Linear Stability Analysis Of An Annular Liquid Sheet Issued Into Compressible Gas Streams

In this paper,the theory of linear stability is used to study the breakup process of an annular liquid sheet entering compressible gas environment.Based on the gas-liquid Navier-Stokes equation(N-S equation),we obtain the differential equation of the liquid phase and the gas phase by dimensionalization and linearization,and the solution of the liquid phase and the gas phase differential equation is found by using the properties of the modified Bessel equation.To derive the dispersion relation of the annular liquid sheet into compressible gas stream,the linearized kinematics and dynamic boundary conditions are used to combine the solution of gas phase and liquid phase differential equation.This dispersion relation explains the function relation between surface wave growth rate (?)r and surface wave number(?).Seen from the dispersion relation,the factors influencing the breakup of the annular fluid sheet are the velocity ratio of the inner and outer gas mediums (?)j,the ratio of gas-liquid density (?)j,the liquid Weber number Wel,the Reynolds number of liquid flow Rel,and the Mach number of the inner and outer air flow Magj etc.In order to study the influence of different flow parameters on the surface wave growth rate,it is necessary to conduct programming and numerical calculation work regarding to the derived dispersion relations.According to the numerical calculation on the annular liquid sheet fracture process,the following conclusions are obtained:1.Under the condition of high liquid Weber number,the para-sinuous wave dominates the breakup of annular liquid sheet;but with the increase of the number of liquid Weber,the para-varicose wave has the same influence as the para-sinuous wave.2.With the increase of gas-liquid velocity ratio,the surface wave growth rate decreases firstly and then increases,and one of the most important factors affecting the liquid sheet breakup is the difference of gas and liquid velocity.3.In order to achieve better atomization effect,when the air velocity is less than twice of the liquid velocity,the effect of air flow on the outer liquid sheet side is greater than the inner side,and when the air flow is greater than twice of the liquid velocity,the effect of air flow on the inner side of the liquid sheet is greater than the outer side.4.When the velocity ratio of gas and liquid is small,the impact factors of liquid sheet breakup is the sum of inside and outside gas-liquid disturbance,but when the velocity ratio of gas and liquid is larger,the influencing factors of liquid film breakup is one of the inner and outer sides which owns larger airflow disturbance,and is not affected by airflow with smaller disturbances.5.For air-assisted atomizers,when the airflow velocity is less than two times of the liquid flow velocity,the atomization is desirable when the airflow velocity approachs to zero,but when the airflow velocity is larger than two times of the liquid flow velocity,the higher the airflow velocity,the better the atomization effect.6.When the inner and outer sheet sides have no aerodynamic effect,the liquid flow Weber number has a stabilizing effect on the liquid sheet,and the gas-liquid density has an inhibitory effect on the breakup of the liquid sheet.However,when the inner and outer sheet sides have the aerodynamic effect,in the small Weber number range,the fluid flow Weber number plays a stabilizing role in the liquid sheet,while in the large Weber number range,the fluid flow Weber number promotes the rupture of the liquid film,and the gas-liquid density promotes the breakup of the liquid sheet when there is aerodynamic effect.7.The liquid Reynolds number has an inhibitory effect on the rupture of the liquid sheet,and the Mach number of the airflow has a promoting effect on the breakup of the liquid sheet.8.The higher the airflow velocity,the greater the different between the compressible model curve and the incompressible model curve.This proves the importance of the study on the annular liquid sheet breakup process under compressible model.9.When the thickness of the liquid film is constant,the outer diameter of the nozzle has an inhibitory effect on the rupture of the liquid sheet,and the liquid sheet thickness can promote the breakup of the liquid film when the outer diameter of the nozzle is constant.