Most unstable waves of a stagnant planar liquid film blown by a high speed viscous gas with a Blasius velocity profile

摘要

The linear most unstable waves generated on the surface of a stagnant planar liquid (gasoline) film with infinite thickness, blown by a high speed viscous gas (air) with a Blasius velocity profile, are computed and analyzed. The free-stream velocity of the gas ranges from 30 m/s to 50 m/s, which is typical of high speed atomization problems. The Reynolds number based on the local thickness of the boundarylayer lies between 200 and 2500. The numerical computation shows that the dimensional wavelength of the most unstable wave is a power functions of the boundary-layer thickness (or Reynolds number) with a power close to 3/4, while the growth rate is inversely proportional to the boundary-layer thickness. When reducing the boundary-layer thickness, the visocus results approach the inviscid results. This result shows that, under the present parameter range, the gas viscosity would have a secondary role on the atomization speed and important influence on the droplet size.