The Takeno Index, introduced in [1], is a product of the gradient of the fuel mass fraction and the gradient of the oxygen mass fraction, giving information on whether a flame regime is premixed or of the diffusion-type.
To me, this seems to be an approach that has to be used with detailed chemistry and a resolved flame – Is this true or could this approach be used in turbulent combustion models with a RANS approach for turbulence?
[1] Yamashita, H., Shimada, M., and Takeno, T., "A numerical study on flame stability at the transition point of jet diffusion flames”, 26th symposium of the Combustion Institute, pp. 27-34, 1996.
In principle, the Takeno index concept has to be applied at a numerical resolution, where most of the flame front can be resolved. If a lot of flame folding and mixture fraction variation is subgrid (as is the case in most RANS simulations), the concept is weak. The concept may still make sense when in a LES the gradients of fuel mass fraction can be largely resolved, but the (partially premixed) flame fronts are underresolved. The we have a situation of premixed flamefronts propagating into a medium of spatially varying fuel-air ratio.
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