In
combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion ...
, Liñán's flame speed provides the estimate of the upper limit for edge-flame propagation velocity, when the flame curvature is small. The formula is named after
Amable Liñán
Amable Liñán Martínez (born 1934 in Noceda de Cabrera, Castrillo de Cabrera, León, Spain) is a Spanish aeronautical engineer working in the field of combustion.
Biography
He holds a PhD in Aeronautical Engineering from the Technical Uni ...
. When the flame thickness is much smaller than the mixing-layer thickness through which the edge flame is propagating, a flame speed can be defined as the propagating speed of the flame front with respect to a region far ahead of the flame. For small flame curvatures (
flame stretch), each point of the flame front propagates at a
laminar planar premixed speed that depends on a local
equivalence ratio
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just ahead of the flame. However, the flame front as a whole do not propagate at a speed
since the mixture ahead of the flame front undergoes thermal expansion due to the heating by the flame front, that aids the flame front to propagate faster with respect to the region far ahead from the flame front. Liñán estimated the edge flame speed to be:
:
where
and
is the
density
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
of the fluid far upstream and far downstream of the flame front. Here
is the stoichiometric value (
) of the planar speed. Due to the thermal expansion, streamlines diverges as it approaches the flame and a pressure builds just ahead of the flame.
The scaling law for the flame speed was verified experimentally In constant density approximation, this influence due to density variations disappear and the upper limit of the edge flame speed is given by the maximum value of
.
[Rajamanickam, P., Coenen, W., Sánchez, A. L., & Williams, F. A. (2019). Influences of stoichiometry on steadily propagating triple flames in counterflows. Proc. Combust. Inst., 37(2), 1971-1977.]
References
{{Reflist
Fluid dynamics
Combustion