Large-eddy simulation, convective instability, and modal causality of coaxial supersonic air–water jets considering a swirl effect

An annular liquid sheet sheared by a coaxial supersonic gas stream with a swirling effect is investigated using Large Eddy Simulation. Despite its wide applications in aerospace and medical devices, the instability and spatial characters have been barely investigated due to the high complexity under supersonic condition. Unlike the conventional use of the temporal dynamic mode decomposition (DMD), DMD is applied in the axial direction to evaluate the transient convective instability. The high-velocity cases show significantly stronger instability in the nozzle near-field. However, swirling has only marginal effects on the convective instability. In addition, proper orthogonal decomposition (POD) extracts the essential spatial topology of velocity, momentum, and pressure fields. Pulsatile and flapping instabilities are observed in the gas flow, where liquid flow demonstrates the schrink/expansion as well as the flapping instabilities. In addition, all POD modes of the pressure field take the form of coherent wavepacket structures, and their wavelength and spatial forms of the wavepackets are dependent on the gas flow speed rather than the swirling. Time coefficients of the leading POD modes of momentum and pressure fields show an interesting correlation. Hence, the causal–effect relationship between these leading modes of momentum and pressure field is quantified via transfer entropy from the information theory. The transfer entropy from the pressure field to the momentum field is generally higher than vice versa, and this trend is enhanced by the swirling in the low-velocity condition.