Turbulence modelling of fast bimolecular reactions using one-dimensional equations of change

Direct numerical simulation (DNS) of one-dimensional equations of change have been made for the fast reaction A + B → R in statistically homogeneous Burgers turbulence. Two classes of initial conditions have been considered.;For initially nonpremixed reactants, the evolution of single-point statistics have been computed from the DNS results at a turbulence Reynolds number Re = 400, at turbulent Damkohler numbers of Da = 102, 10 3 and at Schmidt numbers Sc = 10-3, 10 -2, 10-1, 1. Toor's closure is more reliable for nonpremixed than for partially premixed reactants. Tarbell's closure, which failed for partially premixed reactants, offers improvement over Toor's, as does the closure developed by Kim and Reed (Ind. Eng. Chem. Res. 37, 3710 (1998)) for partially premixed reactants, which also offers an advantage over Tarbell's closure and recognizes the phenomenon of reaction segregation.;For partially premixed reactants, the evolution of reactant and product spectra, EA(k,t)(=EB(k,t)) and ER(k,t) have been computed from the DNS concentration profiles at Re = 400 and Da = 10, 102, 103 for Sc = 10-3 , 1. The interpretation of the reactant spectra hinges on the passive additive spectra Etheta(k,t) having the same initial spectrum as EA(k,t), being convected by the same random velocity field u(x,t) that convects A, B, and R, and having the same Prandtl/Schmidt number as the Sc of A, B, and R. While ER(k,t) depends upon Da and Sc, E A(k,t) depends almost exclusively on Sc.