Dispersion Relation For Viscose Annular Liquid Film Jet In Inner And Outer Gas Stream With Different Velocity

Annular liquid film jet is a tubular beam cone annular liquid membrane. The researchabout it is an important part of the analysis of the atomization process in the diesel enginesand a hot research project in international fluid and combustion fields. Diesel axle-needle jetnozzle works according to the principle of annular liquid film jet, which spraying process iscomplex and effect is unsatisfactory because of the interference of surrounding air.The atomization and breakup of annular liquid jet are of significant importance for thestudy on the science of engine atomization and combustion. The linear stability theory is animportant method for studying on circular liquid jets disintegrated process. To study thefracture process of annular liquid jet into the incompressible gas medium, this paperestablished respectively gas and liquid phase Navier-Stokes equation (it’s the conservation ofmomentum equation and continuity equation), made the control equations linearization, andmade the control equations and boundary conditions dimensionless.For the spatial axle-symmetric two-dimensional flow liquid membrane, for example,annular liquid jet, this paper added the flow function introduced into theadditional boundary condition equation and built Bessel’s equation, then added the analyticsolution into the kinematic boundary conditions and the dynamic boundary conditions, andobtained respectively inner and outer rings dispersion relations of surface wave on thegas-liquid interface.Meanwhile, the paper combined the gas and liquid phase dispersion relations, got surfacewave dispersion relations of varicose, sinuous, para-varicose and para-sinuous, and gotamplitude ratio of surface wave i oon the inner and outer rings gas-liquid interface andphase angle parameter of surface waveei on the gas-liquid interface in the conditions ofpara-varicose and para-sinuous. Finally, according to dispersion relations of the fourwaveforms, the stability limit was obtained, which is the biggest wave numberk0when thegrowth rate of surface wave r0.