Validation of SIMULATE5-K and CASMO5 with the SPERT-III E-Core

1 Introduction

SIMULATE5-K (S5K) is the best-estimate transient nodal reactor analysis tool developed by Studsvik Scandpower, Inc. (SSP). The motivation for the development of S5K was to modernize the existing best-estimate tool SIMULATE-3K and to obtain a solution fully consistent with the licensed advanced core design tool SIMULATE5 (Borkowski et al., 1994; Bahadir and Lindhal, 2009). Previously, the numerical methods for solving the time-dependent neutron diffusion equation for representative reactor transients were demonstrated and verified for numerical benchmark calculations (Bahadir, 2022). This work will validate the use of S5K for transient calculations in realistic Light Water Reactors (LWRs) with comparisons to experimental data.

The Special Power Excursion Reactor Test III (SPERT-III) E-core was an experimental reactor built to perform non-destructive tests of power excursions in typical LWRs. The reactor core was very compact and was designed to perform reactivity excursion events similar to Reactivity Insertion Accidents (RIAs). Several of the prompt-supercritical SPERT-III E-core experiments have been modeled using S5K to add to the validation data available for S5K.

Previous work has focused on using lattice data from CASMO5 to model the experiments in SIMULATE-3K (S3K) (Grandi and Moberg, 2012; Grandi and Ferrer, 2018; Grandi, 2014). Selected validation results with S5K have been presented previously (Dawn et al., 2024b). The results here are more comprehensive and include the details of how the modeling was performed. Additionally, the multi-group capabilities of S5K were used to investigate the energy-group dependence on the results.

1.1 Description of experiments

As these experiments were transients designed to emulate the conditions of RIA in LWRs, these results are particularly important for the validation of S5K. Notably, the design of the SPERT-III E-core was well documented and much experimental data was collected.

1.1.1 Reactor description

The SPERT-III E-core is a small, oxide-fueled Pressurized Water Reactor (PWR) and has similar characteristics (excepting its size) to a commercial nuclear power reactor with no fission product inventory. The core has been described in detail in the original report and has been summarized in previous modeling work (McCardell et al., 1969; Grandi, 2014). The core is approximately cylindrical with an active fuel height of 97.282 cm and a diameter of approximately 66.04 cm. The rated thermal power is 20 MW and the rated flow is nominally 1.26 m³/s at 17.33MPa and 616K. The fuel in the SPERT-III E-core is 4.8% enriched UO 2 fuel rods on a square-lattice with a pin-pitch of 1.4859 cm. The fuel assemblies are each surrounded by flow channel boxes.

There are a total of 60 fuel assemblies in the SPERT-III E-core. The layout of the reactor core is shown in Figure 1 and the different assembly designs are shown in Figure 2. The main “driver” fuel is the 5 × 5 fuel assembly in Figure 2a. The central four assemblies are 4 × 4 fuel assemblies which are slightly smaller to allow the transient control rod to pass through the core. Finally, there are eight control rod assemblies that are composed of a lower 4 × 4 fuel assembly and an upper assembly of borated steel as a neutron absorbing material. These control rod assemblies are fueled-follower control assemblies that are used to modify the excess reactivity in the core for each experiment.

1.1.2 Experimental procedure

The SPERT-III reactor was versatile and could be readily configured to perform many different reactivity excursion experiments. When performing a particular experiment, the reactor operators would first configure the reactor to a particular set of inlet temperature and flow conditions. Then, with the transient control rod fully inserted, the control rod assemblies would be inserted or removed on gang (such that they were all at the same position). The control rod assemblies were positioned such that the excess reactivity (the net reactivity should the transient control rod be fully removed) was set to a prescribed level (e.g., 1.21$). Next, the transient control rod was used to bring the reactor to the critical state. Finally, the transient was initiated by dropping the transient control rod.

2 Methodology

Modeling the SPERT-III E-core in S5K required making several decisions described herein. Some of the newer features of S5K were used to recreate the experimental procedure as closely as possible.

2.1 CASMO5

CASMO5 lattice models were developed for the 5 × 5 fuel assembly, the 4 × 4 controlled/uncontrolled fuel assembly, and the 4 × 4 fueled follower control rod assembly. The one-dimensional reflector modeling in CASMO5 was used for all other non-fissile nodes in the core such as the control rod assembly upper part with the neutron absorbing material. In the one-dimensional modeling for non-fissile materials, the reactor component of interest is modeled as a series of one-dimensional slabs adjacent to a two-dimensional fissile lattice. For example, nuclear data for the control rod upper portion is generated by modeling a series of one-dimensional slabs adjacent to the control rod lower portion. The dimensions of the representative one-dimensional slabs are calculated to preserve the material fractions within the non-fissile assembly. While the control rod assemblies are somewhat geometrically complex, their neutronic data can be well described by a simplified model since the main effect is their significant thermal neutron absorption. Reflector data was computed for top and bottom axial reflectors as well as radial reflectors.

The automatic case-matrix feature in CASMO5 was used to perform CASMO5 calculations at sufficient conditions to “cover” the conditions in the SPERT-III E-core transients. The automatic case-matrix is more extensive than needed for this modeling since depletion is entirely unnecessary and all of the transients are performed with fresh fuel. However, the automatic case-matrix was used to validate that it is broad enough to accurately model these transients.

2.2 SIMULATE5 (steady-state)

SIMULATE5 is used for the steady-state model of the SPERT-III E-core for initialization of the transients. This section will describe the basic discretization of the multi-group neutron diffusion equation and thermal hydraulic modeling as used in this work.

The one-dimensional axial rehomogenization (subnode) method was used in this work. The axial rehomogenization model allows the use of a coarser axial mesh without sacrificing accuracy due to so-called control rod “cusping” effects as control rods move axially.

SIMULATE5 solves the multi-group neutron diffusion with the Analytic Nodal Method (ANM) (Bahadir and Lindhal, 2009). In this work, the SPERT-III E-core is discretized with one node per assembly in the radial direction and 16 axial nodes. The radial node width is 7.62 cm and the axial node height is approximately 6.08 cm.

Similarly, the thermal hydraulics model in SIMULATE5 is discretized with one flow channel per fuel assembly. As each of the assemblies in the SPERT-III E-core are surrounded by solid boxes, there is no crossflow between assemblies. In each flow channel at each axial level, a five-equation model is used to calculate the heat transfer from the fuel into the coolant. The five conservation equations used to model the fluid flow are: liquid and vapor mass, liquid and vapor energy, and mixture momentum. Then, in each node the fuel temperature is computed for a representative fuel pin using a one-dimensional cylindrical heat conduction model. This representative fuel temperature is used to compute the neutron cross sections. Additional information on the SIMULATE5 fuel pin model can be found in (Grandi, 2018).

2.3 SIMULATE5-K (transient)

The S5K model uses the same spatial discretization as the SIMULATE5 model. The same nodal equations for the multi-group neutron diffusion equation are solved in the transient using the Frequency Transform Method (FTM). Additionally, the one-dimensional axial rehomogenization model tracks the delayed neutron precursor concentrations in each fueled axial subnode. This results in accurate treatment of partially-fueled nodes (in the case of control rod assemblies) and accurate resolution of the so-called control rod “cusping” effect as the transient control rod moves through the core (Bahadir, 2022; Dawn et al., 2024a).

The time-dependent thermal hydraulics model in S5K solves the same five-equation model for fluid flow and the same radial heat conduction model accounting for temporal derivatives. The thermal hydraulics models in S5K are used to compute the material temperatures and associated power distribution at each time-step. The power distribution is converged at each time-step and backup time-steps may be performed as necessary for convergence.

The transient control rod position during the SPERT-III E-core transients is not known exactly based on the available data. In this work, an estimate of the transient control rod drop time was used from the original report based on a control rod drop test (McCardell et al., 1969). The transient control rod velocity was assumed to increase linearly (due to gravity) and the velocity was adjusted to match the reported transient control rod drop time.

The temporal discretization in S5K is performed using the FTM by default (Bahadir, 2022). S5K has an adaptive time-stepping capability based on a series of heuristics that track temporal derivatives during the transient. The adaptive time-stepping capability in S5K was used in this work. All of the SPERT-III E-core transients were modeled with a maximum time-step of 1 ms except for the Hot Full-Power (HFP) cases, which were modeled with a maximum time-step of 0.5 ms.

2.4 Modeling procedure

The CMS5 suite is capable of modeling many types of LWRs at many different operational conditions. The capabilities of CMS5 are so diverse that the SPERT-III E-core transient could be modeled following almost the same procedure as the true experiments.

The position of neither the control rod assemblies nor the transient control rod are reported with the experimental data. Instead, the “initial reactivity insertion” is reported in units of $. A value of β e f f is required to convert into absolute units for k e f f. First, a steady-state model of each transient was used to compute the adjoint neutron flux and obtain a value of β e f f for each initial condition. Given a value of β e f f, the target k e f f could be computed aswhere ρ is the reactivity in units of $ and β e f f is in absolute units.

k e f f = 1 1 − ρ β e f f (1)

Next, the transient control rod was moved to the fully-withdrawn position in the SIMULATE5 model. Then, the automated control rod search feature of SIMULATE5 was used to position the control rod assemblies (fueled-followers) to achieve the target value of k e f f from Equation 1. Next, the transient control rod was inserted to achieve criticality in the model and a steady-state calculation was performed for initialization. Finally, the transient control rod was removed using the time-dependent velocity and the transient was followed in S5K.

It is worth noting that the ability to move fueled-follower assemblies such as the control rod assemblies is a relatively new addition to SIMULATE5 and S5K. Originally, this capability was added for modeling fuel-follower assemblies in VVER-440 reactors (Dawn et al., 2024a). However, this work shows that this powerful capability can be used to simplify the modeling of other reactors as well.

3 Results

Using the model described in Section 2, 52 different reactivity insertion experiments were modeled with the SPERT-III E-core and compared to experimental data. As S5K is capable of solving the multi-group form of the time-dependent neutron diffusion equation, the evaluations were performed with two, four, and eight energy groups to observe any impact that the energy discretization may have on the accuracy of the results.

The synthesis of these results is presented in the meta analysis in Section 3.4. Overall, the meta analysis shows that any biases in the comparison between the S5K results and the experimental results is less than the spread of the computed results. Furthermore, the discussion in Section 3.5 shows qualitatively that the uncertainty in the initial condition of the SPERT-III E-core reactivity insertion experiments is expected to explain any differences between the computed and experimental results.

3.1 Transient results of selected cases

The reactivity insertion experiments are broken into five categories: Cold (CLD), Hot Start-Up (HSU) at 259°F, HSU at 500°F, Hot Stand-By (HSB), and Hot Full-Power (HFP). For one transient from each of these categories, the reactor power and reactivity during the transient are compared between the multi-group S5K results and the time-dependent measured data. These comparisons are presented in Figures 3–7. Qualitatively, the results computed with S5K agree well with the experimental results. Although the time of the peak power differs between the computed and experimental results for some cases, the time of the peak power cannot be reasonably compared in these experiments as the initial power is not known with sufficient accuracy. These reactor power and reactivity plots also demonstrate that the two-, four-, and eight-group results are all consistent with each other.

S5K can also be used to investigate the individual reactivity contributions from effects such as the fuel temperature and moderator density. For example, the reactivity components from case number 86 at HFP condition with the eight-group energy structure are shown in Figure 8. As expected for such a rapid transient, the reactivity feedback is due almost entirely to the control rod movement and the fuel temperature (Doppler) effect. Additionally, Figure 8 shows that a significant portion of the total reactivity is due to flux redistribution effects meaning that a simple point-kinetics model may struggle to replicate these results.

3.2 Comparative visualizations

For each transient, three quantities of interest are reported in the original report: peak power, total (integral) energy released until the peak power, and compensated reactivity. Compensated reactivity is defined as the initial reactivity minus the reactivity at the time of the peak power and is used as a measure of the fuel temperature and moderator density feedback mechanisms. Comparison plots are made for each of these quantities of interest comparing the reference (experimental) results to the computed (S5K) results.

Results for the and eight-group energy structure are shown in Figure 9. Results from other energy group structures are nearly identical and are discussed quantitatively in Section 3.3. These comparative plots show that generally, S5K agrees well with the reported experimental data for the cases of interest. Note that in Figure 9C, the experimental uncertainty is not provided in the original report for the HFP and HSB experiments so error bars are omitted for these cases.

Comparative analysis of the peak power suggests that the S5K results systematically over-predict the peak power in the SPERT-III E-core experiments except for the HSB conditions. These differences will be quantified in Section 3.3.

This systematic over-prediction of reactor power had not been observed in previous modeling work of the SPERT-III E-core experiments with S3K (Grandi and Ferrer, 2018; Grandi, 2014; Grandi and Moberg, 2012). It is suggested that the automated search used to determine the initial position the control rod assemblies has resulted in this bias. The bias in peak power would be affected by the values used for β e f f. Additionally, there was large uncertainty in the initial reactivity insertion and this will be further discussed in Section 3.5.

3.3 Quantitative analysis

The results from the 52 reactivity insertion experiments computed with S5K can also be compared to the experimental data quantitatively. The data for the three quantities of interest in this work are presented in Table 1, Tables 2, 3 for two-, four-, and eight-group energy structures respectively. The results do not show any clear trends and the results with the different energy group structures agree well with each other.

TABLE 1. Two-group.

TABLE 2. Four-group.

TABLE 3. Eight-group.

Furthermore, these results computed with CASMO5 and S5K agree well with similar results published in literature. Similar trends in over/under-prediction are seen when comparing to other methods using Serpent 2 data in DYN3D and ATHLET as well as the ANCK code system (Aures et al., 2020; Aoki et al., 2009). These results consistently show predictions within 10%–20% for most quantities with a few experiments as outliers, presumably due to the uncertainty in the initial conditions.

3.4 Meta analysis

The quantitative data can be summarized as a set of results for each of the energy group structures. This meta analysis comparing across all of the reactivity insertion experiments modeled with S5K in this work is presented in Table 4.

TABLE 4. Meta comparison.

The first observation from this meta comparison is that overall, the S5K results are very consistent with the SPERT-III experimental data. For almost all of the results, any biases observed in the results are within one standard-deviation of the mean. Additionally, Table 4 shows that there is no clear effect of the different energy group structures and the default two-group structure is sufficient for modeling these experiments accurately.

The Root-Mean-Squared (RMS) error for any of the quantities of interest with any of the energy groups structures is less than 20.1%. While this may seem significant, it is much less than the uncertainty in the experimental results due to the uncertainty in the initial conditions as will be discussed in Section 3.5.

3.5 Uncertainty in initial conditions

The original experimental data from the SPERT-III E-core experiment included measurement uncertainty in the three quantities of interest here (peak power, total energy released until peak power, and compensated reactivity). Additionally, the experimental report included uncertainty in the initial reactivity insertion. It is noted that these initial reactivity insertion uncertainties are rather large. For example, experiment number 16 was performed at CLD condition and with an initial reactivity insertion of 1.01$ and an uncertainty of 0.04$. Fundamentally, this suggests that there is uncertainty as to whether this reactivity insertion experiment achieved prompt supercriticality (ρ >1$) or not. The relatively large uncertainties in the initial reactivity insertion can explain much of the differences between the results computed with S5K and the experimental results.

To demonstrate the magnitude of these initial reactivity insertion uncertainties and how they affect the results, the transient results from Section 3.1. One case was selected from each of the operating conditions of the SPERT-III E-core (CLD, HSU at °F, HSU at 500°F, HSB, and HFP). For these selected cases, the transient was evaluated with the nominal initial inserted reactivity, the initial inserted reactivity plus the uncertainty, and the initial inserted reactivity minus the uncertainty. These demonstrative cases are shown in Figure 10. For these uncertainty bounding figures, all of the results shown use eight energy groups.

Figure 10 shows the large spread of expected results in the measured quantities of interest. The effect of the uncertainty in the initial reactivity insertion on the reactor power during the transient is especially noteworthy. For all cases investigated here, the initial reactivity insertion uncertainty can change the peak power by a factor of two or more. The effect of the uncertainty in the initial reactivity insertion dwarfs the approximately 20% bias observed in the S5K results from Table 4.

4 Summary and conclusion

This work has described the validation of S5K with the modeling of the SPERT-III E-core experiments. These transient experiments were performed in a small LWR similar to a PWR and were designed to serve as validation experiments for modeling RIAs.

This work demonstrated the capabilities of S5K for modeling RIA. CASMO5 was used to model two-dimensional lattices for each unique assembly type in the SPERT-III E-core. SIMULATE5 was used to solve the multi-group neutron diffusion equation and model the thermal hydraulic feedback in the reactor at steady-state for the prescribed initial conditions of the reactor. Finally, S5K was used to model the transients and the thermal hydraulic feedback during the transient.

New features of SIMULATE5 were used to automate the modeling of the SPERT-III E-core experiments. For each reactor condition of interest, the control rod assemblies were positioned using the criticality search feature in SIMULATE5 to achieve the excess reactivity specified for the experiment.

In this work, 52 different experiments from the SPERT-III E-core were modeled spanning five different initial reactor configurations. Additionally, these transients were modeled using two-, four-, and eight-group cross section libraries to observe if the energy group structure affects the accuracy of the results computed with S5K. It was observed that S5K tends to over-predict the reactor power during these transients. However, it was also shown that any over-prediction of the reactor power for these experiments is much smaller than the effect of the uncertainty in the initial reactivity insertion as described in the experimental report. It was also observed that the number of energy groups does not significantly affect the results in any of the quantities of interest described here. These results validate that the default two-group structure in S5K is sufficient for the modeling of similar RIAs.

Overall, the results presented here validate that S5K can be used to accurately model RIAs similar to those performed in the SPERT-III E-core experiments.

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Footnotes

Edited by: Mark D. DeHart, Abilene Christian University, United States

Reviewed by: Tuan Tran, Nuclear Research and Consultancy Group, Netherlands

Nhu Viet Ha Pham, Vietnam Atomic Energy Institute, Vietnam

Footnotes

ANM, Analytic Nodal Method; BWR, Boiling Water Reactor; CLD, Cold; FTM, Frequency Transform Method; HFP, Hot Full-Power; HSB, Hot Stand-By; HSU, Hot Start-Up; LWR, Light Water Reactor; PWR, Pressurized Water Reactor; RIA, Reactivity Insertion Accident; RMS, Root-Mean-Squared; S3K, SIMULATE-3K; S5K, SIMULATE5-K; SPERT-III, Special Power Excursion Reactor Test III; SSP, Studsvik Scandpower, Inc.