Numerical methodology for spontaneous wrinkling of centrally ignited premixed flames - linear theory

An improved embedded-manifold/Navier-Stokes numerical methodology is developed to simulate the propagation of premixed flames within the context of the hydrodynamic theory. The method is computationally tractable, permitting calculations to not only be extended to larger physical domains but also to span a broader parametric space of physicochemical parameters. The focus of this paper is to examine the susceptibility of centrally ignited, freely propagating and outwardly expanding circular flames to small amplitude disturbances and observe the flame's development through the onset of the hydrodynamic instability. The numerical simulations, validated by a linear stability analysis, show that for mixtures with Lewis numbers above criticality, thermo-diffusive effects exert stabilising influences which dominate at small flame radii, initially suppressing the growth of all disturbances. Consistent with the linear theory, simulations show the flame initially remaining stable and demonstrate the existence of a particular mode which is the first to grow. This mode is said to dictate the cellular pattern observed experimentally at the onset of instability. The variation in critical flame radius with respect to the Markstein length and thermal expansion coefficients are in quantitative agreement with these analytical results.