Thin reaction zones in highly turbulent medium

A big database (23 cases characterized by Damköhler number less than unity) created recently in 3D Direct Numerical Simulation (DNS) of propagation of a statistically one-dimensional and planar, dynamically passive reaction wave in statistically stationary, homogeneous, isotropic turbulence is analyzed. On the one hand, the DNS data well support the classical Damköhler expression, i.e., square-root dependence of a ratio of turbulent and laminar consumption velocities on the turbulent Reynolds number. On the other hand, contrary to the common interpretation of the Damköhler theory and, in particular, to the concept of distributed burning, the DNS data show that the reaction is still localized to thin zones even at Da as low as 0.01, with the aforementioned ratio of the consumption velocities being mainly controlled by the reaction-zone-surface area. To reconcile these apparently inconsistent numerical findings, an alternative regime of propagation of reaction waves in a highly turbulent medium is analyzed, i.e., propagation of an infinitely thin reaction sheet is theoretically studied, with molecular mixing of the reactant and product being allowed in wide layers. In this limiting case, an increase in the consumption velocity by turbulence is solely controlled by an increase in the reaction-sheet area. Based on physical reasoning and estimates, the area is hypothesized to be close to the mean area of an inert iso-scalar surface at the same turbulent Reynolds number. This hypothesis leads to the aforementioned square-root dependence. Thus, both the DNS data and the developed theory show that a widely accepted hypothesis on penetration of small-scale turbulent eddies into reaction zones is not necessary to obtain the classical Damköhler scaling for turbulent consumption velocity

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

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 U T 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, U T /u′ is mainly controlled by the reaction-surface area. Fifth, U T /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 U T /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 U T /u′

Influence of Thermal Expansion on Potential and Rotational Components of Turbulent Velocity Field Within and Upstream of Premixed Flame Brush

Direct Numerical Simulation (DNS) data obtained earlier from two statistically stationary, 1D, planar, weakly turbulent premixed flames are analyzed in order to examine the influence of combustion-induced thermal expansion on the flow structure within the mean flame brushes and upstream of them. The two flames are associated with the flamelet combustion regime and are characterized by significantly different density ratios, i.e. σ= 7.53 and 2.5. The Helmholtz–Hodge decomposition is applied to the DNS data in order to extract rotational and potential velocity fields. Comparison of the two fields shows that combustion-induced thermal expansion can significantly change the local structure of the incoming constant-density turbulent flow of unburned reactants by significantly increasing the relative magnitude of the potential velocity fluctuations when compared to the rotational velocity fluctuations in the flow. Such effects are documented not only within the mean flame brush, but also well upstream of it. The effect magnitude is increased by the density ratio σ, with the effects being well (weakly) pronounced at σ= 7.53 (2.5, respectively). Moreover, the potential and rotational velocity fields can cause opposite variations of the local area of an iso-scalar surface c(x, t) = const within flamelets by generating the local strain rates of opposite signs.\ua0\ua9 2020, Springer Nature B.V