# Deflagration

Deflagration is a process of subsonic combustion that usually propagates through thermoconductivity (hot burning material heats next layer of cold material and ignites it). Deflagration is different from detonation which is supersonic and propagates through shock compression.

## Flame Physics

We can better understand the underlying flame physics by constructing an idealized model consisting of a uniform one-dimensional tube consisting of unburnt and burned gaseous fuel, separated by a thin transitional region of width [itex]\delta[itex] 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 important characteristic timescales which are important for this burning process. The first is the thermal diffusion timescale [itex]\tau_d[itex], which is approximately equal to [itex]\tau_d \simeq \delta^2 / \kappa[itex] Here [itex]\kappa[itex] is the thermal conductivity.

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

In equilibrium, these two rates are equal, which sets the characteristic width [itex]\delta[itex] of the flame front :

[itex]\tau_b \simeq \tau_d[itex]

[itex] \delta \simeq \sqrt {\epsilon \kappa / \dot {w}} [itex]

Now, the thermal flame front propagates at a characteristic speed [itex]S_l[itex], which is simply equal to the flame width divided by the burn time :

[itex]S_l \simeq \delta / \tau_b \simeq \sqrt {\kappa \dot {w} / \epsilon} [itex]

Note that this simplified 1D model neglects the possible influence of turbulence. As a result, this derivation refers to the laminar flame speed -- hence the designation [itex]S_l[itex].

## Applications

In terms of engineering, 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.de:Deflagration nl:Deflagratie pl:Deflagracja sv:Deflagration

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