Spherical flame initiation and propagation with thermally sensitive intermediate kinetics

Spherical flame initiation and propagation with thermally sensitive intermediate kinetics are studied analytically within the framework of large activation energy and quasi-steady assumptions. A correlation describing different flame regimes and transitions among the ignition kernels, flame balls, propagating spherical flames, and planar flames is derived. Based on this correlation, spherical flame propagation and initiation are then investigated. The flame propagation speed, Markstein length, and critical ignition power and radius are found to strongly depend on the Lewis numbers of fuel and radical and the heat of reaction. For spherical flame propagation, the trajectory is shown to change significantly with the fuel Lewis number and a C-shaped solution curve of flame propagation speed as a function of flame radius is observed for large fuel Lewis numbers. The Markstein length is shown to increase/decrease monotonically with the fuel/radical Lewis number. The influence of stretch on flame propagation (i.e. the absolute value of Markstein length) is found to decrease with the heat of reaction. For spherical flame initiation, the critical ignition power and radius are shown to increase with the fuel Lewis number and to decrease with the radical Lewis number and heat of reaction. Three different flame initiation regimes are observed and discussed. Furthermore, the validity of theoretical prediction is confirmed by transient numerical simulations including thermal expansion and detailed chemistry.