Theoretical prediction of flooding velocity in an inclined tube based on viscous Kelvin-Helmholtz instability

Flooding velocity is the upper limit for normal operation of industrial equipment containing countercurrent gas-liquid flow. Nevertheless, predictions for flooding gas velocity are mostly empirical or semi-empirical summarized from experiments. This paper performs the viscous Kelvin-Helmholtz instability analysis with a simplified one-dimensional model. The maximum amplification factor is deemed as the growth rate of the most dangerous waves which can trigger flooding after that the countercurrent flow in an inclined tube becomes unstable. The predicted flooding velocities for both water-air and cryogenic liquid nitrogen-nitrogen vapor are found to satisfactorily accord with both our experimental data and others׳ from available publications. Accordingly, the influences of fluid properties and geometrical parameters on flooding velocities are investigated. The results reveal that surface tension acts as a stabilizing force and cannot be ignored. Smaller liquid viscosity, bigger inclination and larger diameter can all delay the occurrence of flooding respectively, leading to a larger critical gas velocity at a given liquid velocity.