On the critical flame radius and minimum ignition energy for spherical flame initiation

Spherical flame initiation from an ignition kernel is studied theoretically and numerically using different fuel/oxygen/helium/argon mixtures (fuel: hydrogen, methane, and propane). The emphasis is placed on investigating the critical flame radius controlling spherical flame initiation and its correlation with the minimum ignition energy. It is found that the critical flame radius is different from the flame thickness and the flame ball radius and that their relationship depends strongly on the Lewis number. Three different flame regimes in terms of the Lewis number are observed and a new criterion for the critical flame radius is introduced. For mixtures with Lewis number larger than a critical Lewis number above unity, the critical flame radius is smaller than the flame ball radius but larger than the flame thickness. As a result, the minimum ignition energy can be substantially over-predicted (under-predicted) based on the flame ball radius (the flame thickness). The results also show that the minimum ignition energy for successful spherical flame initiation is proportional to the cube of the critical flame radius. Furthermore, preferential diffusion of heat and mass (i.e. the Lewis number effect) is found to play an important role in both spherical flame initiation and flame kernel evolution after ignition. It is shown that the critical flame radius and the minimum ignition energy increase significantly with the Lewis number. Therefore, for transportation fuels with large Lewis numbers, blending of small molecule fuels or thermal and catalytic cracking will significantly reduce the minimum ignition energy.