There are two characteristic timescales which are important here. The first is the thermal diffusion timescale , which is approximately equal to
where is the thermal diffusivity. The second is the burning timescale that strongly decreases with temperature, typically as
where is the activation barrier for the burning reaction and is the temperature developed as the result of burning that can be found from thermodynamics (the so-called "flame temperature").
For a stationary moving deflagration front, these two timescales are equal: The heat generated by burning is equal to the heat carried away by heat transfer. This lets us find the characteristic width of the flame front:
Now, the thermal flame front propagates at a characteristic speed , which is simply equal to the flame width divided by the burn time:
This simplified model neglects the change of temperature and thus the burning rate across the deflagration front. Also this model neglects the possible influence of turbulence. As a result, this derivation gives the laminar flame speed -- hence the designation .
Damage to buildings, equipment and people can result from a large-scale short-duration deflagration. The nature of the 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 maximum flame velocity. When flame velocities are low, the effect of a deflagration is the release of 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 released.
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 try to expand thermally as well. The net result is that the volume of the vessel or structure needs to either expand/fail to accommodate the hot combustion gases, or build internal pressure to contain them. The risks of deflagration inside waste storage drums is a growing concern among storage facilities . see drum deflagration videos