Verification and validation of a Monte Carlo MCS code for high-resolution multiphysics analysis. Verification and validation of a Monte Carlo MCS code for high-resolution multiphysics analysis. An OPR-1000 PWR core operating for 2 consecutive cycles is selected as a target for MP coupling analysis, including verification and validation.
For the MCS MP coupling tool with thermal-hydraulic and fuel performance feedback, excellent agreement with the measured values is observed with a root mean square (RMS) error of 26 ppm for CBC and 1.8% for assembly power. Compared to other codes, MCS MP coupling results have an RMS error of 16 ppm for CBC and 1.8% for composite power.
Introduction
Objective of the thesis
The specific objective of this study is to develop and demonstrate the capability of MCS MP coupling with different feedbacks such as TH coupling (MCS/TH1D and MCS/CTF) and FP coupling (MCS/FRAPCON) for realistic baseline applications. The initial coupling of neutronics/TH MCS codes will be demonstrated using a one-dimensional (1D) single-phase closed-channel model, MCS/TH1D. MCS/TH1D feedback is based on a 1D model of a single-phase closed channel without cross-current between adjacent channels.
The MCS/CTF is similar to the TH1D in that it receives power from the MCS and updates the coolant density and fuel/coolant temperature distribution. Finally, the MCS updates the coolant densities and coolant/fuel temperatures for the next transport step from the FRAPCON results.
Analysis Methodology
MCS Monte Carlo code
MCS sends the fuel pin power distribution to the solver, and the calculated coolant density and fuel/coolant temperature distributions based on the inlet temperature and flow rate in TH1D will be updated to MCS. The MCS code aims to develop a high-fidelity tool capable of supporting large-scale nuclear reactor analysis such as PWRs. The MCS exhaustion capability is implemented by adopting the Chebyshev Rational Approximation Method (CRAM) to solve the Batman equation and uses the Gauss-Seidel iterative method to speed up the exhaustion calculation in the CRAM solver.
The TH feedback implemented in MCS based on the MP link with the TH code (TH1D, CTF) and/or FP code (FRAPCON) is described in the next section. The flowchart of the main feedback algorithm implemented in MCS code is shown in Figure 1.
MCS coupling mechanism
In a single flow, the TH1D solves 1D equations in an axial direction of the mass and energy conservation at a steady state to obtain the coolant temperature/density at each single coolant channel, as expressed in Eq. 1); the diagram illustrating the TH analysis is in Figure 2 (left). Another important feature of the CTF model is that it uses channel-centered geometry instead of rod-centered geometry normally used in the neutronic simulation as in TH1D and FRAPCON codes. The code can accurately calculate and predict all significant fuel rod variables such as fuel and cladding temperature, fission gas emission, pressure, fuel rod deformation and cladding oxidation as a function of time dependent fuel rod force and coolant boundary condition.
FRAPCON is then treated as an FP solver for the MCS code by calculating: 1) fuel and cladding temperature, 2) fuel and cladding deformation, 3) fission product generation and release, void volume and internal gas pressure fuel rod. 15] proved that differences in the coolant temperature distribution of the three MCS junctions cause different versions of the steam table used in each solver.
Verification and Validation of MCS Multi-physics Coupling Model
Fuel pin model
The details of the pin cell parameters are listed in Table 2 with the top and side view image created on the MCS chart. The fuel assembly with a slightly enriched UO2 rod and Gd2O3 rod is studied for the comparison of three coupled MCS systems. Each fuel needle in this study is unevenly divided into 44 grids in the axial direction, and each location of the dividing grid is counted as 1 axial grid.
OPR-1000 core
Code for comparison
Verification and validation of the MCS MP coupling system
Fuel pin
The pin power and flux rating in Table 2 are calculated by dividing the total number of pins in the entire core by the total power and flux of the core. However, the total execution time for the CTF is similar to TH1D because the single-pin model in the CTF has only four subchannels and does not need to consider the effect of cross-current from adjacent pins. Ten small depths corresponding to ten locations of the spacer grid in the active fuel region are observed in the axial distribution of fuel power and temperature.
The calculated fuel temperature distribution shows a significant difference in the FRAPCON model and has the highest fuel temperature value compared to those in TH1D and CTF. The discrepancies in the calculation of thermal conductivities and the use of dynamic slot conduction in the FRAPCON solver [13] affect the fuel temperature calculation, as shown in Eq. 18) and (19), while the TH1D and CTF solver used the constant gap conductance. Another notable result is that the calculated fuel temperature distribution in FRAPCON does not show great depth at the spacing grid location as in TH1D and CTF, since high-fidelity FP parameters such as thermal fuel expansion and fission gas release are taken into account in the FRAPCON model.
In contrast, the calculated output temperature, which will be used to update the temperature in the next exhaust step of the coupled systems, does not show significant differences between them. However, a 16x16 fuel assembly (236 fuel pins, 5 guide tubes placed in 25 fuel pins) will consider 289 subchannels during the calculation of TH parameters in the CTF model, which will increase the simulation time. In general, the power distribution and average fuel temperatures of the three modules are similar.
However, the calculated fuel temperature in the FRAPCON module has a large deviation, within 47 K, compared to the TH1D module, which, as mentioned earlier, is due to the consideration of dynamic gap conductivity and thermal conductivity in the FRAPCON model. The biggest difference of calculated fuel temperature in CTF and TH1D module is at low power gadolinium pin, because CTF calculated fuel temperature as the average of the surface value of 4 fuel pins, and adjacent subchannels of CTF have higher temperature than in gadolinium pin, while TH1D does not. The differences arise from the consideration of cross-flow, where fuel and coolant temperatures are calculated by averaging results from adjacent subchannels in the CTF model, while TH1D and FRAPCON use a closed channel model that does not consider heat exchange between adjacent channels.
Checkboard 2x2 assemblies
Multi-physics full core results
The calculated CBC of MCS underestimates the measured data with a maximum difference of about 44 ppm (1σ = 1 ppm) at 6 GWD/MTU. The power distribution is flatter as the burnout increases with decreasing peak power at BOC compared to EOC. Therefore, the study of MCS/CTF and /FRAPCON will be simulated for the OPR-100 quaternary system at Cycle 1 with the same conditions (number of particles, number of splits in axial and radial radiation) as in MCS/TH1D.
It shows that MCS/CTF required a larger number of simulations compared to MCS/TH1D and MCS/FRAPCON and MCS/TH1D required less memory than others. The changes of CBC as a function of burnup stage and the difference compared to measured data are shown in Figure 28. The relative error of the MCS radial power distribution compared to the reference at BOC, MOC and EOC is shown in Figure 29-Figure 32.
Overall, good agreement of MCS coupling results compared to reference is illustrated with RMS of relative difference of less than 1.8%. MCS results are compared with NDR at BOC due to the unavailability of measured data. NDR composite power (top left) and relative error compared to MCS MP coupling results at BOC (0.05 GWD/MT) cycle 01.
Measured mounting capacity and relative error compared to MCS MP couplings at MOC (6.0 GWD/MT) cycle 01. Measured mounting capacity and relative error of MCS MP couplings at EOC (13.8 GWD/MT) cycle 01. The axial integrated pin- The results of the sensible distribution of MCS/TH1D and the relative difference compared to MCS/CTF and MCS/FRAPCON at BOC and EOC are shown in Figure 36-Figure 43.
However, the relative power difference of MCS/TH1D compared to MCS/CTF and MCS/FRAPCON also increased as a function of combustion due to the negative feedback of fuel temperature decrease with higher combustion [17]. The comparison of the fuel temperature distribution of MCS/FRAPCON with MCS/TH1D and MCS/CTF shows large differences with the maximum relative difference at BOC being 6.3% and 6.9%, respectively, for three reasons.
MCS Multi-cycle Simulation Analysis
Coolant density distribution of MCS and relative differences at EOC cycle 01. . assemblies for cycle 2 BOC are new fuel assemblies removed from the figure for clarity). The MCS multicycle results are compared to measured data and are the result of ST/R2 and NDR in Figure 45-49. The calculated CBC from MCS underestimates the measured data with a maximum difference of approximately 37 ppm (1σ = 1 ppm) at 4 GWD/MT.
The CBC for MCS is within 22 ppm compared to the NDR data, ST/R2 and ST3D code results. Good agreement is observed between the MCS and the references, with a maximum RMS error of less than 1.9% in all states.
Conclusion and Perspective
Herman, et al., OpenMC: A state-of-the-art Monte Carlo code for research and development, Ann. Zhang, et al., MCS – A Monte Carlo particle transport code for large-scale power reactor analysis, Ann. Kim, et al., Coupling FRAPCON for fuel performance analysis in the Monte Carlo code MCS, Comput.
Kim, et al., Cycle 2 depletion simulations of the BEAVRS benchmark with the MCS/CTF coupling system, Nucl. Lemaire, et al., Neutron/thermal-hydraulic/fuel-based fusion with CTF and FRAPCON, Comput. Kim, et al., Preliminary coupling of thermal/hydraulic solvers in Monte Carlo MCS code for practical LWR analysis, Ann.
Lemaire, et al., Fuel efficiency analysis of BEAVRS reference cycle 1 depletion with coupled MCS/FRAPCON system, Ann. Choi, et al., MCS/TH1D analysis of multi-cycle VERA full-core depletion problems, Ann. Jeong, et al., Validation of the UNIST Monte Carlo MCS code for critical safety analysis of a PWR spent fuel pool and storage cask, Ann.
Lemaire, et al., Extension of the Monte Carlo MCS code to spent fuel drum protection analysis, Int. Du, et al., Neutron simulation of China's fast reactor experimental start-up test - Part II: MCS Monte Carlo code calculation, Ann. Cho, et al., Solving the BEAVRS benchmark using the nTRACER direct kernel computation code, J.
