Thin reaction zones in constant-density turbulent flows at low Damköhler numbers: Theory and simulations

Abstract

Propagation of a single-reaction wave in a constant-density turbulent flow is studied by considering reaction rates that depend on the reaction progress variable c in a highly nonlinear manner. Analysis of Direct Numerical Simulation (DNS) data obtained recently from 26 reaction waves characterized by low Damköhler (0.01 < Da < 1) and high Karlovitz (6.5 < Ka < 587) numbers reveals the following trends. First, the ratio of consumption velocity UT to rms turbulent velocity u′ scales as square root of Da in line with Damköhler’s classical hypothesis. Second, the ratio of fully developed turbulent wave thickness to an integral length scale of turbulence decreases with increasing Da and tends to scale with inverse square root of Da, in line with the same hypothesis. Third, contrary to the widely accepted concept of distributed reaction zones, reaction-zone broadening is quite moderate even at Da = 0.01 and Ka = 587. Fourth, contrary to the same concept, UT/u′ is mainly controlled by the reaction-surface area. Fifth, UT/u′ does not vary with the laminar-reaction-zone thickness, provided that Da is constant. To explain the totality of these DNS results, a new theory is developed by (i) exploring the propagation of a molecular mixing layer attached to an infinitely thin reaction sheet in a highly turbulent flow and (ii) hypothesizing that the area of the reaction sheet is controlled by turbulent mixing. This hypothesis is supported by order-of-magnitude estimates and results in the aforementioned Damköhler’s scaling for UT/u′. The theory is also consistent with other aforementioned DNS results and, in particular, explains the weak influence of the laminar-reaction-zone thickness on UT/u′.