The analysis of void wave propagation in adiabatic monodispersed bubbly two-phase flows using an ensemble-averaged two-fluid model

Abstract

A three-dimensional two-fluid model has been developed using ensemble-averaging techniques. The two-fluid model was closed for adiabatic two-phase bubbly flows using cell averaging which accounted for the dispersed phase distribution in the region of the averaging volume. The phasic interfacial momentum exchange includes the surface stress developed on the interface which is induced by the relative motion of the phases. The surface stress has been obtained by treating the interface as an elastic spherical shell. A characteristic analysis revealed that the one-dimensional system of two-fluid conservation equations which were derived is well-posed over a range of void fractions with increased value of the interfacial pressure. The propagation of void fraction disturbances (i.e. the void wave) has also been analyzed by performing a dispersion analysis. The speed, stability and damping of the linear void waves have been obtained. To study finite amplitude void waves, the system of equations has been transformed into a moving coordinate system, and asymptotic solutions of the transformed nonlinear void wave equation have been obtained. The speed and the stability of different types of nonlinear void waves have been found to be sensitive to the closure relations of the two-fluid model. Among the different constitutive parameters, the interfacial pressure difference in the continuous phase and the void fraction gradient in the non-drag force are found to be the most significant in determining behavior of void waves in bubbly flows. The derived void wave speed agrees well with the void wave data of bubbly air–water flow.