A gas turbine combustor will act in a desired way only if its components, specially the fuel injector perform satisfactorily producing fine homogeneous droplets. Stability analysis of liquid, a rich classical fluid mechanics problem, when applied to fuel injector studies can enhance our knowledge leading towards the design of an advanced efficient atomizer. In this work, we analyzed the instability of a swirling annular liquid, exposed to co-flowing inner and outer air streams, by a temporal linear stability analysis using perturbation method. This temporal analysis discusses the effect of liquid Weber number, liquid swirl strength, both inner and outer gas-to-liquid velocity ratio and outer air gas swirl strength on the growth rate of interface instability. Another interesting inclusion in this work is the effect of confinement of the outer air stream which leads to a finite thickness of the outer air stream. Our results show a higher optimum growth rate obtained at a higher axial wave number in the presence of confinement compared to that when the outer air stream extends to infinity. This leads to the formation of smaller droplets which increases the efficiency of atomization. A comparative study between different helical modes revealed that the helical modes are dominant compared to the axisymmetric mode in presence of outer air swirl, whereas reverse phenomenon occurs in its absence.

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