Effects of the spatial distribution of CO₂ dilution on localised forced ignition of stoichiometric CH₄ - CO₂ - air mixtures

Abstract

The localised forced ignition and subsequent flame propagation have been analysed for stoichiometric $\text{C}{\text{H}}_4-\text{C}{\text{O}}_2-\text{air}$ mixtures with different spatial distributions and mean levels of $\text{C}{\text{O}}_2$ dilution (i.e. mole fraction of $\text{C}{\text{O}}_2$ in $\text{C}{\text{H}}_4/\text{C}{\text{O}}_2$ blend) for different flow conditions (e.g. quiescent laminar condition and different turbulence intensities) using three-dimensional Direct Numerical Simulations. The $\text{C}{\text{H}}_4+\text{C}{\text{O}}_2$ mixture is taken to represent biogas, as $\text{C}{\text{H}}_4$ and $\text{C}{\text{O}}_2$ are its two principal constituents. A two-step chemical mechanism, which has been demonstrated to capture the effects of $\text{C}{\text{O}}_2$ dilution on the laminar burning velocity with sufficient accuracy, has been used for the purpose of a parametric analysis in terms of the mean value, standard deviation and integral length scale of the initial spatial Gaussian distributions of $\text{C}{\text{O}}_2$ dilution in the unburned gas. An increase of mean $\text{C}{\text{O}}_2$ dilution level was found to reduce the maximum values of temperature and the reaction rate magnitude of $\text{C}{\text{H}}_4$. Moreover, an increase of mean $\text{C}{\text{O}}_2$ dilution acts to reduce the probability of finding large reaction rate magnitudes of $\text{C}{\text{H}}_4$, which also leads to a decreasing trend of burned gas volume $\text{C}{\text{O}}_2$ irrespective of flow conditions. Furthermore, an increase in turbulence intensity acts to reduce the burned gas volume irrespective of mixture composition due to the enhancement of heat transfer from the hot gas kernel. However, the initial values of integral length scale and standard deviation of $\text{C}{\text{O}}_2$ dilution variation (i.e. $l_{\psi }$ and ${\sigma }^{\psi }$) have been found not to have significant influences on the burned gas volume for the parameter range considered here. Although a small value of $l_{\psi }$ promotes high rates of mixing of $\text{C}{\text{O}}_2$ within the unburned gas, the overwhelming probability of finding $\text{C}{\text{O}}_2$ dilution close to its mean value eclipses the effects of $l_{\psi }$ and ${\sigma }^{\psi }$ even under laminar conditions, and this trend strengthens further under high turbulence intensities due to enhanced mixing.

Keywords:

• Localised forced ignition
• biogas-air mixture
• CO₂ dilution
• turbulence intensity
• direct numerical simulations

Acknowledgements

The financial support of the British Council and EPSRC (EP/R029369/1) and the computational support of Rocket and ARCHER are gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by British Council; Engineering and Physical Sciences Research Council [Grant Number EP/R029369/1].