In this study, a trans-critical $CO_2$ cycle is designed and analyzed for evaluating the energy conversion cycle for a nuclear marine application. A concept of 13MWe Small Modular Reactor (SMR) system with a trans-critical $CO_2$ cooled direct Rankine cycle is designed for generating electricity or power in the ocean condition.
To analyze the trans-critical $CO_2$ Rankine cycle, phenomena of heat transfer and pressure drop when $CO_2$ condensation occurs near the critical point are studied. A HEM (Homogeneous Equilibrium Model) approach is used to evaluate the prediction methods of heat transfer and pressure drop. Therefore, a system transient analysis code adopting the HEM approach is developed in this study namely KAIST-STA (System Transient Analysis) code. The experiment was performed with the $CO_2$ test facility called SCO2PE (Supercritical $CO_2$ Pressurizing Experiment) in KAIST. The heat transfer and pressure drop tests in the $CO_2$ two-phase region were conducted with the PCHE (Printed Circuit Heat Exchanger) in the facility, a $CO_2$ to water heat exchanger, having 896 channels with a 1.8mm diameter. Moreover, the two-phase pressure drop test in a pipe was carried out with the test section of S$CO_2$PE having 1 1/2'' inner diameter.
Among many correlations found from previous works, the correlations that showed a good accuracy in $CO_2$ condensation but having different geometry, and the correlations for $CO_2$ single-phase flow but having similar geometry were selected and compared to the experimental data from SCO2PE facility. The heat transfer correlation of Baik and the pressure drop correlation developed by Muller-Steinhagen and Heck showed the best-performances near the critical point of $CO_2$. It is noteworthy that the Baik’s heat transfer correlation gives the best performance in $CO_2$ two-phase region even if it was originally developed in $CO_2$ single-phase flow conditions. This means that the two-phase flow of $CO_2$ close to the critical point would not be much different from $CO_2$ single-phase flow in terms of heat transfer. Since none of the existing correlations can be used for the $CO_2$ two-phase flow in PCHE, a new correlation is suggested. The pressure drop of the PCHE is predicted with the Baik’s pressure loss correlation, the HEM 2-phase multiplier from Cicchitti’s viscosity and the suggested correction factor, and showed satisfactory agreement. The correction factor to the pressure drop reflecting the amplifying PCHE zig-zag channel form loss effect as the fluid conditions move away from the critical point is newly suggested. The SCO2PE loop was analyzed with the selected heat transfer and pressure drop correlations, and the HEM approach. The analyzed conditions include transient $CO_2$ two-phase flow near the critical point. The comparison results are satisfactory, which means that the HEM is a good assumption for modeling two-phase flow near the critical point.
Since the designed trans-critical $CO_2$ Rankine cycle is for the nuclear marine application, a load follow analysis is necessary to check if the system can successfully respond to the power demand variation. Therefore, on the basis of the trans-critical $CO_2$ Rankine cycle design, the modeling and load follow analyses of the system from 100% to 0% loads and 100-50-75% loads are conducted. The analyses are performed by using the developed system analysis code based on HEM and suitable constitutive relations. As a result, the designed system demonstrated that it can follow the load variation in a satisfying way.