Numerical simulation of single-wave Kelvin-Helmholtz instability in two-phase channel flow

A major critical aspect of the modern injection systems of low Nox emission aeronautical combustors is the formation of the fuel liquid film and its subsequent break-up in the presence of air blast co-flow. The configuration under study in the present work refers to a stratified two-phase gas-liquid flow confined in a horizontal channel. Contrary to previous papers of the literature, where a parallel flow configuration is classically analyzed with plug velocity profile in both fluids, in the present paper the flow is spatially developing, starting from a plug-plug profile at the channel entrance. The sudden change of interface boundary condition produces the flow development and the emergence of a solitary Kelvin-Helmholtz wave, whose formation and evolution are numerically studied. Computer simulations are carried out by means of a home-made modified version of the SURFER code, which is based on the Volume of Fluid (VOF) technique. Two types of possible instabilities are detected. The most physically relevant one is due to non-linear amplification of finite-amplitude entrance disturbances linked to the sudden change of inlet boundary condition and manifests itself as the formation and propagation of a solitary Kelvin-Helmholtz wave. The second one is produced by the linear amplification of very small numerical disturbances generated by the so called spurious currents which may arise around the interface region not yet reached by the traveling wave.