Journal of Fluid Mechanics


On transition to cellularity in expanding spherical flames

G. JOMAASa1, C. K. LAWa1 and J. K. BECHTOLDa2

a1 Princeton University, Princeton, NJ 08544, USA

a2 New Jersey Institute of Technology, Newark, NJ 07102, USA


The instant of transition to cellularity of centrally ignited, outwardly propagating spherical flames in a reactive environment of fuelx–oxidizer mixture, at atmospheric and elevated pressures, was experimentally determined using high-speed schlieren imaging and subsequently interpreted on the basis of hydrodynamic and diffusional–thermal instabilities. Experimental results show that the transition Péclet number, Pec = RcL, assumes an almost constant value for the near-equidiffusive acetylene flames with wide ranges in the mixture stoichiometry, oxygen concentration and pressure, where Rc is the flame radius at transition and ℓL the laminar flame thickness. However, for the non-equidiffusive hydrogen and propane flames, Pec respectively increases and decreases somewhat linearly with the mixture equivalence ratio. Evaluation of Pec using previous theory shows complete qualitative agreement and satisfactory quantitative agreement, demonstrating the insensitivity of Pec to all system parameters for equidiffusive mixtures, and the dominance of the Markstein number, Ze(Le – 1), in destabilization for non-equidiffusive mixtures, where Ze is the Zel'dovich number and Le the Lewis number. The importance of using locally evaluated values of ℓL, Ze and Le, extracted from either computationally simulated one-dimensional flame structure with detailed chemistry and transport, or experimentally determined response of stretched flames, in the evaluation of Pec is emphasized.

(Received April 29 2006)

(Revised January 07 2007)