Study on critical flow model of supercritical $CO_2$ power cycle for the next generation nuclear system application

Abstract

In this study, $CO_2$ critical flow model under single- and two-phase flow conditions was developed and evaluated for the next generation nuclear system application. The study of seals for an S-$CO_2$ Brayton cycle was conducted and the labyrinth seal was preferentially selected because it is easier to analyze the internal flow due to the geometry simplicity and it is more economically feasible. The sensitivity analysis showed that the pre-cooler inlet is the best point for the $CO_2$ inventory recovery point when the leakage was discharged to ambient conditions and $CO_2$ from the gas tank was refilled. A literature review of the labyrinth seal equations was conducted to provide a detailed discussion on all the existing leakage models. Also, various experiment of $CO_2$ critical flow was performed to validate the $CO_2$ critical flow model with experimental results. This study included the experimental data obtained under various conditions including not only single-phase flow such as supercritical and gaseous states but also two phase (liquid and gas) flow. A $CO_2$ critical flow simulation with thermal-hydraulic transient analysis code was conducted to evaluate if the existing MARS code can estimate the $CO_2$ critical flow behavior in the seals. Through three experiment cases, it was identified that MARS and experimental results show a good agreement for simple geometry nozzle. However, MARS results with labyrinth seal geometry nozzle were inaccurate due to over estimated loss coefficients. Since the existing MARS code is complex and not capable of reflecting the number of tooth effect, an isentropic $CO_2$ critical flow model was selected from the literature and compared to the experimental results with single-phase flow (supercritical and gaseous states). The comparison with experimental results with single-phase $CO_2$ flow showed that the isentropic $CO_2$ critical flow model is sufficient to predict the $CO_2$ critical and subcritical flows when the nozzle geometry is simple. Furthermore, the experimental data confirmed that the leak rate is reduced as the nozzle diameter decreases even though the total nozzle length is the same. To correctly capture the labyrinth seal geometry effect on the leakage flow, Hodkinson’s and Vermes’ equations were adopted. The combination of Hodkinson’s equation and Vermes’ equation was used to reflect both compressibility effect and labyrinth seal geometry effect. By updating the empirical formula, it became more suitable for $CO_2$ single-phase condition regardless of the upstream condition at the supercritical state or the gaseous state. The experimental data and model results confirmed that the leak rate is reduced as the number of tooth increases even though the total nozzle length is the same. With $CO_2$ critical flow model based on the Hodkinson’s and Vermes’ equations, mass flux change with cavity length was verified. The analysis results showed that the mass flux is decreased as cavity length is increased. Also, mass flux change with different tooth number was verified. It was verified that there is an optimum tooth number which leads to the minimum leakage rate since inserting more teeth cannot bring more benefits to decrease leakage as cavity length becomes too small. To compare the $CO_2$ critical flow model with $CO_2$ turbo-machine test data, gas foil journal bearing type compressor test results from SCIEL was used. By applying the modified $CO_2$ labyrinth seal equation, the model could estimate the experimental mass flow rate very well within 4.4 percent average error when the flow is expanding from supercritical phase to supercritical phase. Moreover, optimization of tooth number per unit length was conducted to minimize the $CO_2$ leakage from gas foil journal bearing type compressor installed in SCIEL. By increasing the tooth number from twelve to nineteen, the $CO_2$ leakage could be reduced about 8.23 percent. The two-phase critical flow experiment was performed to observe the Joule-Thomson effect in the labyrinth seals. The experiment results identified that the temperature at nozzle exit sharply decreases below -10ºC due to the Joule-Thomson effect after expansion through the nozzle. Therefore, special attention is needed when using a labyrinth seal for the S-$CO_2$ turbomachinery. To estimate the dynamic behavior of $CO_2$critical flow under two-phase condition, Henry-Fauske model is evaluated. To reflect the $CO_2$ characteristic of thermodynamic and transport properties to the two-phase critical flow model, modification of Henry-Fauske model was needed. From experimental results of $CO_2$ leak flow in two-phase condition, the modified Henry-Fauske model became more suitable for $CO_2$ two-phase condition within the equilibrium quality from 0.6 to 0.7 by updating the parameter in the model.