Study On The Linear Instability Of The Convective And Absolute Modes Of Primary Atomization Of Plane Liquid Film

The analysis of the fragmentation mechanism of the plane liquid film is the basis for the study of typical jets.In power machinery,the plane liquid film nozzle can be applied to diesel spray in the combustion chamber of continuous working engines such as gas turbines.The quality of the spray directly affects the combustion efficiency of the engine,and then affects its power performance,economy and emission performance.In the theoretical research on the linear instability of jet fragmentation,there are more studies on temporal mode,less on convective mode and absolute mode,and less on the conversion relationship between the three modes.The theoretical system of spray research is not complete yet,and the research methods need to be improved.In this paper,based on the study of the linear instability of the temporal mode,we analyze the linear instability of convective mode and absolute mode of the plane liquid film Rayleigh wave,and compare them with temporal mode.First,we define and divide the surface wave disturbance amplitude expressions of the three modes used internationally,and analyze the parameter relationships between the modes and the mutual conversion mechanism.By introducing the concepts of group velocity and phase velocity,the coordinate transformation of the vertical and horizontal coordinates of the absolute mode’s curve graph can be carried out,and the three-dimensional surface graph can be replaced by the three-dimensional curve graph.From this,the efficiency of numerical calculation is improved.After improving the research methods,we need to establish the physical models of convective mode and absolute mode,and then study and derive the dispersion relation and stability limit.After that,we compile the Fortran language numerical calculation program,use the Muller iteration method to calculate the dispersion relation,and plot the surface wave growth rate curve of convective mode and absolute mode.Finally,the linear instability analysis can be carried out.The main conclusions are as follows:(1)In the case of large Weber number and low gas-liquid density ratio,the surface wave growth rate curves of convective mode almost coincide with those of temporal mode,while in the case of small Weber number and high gas-liquid density ratio,the surface wave growth rate curves of the two modes are different.It is shown that the temporal domain characteristics of surface waves at the gas-liquid interface are similar to those in the spatial domain.(2)For absolute mode,by drawing the f(-ωi,ωr,kr)=0 curve of the surface wave growth rate on the temporal axis and the f(-ki,ωr,kr)=0 curve of the surface wave growth rate on the spatial axis,we found that in the case of low gas-liquid density ratio and large Weber number,no matter whether the physical parameters of the fluid change or not,the temporal axis and spatial axis surface wave growth rate curves are almost exactly the same in changing trend and numerical value.The three-dimensional curve of absolute mode is located at the angle of 45° on the plane of wave number ωr-kr.The temporal domain characteristics of the jet surface wave are equivalent to the spatial domain characteristics,and their manifestations are similar.However,under high gas-liquid density ratio and small Weber number,the temporal axis surface wave growth rate curve is separated from the spatial axis surface wave growth rate curve,and the temporal domain characteristics and the spatial domain characteristics are no longer balanced.The characteristic frequency corresponding to the growth rate of the temporal axis surface wave becomes smaller and the wave number becomes larger.The characteristic frequency corresponding to the growth rate of the spatial axis surface wave becomes larger and the wave number becomes smaller.The vector vg1 and vg2 of the mean group velocity does not necessarily point to the 45° angle of the wavenumber plane,but the functional relationship(?)and(?)with the critical wavenumber and the cutoff wavenumber still exists.The highest point of the surface wave growth rate curve on the temporal axis and spatial axis is the special case of temporal mode and convective mode.The growth rate of surface wave on the temporal axis and spatial axis shows a trade-off relationship,one increases,the other decreases,and vice versa.The two ends of the three-dimensional curve of absolute mode will extend downward through the critical wavenumber point and the cut-off wavenumber point located in the zero plane,and enter the stable area of the jet to reach the stable state.As-(?)i/-(?)i increases,-(?)i/-(?)i decreases,and the part of absolute mode curve located in the unstable region decreases,while the part located in the stable region increases.(3)The difference of gas-liquid velocity ratio on both sides of liquid film,gas-liquid density ratio,liquid Reynolds number,Weber number,Euler number and gas Mach number are the instability factors of plane liquid film fragmentation.With the increase of temperature,the kinematic viscosity coefficient and surface tension coefficient of the liquid decrease,and the instability of the plane liquid film increases.At the same temperature,the surface tension coefficient of diesel is smaller than that of water,while the kinematic viscosity coefficient is larger than that of water.The surface wave growth rate of diesel film is larger than that of water film,and the diesel film is more easily broken than water film.Compared with viscosity,surface tension has a greater influence on the instability of plane liquid film.