Numerical analysis of the temporal and spatial instabilities on an annular liquid jet

A numerical study of the temporal and spatial instabilities appearing on the interface of an annular liquid jet emerging from an orifice and flowing into a high pressure gas medium has been performed using Direct Numerical Simulation. The purpose of this study is to gain a better insight into the dominant mechanisms in the atomization of annular liquid jets during the start-up portion of the injection. The effects on the growth rate and wavelength of the emerging Kelvin-Helmholtz and Rayleigh-Taylor instabilities of various flow parameters have been investigated: the Reynolds and Weber numbers; fluids properties like gas-to-liquid density and viscosity ratios; and geometrical parameters involved in the problem such as thickness-to-diameter ratio of the liquid sheet. The Reynolds numbers used in this study are in the range from 3,000 to 30,000, and the Weber numbers are in the range of 6,000 up to 150,000. The convergence rate and length of the liquid jet has been also computed and compared for different cases. A characteristic convergence time has been proposed based on the obtained results. Use has been made of an unsteady axisymmetric code with a finite-volume solver of the Navier-Stokes equations for liquid streams and adjacent gas and a level-set method for the liquid/gas interface tracking.Two significant velocity reversals were detected on the axis of symmetry for all flow Reynolds numbers; the one closer to the nozzle exit being attributed to the recirculation zone, and the one farther downstream corresponding to the annular jet collapse on the centerline. The effects of different flow parameters on the location of these velocity reversals are studied. The results indicate that the convergence length and time increase significantly with the gas density and liquid viscosity and decrease with the liquid sheet thickness, while the effects of the gas viscosity and the surface tension are not so considerable.The range of unstable Kelvin-Helmholtz and Rayleigh-Taylor wavelengths have been also studied. The statistical data obtained from the numerical results show that, the average normalized wavelength of the KH instabilities decreases with the Reynolds and Weber numbers and the sheet thickness, and increases with the gas-to-liquid density ratio, and is independent of the viscosity ratio. The wavelength of the KH instabilities were observed to increase in time, except for the very thin liquid sheet, where the average KH wavelength oscillates between two values, indicating occurrence of different sheet breakup cycles. The sheet breakup times and lengths were reported up to the second sheet breakup, and it is shown that the later sheet breakups happen closer to the nozzle exit plane. The RT wavelengths tend to decrease during the start-up period of injection