A generalized rate law for inhomogeneous system and turbulence-chemistry decoupling of reaction rate calculation in combustion

TL;DR

This paper develops a generalized rate law for inhomogeneous systems in combustion, enabling accurate reaction rate calculations through sub-grid modeling without explicitly considering turbulence-chemistry interactions.

Contribution

It introduces a new formulation of reaction rates for inhomogeneous concentration distributions using spatial integration, validated with various distribution examples.

Findings

Reaction rates can be accurately computed with proper sub-grid concentration modeling.

The method reduces the need to explicitly model turbulence-chemistry interactions.

Validated with different one-dimensional concentration distributions.

Abstract

In this work, the rate law for inhomogeneous concentration distributions has been formulated, by applying spatial integration over the products of species concentrations. Reaction rates for typical reactions have been investigated by assuming a linear concentration distribution in the grid. A few examples of one-dimensional concentration distributions, straight line, piecewise, and sine function, for a selected second order reaction have been taken to illustrate the validations of the method developed. Difference between the reaction rates by spatial integration and by mean concentrations have been discussed. It is revealed that the chemical reaction rates for combustion simulation can be calculated by appropriate sub-grid modeling of concentration distributions, without needs of the explicit consideration of turbulent combustion interactions, and the reaction rates for the species transport equation in turbulent combustion simulations can be accurately calculated if the concentration distributions of species within the grid are correctly defined.