Effect of gas-liquid axial velocity continuity on the axisymmetric and asymmetric instabilities of a viscoelastic liquid core in a swirling gaseous co-flow

When liquid jets eject into a co-flowing gas stream with unequal velocities, the axial velocity discontinuity between the two phases may cause jet instability; it then moves into the surface-driven instability with the gas-liquid axial velocity continuity. This paper expands the issue to include instability of a three-dimensional viscoelastic liquid jet subjected to a swirling gas. In the solid-body-rotation gas velocity profile, the dispersion relationship was obtained by conducting a linear instability analysis in the temporal mode. Results showed that a viscoelastic liquid jet can behave with greater instability than its Newtonian counterpart. Liquid elasticity is a destabilizing factor, while liquid viscosity and deformation retardation time enhance the stability of viscoelastic jets. In an axisymmetric jet, the liquid Weber number has no influence on jet instability with gas-liquid axial velocity continuity; however, the liquid Weber number makes the jet more unstable when a gas-liquid axial velocity discontinuity exists. Gas density stabilizes the jet while destabilizing it in situations both with and without axial velocity continuity, respectively. Further investigation indicated that gas-liquid axial velocity discontinuity can enhance the effects of flow parameters on jet instability. With large swirl strength, the asymmetric mode can prevail over its axisymmetric counterpart and dominate jet instability. The solid-body-rotation profile has a more significant effect on instability of viscoelastic liquid jet with gas-liquid axial velocity discontinuity than a free-vortex profile; however, these two velocity profiles have an identical effect on velocity continuity.