Analysis Of Rayleigh-Taylor(R-T) Surface Wave Linear Stability For Circular Jet

In this paper,a two-dimensional composite airflow model of θ-z direction and a three-dimensional composite airflow of r-θ-z direction are set up.Linearization and dimensionalization of the continuity equations and the Navier-Stokes equations,kinematic boundary conditions,additional boundary conditions,and dynamic boundary conditions are derived,and the dispersion criterion relationship is derived.The numerical calculation of the dispersion criterion relation was performed using MATLAB software,and the stability analysis of the numerical calculation results was obtained,and the following conclusions were obtained:（1）The derivation of the stability limit shows that when the T wave does not exist,the R wave still exists;but when the R wave does not exist,the T wave no longer exists.Therefore,the R wave is the primary wave and the T wave is the secondary wave.The R wave plays a leading role in the fragmentation process of the liquid film.（2）For the R wave,the surface wave growth rate?（?）_r increases first and then decreases with the increase of the wave number （?）_z.There is a dominant surface wave growth rate?（?）_r-domand a corresponding dominant wave number （?）_z-dom.For T wave,the dominant surface wave growth rate?（?）_r-domis located at k_θ=0,which indicates that the surface wave is the most unstable when there is only R wave and no T wave.It proves again that R wave is the main wave,and the fragmentation of the jet mass Plays a leading role.When k_θ>0,there are both R waves and T waves.Although the T wave cannot increase the instability of the jet clumps,it together with the R wave plays an important role in the formation of discrete tiny satellite droplets on the jet surface.（3）The surface wave growth rate decreases slightly with the increase of the liquid flow Weber number We_l and Reynolds number Re_l,and then increases significantly,with the increase of the gas-liquid velocity ratio （?）_z and （?）_θ,the gas flow Mach number Ma_zg,and the gas-liquid density ratio （?）.（4）Regardless of whether there is only axial airflow or only rotating airflow or composite airflow,as the order n increases,the surface growth rate decreases slightly,the jet tends to stabilize,and the probability of occurrence decreases.（5）The growth rate of surface waves with only axial airflow is greater than the growth rate of surface waves with rotating airflow only;under composite airflow conditions,the effect of axial airflow on surface wave stability is greater than that of rotating airflow.（6）With the increase of Ma_zg and Ma_θg,the growth rate of R-wave and T-wave surface waves,the growth rate of dominating surface waves,the number of dominating waves,and the number of truncated waves all increase.Under the condition of compressible air flow with Ma_zg>0.3,the growth rate increases significantly.（7）With the increase of the strength of the rigid eddy current and the potential eddy current,the growth rate of the R wave and the T wave of the varicose wave and the sinuous wave both increase,and the liquid beam becomes more unstable.