Linear and nonlinear instabilities of a co-current gas-liquid flow between two inclined plates analyzed using the Navier–Stokes equations

Abstract

The paper is devoted to a theoretical analysis of a co-current gas-liquid flow between two inclined plates. As a first step, we linearized the Navier-Stokes equations in both phases and carried out a linear stability analysis of the basic steady-state solution over a wide variation of the liquid Reynolds number and the gas superficial velocity. We obtained two modes of the unstable disturbances and computed the wavelength and phase velocity of their neutral and the fastest growing disturbances varying the liquid and gas Reynolds number. The first mode corresponds to the Kapitza's waves at small values of the gas superficial velocity. The second mode of the unstable disturbances corresponds to the transition to a turbulent flow in the gas phase. We found that the co-current gas velocity destabilize the film flow at all values of the inclination angle and distance between the plates considered in the paper. The range of the wavelength of the unstable disturbances essentially increases with the gas velocity increasing. As a second step, we have performed the systematic study of nonlinear wave regimes. We found that the gas flow affects significantly the wave characteristics decreasing the amplitude and increasing the phase velocity. The complex multi-fold and multi-sheet surface, found on the plane of parameters (wavelength and the liquid Reynolds number) for the gravitational film flow, exists at all velocities of the co-current gas flow. We carried out investigation of the “optimal” waves for several folders and presented comparison with the regimes observed in experiments. Using of the strict equations without any additional assumptions is an important feature of this paper.