Direct numerical simulations of turbulent premixed cool flames: Global and local flame dynamics analysis

The cool flame dynamics, especially in turbulent flows, is of great interest for both practical application and fundamental research. In this study, a series of direct numerical simulations of turbulent premixed n-C${}_7$H₁₆/O${}_2$/O${}_3$/N${}_2$ cool flames are performed, with the focus on the influence of turbulence intensity ($u^{\prime }/S_L$, where $S_L$ is the laminar flame speed) on the flame structure as well as the global and local cool flame dynamics. It is found that the cool flame front is considerably wrinkled by turbulence at high $u^{\prime }/S_L$, leading to significantly thickened turbulent cool flame brush and largely altered local reactivity compared with the reference laminar flame. However, the turbulent flame structure in the temperature space is found to be insensitive to $u^{\prime }/S_L$. Besides, with increasing $u^{\prime }/S_L$, the normalized turbulent cool flame speed ($S_T/S_L$) is monotonically increased, attributed to substantial augmentation on the flame surface area ($A_T/A_L$), while the stretching factor ($I_0$) remains almost constant and is smaller than 1. The underlying mechanisms for such variations are revealed through local flame dynamics analysis. Specifically, the local flame displacement speed $S_d$ is found to be strongly negatively correlated with flame curvature; meanwhile, such negative correlation and the probability distribution function (PDF) of flame curvature are barely influenced by $u^{\prime }/S_L$, leading to a weak dependence of $I_0$ on $u^{\prime }/S_L$. In contrast, the PDF of the tangential strain rate is found to span a much wider range and shift to the positive side as $u^{\prime }/S_L$ increases, suggesting that the enhanced tangential strain rate is the main cause for the increase in surface area of the turbulent premixed cool flame. Finally, the influence of equivalence ratio on above findings is found to be insignificant, indicating that although the local reactivity of turbulent premixed cool flames is altered due to the differential diffusion, the resultant flame-stretch interaction is insensitive to the equivalence ratio. This study presents some unique cool flame dynamics that are distinct from hot flames, which can help improve the understanding and modeling of turbulent cool flames.

Novelty and Significance Statement

The novelty of this work is that the combined global and local flame dynamics analyses are conducted for isolated turbulent premixed cool flames for the first time. It is found that with increasing turbulence intensity, the normalized turbulent cool flame speed increases monotonically due to substantial increase on flame surface area, whereas the stretching factor remains almost constant. The underlying mechanisms for these trends are revealed through the local flame dynamics analysis. Besides, the influence of equivalence ratio is found to be insignificant on the cool flame dynamics. Results from this work demonstrate that the turbulent premixed cool flame features some similar characteristics as the turbulent hot flames with Lewis number larger than 1, but more importantly, it also present some unique characteristics which are distinct from hot flames. Therefore, this study contributes to a better understanding of cool flame dynamics.