One-dimensional three-field model of condensation in horizontal countercurrent flow with supercritical liquid velocity

Abstract A one-dimensional three-field model was developed to predict the flow of liquid and vapor that results from countercurrent flow of water injected into the hot leg of a PWR and the oncoming steam flowing from the upper plenum. The model solves the conservation equations for mass, momentum, and energy in a continuous-vapor field, a continuous-liquid field, and a dispersed-liquid (entrained-droplet) field. Single-effect experiments performed in the upper plenum test facility (UPTF) of the former SIEMENS KWU (now AREVA) at Mannheim, Germany, were used to validate the countercurrent flow limitation (CCFL) model in case of emergency core cooling water injection into the hot legs. Subcooled water and saturated steam flowed countercurrent in a horizontal pipe with an inside diameter of 0.75 m. The flow of injected water was varied from 150 kg/s to 400 kg/s, and the flow of steam varied from 13 kg/s to 178 kg/s. The subcooling of the liquid ranged from 0 K to 104 K. The velocity of the water at the injection point was supercritical (greater than the celerity of a gravity wave) for all the experiments. The three-field model was successfully used to predict the experimental data, and the results from the model provide insight into the mechanisms that influence the flows of liquid and vapor during countercurrent flow in a hot leg. When the injected water was saturated and the flow of steam was small, all or most of the injected water flowed to the upper plenum. Because the velocity of the liquid remained supercritical, entrainment of droplets was suppressed. When the injected water was saturated and the flow of steam was large, the interfacial shear stress on the continuous liquid caused the velocity in the liquid to become subcritical, resulting in a hydraulic jump. Entrainment ensued, and the flow of liquid to the end of the hot leg was greatly reduced. The influence of condensation on the transition from supercritical to subcritical flow as observed in the experimental data is also predicted with the three-field model. When the injected water was subcooled, condensation on the flow of continuous liquid caused a reduction in the flow of vapor and, consequently, a reduction in the interfacial shear stress. Therefore, the flow of liquid remained supercritical to the end of the hot leg at the upper plenum. The entire flow of injected water flowed to the end of the hot leg at higher flows of steam when the injected water was subcooled than when it was saturated. When the flow of vapor was large enough to cause a hydraulic jump in the subcooled liquid, the rate of entrained droplets was greatly increased. The interfacial surface area of the droplets was several orders of magnitude greater than for the continuous-liquid field, and condensation rate on the droplet field was also several orders of magnitude greater. When the flow of vapor from the upper plenum was at its greatest, most of the flow in the continuous liquid was entrained before reaching the upper plenum. The large flow of subcooled droplets caused three-quarters of the steam to condense.