An accurate prediction of a critical flow discharged from a pressurized pipe system is of most importance in such a safety analysis of nuclear power plants, since it provides the transient boundary conditions during the depressurization transients initiated by a pipe break in primary or secondary systems and during the over-pressurization transients resulting in a relief of coolant through valves. Mass and energy discharge through the opening of pressure boundary affects the system thermal hydraulic responses, that is, phase changes and flow distribution in the system, and the mass inventory remaining in the system necessary to remove core decay heat of a nuclear reactor. Therefore, the safety significance relating to the critical flow led to a development of various empirical and mechanistic critical flow models. However, the accuracies of these models are still in question especially during two-phase critical flow condition. A good example of that is a homogeneous equilibrium model (HEM). The HEM is the basis of several system codes, such as early versions of RELAP, for nuclear loss-of-coolant accident (LOCA). The major non-equilibrium phenomena that are ignored in the HEM are vapor bubble nucleation and interface heat, mass, and momentum transfer. Henry-Fauske empirically handled non-equilibrium vapor generation by introducing a non-equilibrium parameter that allows only a fraction of the equilibrium vapor generation to occur. This approach boils down in essence to a correlation of the deviation between the measured flow rate and the prediction from the HEM: The details of the flow path do not have to be worked out and only needs to know the upstream conditions. However, if we treat non-equilibrium phenomena with this model, it requires an empirical database of the non-equilibrium parameters or their correlations that are so far unknown. Further, because the coefficients are not applied separately to the subcooled liquid and two-phase mixture, we have not been able to treat the non-equilibrium phenomena with the phase change properly. For this reason, we propose the non-equilibrium parameters for subcooled liquid and two-phase mixture, respectively, and then we adopt their combinations according to the flow conditions through the phase change process using the RELAP5/MOD3 code. In addition, we discuss the assessment results of Marviken LBLOCA tests using these non-equilibrium parameter sets with those from the non-equilibrium model by Trapp-Ransom and Chung et al.
Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media
