Non-modal analysis of transient growth in a liquid annular jet surrounded by gas flow

Transient energy growth is a common mathematical concept in many fluid flow systems, and it has been widely investigated in recent years using non-modal analysis. Non-modal analysis can characterize the short-term energy amplification of perturbations, which is influenced by the Reynolds number, the Weber number, and the initial conditions such as the wavenumber. In gas–liquid coaxial nozzles, annular jets are often produced, and their breakup process is influenced by transient energy growth. However, research in this area has been limited so far. This paper for the first time investigates the transient energy growth of an annular liquid jet in static gas and validates it using a modified annular jet model. In the derivation process, the gas–liquid interfaces inside and outside the annular liquid film are taken into account. It has been found that there exists an optimal initial condition for a certain Reynolds number and a Weber number. The increase in the Reynolds number and ratio of inner and outer radius of the annular jet can maximize the transient growth under a specific initial wavenumber, while the increase in gas/liquid density ratio and the Weber number will minimize the transient growth. It is also found that transient energy growth is caused by the displacement of the free boundary.