A Reduced Nonlinear Model for the Simulation of Two Phase Flow in a Horizontal Pipe

In the last 10 years many 3D numerical schemes have been developed for the study the flow of a mixture of liquid and gas in a pipeline (Frank, Numerical simulation of slug flow regime for an air-water two-phase flow in horizontal pipes. In: The 11th international topical meeting on nuclear reactor thermal-hydraulics (NURETH-11), Avignon, 2005; Vallée et al., Nucl Eng Des 238(3):637–646, 2008; Höhne, Experiments and numerical simulations of horizontal two-phase flow regimes. In: Proceeding of the seventh international conference on CFD in the minerals and process industries, Melbourne, 2009; Bartosiewicz et al., Nucl Eng Des 240(9):2375–2381, 2010) but although they offer a very good accuracy, they are rarely fit for modelling a long pipe, due to the high computational costs. Then one is usually led to consider 1D models, see e.g. the works of Issa and his group (Issa and Kempf, Int J Multiphase Flow 29(1):69–95, 2003). Such models offer much faster simulations than 3D schemes, on the other hand they almost completely miss the dynamics in the transversal direction. Here we present a model able of representing the full 3D dynamics, but with the computational cost typical of 1D simulation. The main feature of our model consists in describing the dynamical variables in the direction transversal to the pipe by means of a family of functions depending on a set of parameters. The model is then solved by a standard finite volume scheme.