Analysis of pulsating spray flames propagating in lean two-phase mixtures with unity Lewis number

Pulsating (or oscillatory) spray flames have recently been observed in experiments on two-phase combustion. Numerical studies have pointed out that such front oscillations can be obtained even with very simple models of homogeneous two-phase mixtures, including elementary vaporization schemes. The paper presents an analytical approach within the simple framework of the thermal-diffusive model, which is complemented by a vaporization rate independent of gas temperature, as soon as the latter reaches a certain thermal threshold (θv in reduced form). The study involves the Damköhler number (Da), the ratio of chemical reaction rate to vaporization rate, and the Zeldovich number (Ze) as essential parameters. We use the standard asymptotic method based on matched expansions in terms of 1/Ze. Linear analysis of two-phase flame stability is performed by studying, in the absence of differential diffusive effects (unity Lewis number), the linear growth rate of 2-D perturbations added to steady plane solutions and characterized by wavenumber k in the direction transverse to spreading. A domain of existence is found for the pulsating regime. It corresponds to mixture characteristics often met in air-fuel two-phase systems: low boiling temperature (θv≪1), reaction rate not higher than vaporization rate (Da<1, i.e., small droplets), and activation temperature assumed to be high compared with flame temperature (Ze⩾10). Satisfactory comparison with numerical simulations confirms the validity of the analytical approach; in particular, positive growth rates have been found for planar perturbations (k=0) and for wrinkled fronts (k≠0). Finally, comparison between predicted frequencies and experimental measurements is discussed.