A two-fluid model for critical vapour-liquid flow

One-dimensional two-fluid equations are used to calculate the mass flux of initially saturated or subcooled water discharging from a pipe in critical flow. The model allows in a general way for thermal non-equilibrium between the liquid and vapour bubbles, and for interphase relative motion. The theory is shown to be in good agreement with the measured critical flow-rates of pressurised water over a wide pressure range for a single choice of parameters characterising (i) the density of nucleation sites in the liquid, (ii) the liquid superheat required to cause bubble nucleation. Predictions are made of the critical mass flux of initially saturated water in pipes of the range of sizes of interest in water-reactor blowdown safety analysis. Results indicate that for pipes up to ten diameters in length flows will be significantly higher than values obtained from conventional homogeneous thermal equilibrium flow theory.