Liñán's flame speed explained

S _{L} that depends on a local equivalence ratio \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:(U)/(S ^{0} _{L}) \sim \left( (\rho _{u})/(\rho _{b}) \right) ^{1/2} ,

where

\rho _{u} and \rho _{b} is the density of the fluid far upstream and far downstream of the flame front. Here S ^{0} _{L} 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^{[2] [3]} 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} .^[4]

Notes and References

1. Ruetsch, G. R., Vervisch, L., & Liñán, A. (1995). Effects of heat release on triple flames. Phys. Fluids, 7(6), 1447-1454.
2. Cha, M. S., & Ronney, P. D. (2006). Propagation rates of nonpremixed edge flames. Combust. Flame, 146(1-2), 312-328.
3. Song, H., Wang, P., Boles, R. S., Matinyan, D., Prahanphap, H., Piotrowicz, J., & Ronney, P. D. (2017). Effects of mixture fraction on edge-flame propagation speeds. Proc. Combust. Inst., 36(1), 1403-1409.
4. 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.