Linear Stability Analysis on Free-Surface Liquid Jet with Different Simplification of Velocity Profile

Abstract

Free surface wave arisen from the shear layer instability on a liquid jet is investigated experimentally and theoretically. The stability analysis is conducted for initially laminar free-surface shear layer with different levels of simplification of velocity profile (i.e., numerical shear-layer profile separated from nozzle exit and two kinds of simplified velocity profiles obtained through linear and piecewise-linear fitting of numerical profile). It is shown that the linear perturbation equation has temporally-neutral, spatially-unstable solutions by substituting all kinds of local velocity profiles. On the other hands, the periodic two-dimensional waves on liquid jet are measured by using a laser beam refraction technique. The frequency of the most-unstable solutions shows fair agreement with the measured dominant frequency of free surface waves. The linear stability analysis can be simplified drastically by introducing linear or piecewise linear approximation of the velocity profile. Such simplification does not result in large discrepancy from the detailed-model, or experimental data, except in the initial region of the jet where arbitrariness exists in simplification of velocity profiles.

Keywords

• liquid jet
• shear layer instability
• free surface wave
• optical measurement
• linear stability analysis
• velocity profile