Linear instability of an annular liquid jet with gas velocity oscillations

Pressure fluctuation produced in liquid rocket engines affects atomization of the annular liquid jet in the combustion chamber. A linear stability analysis of an annular liquid jet under acoustic oscillations was conducted in this work. Parametric instability was applied to study the problem, and the oscillations of the gas velocity were considered. The Floquet theory was used to solve the disturbance, from which the dispersion equation containing the coefficients of the infinite order matrix was derived; the order of the coefficient matrix affected the accuracy of the results. There were several unstable regions in the wavenumber range, obtained by solving the dispersion matrix. When the gas velocity oscillated, the amplitude of the surface wave displacement also oscillated. In various unstable regions, the growth of the surface wave of the annular liquid sheet was also different, but the crest never passed through the equilibrium position, which was more complicated than in the planar liquid sheet. Increasing oscillation frequency contributed to an increase in the wavenumber corresponding to the unstable area. Increasing the oscillation amplitude increased the maximum growth rate. The effect of physical parameters on the instability of the annular liquid jet was also discussed.