| In this paper,a physical model of a viscous annular liquid film spraying into a compressible θ-z composite airflow is established.The gas-liquid two-phase continuity equation and the Navier-Stokes equations,kinematic boundary conditions,additional boundary conditions,and dynamic boundaries Conditions,the dimension-dispersion criterion relationship and stability limit are obtained.Using MATLAB to write a program for numerical calculations to obtain the relationship between the surface wave growth rate of different parameters as a function of wave number kz,kθ.Finally,a linear stability analysis of the annular liquid film Rayleigh-Taylor wave(R-T wave)was performed.At the same time,the theoretical derivation part of the viscous annular liquid film jet into the compressible r-θ-z composite airflow is completed,and the dimension-dispersion criterion relationship and stability limit are obtained.According to the derivation of the dispersion relation,it can be known that when Taylor wave(T wave)does not exist,Rayleigh wave(R wave)still exists;when R wave does not exist,T wave does not exist.From the linear stability analysis,we can know that:(1)For R-T waves under compressible airflow,the surface wave growth rate of varicose is generally greater than that of sinuous.(2)Under general circumstances,the surface wave growth rate of the R wave ωr increases first and then decreases with the increase of the wave number kz,and there is a dominant surface wave growth rate ωr-dom and a corresponding dominant wave number kz-dom.For T waves,the surface wave growth rate ωr continues to decrease as the wave number kθ increases until it is zero.T wave that dominates the growth rate of surface waves locate kθ=0,which indicates that surface waves are the most unstable when there are only R waves and no T waves.Prove that the R wave is the main wave and plays a leading role in the fragmentation of the jet mass.But T wave together with R wave play an important role in the formation of discrete tiny satellite droplets on the jet surface.When the T-wave curve first increases and then decreases,the T wave that dominates the growth rate of the surface wave locate ke>0.It shows that in the case of both R wave and T wave,T wave and R wave together affect the fragmentation of the annular liquid film mass and the formation of satellite droplets.(3)In the case of only forward airflow and no rotating airflow,when the Mach number is small,the R wave is the main wave;when the Mach number is large,the R wave is no longer the main wave,and the T wave and the R wave will be against the liquid The fragmentation of the clumps and the formation of satellite droplets have an impact.In the case of no forward airflow,when the rotating gas-liquid flow velocity is relatively small or the rotating airflow Mach number is small,the R wave is the main wave;When the rotating gas-liquid velocity is large or the Mach number of the rotating gas is large,the influence of the T wave begins to appear,and the T wave turns into a main wave;In the case of a composite airflow,the effect of the T wave will begin to appear in advance at a smaller gas-liquid velocity ratio or a smaller airflow Mach number.The main wave conversion of R wave and T wave will be advanced.(4)When the forward or rotating gas-liquid flow rate is relatively small,the unilateral gas flow in the outer ring of the tissue is most conducive to the fragmentation of the annular liquid membrane.On the contrary,the gas flow on both sides of the inner and outer rings of the tissue is most conducive to the fragmentation of the annular liquid membrane.(5)Increasing the gas-liquid density ratio p will promote the fragmentation of the annular liquid film.(6)When Wel is small,the siphon effect of surface tension is the main factor affecting the cracking of the liquid film.The annular liquid film is more likely to crack as the surface tension increases,and the aerodynamic effect is small.When Wel is larger,the aerodynamic effect gradually appears with Wel increase,which promotes the fragmentation of the annular liquid film,and the surface tension in turn functions to stabilize the liquid film.(7)The increase of rigid vortex intensity Γj,and potential vortex intensity χj of the inner and outer rings will promote the fragmentation of the annular liquid film. |
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