Effects of substituting fuel spray for fuel gas on flame stability in lean premixtures

We analyze flame propagation through a homogeneous three-component premixture composed of fuel gas, small fuel droplets, and air. This analytical study is carried out within the framework of a diffusional–thermal model with the simplifying assumption that both fuels—the fuel in the gaseous phase and the gaseous fuel evaporating from the droplets—have the same Lewis number. The parameter that expresses the degree of substitution of spray for gas is δ, the liquid loading, i.e., the ratio of liquid fuel mass fraction to overall fuel mass fraction in the fresh premixture. In this substitution of liquid fuel for gaseous fuel, the overall equivalence ratio is lean and is kept identical. We hence obtain a partially prevaporized spray, for which we analytically study the dynamics of the plane spray-flame front. The investigated model assumes the averaged distance between droplets to be small compared with the premixed flame thickness (i.e., small droplets and moderate pressure). Le, the Lewis number, Ze, the Zeldovich number, and δ are the main parameters of the study. Our stability analysis supplies the stability diagram in the plane { Le , δ } for various Ze values and shows that, for all Le, the plane front becomes unstable for high liquid loading. At large or moderate Lewis number, we show that the presence of droplets substantially diminishes the onset threshold of the oscillatory instability, making the appearance of oscillatory propagation easier. Oscillations can even occur for Le < 1 when sufficient spray substitution is operated. The pulsation frequency occurring in this regime is a tunable function of δ. At low Lewis number, substitution of spray for gas leads to a more complex situation for which two branches can coexist: the first one still corresponding to the pulsating regime, the other one being related to the diffusive–thermal cellular instability.