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

TL;DR

The paper addresses inaccuracies in turbulent combustion modeling that arise when mean concentrations are used in standard rate laws. It develops a generalized rate law (GRL) by formulating the grid-averaged reaction rate as a spatial integral of local concentrations, $\widehat{R}_{\mathrm{A}} = - \frac{k}{V} \int c_{\mathrm{A}}^{\alpha} c_{\mathrm{B}}^{\beta} \cdots dv$, which reduces to the classical form in homogeneous systems. By applying this GRL to first-, second-, Lindemann unimolecular, and trimolecular/global mechanisms, it shows that chemical source terms can be computed from sub-grid concentration distributions without explicit turbulence parameters, enabling a turbulence-chemistry decoupling. Numerical examples with one-dimensional concentration distributions (straight-line, sine, piecewise) illustrate how the exact integrals compare to mean-concentration predictions and how grid refinement reduces error, highlighting the dependence of reaction rates on mixing and distribution shape. The work offers a theoretical framework for more accurate sub-grid chemistry in LES and related turbulent reacting-flow simulations, with potential extensions to more realistic distributions and kinetic schemes.

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.

Figures (4)

• Figure 1: Diagram of one-dimensional linear concentration distributions.
• Figure 2: Linear concentration distributions of H2 and O2 in grid.
• Figure 3: Sine function distributions of $c_{\rm{O}_2}$ and $c_{\rm{H}_2}$.
• Figure 4: piecewise distributions of $c_{\rm{O}_2}$ and $c_{\rm{H}_2}$.