Quasi-Decoupling of Shvab-Zel’dovich Variables

A paper presents some novel conclusions concerning the Shvab-Zel’dovich (SZ) vari- ables, which are linear combinations of dep- endent variables in mathematical models of multicomponent, chemically reacting flows. The SZ variables represent scalar quantities that are conserved, that is, are not affected by chem- istry. The role of SZ variables is to decouple the conservation equations and make it simpler to solve them. However, SZ variables that entirely decouple the system of equations are generally defined only under the restrictive assumption that all Lewis numbers are unity (ALeU). Each Lewis number represents the ratio of a single species mass-diffusion characteristic time to the thermal conduction characteristic time. The present paper discusses the foregoing issues and further presents a mathematical analysis addressing the question of whether the ALeU assumption is a necessary condition for such decoupling. The conclusion reached in the analysis is that the ALeU assumption is sufficient but not necessary and that quasi-decoupling (that is partial decoupling) may be performed in the absence of thermal diffusion. When thermal diffusion is present, quasi-decoupling may still be performed subject to a controllable error.