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.
This work was done by Josette Bellan of Caltech and Sau-Hai (Harvey) Lam of Princeton University for NASA’s Jet Propulsion Laboratory.
This Brief includes a Technical Support Package (TSP).
Qusai-Decoupling of Shvab-Zel'dovich Variables
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Overview
The document is a technical support package from NASA detailing research on the quasi-decoupling of Shvab-Zel'dovich (SZ) variables in the context of multicomponent, chemically reacting flows. Authored by Josette Bellan from Caltech and Sau-Hai Lam from Princeton University, the work addresses the complexities involved in solving conservation equations for reactive flows, where the characteristic time of chemical reactions is significantly shorter than that of the flow itself.
Traditionally, it was believed that the conservation equations could only be decoupled under the restrictive assumption that all Lewis numbers are equal to one (ALeU). The Lewis number represents the ratio of mass diffusion time to thermal conduction time for a species. The research presented in this document challenges this notion, demonstrating that while the ALeU assumption is sufficient for complete decoupling, it is not strictly necessary. The authors propose that quasi-decoupling—partial decoupling of the equations—can be achieved even when thermal diffusion is present, albeit with a controllable error.
The significance of SZ variables lies in their ability to represent conserved scalar quantities that are unaffected by chemical reactions, thus simplifying the mathematical modeling of reactive flows. By utilizing these variables, the authors aim to facilitate the solution of complex conservation equations, which are often difficult to manage due to the interplay of chemical kinetics and fluid dynamics.
The document outlines the methodology for handling fast chemistry modes and emphasizes the need to modify the diffusion term in reduced chemistry models. This modification is crucial to ensure accurate predictions in scenarios where the chemistry has been simplified.
In summary, this research provides a novel approach to the decoupling of conservation equations in reactive flows, offering a more flexible framework that can be applied under a broader range of conditions than previously thought. The findings have implications for improving the modeling and understanding of combustion processes and other applications involving chemically reacting flows, potentially leading to advancements in both theoretical and practical aspects of fluid dynamics.
