Outwardly Propagating Spherical Flames with Thermally Sensitive Intermediate Kinetics and Radiative Loss

Abstract

The outwardly propagating spherical flames with thermally sensitive intermediate kinetics and radiative loss are analyzed within the framework of large activation energy and quasiplanar assumptions. The relationship between the flame propagation speed and flame radius are derived in theoretical analysis. Based on this relationship, the spherical flame propagation and extinction are analyzed. The flame propagation speed and extinction limit are shown to be strongly affected by fuel and radical Lewis numbers and radiative loss. It is demonstrated that the spherical flame propagation is always enhanced by the increase of the radical Lewis number, and that the flame propagation speed correlates well with the peak radical concentration. The radiative loss is shown to affect quantitatively but not qualitatively the dependence of the Markstein length on the fuel and radical Lewis numbers. Moreover, it is found that the flammable region of positively stretched spherical flame can be extended by decreasing the fuel Lewis number or increasing the radical Lewis number, and that the self-extinguishing flame can be observed for mixtures with small fuel Lewis number and/or large radical Lewis number. The linear and quartic heat loss models are compared, and these two models are found to have qualitatively and even quantitatively similar influence on spherical flame propagation when the heat loss intensities are properly specified. Furthermore, transient numerical simulations of spherical flame propagation at finite reaction rate are conducted to demonstrate the validity of theoretical results.

Keywords:

• Extinction limit
• Lewis number
• Propagating spherical flame
• Radiative loss
• Two-step chemistry

ACKNOWLEDGMENTS

This work was sponsored by the National Natural Science Foundation of China (No. 50976003 and No. 51136005) and Doctoral Fund of Ministry of Education of China (Grant No. 20100001120003). The authors thank Professor Yiguang Ju at Princeton University for helpful discussions.

Notes

The current affiliation for Huangwei Zhang is Department of Engineering, University of Cambridge, Cambridge, UK.