Deflagration

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Image:Log in fireplace.jpg Deflagration is a process of subsonic combustion that usually propagates through thermal conductivity (hot burning material heats the next layer of cold material and ignites it). Deflagration is different from detonation which is supersonic and propagates through shock compression.

Applications

In engineering terms, deflagrations are easier to control than detonations. Consequently, they are better suited when the goal is to move an object (a bullet in a gun, or a piston in an engine) with the force of the expanding gas. Typical examples of deflagrations are combustion of a gas-air mixture in a gas stove or a fuel-air mixture in an internal combustion engine, a rapid burning of a gunpowder in a firearm or pyrotechnic mixtures in fireworks.

In astrophysics, flame fronts are believed to play a crucial role in Type Ia supernovae. There, the energy is supplied not by chemical processes as is the case with all terrestrial flames, but rather by thermonuclear burning.

Flame Physics

We can better understand the underlying flame physics by constructing an idealized model consisting of a uniform one-dimensional tube of unburnt and burned gaseous fuel, separated by a thin transitional region of width <math>\delta</math> 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.

There are two characteristic timescales which are important here. The first is the thermal diffusion timescale <math>\tau_d</math>, which is approximately equal to <math>\tau_d \simeq \delta^2 / \kappa</math> where <math>\kappa \;</math> is the thermal conductivity.

The second is the burning timescale <math>\tau_b</math>, which is approximately equal to <math>\tau_b \simeq \epsilon / \dot {w} </math> where <math>\epsilon</math> is the total energy released by burning per unit mass, and <math>\dot {w}</math> is the burn rate (eg, the rate of increase of specific thermal energy).

In equilibrium, these two rates are equal: The heat generated by burning is equal to the heat carried away by heat transfer. This lets us find the characteristic width <math>\delta</math> of the flame front :

<math>\tau_b \simeq \tau_d</math>

<math> \delta \simeq \sqrt {\epsilon \kappa / \dot {w}} </math>

Now, the thermal flame front propagates at a characteristic speed <math>S_l</math>, which is simply equal to the flame width divided by the burn time :

<math>S_l \simeq \delta / \tau_b \simeq \sqrt {\kappa \dot {w} / \epsilon} </math>

This simplified one-dimensional model neglects the possible influence of turbulence. As a result, this derivation gives the laminar flame speed -- hence the designation <math>S_l</math>.de:Deflagration fr:Déflagration nl:Deflagratie pl:Deflagracja ru:Дефлаграция sv:Deflagration