Analysis of two phase critical flow with a non-equilibrium model

Highlights: • A six-equation two phase critical model was developed. • The virtual mass force and the force for interfacial momentum transport were better implemented. • The prediction of the critical flow was in the range of −7% to +4% compared to measurements. Critical (choked) flow is a highly concerned phenomenon in safety analysis for nuclear energy. During the accident, a large amount of fluid with the aerosol in nuclear power plant (NPP), which are hazardous for environment, may be released accompanying the fluid discharge. The prediction of the amounts of discharge fluid is crucial for engineering design and emergency response in case of nuclear accidents. Unfortunately, the critical flow is difficult to predict especially when two phase flow exists. Based on the literature, a six-equation two phase critical model, which considers the interphase interaction terms for momentum, heat transfer and mass, was developed to allow the calculation of critical flow rates for steam-water mixtures. Certain constitutive correlations, which account for different flow regimes, were included into this model. New virtual mass force and the force for interfacial momentum transport were used in this model. The six equations used in this two phase critical flow model form a system of stiff ordinary differential equations (stiff ODEs), which were solved by using a variable step implicit Runge-Kutta procedure. Furthermore, the shooting method was used to split the given boundary value problem into several initial value problems, since the choked point of the discharge pipe for a given mass flow is not a-priori known (ODEs should be solved each time). The numerical results were then compared with the experimental data involving critical flows for different geometries (long pipe and orifice). It came out that the non-equilibrium model predicts well the critical flow rate, pressure distribution along the tube, and the tube outlet pressure. In addition, the errors made in the prediction of the critical flow are between −7% and + 4%, better than other models in literatures, most probably as a pay-back for the modification of the virtual mass force and of the force corresponding to the interfacial momentum transport. The choking process was understood more clearly by analyzing the main constitutive parameters, aspect with little payed attention in other works. This study contributes to a detailed understanding of the critical flow phenomenon and its results may be implemented into related code development (especially for system thermal hydraulics STH codes) and used for safety analysis.