Thermo-diffusive and hydrodynamic instabilities occur in premixed gas flames and result in cellular, pulsating, traveling wave, complex and chaotic spatio-temporal flame structures and dynamics. More often than not, these instability mechanisms are coupled and may lead to extraordinarily complex flame dynamics. This paper explores numerically the two-dimensional temperature and species distributions owed to reactive-diffusive couplings, neglecting the hydrodynamic instability in an effort better understand the occurrence of target and spiral wave patterns observed in high-Lewis number premixed gas combustion.

Using the reactive-diffusive Sal'nikov model, taken from the work of Scott, Wang, and Showalter [1] as a baseline, the species conservation and energy balance equations are solved numerically including diffusive fluxes of heat and species. The roles of: (1) diffusive fluxes (i.e., Le), (2) heat loss to heat generation ratio, (3) initial reactant concentration and initial temperature as well as (4) reactant consumption are numerically explored, extending the work reported in [1]. Additionally, the interaction between multiple counter-propagating wave fronts is studied. In a bulk medium near extinction, it is perhaps possible that local oscillations ("pacemaker sites") may occur at different spatial locations each with a different characteristic frequency, local temperature and local species distribution. These oscillatory inhomogenieties can propagate into the bulk mixture through diffusional couplings, thereby inducing multiple interacting waves. The waves may annihilate one another when they interact due to reactant consumption, the waves induced by the faster "pacemaker" may engulf those induced by the slower pacemaker(s), and complex patterns result.

[1] Scott, S. Wang, J. and Showalter, K. "Modelling studies of spiral waves and target patterns in premixed flames," J. Chem. Soc., Faraday Trans., 1997, 93(9), 1733.