the result of burning; the value of this so-called "flame temperature" can be determined from the laws of thermodynamics.

For a stationary moving deflagration front, these two timescales must be equal: the heat generated by burning is equal to the heat carried away by heat transfer. This makes it possible to calculate the characteristic width ${\displaystyle \delta \;}$ of the flame front:

${\displaystyle \tau _{b}=\tau _{d}\;}$,

thus

${\displaystyle \delta \simeq {\sqrt {\kappa \tau _{b}}}}$.

Now, the thermal flame front propagates at a characteristic speed ${\displaystyle S_{l}\;}$, which is simply equal to the flame width divided by the burn time:

${\displaystyle S_{l}\simeq \delta /\tau _{b}\simeq {\sqrt {\kappa /\tau _{b}}}}$.

This simplified model neglects the change of temperature and thus the burning rate across the deflagration front. This model also neglects the possible influence of turbulence. As a result, this derivation gives only the laminar flame speed—hence the designation ${\displaystyle S_{l}\;}$.

Damaging events

Damage to buildings, equipment and people can result from a large-scale, short-duration deflagration. The potential damage is primarily a function of the total amount of fuel burned in the event (total energy available), the maximum flame velocity that is achieved, and the manner in which the expansion of the combustion gases is contained.

In free-air deflagrations, there is a continuous variation in deflagration effects relative to the maximum flame velocity. When flame velocities are low, the effect of a deflagration is to release heat. Some authors use the term flash fire to describe these low-speed deflagrations. At flame velocities near the speed of sound, the energy released is in the form of pressure and the results resemble a detonation. Between these extremes, both heat and pressure are generated.

When a low-speed deflagration occurs within a closed vessel or structure, pressure effects can produce damage due to expansion of gases as a secondary effect. The heat released by the deflagration causes the combustion gases and excess air to expand thermally. The net result is that the volume of the vessel or structure must expand to accommodate the hot combustion gases, or the vessel must be strong enough to withstand the additional internal pressure, or it fails, allowing the gases to escape. The risks of deflagration inside waste storage drums is a growing concern in storage facilities.

See also

• Conflagration
• Deflagration to detonation transition
• Pressure piling

References

1. UK Fire Service advice on chip pan fires
2. Williams, F. A. (2018). Combustion theory. CRC Press.
3. Landau, L. D. (1959). EM Lifshitz, Fluid Mechanics. Course of Theoretical Physics, 6.
4. Linan, A., & Williams, F. A. (1993). Fundamental aspects of combustion.
5. Zeldovich, I. A., Barenblatt, G. I., Librovich, V. B., & Makhviladze, G. M. (1985). Mathematical theory of combustion and explosions.