Effects of thermal expansion on Taylor dispersion-controlled diffusion flames

TL;DR

This paper develops a theoretical model to analyze how gas expansion from heat release affects unsteady diffusion flames in pipe flow, focusing on Taylor dispersion-controlled mixing and extending previous thermo-diffusive theories.

Contribution

It extends existing thermo-diffusive models by incorporating gas expansion effects into the analysis of Taylor dispersion-controlled diffusion flames.

Findings

Gas expansion has a small first-order effect on pressure gradients at large times.

Corrections to velocity and mixing variables are derived for Burke-Schumann flames.

Gas density dependence leads to notable deviations from previous models.

Abstract

A theoretical analysis is developed to investigate the effects of gas expansion due to heat release on unsteady diffusion flames evolving in a pipe flow in which the mixing of reactants is controlled by Taylor's dispersion processes thereby extending a previously developed theory based on the thermo-diffusive model. It is first shown that at times larger than radial diffusion times, the pressure gradient induced by the gas expansion is, in the first approximation, small in comparison with the prevailing pressure gradient driving the flow, indicating that corrections to the background velocity profile are small. The corrections to the velocity components along with the leading-order mixing variables such as the concentrations, temperature and density are solved for a Burke-Schumann flame. Due to the dependence of the effective Taylor diffusion coefficients on the gas density, quantitative and sometimes qualitative departures in predictions from the thermo-diffusive model are observed.