Functional formulation of nonisothermal turbulent reactive flows

Abstract

The two familiar functional formalisms in turbulence are applied to the simultaneous turbulent mixing and chemical reaction of scalar fields. One-step, second-order, irreversible, exothermic chemical reactions with an Arrhenius-type rate constant are considered. The problem is formally posed in terms of initial and boundary conditions. For the special case of equal mass-diffusivities and a Lewis number of one the functional equations are decoupled into a turbulent binary mixing study and a reactive problem. The Lewis-Kraichnan formalism is used in order to obtain exact functional solutions of the binary mixing case in final period turbulence. Driving forces are included in the thermal energy equation. These solutions are used to obtain detailed information about the binary mixing problem and the behavior of very rapidly reacting species in the final period.