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ABSTRACT: Two-phase gravity-driven and gravity-stratified flow regime inside a pipe, which is present in many engineering applications, is an attractive option for solar cooling/heating/power production using Rankine cycles, absorption cycles or any other thermodynamic application by means of vapor as working fluid. This paper offers a numerical model of this flow configuration that copes with transient phenomena, like unsteadiness of solar radiation, among others. The mathematical model consists of 1-D balance equations for mass and momentum for both fluids and energy for both fluids and the wall of the pipe that absorbs the solar radiation. The model is characterized by the fact that the area (or height) of the liquid layer is treated as a dependent variable forming part of the solution. The numerical method consists in a finite volume staggered grid discretization of the governing equations. Mass flow and liquid area are calculated with a semi-implicit pressure based method and the transient terms are treated with the explicit first stage singly implicit Runge-Kutta (ESDIRK) method. The calculation of the mass transfer rate from liquid to vapor is calculated iteratively by a guess-and-correct mass transfer algorithm, specially developed for stratified flows. The results show the applicability and benefits of this model for the not so well known counter-current stratified two-phase with evaporation/boiling. Additionally, the performance of the mass transfer algorithm is discussed showing that it is monotonic decreasing and linearly convergent.
1-d two-phase flows; runge-kutta methods; finite volume method; quasi-homogeneous model; solar collectors; direct steam production; gravity driven and stratified counter-current flow