A finite-volume based computational model for one dimensional, unsteady two fluid flow in a pipe

This paper describes a computational model based on finite volume method to model the two-phase flow that occurs in a standpipe. Both phases are treated as continuums. Pressure field, which is treated as common to both fluids, is obtained using the SIMPLE algorithm. Field variables are stored in a staggered-grid fashion; pressures are stored at the center of a cell while the velocities and void fractions are stored at the cell faces. Separate momentum equations are used to calculate the velocities for each phase and thus allowing slip. Pressure is assumed to be of the same value for both phases. It is assumed that the resistance due to the motion of the second fluid on the first is proportional to the velocity difference (slip velocity) between the fluids. At the beginning of a time step, pressure field is obtained by integrating the combined momentum equations for both fluids. This is followed by the solution of velocity field for both fluids. Void fractions for both fluids are obtained at each cell by imposing the continuity condition at that cell. Then a cell-wise pressure correction is carried out based on the overall continuity error in that cell. Using the model, quantitative predictions are made on the influence of the friction factor between the two phases on the settling time of the heavier phase.