On revised mixture fraction describing multi-stream mixing

Multi-stream mixing is common in practice but cannot be modeled using the traditional Bilger mixture fraction defined for only two streams. This work was intended to define the multi-stream mixture fractions that can be adopted in flamelet-tabulated combustion models to simulate the multi-stream mixing and combustion. These mixture fractions are expressed as linear combinations of species mass fractions like the Bilger mixture fraction. The present definition is special as the new mixture fractions are nonconservative and can include the preferential diffusion (PD) effects which were often ignored before. Meanwhile, it can be appliable for any number of inlet streams. The multi-stream mixture fractions are derived based on some basic conserved scalars, like the element mass fractions, enthalpy, and transported scalars. Governing equations for the multi-stream mixture fractions are also presented.