A computational study of the transition from localized ignition to flame ball in lean hydrogen/air mixtures

A computational study has been conducted to determine the critical conditions for the transition from localized flame ignition and propagation to the establishment of a flame ball. Lean H₂/air mixtures are investigated using a time-dependent, spherically symmetric code with detailed chemistry, transport, and radiation submodels. Results show that outwardly propagating spherical flames can be ignited for hydrogen mole fractions X_H2 larger than ∼3.5%. Furthermore, assuming optically thin radiative heat loss, flame balls can be established from centrally ignited premixed spherical flames only within a narrow range of mixture compositions (i.e., ∼3.5% < X_H2 < ∼6.5%). For ∼6.5% < X_H2 ∼11%, flames propagate until radiative extinction, never evolving into flame balls, while for X_H2 > ∼11%, the expanding spherical flames develop asymptotically into planar propagating flames. These findings corroborate the experimental result that the range of mixtures within which flame balls have been observed is much narrower than that predicted by previous one-dimensional instability analysis of the flame ball, where it was shown that steady flame balls exist for 3.5% < X_H2 < 10.7%. The present simulation also shows that the dynamic transition from a spherically propagating flame to the flame ball controls the range of mixtures for which flame balls can be reached, with radiative loss being both the requisite mechanism for and the limiting mechanism against the dynamic transformation. Additional calculations show that the size of the flame ball is noticeably enlarged when radiative reabsorption is incorporated.