Fluctuations and correlations of reactive scalars near chemical equilibrium in incompressible turbulence

TL;DR

This paper investigates how chemical reactions influence scalar fluctuations and correlations in turbulent flows, introducing a Damköhler number that predicts the balance between reaction effects and turbulence, validated by simulations.

Contribution

It introduces a Damköhler number-based framework to predict scalar fluctuations and correlations near chemical equilibrium in turbulence, supported by analytical and numerical validation.

Findings

Scalar fluctuations decrease with increasing Damköhler number.

Correlations between reactants increase with Damköhler number.

A saturation point occurs at Damköhler number around 10.

Abstract

The statistical properties of species undergoing chemical reactions in a turbulent environment are studied. We focus on the case of reversible multi-component reactions of second and higher orders, in a condition close to chemical equilibrium sustained by random large-scale reactant sources, while the turbulent flow is highly developed. In such a state a competition exists between the chemical reaction that tends to dump reactant concentration fluctuations and enhance their correlation intensity and the turbulent mixing that on the contrary increases fluctuations and remove relative correlations. We show that a unique control parameter, the Damkh\"{o}ler number ($Da_\theta$) that can be constructed from the scalar Taylor micro-scale, the reactant diffusivity and the reaction rate characterises the functional dependence of fluctuations and correlations in a variety of conditions, i.e., at changing the reaction order, the Reynolds and the Schmidt numbers. The larger is such a Damkh\"{o}ler number the more depleted are the scalar fluctuations as compared to the fluctuations of a passive scalar field in the same conditions, and vice-versa the more intense are the correlations. A saturation in this behaviour is observed beyond $Da_\theta \simeq \mathcal{O}(10)$. We provide an analytical prediction for this phenomenon which is in excellent agreement with direct numerical simulation results.