On conserved scalars that preserve stoichiometric mixture fraction

With the increasing use of carbon-free fuels in hydrocarbon blends, multiple definitions are appearing for conserved scalars that are employed in the formulation of mixture fraction. One essential requirement for such scalars is the preservation of stoichiometric mixture fraction under conditions where the elemental ratios change locally due to preferential diffusion. This short communication clarifies that the scalar introduced by Bilger in 1989, namely beta = 2YC WC +2WHYH - WOYO does satisfy these conditions regardless of the gaseous fuel blend, as long as the products of complete combustion are assumed to be CO2 and H2O. An explanation of the underlying foundation of this conserved scalar is provided along with an example for the generalised cases where dilution and partial premixing may be present.