## Abstract

Feedback reactivity caused by core deformation is one of the inherent safety features in a sodium-cooled fast reactor (SFR). To validate the evaluation models of the reactivity feedback equipped in the in-house plant dynamics analysis code, named Super-COPD, we have been conducting the benchmark analyses for the unprotected loss of heat sink (ULOHS) tests of balance of plant (BOP)-302R and BOP-301 as one of the representative issues in Experimental Breeder Reactor-II (EBR-II), a pool-type experimental SFR in the United States. During the transient of the ULOHS tests, the reactor power decreased to the decay heat level due to the negative reactivity caused by the radial expansion of the core. Developing the evaluation models of the reactivity feedback is essential for predicting the plant behavior in unprotected events, such as ULOHS events, and the numerical analyses modeling the feedback reactivity were conducted. By comparing the numerical results and the experimental data, the increment temperature profiles of the core inlet and the decreasing reactor power profile calculated by Super-COPD were comparable with experimental data. The applicability of the evaluation models for the reactivity feedback was indicated during the ULOHS event. In addition, through the sensitivity analyses on the cold pool model, it was found that the modification of the plenum model of the cold pool to take into account the thermal stratification was required to improve the core inlet temperature profile.

## 1 Introduction

The feedback reactivity caused by the core deformation is one of the most important factors of inherent safety features in sodium-cooled fast reactors (SFRs). In particular, the negative reactivity caused by the increase of the fuel assemblies (FAs) pitches in the core by the core support plate's radial expansion according to the increase of the core inlet temperature, namely, core radial expansion reactivity is essential in unprotected loss of heat sink (ULOHS) event.

Japan Atomic Energy Agency (JAEA) has been developing a one-dimensional plant dynamics analysis code, named Super-COPD (S-COPD) [1] to predict the plant behaviors in the design investigation and the safety analyses of SFRs. Although the feedback reactivity models' validation has been carried out with several plant test data such as Joyo, Monju, and Experimental Breeder Reactor-II (EBR-II) [25], there is still some room for improving the evaluation accuracy of the feedback reactivity for the design study of the SFRs and the safety assessment of the events in S-COPD.

In this paper, numerical analyses of the balance of plant (BOP) tests [6] performed in the EBR-II were performed from the viewpoint of validating the evaluation models of the feedback reactivity equipped in S-COPD. The detail of the analytical models and the numerical results by S-COPD of the ULOHS tests in EBR-II was described. We joined the benchmark analyses program of the BOP tests launched in the framework of Generation-IV International Forum (GIF) [7]. In the analyses, the primary heat transport system (PHTS), including the core, was modeled by a one-dimensional flow network model, and the reactor power was calculated by solving the point kinetics equations in S-COPD. The reactivity models were constructed taking into account the effects on the core radial expansion, Doppler, fuel axial expansion, coolant density, wrapper tube density, and fuel cladding density as the function of the representative temperature in the core. The applicability of the feedback reactivity models to the ULOHS tests was examined by comparing the results of the S-COPD with the measured data of the plant dynamics. Finally, future works were discussed through sensitivity analyses on the cold pool model to improve the accuracy of the numerical results by S-COPD.

## 2 Balance of Plant-302R and Balance of Plant-301 ULOHS Tests in EBR-II

### 2.1 Plant Overview of EBR-II.

Figure 1 shows the overview of the components in the PHTS of EBR-II. EBR-II is a pool-type experimental SFR in the United States. All the major components in the PHTS, such as the core, the upper plenum in the reactor vessel (RV), the intermediate heat exchanger (IHX), the pipe connecting the upper plenum in the RV, and the IHX which is called the Z-shaped pipe (Z-pipe), the two primary pumps, the high-pressure plenum (HPP), and the low-pressure plenum (LPP), were installed in the cold pool. The liquid sodium as coolant through the core was mixed in the upper plenum in the RV and flowed into the IHX through the Z-pipe. The sodium-cooled in the IHX flowed into the cold pool, and the sodium pressurized by the two primary pumps flowed into the HPP and the LPP.

Fig. 1
Fig. 1
Close modal

### 2.2 Outline of Balance of Plant-302R and Balance of Plant-301 Tests.

In EBR-II, various tests were carried out to develop fuels, components, and associated technologies, including computer codes for a large-scale SFR development [8]. The benchmark analyses of the SHRT-17 test for protected loss of flow event and SHRT-45R test for unprotected loss of flow event have already been performed in the framework of the IAEA Coordinated Research Project [9]. BOP-302R and BOP-301 tests performed as one of the ULOHS events were employed as the benchmark analysis problems in the framework of the GIF [7]. The BOP tests have advantages over the SHRT tests in that the applicability of the analysis models can be investigated without the uncertainty of the primary flowrate because the primary pumps were not tripped and the flowrate was kept on. BOP-302R and BOP-301 tests were initiated from 100% power operation condition and 50% power condition, respectively. In both tests for the ULOHS event, the sequence of the plant transient was initiated after the secondary sodium pump tripped without scram nor tripping the primary pumps. The heat sink by means of the air-cooler was isolated immediately by the secondary pump trip. The core inlet temperature began to increase due to the loss of the heat sink, and the reactor power decreased to the decay heat level. At the end of the sequences, the decay heat was balanced with the heat dissipation from the components. All the experimental data of the BOP tests are worthwhile for validating analytical codes in ULOHS events.

## 3 Analytical Model of Balance of Plant Tests in EBR-II

### 3.1 Thermal-Hydraulics Model.

Figure 2 shows the one-dimensional EBR-II flow network model. The two primary heat transport loops were modeled independently. The plena, such as the HPP, the LPP, and the cold pool, were modeled by the perfect mixing volume, and the flow connecting the plena was formulated with the flow network. The models for the major piping are listed in Table 1. For the modeling simplicity, heat transfer from the coolant in the piping to the structures was not modeled because it's influence on the whole plant behavior was negligibly small in full-power circulation conditions.

Fig. 2
Fig. 2
Close modal
Table 1

Nodalization of major piping

LocationsNumber of nodes (–)
Z-Pipe57
Pump outlet piping10
High-pressure piping30
Throttle valve inlet piping24
Low-pressure piping52
Intermediate inlet piping33
Intermediate outlet piping15
LocationsNumber of nodes (–)
Z-Pipe57
Pump outlet piping10
High-pressure piping30
Throttle valve inlet piping24
Low-pressure piping52
Intermediate inlet piping33
Intermediate outlet piping15

Figure 3 shows the thermal-hydraulics model of the core in EBR-II. All FAs were modeled by the independent flow channels to simulate the radial heat transfer between the FAs through the sodium in their gap. The core model was connected to the HPP, the LPP, and the upper plenum in the flow network model, as shown in Fig. 2. The reactor power was calculated by solving point kinetics equations with the reactivity model coefficients in S-COPD.

Fig. 3
Fig. 3
Close modal
Table 2 shows the friction factors and heat transfer coefficient correlations employed in the EBR-II numerical analysis. The friction factor, λ, on the outside wall of the wrapper tube of FA is as follows:in laminar flow regime
$λ=96Re$
(1)
and in turbulent flow regime
$λ=0.3164Re0.25$
(2)
Table 2

Correlations used in S-COPD

PhenomenaLocationsCorrelations
Friction factorFuel pin bundleCheng-Todreas correlation [10]
Inter-wrapper tubeParallel plate correlation in Eqs. (1) and (2) [11]
IHX tube bundlePipe flow correlation in Eqs. (3) and (4) [11]
Heat transfer coefficientFuel pin bundleLyon correlation [12]
Wrapper tubeThermal conductivity (sodium)
IHX tube bundleMikityuk correlation [13]
PhenomenaLocationsCorrelations
Friction factorFuel pin bundleCheng-Todreas correlation [10]
Inter-wrapper tubeParallel plate correlation in Eqs. (1) and (2) [11]
IHX tube bundlePipe flow correlation in Eqs. (3) and (4) [11]
Heat transfer coefficientFuel pin bundleLyon correlation [12]
Wrapper tubeThermal conductivity (sodium)
IHX tube bundleMikityuk correlation [13]

The friction factor, λ, on the wall of the IHX tube bundle is as follows:

in laminar flow regime
$λ=64Re$
(3)
and in turbulent flow regime
$λ=0.3164Re0.25$
(4)

### 3.2 Reactivity Model in Neutronics Analysis.

In the benchmark analyses, each participant can use their own reactivity model. The original reactivity models equipped in S-COPD were developed using the neutronics calculation methods in JAEA [14], and the reactivity coefficients were determined based on the neutronics benchmark specifications in SHRT-45R [15]. In this study, the following reactivity models of the core radial expansion, Doppler, fuel axial expansion, coolant density, the wrapper tube density, and fuel cladding density were used in the analyses by S-COPD. The values of the reactivity coefficients used in the analyses are summarized in Table 3.

Table 3

Values of reactivity coefficients

ReactivitySymbolValue
(i) Core radial expansionαr1.91565 × 10−5 (Δk/k·K)
(ii) DopplerβD4.33977 × 10−4 (Δk/k)
(iii) Fuel axial expansionInner coreαa,11.92491 × 10−6 (Δk/k·K)
Outer core reflectorαa,20.00000 (Δk/k·K)
Outer core blanketαa,30.00000 (Δk/k·K)
(iv) Coolant densityInner coreαNa,11.59931 × 10−5 (Δk/k·K)
Outer core reflectorαNa,21.68507 × 10−6 (Δk/k·K)
Outer core blanketαNa,36.79852 × 10−8 (Δk/k·K)
(v) Wrapper tube densityInner coreαw,14.80547 × 10−7 (Δk/k·K)
Outer core reflectorαw,21.70566 × 10−8 (Δk/k·K)
Outer core blanketαw,37.14921 × 10−10 (Δk/k·K)
(vi) Cladding densityInner coreαc,14.66626 × 10−7 (Δk/k·K)
Outer core reflectorαc,20.00000 (Δk/k·K)
Outer core blanketαc,35.61635 × 10−9 (Δk/k·K)
ReactivitySymbolValue
(i) Core radial expansionαr1.91565 × 10−5 (Δk/k·K)
(ii) DopplerβD4.33977 × 10−4 (Δk/k)
(iii) Fuel axial expansionInner coreαa,11.92491 × 10−6 (Δk/k·K)
Outer core reflectorαa,20.00000 (Δk/k·K)
Outer core blanketαa,30.00000 (Δk/k·K)
(iv) Coolant densityInner coreαNa,11.59931 × 10−5 (Δk/k·K)
Outer core reflectorαNa,21.68507 × 10−6 (Δk/k·K)
Outer core blanketαNa,36.79852 × 10−8 (Δk/k·K)
(v) Wrapper tube densityInner coreαw,14.80547 × 10−7 (Δk/k·K)
Outer core reflectorαw,21.70566 × 10−8 (Δk/k·K)
Outer core blanketαw,37.14921 × 10−10 (Δk/k·K)
(vi) Cladding densityInner coreαc,14.66626 × 10−7 (Δk/k·K)
Outer core reflectorαc,20.00000 (Δk/k·K)
Outer core blanketαc,35.61635 × 10−9 (Δk/k·K)

#### 3.2.1 Core Radial Expansion Reactivity.

The reactivity induced by the radial movement in the fuel region due to the core expansion or constriction is represented as follows:
$ρr=αr(TNa,in,1−TNa,in,1,ini)$
(5)

where αr (Δk/k·K) is the reactivity coefficient by the core radial expansion, and TNa,in,1 (K) is the average inlet temperature of the coolant in the inner core.

#### 3.2.2 Doppler Reactivity.

The reactivity induced by the variation of the neutron absorption cross section due to that of the fuel temperature is represented as follows:
$ρD=βDln(Tf,1Tf,1,ini)$
(6)

where βD (Δk/k) is the reactivity coefficient by the Doppler effect, Tf,1 (K) is the average temperature of the fuel in the inner core.

#### 3.2.3 Fuel Axial Expansion Reactivity.

The reactivity induced by the axial expansion or contraction of the fuel is represented as follows:
$ρa=∑j=13αa,j(Tf,j−Tf,j,ini)$
(7)

where αa,j (Δk/k·K) is the reactivity coefficient by the fuel axial expansion in the region of j, Tf,j (K) is the average temperature of the fuel in the region of j, where j means “in the inner core”, “in the outer core reflector”, and “in the outer core blanket” by the indexes of 1, 2, and 3, respectively.

#### 3.2.4 Coolant Density Reactivity.

The reactivity induced by the effects of the neutron leakage, the moderation, and the reflection due to the coolant densities is represented as follows:
$ρNa=∑j=13αNa,j(TNa,j−TNa,j,ini)$
(8)

where αNa,j (Δk/k·K) is the reactivity coefficient by the change of the coolant temperature in the region of j, TNa,j (K) is the average temperature of the coolant in the region of j, where j means “in the inner core,” “in the outer core reflector,” and “in the outer core blanket” by the indexes of 1, 2, and 3, respectively.

#### 3.2.5 Wrapper Tube Density Reactivity.

The reactivity induced by axial expansion or contraction of wrapper tubes is represented as follows:
$ρw=∑j=13αw,j(Tw,j−Tw,j,ini)$
(9)

where αw,j (Δk/k·K) is the reactivity coefficient by the change of the wrapper tube temperature in the region of j, Tw,j (K) is the average temperature of the wrapper tube in the region of j, where j means “in the inner core”, “in the outer core reflector”, and “in the outer core blanket” by the index of 1, 2, and 3, respectively.

The reactivity induced by axial expansion or contraction of fuel claddings is represented as follows:
$ρc=∑j=13αc,j(Tc,j−Tc,j,ini)$
(10)

where αc,j (Δk/k·K) is the reactivity coefficient by the change of the fuel cladding temperature in the region of j, Tc,j (K) is the average temperature of the fuel cladding in the region of j. The indexes of 1, 2, and 3 in j, indicate “in the inner core”, “in the outer core reflector”, and “in the outer core blanket”, respectively.

### 3.3 Boundary Conditions.

In both analyses of BOP-302R and BOP-301 tests, the transient data of flowrate at the intermediate heat transport system (IHTS), the temperature at the inlet of the IHX on the IHTS side, the rotational speed of the primary pumps, and the electromagnetic pump head were given as boundary conditions from Ref. [6] for the test definitions. The decay heat curve in SHRT-17 [16], as shown in Fig. 4, was adopted tentatively because no information was provided about it in Ref. [6], and it was considered that it would have little impact on the behavior of the whole plant.

Fig. 4
Fig. 4
Close modal

### 3.4 Initial Conditions of Balance of Plant-301.

Table 4 shows the initial heat balance around the core and the IHX on the IHTS side in the BOP-301 test. The IHX outlet temperature in the IHTS calculated from the measured data of the inlet temperature of IHX, and the flowrate in the IHTS exceeded the core outlet temperature. This problem was regarded to be due to the lack of consideration of the heat radiation from the cold pool to the atmosphere, as discussed in Sec. 4.1. The inlet temperature of IHX in the IHTS was set at 543 K to obtain the initial heat balance, 10 K lower than that provided as boundary conditions in Ref. [6]. This modification was considered to have a negligible effect on the whole plant response of the PHTS because the heat removal by the intermediate loop is isolated just after the transient.

Table 4

Initial heat balance in BOP-301

Inlet temperature, (K) (Given values)Mass flow rate, (kg/s) (Given values)Outlet temperature, (K) (calculation results)
Core617473668
IHX on IHTS side553202671
Inlet temperature, (K) (Given values)Mass flow rate, (kg/s) (Given values)Outlet temperature, (K) (calculation results)
Core617473668
IHX on IHTS side553202671

## 4 Results and Discussion

The analysis results were compared with the measured data. The typical uncertainties of the measured reactor power and the fluid temperature can be estimated as 2% and 0.5% [9] of the steady-state, which are 1.2 MW and 3.6 K at the maximum, respectively. The differences between the analysis results and the measured data beyond the uncertainties are discussed in the following sections.

### 4.1 Steady State Analysis Results.

Tables 5 and 6 show the measured data and the analysis results in the steady-state of BOP-302R and BOP-301, respectively. In both tests, all the parameters calculated by S-COPD agreed well with the measured data.

Table 5

Comparisons of initial conditions of BOP-302R between S-COPD analysis and experiment

ParametersExperimental dataS-COPD
Reactor power (MW)59.8959.98
Inner core mass flow rate (kg/s)391.4390.7
Outer core mass flow rate (kg/s)75.573.3
Core bypass mass flow rate (kg/s)3.93.9
IHX Inlet temperature in IHTS (K)562.4Boundary conditiona
IHX Outlet temperature in IHTS (K)707.1714.1
Mass flow rate in IHTS (kg/s)307.2Boundary conditiona
IHX inlet temperature in PHTS (K)706.0716.7
IHX outlet temperature in PHTS (K)619.3615.6
HPP inlet temperature (K)616.2616.6
LPP inlet temperature (K)617.2616.6
Z-pipe inlet temperature (K)715.9716.7
ParametersExperimental dataS-COPD
Reactor power (MW)59.8959.98
Inner core mass flow rate (kg/s)391.4390.7
Outer core mass flow rate (kg/s)75.573.3
Core bypass mass flow rate (kg/s)3.93.9
IHX Inlet temperature in IHTS (K)562.4Boundary conditiona
IHX Outlet temperature in IHTS (K)707.1714.1
Mass flow rate in IHTS (kg/s)307.2Boundary conditiona
IHX inlet temperature in PHTS (K)706.0716.7
IHX outlet temperature in PHTS (K)619.3615.6
HPP inlet temperature (K)616.2616.6
LPP inlet temperature (K)617.2616.6
Z-pipe inlet temperature (K)715.9716.7
a

The experimental data in the column on left side was used in S-COPD as the boundary conditions.

Table 6

Comparisons of initial conditions of BOP-301 between S-COPD analysis and experiment

ParametersExperimental dataS-COPD
Reactor power (MW)30.98a30.97
Inner core mass flow rate (kg/s)392.9390.9
Outer core mass flow rate (kg/s)75.873.3
Core bypass mass flow rate (kg/s)3.93.9
IHX inlet temperature in IHTS (K)553.4543.4
IHX outlet temperature in IHTS (K)666.3661.6
Mass flow rate in IHTS (kg/s)202.2Boundary conditionb
IHX inlet temperature in PHTS (K)665.6667.2
IHX outlet temperature in PHTS (K)619.6615.2
HPP inlet temperature (K)616.5615.7
LPP inlet temperature (K)617.1615.7
Z-pipe inlet temperature (K)666.9667.2
ParametersExperimental dataS-COPD
Reactor power (MW)30.98a30.97
Inner core mass flow rate (kg/s)392.9390.9
Outer core mass flow rate (kg/s)75.873.3
Core bypass mass flow rate (kg/s)3.93.9
IHX inlet temperature in IHTS (K)553.4543.4
IHX outlet temperature in IHTS (K)666.3661.6
Mass flow rate in IHTS (kg/s)202.2Boundary conditionb
IHX inlet temperature in PHTS (K)665.6667.2
IHX outlet temperature in PHTS (K)619.6615.2
HPP inlet temperature (K)616.5615.7
LPP inlet temperature (K)617.1615.7
Z-pipe inlet temperature (K)666.9667.2
a

Page 5 in Ref. [6].

b

The experimental data in the column on left side was used in S-COPD as the boundary conditions.

The difference between the IHX inlet and outlet temperature in the IHTS calculated by S-COPD was 7 K and 5 K smaller than the measured data in BOP-302R and BOP-301, respectively. These discrepancies were supposed to be caused by the heat sink effect other than that from the IHTS, e.g., heat radiation from the cold pool to the atmosphere. The problem in acquiring the initial heat balance in BOP-301 would be fixed by considering this phenomenon. As shown in Table 4 in Sec.3.4, the IHX outlet temperature in the IHTS was estimated assuming that all the reactor power was transferred to the IHTS. Taking into account the heat radiation effect from the cold pool, the initial heat balance in BOP-301 would be improved.

### 4.2 Transient Analysis Results

#### 4.2.1 Intermediate Heat Exchanger Inlet and Outlet Temperatures in Intermediate Heat Transport System and Primary Heat Transport System.

Figures 5 and 6 compare the analysis results and the measured data of the IHX inlet and outlet temperatures in IHTS in BOP-302R and BOP-301, respectively. The analysis results of the temperature difference between the IHX inlet and IHTS outlet followed the measured data profile within the discrepancies at 22 K as the maximum value. These discrepancies were considered to be caused by the difference in the heat transfer characteristics of the IHX between the numerical model and the actual one when the intermediate flowrate was close to zero by the pump trip on the intermediate side.

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal

Figures 7 and 8 compare the analysis results and the measured data of the IHX inlet and outlet temperature in PHTS in BOP-302R and BOP-301, respectively. The maximum discrepancy degree of the IHX inlet temperature in PHTS between the analysis results and the measured data was approximately 11 K. This could be explained by the profiles of the core outlet temperature described in Sec. 4.2.3. As for the IHX outlet temperature in PHTS, the analysis results showed a sharp increase just after starting the transient. Moreover, large discrepancies were observed between the analysis results and the measured data at approximately 78 K in BOP-302R and 34 K in BOP-301, as shown in Figs. 7 and 8, respectively. Figure 9 shows the temperature distribution around the IHX outlet at 50 s calculated by the computational fluid dynamics (CFD) code (FLUENT) [17]. Since the thermocouples at the IHX outlet in PHTS were located about 2 inches outside the IHX tubes [9], the temperature discharged from the IHX outlet was not captured by the thermocouples, as shown in Fig. 9.

Fig. 7
Fig. 7
Close modal
Fig. 8
Fig. 8
Close modal
Fig. 9
Fig. 9
Close modal

#### 4.2.2 Reactor Power and Reactivity.

Figures 10 and 11 compare the analysis results and the measured data of the reactor power in BOP-302R and BOP-301, respectively. The total power calculated by S-COPD agreed to the measured data within 7.0 MW and 1.4 MW, corresponding to 11.5% and 4.5% of the initial value in BOP-302R and BOP-301, respectively. These discrepancies were considered to be caused mainly by the slower increase in the core inlet temperature than the measured data shown in Sec. 4.2.3. This indicates the modification of the cold pool model with the perfect mixing volume was required, as described in Sec. 4.3.

Fig. 10
Fig. 10
Close modal
Fig. 11
Fig. 11
Close modal

Figures 12 and 13 show the analysis results of the reactivities calculated by S-COPD in BOP-302R and BOP-301, respectively. The reactor power was decreased mainly due to the reactivity by the core radial expansion in both tests. The increase in the fuel axial expansion and the coolant density reactivities of the BOP-302R was larger than the BOP-301. These differences were considered to be caused by the larger decrease in the core average temperature in BOP-302 than in BOP-301.

Fig. 12
Fig. 12
Close modal
Fig. 13
Fig. 13
Close modal

#### 4.2.3 Core Inlet and Outlet Temperatures.

Figures 14 and 15 compare the analysis results and the measured data of the core inlet temperature in the HPP and LPP, and the outlet temperature at the Z-pipe inlet in BOP-302R and BOP-301, respectively. In the analysis, during 500 s from the initial in both tests, the increment rate of the core inlet temperature was slower than the measured data. The perfect mixing volume model of the cold pool in which the thermal stratification would occur was considered to cause this difference. The inlet temperature of the core in the analysis was approximately 14 K and 7 K higher than measured data in BOP-302R and BOP-301, respectively.

Fig. 14
Fig. 14
Close modal
Fig. 15
Fig. 15
Close modal

The feedback reactivity due to the smaller expansion of the core support plate was found to be underestimated because of the slower increase in the core inlet temperature than the measured one. As shown in Fig. 10, the reactor power calculated in BOP-302R decreased more slowly than the measured data. In BOP-301, however, the reactor power calculated by the S-COPD decreased a little faster than the measured data, though the inlet temperature of the core increased slower than the measured data, as shown in Fig. 11. This indicates that the current reactivity models underestimated the total reactivity, and further investigation of the reactivity model would be required to bring positive reactivity; for example, adding the core bowing reactivity can be a strategy to bring positive reactivity. The sodium temperature at the elevation of the upper load pad located near the core outlet decreased, as shown in Figs. 14 and 15. As a result, at the middle height of the core, FAs moved inward due to the thermal deformation by the structure shrinkage on the height of the upper load pad, and the positive reactivity was supposed to be inserted.

As shown in Figs. 14 and 15, the measured temperature at the inlet of the HPP was higher than that of the LPP in both tests. In the analysis results, however, temperature profiles were traced at the inlet of the HPP and the LPP with the same trend. Considering the difference in the piping lengths, modeling the heat transfer to the cold pool from the high- and low-pressure pipings connected to the HPP and the LPP, would improve the temperature transition profile.

### 4.3 Sensitivity Analyses of Mixing Volume of Cold Pool.

The lower increase in the core inlet temperature and the slighter decrease in the reactor power than the measured data were simulated, as shown in Secs. 4.2.2 and 4.2.3, due to the perfect mixing volume model of the cold pool. Then, the sensitivity analyses of the mixing volume of the cold pool were carried out to investigate the influence of the thermal stratification in the cold pool on the behavior of the whole plant.

Figure 16 shows the outline of the cold pool model of the sensitivity analyses. The cold pool was divided into two regions at the middle height of the IHX outlet window, and only the upper region of the cold pool was assumed to be mixed as the minimum mixing volume for the thermal stratification in the cold pool.

Fig. 16
Fig. 16
Close modal

Figures 17 and 18 compare the numerical results of the core inlet and outlet temperatures between the sensitivity analyses and the original analyses in BOP-302R and BOP-301, respectively. Figures 19 and 20 compare the numerical results of the reactor power between the sensitivity analyses and the original analyses in BOP-302R and BOP-301, respectively. In the sensitivity analyses, the core inlet temperature increased to approximately 19 K and 12 K higher than in the original analyses in BOP-302R and BOP-301, respectively. Moreover, in the sensitivity analyses, the reactor power decreased more rapidly than in the original analyses. The maximum differences in the reactor power were 15 MW and 7 MW in BOP-302R and BOP-301, respectively. It was found that the effective mixing volume of the cold pool greatly impacted the behaviors of the whole plant. In addition, the thermal stratification estimated to occur in the cold pool should be clarified by using tools such as CFD codes.

Fig. 17
Fig. 17
Close modal
Fig. 18
Fig. 18
Close modal
Fig. 19
Fig. 19
Close modal
Fig. 20
Fig. 20
Close modal

## 5 Conclusion

The reactor power calculated by S-COPD agreed to the experimental data within 11.5% of the initial value. In addition, the applicability of the evaluation models of the feedback reactivity, including those obtained by the effect of the core radial expansion on the ULOHS events, was successfully confirmed.

In the analyses, the cold pool in which the thermal stratification would occur was modeled by one perfect mixing volume, and the increment rate of the core inlet temperature was slower than the measured data. Additionally, the simulated reactor power in the BOP-301 test decreased slightly faster than the measured data despite of the slower increase in the core inlet temperature. This indicated that the present reactivity models underestimated the total reactivity.

Further studies and model improvements are required on the addition of the core bowing reactivity, the modeling of the heat radiation from the cold pool to the atmosphere and the heat transfer from the high-pressure piping or the low-pressure piping to the cold pool, and the refinement of the cold pool model by taking account of the thermal stratification referring to the results of CFD analyses.

## Acknowledgment

The authors would like to express our gratitude to Dr. T. Sumner in Argonne National Laboratory (ANL) for providing the experimental data of BOP-302R and BOP-301.

## Nomenclature

Re =

Reynolds number

T =

temperature (K)

α =

reactivity coefficient (Δk/k·K)

β =

reactivity coefficient (Δk/k)

λ =

friction coefficient

ρ =

reactivity (Δk/k)

### Subscripts

Subscripts
1 =

inner core

2 =

outer core reflector

3 =

outer core blanket

a =

fuel axial expansion

c =

D =

Doppler

f =

fuel

in =

inlet

ini =

initial conditions

j =

variable of locations

Na =

coolant

r =

w =

wrapper tube

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