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

Abstract

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 H 2 /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 larger than ϳ3.5%. Furthermore, assuming optically thin radiative heat loss, flame balls X H 2 can be established from centrally ignited premixed spherical flames only within a narrow range of mixture compositions (i.e., ϳ3.5% Ͻ Ͻϳ6.5%). For ϳ6.5% Ͻ Ͻϳ11%, flames propagate until radiativeextinction, never evolving into flame balls, while for Ͼ ϳ11%, the expanding spherical flames develop X H 2 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% Ͻ Ͻ 10.7%. The present simulation also shows that the dynamic transition from a X H 2 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.

Flame balls with thermally sensitive intermediate kinetics

“…Indeed, asymptotic and numerical predictions of some phenomena, such as the negative propagation speed of the flame edges [23][24][25][26] and the existence of stable flame balls [27][28][29][30][31][32][33], preceded and indeed motivated their observation experimentally [26,[31][32][33]. There is now a growing theoretical literature of flame-ball studies based on one-step chemistry [34][35][36][37][38][39][40][41][42], supplemented by numerical studies based on detailed chemical, transport and radiative models [43][44][45][46].…”

“…Several studies of flame balls using one-step kinetics have considered the relative importance and differing effects of non-linear radiative heat losses and linear heat losses, for example [30,38] and [44][45][46]. In dimensional terms, Stefan's law would give a rate of heat loss that is proportional to T 4 − T while it also has a maximum value of the order of (T 0 + T s ) 4 .…”