Scale model for investigating two-phase flow instability in a PWR passive residual heat removal system

Abstract

To design a scale model of a PWR passive residual heat removal system that preserves and controls the two-phase flow instability, defined as unstable oscillations of the condensate water level at the saturated steam/water interface in the vertical condensate pipe column, non-dimensional (Pi) groups were derived using the top-down (macroscopic) modeling approach known as the Buckingham Pi Theorem. Subsequently, the scaling ratios and scaling laws for the two-phase flow instability-related parameters of the system design—expressed in terms of the ratios of pipe length and diameter between the scale model and the full-size system—were derived based on the relationships between the Pi groups. The scaling ratios obtained for the parameters such as length, diameter, area, volume, time, oscillation frequency, mass flow rate, heat input, and pressure drop were compared with those derived from bottom-up (microscopic/fine structure) modeling approaches, including the three-level and hierarchical two-tiered scaling methods. As a result, the findings of this study align with those obtained using either the three-level or hierarchical two-tiered scaling method, except for the heat input (power) scaling ratio and the power-volume scaling ratio. From a dimensional similarity perspective, the present method appears to yield physically consistent values for the heat input and power-volume scaling ratios, which are defined as the product of the length scaling ratio and the corresponding scaling ratio derived from either the three-level or hierarchical two-tiered scaling method. Consequently, this study makes a significant contribution to engineering literature by demonstrating that the Buckingham Pi Theorem can establish scaling laws for designing a scale model to predict and interpret full-scale system behavior without requiring a comprehensive understanding of transient two-phase flow phenomena, unlike bottom-up approaches that necessitate detailed knowledge of the underlying phenomena.