The dissipation rate of a scalar variance is related to the mean heat release rate in turbulent combustion. Mixture fraction is the scalar of interest for non-premixed combustion, and a reaction progress variable is relevant for premixed combustion. A great deal of work is conducted in past studies to understand the spectra of passive scalar transport in turbulent flows. A very brief summary of these studies to bring out the salient characteristics of the passive scalar spectrum is given first. Then, the classical analysis of the reactive scalar spectrum is revisited in the lights of recent understanding gained through analyzing the scalar spectrum deduced from direct numerical simulation data of both non-premixed and premixed combustion. The analysis shows that the reactive scalar spectral density in premixed combustion has a dependence on Karlovitz and Damköhler numbers, which comes through the mean scalar dissipation rate appearing in the spectral expression. In premixed combustion, the relevant scale for the scalar dissipation rate is shown to be of the order of the chemical length scale, and the dissipation rate is not influenced by the scales in the inertial-convective range unlike for the passive scalar dissipation rate. The scalar fluctuations produced near the chemical scales cascade exponentially to larger scales. These observations imply that the passive scalar models cannot be extended to premixed combustion.
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2021
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