Studies on the Outwardly and Inwardly Propagating Spherical Flames with Radiative Loss

Abstract

Outwardly and inwardly propagating spherical flames (OPF and IPF) with radiative loss are studied analytically and numerically. Emphasis is placed on investigating the effects of radiation on flame propagating speed, Markstein length, and flame extinction, as well as on examining whether the reactant can be completely consumed via an IPF. A general correlation between flame propagating speed and flame radius for OPF and IPF of large flame radii is derived and utilized to study the effects of radiative loss and Lewis number on flame propagation and extinction. A correlation for Markstein length at different Lewis numbers and radiative loss is also presented. It is shown that the Markstein length is strongly affected by radiative loss as well as Lewis number, and that only for mixtures not close to their flammability limits and without CO₂ dilution is the effect of radiation on the Markstein length measured from expanding spherical flames negligible. Furthermore, the theoretical results are validated by numerical simulations. It is found that when radiative loss is considered, there exists unconsumed reactant after the extinction of IPF for mixture with Lewis number less than unity.

Keywords:

• Extinction
• Markstein length
• Propagating spherical flame
• Radiative loss

ACKNOWLEDGMENT

This work was partially supported by National Natural Science Foundation of China (Grant no. 50976003), State Key Laboratory for Turbulence and Complex Systems, and the U.S. Department of Energy. It is also a pleasure to acknowledge helpful discussions with Mr. Michael P. Burke at Princeton University.