Reaction analogy based forcing for incompressible scalar turbulence

Abstract

We present a novel reaction analogy (RA) based forcing method for generating stationary scalar fields in incompressible turbulence. The new method can produce more general scalar PDFs (e.g. double-delta) than current methods, while ensuring that scalar fields remain bounded. Such features are useful for generating initial fields in non-premixed combustion or for studying non-Gaussian scalar turbulence. The RA method mathematically models hypothetical chemical reactions that convert reactants in a mixed state back into its pure unmixed components. Various types of chemical reactions are formulated and the corresponding mathematical expressions derived such that the reaction term is smooth in the scalar space and is consistent with mass conservation. For large values of the scalar dissipation rate, the method produces statistically steady double-delta scalar PDFs. Quasi-uniform, Gaussian, and stretched exponential scalar statistics are recovered for smaller values of the scalar dissipation rate. The shape of the scalar PDF can be further controlled by changing the stoichiometric coefficients of the reaction. The ability of the new method to produce fully developed passive scalar fields with quasi-Gaussian PDFs is also investigated, by exploring the convergence of the third order mixed structure function to the "four-thirds" Yaglom's law.