*3.2. Code-to-Code Comparison*

Figure 7 depicts the code-to-code comparison of one- and multi-dimensional results by both codes, respectively. The results clearly showed that TRACE predicted high void fractions compared to MARS-KS in both one- and multi-dimensional cases. As listed in Table 3, the results of the one-sample t-test based on absolute error samples of each code against the measured data also supported the significant difference in the void prediction between the codes. The negative t-values of MARS-KS for all categories proved that its prediction did not exceed the allowed measurement error, 2σ, generally. However, as TRACE showed positive *t*-values significantly, this supported that its prediction generally exceeded the allowable range. In other words, this meant that TRACE showed poor prediction capability compared to MARS-KS. It was found that such a significant overprediction tendency of TRACE came from the difference in crossflow calculation. As depicted in Figure 8, it was clearly confirmed that TRACE generally calculated much less vapor crossflow compared to MARS-KS for

all test cases. Moreover, in the multi-dimensional cases, TRACE calculated the net vapor inflow to the measuring sections, whereas MARS-KS generally calculated significant vapor outflow from the measuring sections. As the accompanying liquid crossflow showed no significant difference, the difference in the void fraction prediction was totally attributable to the vapor crossflow. From these, it was clearly identified that TRACE had the tendency to keep more vapor in the central channel with much less vapor crossflow. Thus, the higher void fraction in the measuring section was the result.

**Figure 7.** Code comparisons: (**a**) 1D void predictions; (**b**) 3D void predictions.


**Table 3.** Results of one-sample *t*-test for assessing code predictions.

**Figure 8.** Code comparisons: (**a**) 1D vapor crossflow; (**b**) 1D liquid crossflow; (**c**) 3D vapor crossflow; (**d**) 3D liquid crossflow.

#### *3.3. Influence of Crossflow-to-Code Predictions*

As it was found that there was a significant difference in crossflow calculations between both codes, and the difference made TRACE predict higher void fractions compared to MARS-KS, crossflow was considered as the root cause of the overprediction tendency. Therefore, an additional evaluation of the sensitivity against crossflow was conducted in order to clearly identify the influence of crossflow on each code prediction. For this, a simple modification of the one-dimensional model of each code, which was convenient to modify, was made as depicted in Figure 9. The modification was made by deleting crossflow junction connections and giving averaged mass flow conditions to the central measuring channel and peripheral channel, respectively. Except for test series B7, of which the averaged central mass flow fraction was 13%, the nominal mass flow condition for the central channel was given as 15% of total mass flow. The calculated result of each modified model was compared with the previous one-dimensional results of each system code, as depicted in Figure 10. Especially in the case of MARS-KS, the influence of crossflow was clearly captured, as the results showed that the modified model predicted higher void fractions compared to the default model when the crossflow was disabled. Moreover, the comparison of the modified model showed higher void fractions from MARS-KS compared to TRACE. In addition, in the case of TRACE, there was no drastic change by the crossflow because of negligible crossflow even with the default model. From these, it was clearly concluded that crossflow was the root cause of the overpredictions. Thus, further improvement to the crossflow model is necessary in order to reduce the significant overpredictions of TRACE and to improve the predictions

of MARS-KS as well. For the improvement, additional constitutive models should be employed to improve the prediction of two-phase crossflow. This could be done by employing a turbulent mixing model based on the Equal Volume and Void Drift (EVVD) method, which is adopted by state-of-the-art subchannel analysis codes, in order to enhance two-phase crossflow [15]. The EVVD method enables direct mass and energy mixing between channels, by which void drift from a higher void channel to a lower void channel is induced by not only inter-channel void difference but also net liquid flow from low void to high void. Therefore, it is expected that this model will enable the enhancement of two-phase crossflow for both codes by modeling additional net mass and energy exchanges directly in the field equation of each code.

**Figure 9.** Modified one-dimensional model for crossflow influence test: (**a**) nodalization of MARS-KS; (**b**) nodalization of TRACE.

**Figure 10.** *Cont.*

**Figure 10.** Comparisons for checking influence of crossflow-to-code predictions: (**a**) code comparison of modified models, in which the crossflows are disabled; (**b**) void difference between modified models of MARS-KS and TRACE; (**c**) model comparison of TRACE; (**d**) model comparison of MARS-KS.

#### **4. Conclusions**

As a follow-up study, a further assessment of void fraction predictability of the system codes, MARS-KS 1.4 and TRACE V5.0, was performed with one- and multi-dimensional models, mainly to find the root cause of overprediction tendencies in bundle cases identified by the previous study. In total, 219 steady-state bundle test cases from the OECD/NRC PSBT benchmark were utilized for the assessment. From the model comparison of each system code, it was found that each code showed no significant difference in void prediction between one- and multi-dimensional models. In the case of MARS-KS, because the multi-dimensional model cannot implement direct mass and energy exchange due to turbulence, no clear difference emerged when compared to the one-dimensional model of itself. Therefore, it was concluded that the turbulent mixing model of MARS-KS is not appropriate to cover two-phase mixing flow within the bundle. Meanwhile, as TRACE showed significant void predictions due to fewer crossflow calculations compared to MARS-KS, crossflow was considered as the root cause of the overprediction tendency. From the additional assessment with the modified one-dimensional models, it was clearly confirmed that crossflow significantly affects the code predictions, and thus crossflow is the root cause of the overpredictions in the bundle cases. From these, it was concluded that further improvement of the crossflow model is necessary in order to predict the void fraction more realistically. As state-of-the-art subchannel codes adopt the Equal Volume and Void Drift (EVVD) method as the turbulent mixing model to improve the inter-channel crossflow, this study concludes that an improvement should be made with the application of the EVVD method to model the direct net mass and energy interchanges between channels under two-phase flow conditions. Therefore, as a future work, modification of the crossflow model will be made by applying the EVVD method to both one- and multi-dimensional solutions of each system code, respectively.

**Author Contributions:** Conceptualization, funding acquisition, project administration, resources, and supervision, T.K.; methodology and investigation, Y.L. and T.K.; formal analysis, validation, visualization, writing—original draft preparation, and writing—review and editing, Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by Incheon National University (International Cooperative) Research Grant in 2018.

**Conflicts of Interest:** The authors declare no conflicts of interest.
