Scaling of reaction progress variable variance in highly turbulent reaction waves
Journal article, 2021
Self-propagation of a reaction wave, which consists of an infinitely thin reaction zone (front) and a thick inert mixing layer adjacent to the front, in constant-density statistically stationary, homogeneous isotropic turbulence unaffected by the wave is analytically studied. In the asymptotic case of a high turbulent Reynolds number, high Karlovitz number, and low Damk_ohler number Da, the scalar variance c02 is shown to be proportional to Da for the statistically stationary stage of the wave evolution. This scaling is supported by newly analyzed Direct Numerical Simulation data discussed in detail by Sabelnikov et al. ["Thin reaction zones in constant-density turbulent flows at low Damk_ohler numbers: Theory and simulations," Phys. Fluids 31, 055104 (2019)]. The obtained analytical results also show that, under conditions of the present study, spatial gradients of reactant concentration non-uniformities due to the reaction and spatial gradients of reactant concentration non-uniformities due to the turbulence are of the same order of magnitude. Accordingly, major statistical characteristics of the scalar field c(x, t) such as the mean area of an iso-scalar surface c(x, t) = const, the mean molecular flux through this surface, etc., can be found adopting results known in the theory of inert and passive turbulent mixing. Nevertheless, the reaction indirectly affects these characteristics by controlling the mean thickness of the reaction wave and, consequently, the spatial gradient of the mean reaction progress variable. Published under an exclusive license by AIP Publishing.