Study On Nonlinear Stability Of Circular Liquid Jet Multi-level Surface Wave

In this paper,the nonlinear physical model of non-viscous circular jet injection into the uncompressible axial flow is established.The continuity control equation,kinematics and dynamic boundary conditions of nonlinear dimensionalization are derived,and then The expression of the apparent complex circular frequency and surface wave amplitude of the secondary wave varicose waveform is deduced.Draw the waveforms of the first and second wave,as well as the waveforms and crests of the first and second wave waveforms.The results show that:?1?Due to the ordinate symmetry of hyper cosine cosh,the positive and negative of the growth rate of surface wave ???_i1 have no effect on the numerical calculation results.?2?Under the condition of the same input parameters and low liquid viscosity,The numerical results of the nonlinear explicit growth parameters-the dominant surface wave growth rate ???_i1-dom,the fluctuation term parameters-the dominant ???_{r 1-dom} 1-dom and dominant wave numbersk_1-dom,The result of Gaster transformation is almost the same as that of the linear implicit Temporal dispersion criterion obtained by Muller's method,which can be substituted to simplify the calculation process.?3?The amplitude of the secondary wave is smaller and increases with time.?4?the primary wave will cause the circular jet to fragment.Since the amplitude of the secondary wave is too small compared with that of the primary wave,it will have almost no effect on the fragmentation time and the fragmentation length after superposition.Therefore,the primary wave will dominate the fragmentation of the circular jet,whereas the secondary wave will only play a major role in the formation of satellite droplets around the circular jet.