Stability analysis of vertical annular flows with the 1D Two–Fluid Model: effect of closure relations on wave characteristics

Abstract

For several industrial applications involving two-phase gas-liquid flows, the one-dimensional Two–Fluid Model equations are typically solved for flow simulation. To ensure reliable predictions, it is very important to assess the stability properties and grid dependency of one-dimensional formulations, which are known to be largely affected by the closure relations and numerical schemes employed. In this work, a stability analysis of the transient one-dimensional Two–Fluid Model was performed for vertical annular flows. A viscous approach of differential and discretized formulations was analysed. The influence of the momentum flux parameter, interfacial pressure jump due to surface tension and a dynamic pressure model were investigated. The analytical results were compared to those obtained by numerical solution of the model equations with the Finite Volume Method, for various experimental configurations taken from the literature. Results showed that closure models largely affect the wave frequencies and the growth rates captured by the model. The surface tension term introduced a cut-off frequency in the differential formulation rendering the model well-posed and effectively stabilizing short waves. The introduction of the dynamic pressure term considered here did not affect the cut-off values. However, the wave growth rates decreased compared to the case without this term. The liquid momentum flux parameter greater than 1 presented a stronger influence on the evolution of interfacial waves in a broadband of frequencies than the other closures and leads to more regular waves and a more uniform flow field but much higher values may excessively damp the solution, which blocks the natural formation of larger waves in vertical annular flows. The numerical solution of the model equations showed very good agreement with the discrete stability analysis performed and was able to capture the wave frequencies and associated (linear) growth rates in the wave formation region. Concerning the momentum flux parameter, the bandwidth of the most damped disturbances in the linear and nonlinear region was similar. This suggests that the frequency response in this case was not very different from linear to nonlinear wave regimes. The methodology proved to be an important tool for further development of closure models and numerical schemes applied to vertical annular flows.