Study on 1-D critical flow model of supercritical CO$_2$ for safety analysis of the next generation nuclear system

Abstract

Supercritical carbon dioxide (S-CO$_2$) is being considered as a promising working fluid in nuclear power applications because it has interesting characteristics suitable for the next generation nuclear systems such as Small Modular Reactor (SMR). For the operation, management and safety of an S-CO$_2$ system, it is necessary to predict the critical flow rate under the supercritical carbon dioxide condition. Thus, it is necessary to develop a critical flow rate model suitable for S-CO$_2$. Most critical flow models developed by prior researchers are ideal gas equation or homogeneous-equilibrium model (HEM). However, in the S-CO$_2$ power cycle operating region, thermodynamic state ranges from the vicinity of supercritical point to the region where condensation occurs. Therefore, it is necessary to develop a model that can consider non-equilibrium effects. In this thesis, a non-equilibrium model is developed based on the 1-D analytical critical flow model, which has low computational cost and good applicability to the existing nuclear thermal hydraulic system safety analysis code. Moody's slip ratio is adopted for mechanical non-equilibrium, and a new thermal non-equilibrium correlation for supercooling is proposed for thermal non-equilibrium. To systematically evaluate the developed model, a critical flow experiment using an orifice is conducted to expand the range of previously published data. From the evaluation with newly obtained data as well as data available in the open literature, the validity of the developed non-equilibrium model and 1-D analytical critical flow model is confirmed under the S-CO$_2$ system operating conditions. In addition, discharge coefficients of an orifice required for both models are recommended. The impact of the critical flow model is examined by modifying a nuclear system analysis code, MARS. Pre-designed S-CO$_2$ systems, KAIST-MMR and ATOM-sCO$_2$, are analyzed. In the case of KAIST-MMR, no significant change in safety margin with respect to the change of the critical flow model is observed due to sufficient heat removal performance of the system. In the case of ATOM-sCO$_2$, a notable change in MDNBR safety margin is observed due to the change in the critical flow model. From the safety analysis results, it can be confirmed that the critical flow model affects the system’s transient behavior, but the degree to variation in safety margin depends on the design characteristics and the type of accidents.