A numerical study of primary instability on viscous high-speed jets

A fully nonlinear model incorporating a weak viscous treatment has been developed to assess the time-dependent evolution of an axisymmetric liquid jet using a boundary element method. Prior research has indicated the importance of the boundary layer structure at the orifice exit plane in generating instabilities just downstream of the injection point. By focusing on the boundary layer instability mechanism, simulations are compared against the experimental results and linear theory. In order to assess viscous effects, the weak viscous method of Lundgren and Mansour is utilized and various parametric studies are performed. Results show that the boundary layer thickness is the dominant factor affecting the nonlinear wave growth near the exit plane of the orifice. Viscosity and surface tension are shown to play minor roles in the initial primary instability. The most unstable wavelength calculated by the model matches linear boundary layer instability theory reasonably well.