# Laminar flame speed

Laminar flame speed is an intrinsic characteristic of premixed combustible mixtures [1] that plays a key role in understanding a mixture’s reactivity, diffusivity, and exothermicity.[2][3][4] It is the speed at which an un-stretched laminar flame will propagate through a quiescent mixture of unburned reactants. Laminar flame speed is defined as the normal component of velocity of flame relative to unburned gas.[5] Laminar flame speed is given the symbol sL. According to the thermal flame theory of Mallard and Le Chatelier, the un-stretched laminar flame speed is dependent on only three properties of a chemical mixture: the thermal diffusivity of the mixture, the reaction rate of the mixture and the temperature through the flame zone:

${\displaystyle s_{\mathrm {L} }^{\circ }={\sqrt {\alpha {\dot {\omega }}\left({\dfrac {T_{\mathrm {b} }-T_{\mathrm {i} }}{T_{\mathrm {i} }-T_{\mathrm {u} }}}\right)}}}$

${\displaystyle \alpha }$ is thermal diffusivity,

${\displaystyle {\dot {\omega }}}$ is reaction rate,

and the temperature subscript u is for unburned, b is for burned and i is for ignition temperature.

Laminar flame speed is a property of the mixture (fuel structure, stoichiometry) and thermodynamic conditions upon mixture ignition (pressure, temperature). Turbulent flame speed is a function of the aforementioned parameters, but also heavily depends on the flow field. As flow velocity increases and turbulence is introduced, a flame will begin to wrinkle, then corrugate and eventually the flame front will be broken and transport properties will be enhanced by turbulent eddies in the flame zone. As a result, the flame front of a turbulent flame will propagate at a speed that is not only a function of the mixture's chemical and transport properties but also properties of the flow and turbulence.