Thin Reaction Zones in Highly Turbulent Medium

TL;DR

This paper introduces and studies a new regime where reaction waves propagate as infinitely thin sheets in highly turbulent media, emphasizing the role of reaction-zone surface area in turbulent consumption velocity.

Contribution

It proposes a theoretical and numerical analysis of thin reaction sheets in turbulence, challenging the traditional distributed reaction zone model at low Damköhler numbers.

Findings

Reaction zones remain thin even at low Da values.

Turbulent consumption velocity correlates with reaction-zone surface area.

Theoretical predictions are validated by 3D DNS data.

Abstract

In a highly turbulent medium characterized by a low Damk\"ohler number Da, reactions are commonly considered to occur in distributed zones broadened by small-scale turbulent eddies. In the present communication, an alternative regime of propagation of reaction waves in a highly turbulent medium is introduced and studied theoretically and numerically. More specifically, propagation of an infinitely thin reaction sheet in a turbulent medium is analyzed, 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 a relation for the turbulent consumption velocity, which is similar to the well-known Damk\"ohler scaling associated commonly with distributed reaction zones at a low Da. The obtained theoretical results are validated by analyzing a big database (23 cases characterized by 0.01<Da<1) created recently in 3D direct numerical simulations of propagation of a statistically planar, one-dimensional, dynamically passive reaction wave in statistically stationary, homogeneous, isotropic turbulence. The DNS data well support the aforementioned relation. They also show that the reaction is localized to thin zones even at Da as low as 0.01, with a ratio of the turbulent and laminar consumption velocities being mainly controlled by the reaction-zone-surface area.