Energy-conserving formulation of the two-fluid model for incompressible two-phase flow in channels and pipes

We show that the one-dimensional (1D) twouid model (TFM) for strati ed ow in channels and pipes (in its incompressible, isothermal form) satis es an energy conservation equation, which arises naturally from the mass and momentum conservation equations that constitute the model. This result extends upon earlier work on the shallow water equations (SWE), with the important di erence that we include nonconservative pressure terms in the analysis, and that we propose a formulation that holds for ducts with an arbitrary cross-sectional shape, with the 2D channel and circular pipe geometries as special cases. The second novel result of this work is the formulation of a nite volume scheme for the TFM that satis es a discrete formof the continuous energy equation. This discretization is derived in amanner that runs parallel to the continuous analysis. Due to the non-conservative pressure terms it is essential to employ a staggered grid, which requires careful consideration in de ning the discrete energy and energy uxes, and the relations between them and the discrete model. Numerical simulations con rm that the discrete energy is conserved.

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