Stability analysis of stratified two-phase liquid-gas flow in a horizontal pipe

This study aimed at linear stability analysis of the stratified two-phase liquid-gas flow in a horizontal pipe. First, equations governing the linear stability of flow in each phase and boundary conditions were obtained. The governing equations were eigenvalue Orr Sommerfeld equations which are difficult and stiff problems to solve. After obtaining the velocity profiles of the gas and liquid phases in the pipe, the instability equations for each phase with related boundary conditions were coupled and simultaneously solved by using the Chebyshev Tau - QZ polynomial method. The instability spectra for some points has been plotted and some curves about instability conditions the same as neutral stability curve which shown stable and unstable region respect to Reynolds number had been drown. According to the neutral stability curve for each phase, the liquid phase is more exposed to instability than the gas phase. The liquid phase was unstable in low Reynolds numbers and a large amplitude of the wave velocity α but gas was unstable in higher Reynolds number and small amplitude of α.