Nonlinear Stability Analysis Of Plane Viscous Liquid Film In A Stationary Air Medium

Spray and atomization in internal combustion engine working process are foundation of liquid fuel mass and energy transfer. Arrange spray and atomization at a proper time can improve ICE's efficiency. Study on disintegration is one of the most important and difficulty directions and still in developing. Using nonlinear stability theory to study absolute model that plane viscous liquid film spray into compressible airstream on the base of Reynolds equation is ultimate objective.My supervisor Prof. Cao Jianming derived nonlinear dimensionless dispersion relations of viscous liquid wave from viscous nonlinear Navier-Stokes equations and boundary control equations in which the mass conservation equation is linear while the momentum conservation equation is nonlinear and nonlinear perturbed velocity of convection is retained. So it can be used for nonlinear stability study of viscous vortex spray. This paper based on the nonlinear dimensionless dispersion relations in a stationary air medium, programmed to computation with Fortran language and got numerical solutions with Miller method. The results showed that with the increase of axial displacement x , the wave number k and the wave growth rateωr decreased. This suggested that liquid film breakup length is shorted with wave growth rate increased which can be effectually used to evaluate stability liquid film breakup process.According to numerical computation curves and disintegration conditions, we analyzed stability of plane viscous liquid film moving in a stationary air medium and foundω_r/ Rel,ω_r/ Welandω_r/ Eulcan be used to evaluate stability in a low velocity Rayleigh spray region.ω_r/ Relandω_r/ Weldecreased with the increase of velocity U l or half water film thickness a whileω_r/ Eul had a contrary tendency. When half water film thickness a remained constant, there is every group of (ω_r/ Rel)b,(ω_r/ Wel)b and (ω_r/ Eul)b in every axial position. Decrease velocity U lor a andω_r/ Rel,ω_r/ Welare greater than (ω_r/ Rel)b,(ω_r/ Wel)b whileω_r/ Eul is smaller than (ω_r/ Eul)b, the water film will break up and vice versa. Water film is prolonged and break up untilω_r/ Rel,ω_r/ Wel andω_r/ Eulreached another smallerω_r/ Rel,ω_r/ Weland bigger (ω_r/ Eul)b.