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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 S_L that depends on a local
equivalence ratio Equivalence or Equivalent may refer to: Arts and entertainment *Album-equivalent unit, a measurement unit in the music industry *Equivalence class (music) *'' Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre *'' Equiva ...
\phi just ahead of the flame. However, the flame front as a whole do not propagate at a speed S_L 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: :\frac \sim \left(\frac\right)^, where \rho_u and \rho_b 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 S_L^0 is the stoichiometric value (\phi=1) 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 S_L.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