7. MODELS AND RESULTS
7.3.5. Final results, data comparisons
Based on the blind benchmark analyses of SHRT-17 and SHRT-45R, three aspects needed to improve. First, the simulated temperature of the IHX was so much higher than the recorded data. According to the analyses of temperatures of the Z-Pipe and IHX, the problem does not result from the predicted temperature of the core but may be the heat loss in the Z-Pipe.
Therefore, a heat transfer model for the Z-Pipe was added. Second, the simulated mass flow during natural circulation was higher than the recorded data, which might have been caused by neglecting thermal stratification of the cold pool. Therefore, a three-layer pool model was
added. Third, the calculated temperatures of XX10 were much lower than the experiment data. XX10 was a non-fueled subassembly surrounded by driver subassemblies. Sodium has the property of high thermal conductivity. The heat transfer between XX10 and the surrounding subassemblies may raise the temperature in XX10. Hence, the inter-wrapper model was used.
With the improved models and the more comprehensive knowledge of EBR-II, the final CRP results are in better agreement with the experiment data.
7.3.5.1. SHRT-17
FIG. 73 displays comparison of final results and experiment data for SHRT-17. For SHRT-17, it was discovered that no Z-Pipe inlet temperature was recorded, and the data shown are actually an average of several subassembly outlet temperatures. The mass flow of pump #2 was more reasonable than the Phase 1 result.
Comparing FIG. 68 and FIG. 74, it can be seen that the predicted temperatures in XX09 are closer to the experiment data with the above modification.
FIG. 73. Comparison of final results and experimental data for SHRT-17.
FIG. 74. Comparison of final results and experimental data in XX09 for SHRT-17.
After the addition of the inter-wrapper model, the temperature of XX10 increased and agreed well with the experiment data, as can be seen by comparing FIG. 69 and FIG. 75. The reverse flow in XX10 also disappeared.
FIG. 75. Comparison of final results and experimental data in XX10 for SHRT-17.
7.3.5.2. SHRT-45R
In FIG. 76, the simulated IHX primary inlet temperature and IHX intermediate outlet temperature are closer to the data in phase 2 than were the phase 1 results. The mass flow rate of pump #2 was a better fit to the data than was the phase 1 result.
FIG. 76. Comparison of final results and experimental data for SHRT-45R.
Comparing FIG. 71 and FIG. 77, it can be seen that the peak temperature in XX09 decreased but the temperature late in the transient was higher than the experiment data, possibly caused by overestimation of the power.
Looking at FIG. 72 and FIG. 78, the phase temperature of XX10 increased and agreed well with the experiment data, which proves the significance of heat transfer through the inter-wrapper sodium.
FIG. 77. Comparison of final results and experimental data for XX09 for SHRT-45R.
FIG. 78. Comparison of final results and experimental data in XX10 for SHRT-45R.
7.3.5.3. Model improvements
As a result of analyses of the phase 1 results, the three-layer model of the sodium pool, heat transfer between the Z-Pipe and the cold pool, and the inter-wrapper flow model were added.
A comparison between the simulation results with the three-layer pool model and with the perfect mixing model are presented in FIG. 79 for SHRT-17 and in FIG. 80 for SHRT-45R. In both cases, the results using the three-layer model agree with the measured data significantly better than did the results using the perfect mixing model. The three-layer model allowed inclusion of component heat transfer that could cause stratification of the cold pool.
FIG. 79. Comparison between the perfect mixing model and the three-layer model for the cold pool during SHRT-17.
FIG. 80. Comparison between the perfect mixing model and the three-layer model for the cold pool during SHRT-45R.
Since the heat transfer from surrounding subassemblies affects the temperature distribution of XX10 significantly, the inter-wrapper flow model was developed. Comparing FIG. 75 and FIG. 78 clearly shows that, for XX10, heat transfer between subassemblies is significant.
7.4. IRSN (FRANCE)
7.4.1. Geometry/discretization
The CATHARE nodalization of the EBR-II primary circuit is shown in FIG. 81. The modelling of the intermediate circuit is limited to the heat exchangers (IHX), with experimental data as boundary conditions for secondary sodium flow rate and inlet temperature.
The primary circuit is described by a set of:
(a) 0-D modules (VOLUME) for the tank, the inlet plena and the upper plenum;
(b) 1-D modules (Axial) for the core, the inlet piping and the Z-Pipe.
FIG. 81. CATHARE nodalization of the EBR-II primary circuit.
7.4.2. Thermal hydraulics methods and models 7.4.2.1. Code(s) used
The CATHARE system code (version V2.5_3) was used to simulate the 17 and SHRT-45R tests (see the brief description in Section 5.1.1).
7.4.2.2. Model
The main features and assumptions of the CATHARE model are given below:
(a) Tank
Single volume (thermal stratification not taken into account);
Free level (argon cover);
Heat losses neglected (short term transient).
(b) Primary pumps
Two primary pumps with associated piping modelled individually;
Characteristics described by homologous curves (head and torque by octant), with assumptions for the low flow rate regime, as primary pumps are not totally defined in the benchmark specifications.
(c) Inlet plena
Single volume (perfect mixing).
(d) Core
4 channels for the high pressure zone (fissile subassemblies, blanket subassemblies, XX09 and XX10 instrumented subassemblies);
2 channels for the low pressure zone (blanket subassemblies, reflector subassemblies);
Singular pressure drop coefficients at channels inlet tuned to match the steady state core mass flow rate distribution for run 129-C;
Specific friction law used for wire-wrapped fuel pins (Pontier’s correlation [80]);
Thimble flow region for XX09 and XX10 subassemblies not modelled;
Heat exchange between subassemblies not modelled.
(e) Upper plenum
Single volume (perfect mixing);
Horizontal and vertical baffles not taken into account.
(f) Z-pipe
Double-wall structure modelled;
Stagnant sodium between the inner and outer piping;
Heat transfer from the Z-Pipe to the tank taken into account and tuned with the help of a heat exchange coefficient (use of a heat transfer correlation for liquid metal in natural convection from the literature as a first approach).
(g) Auxiliary electromagnetic pump
Specific CATHARE pump model (flow rate proportional to voltage);
Only used for the SHRT-45R test.
(h) IHX
Two counter-current pipes;
Inlet boundary conditions imposed at the secondary side (experimental data).
The experimental power evolution is directly used as a boundary condition for the SHRT-17 test. The radial power distribution given in the benchmark specifications for run 129-C was used. A uniform axial power distribution is assumed (no information in the benchmark specifications). A point-kinetics model is used for the SHRT-45R test. The reactivity feedback coefficients used (Doppler, radial fuel expansion, axial fuel expansion, axial cladding expansion, radial core expansion) are based on the information provided in the benchmark specifications.
Leakage flows throughout the primary circuit (3.2% of the primary flow rate in steady state according to the benchmark specifications) are neglected.
7.4.3. Blind results 7.4.3.1. SHRT-17
The key parameter for this test is the natural circulation mass flow rate after the trip of the primary pumps. The mass flow rate has been measured for primary pump #2 (no data available for primary pump #1) and the instrumented subassemblies. The predicted values are higher than the measurements for the blind calculation. With CATHARE, the total core flow rate drops from 460 kg/s to 13 kg/s within 65 s after the primary pumps trip (6.5 kg/s for the for primary pump #2 as compared to the measured value of 2.96 kg/s, and 8.9x10-2 kg/s for the XX09 subassembly as compared to the measured value of 2.3x10-2 kg/s). Then, with the development of natural circulation, the core flow rate increases slowly up to 17 kg/s (8.5 kg/s for the primary pump #2 as compared to the measured value of 5.7 kg/s, and 9.7x10-2 kg/s for the XX09 subassembly as compared to the measured value of 4.5x10-2 kg/s).
This result leads to a significant underestimation of the sodium temperature in the core. The temperature decrease caused by the reactor scram and the temperature increase occurring immediately after is reproduced by CATHARE, but with smaller amplitudes. The peak sodium temperature at the core top for the XX09 subassembly (between 850 and 890°C according to the thermocouples location) is underestimated by 100°C approximately.
The first temperature measurement available downstream of the core is located at the Z-Pipe inlet. The temperature decrease and increase are both largely underestimated (by 30–40°C).
Conversely, the IHX primary inlet temperature is overestimated by 60°C. The temperature decrease during the second part of the transient is not as sharp with CATHARE.
The inlet plena temperatures, almost constant during the whole transient (900 s), are well predicted by CATHARE. The slight decrease of the low pressure inlet plenum temperature during the last part of the transient is not reproduced, though.
XX09 and XX10 instrumented subassemblies were modelled by specific channels, but the 1-D modelling (single pin model) restricted the code-to-data comparisons. Other participants used subchannel or computational fluid dynamics (CFD) models to calculate the detailed radial temperature distribution in the subassembly.
7.4.3.2. SHRT-45R
The SHRT-45R test was calculated, but it was decided to mainly focus on the SHRT-17 test as a first step. The power evolution is not a boundary condition for this transient: the reactivity feedback effects need to be calculated. Nevertheless, it was a good opportunity to test the CATHARE point-kinetics model and the electromagnetic pump model (the auxiliary pump was on for this test). The results obtained are consistent overall, with similar trends as those observed for the SHRT-17 test. An in-depth analysis still needs to be conducted.
7.4.4. Final results, data comparisons 7.4.4.1. SHRT-17
Modelling improvements for the final calculations are listed in the next paragraph.
Comparisons of final results against temperature and flow rate measurements show significant improvements. With CATHARE, the total core flow rate drops from 460 kg/s to 6.2 kg/s within 55 s after the primary pumps trip (4 kg/s for primary pump #2 as compared to the measured
value of 2.96 kg/s, and 4.96x10-2 kg/s for the XX09 subassembly as compared to the measured value of 2.3x10-2 kg/s). Then, with the development of natural circulation, the core flow rate increases slowly up to 10.5 kg/s (5.4 kg/s the for primary pump #2 as compared to the measured value of 5.7 kg/s, and 6.2x10-2 kg/s for the XX09 subassembly as compared to the measured value of 4.5x10-2 kg/s).
The peak sodium temperature at the core top for the XX09 subassembly is better predicted as well (878°C with CATHARE as compared to the measured values of 8508–90°C).
However, large discrepancies remain between the measured and calculated temperatures at the Z-Pipe inlet and IHX inlet. It could be explained by different reasons:
(a) A perfect mixing model seems to be inadequate for the upper plenum: horizontal and vertical baffles may have a significant impact on flow paths;
(b) According to Argonne, the thermocouple reading at the Z-Pipe inlet was not recorded correctly: the measurement seems actually to be a combination of outlet temperature measurements from several subassemblies;
(c) Thermal stratification may occur during the establishment of natural circulation. As a consequence, the sensor might not give a mean value;
(d) Heat losses from the Z-Pipe affect the temperature at the IHX inlet, but sensitivity calculations seem to indicate that it cannot explain the large discrepancies observed.
7.4.4.2. SHRT-45R
Model improvements made for the SHRT-17 test were taken into account for the SHRT-45R test and led to better results. No specific sensitivity calculations (except for the auxiliary electromagnetic pump) were performed to further improve these results.
7.4.4.3. Model improvements
Model improvements for the final calculations are listed below:
Inlet piping
A single set of inlet piping (from primary pumps to inlet plena), with one equivalent primary pump (weight of 2) was used for the blind calculations. As the pump speed differs slightly between the two primary pumps, the inlet piping mass flow rates could not be well predicted with this simplified model. Two sets of inlet piping, with independent primary pumps, were used for the final calculations. A dissymmetrical behaviour and flow inversions are now observed in the inlet piping during the natural convection onset.
Singular pressure drop coefficients at low flow rates
Constant singular pressure drop coefficients were used for the blind calculations. They were tuned to match the nominal flow rate and the core flow rate distribution. No information was available in the benchmark specifications concerning singular pressure drop at low flow rate (for the core and primary pumps). As singular pressure drop coefficients increase at low flow rates [81], a sensitivity calculation was performed with higher values (multiplied by 10) for low flow rates. Better mass flow rate results are found with this modification. This sensitivity calculation also showed, as expected, the strong influence of the core mass flow rate on the core temperatures. Particular attention should be paid to the values used, though. A fine-tuning may hide modelling weaknesses or errors.
Auxiliary electromagnetic pump (SHRT-45R)
Only two voltage values (step) were used for the blind calculations. The accurate voltage evolution from the benchmark specifications was taken into account for the final calculations.
Better mass flow rate results are found particularly at the time when the EM pump voltage increases (around 600 s).
Other modelling issues need to be investigated, in particular:
(a) Leakage paths throughout the primary circuit;
(b) Axial power distribution;
(c) Heat exchange between subassemblies;
(d) Heat transfer between the Z-Pipe and the cold pool.
7.4.5. Conclusions
The objective of this benchmark exercise was to assess the CATHARE capability in simulating the thermal hydraulics behaviour of the EBR-II reactor under natural circulation conditions. The analysis conducted mainly focused on the SHRT-17 test (experimental power evolution used as a boundary condition and auxiliary electromagnetic pump off).
The main conclusions are summarized below:
(a) A good agreement was obtained in steady state;
(b) Trends of mass flow rate and sodium temperature in the core are well predicted during establishment of natural circulation with appropriate singular pressure drop coefficients. Precise information concerning primary pump characteristics and singular pressure drops in subassemblies for the low flow rate regime is necessary, as fine-tuning may hide modelling weaknesses or errors;
(c) The 1-D modelling (with single pin model) for instrumented subassemblies restricted the code-to-data comparisons;
(d) Large discrepancies between calculated and measured temperatures are observed at the Z-Pipe inlet and the IHX inlet:
(i) The comparison is quite limited by the lack of reliability and relevance of the measurements: the thermocouple reading at the Z-Pipe inlet was not recorded correctly according to Argonne, and the thermocouple at the IHX inlet may not give an average value due to thermal stratification in the Z-Pipe during establishment of natural circulation;
(ii) Modelling issues related to mixing and thermal stratification for the upper plenum and the Z-Pipe cannot be address with a 0-D/1-D modelling.
(e) Some modelling assumptions (axial power distribution, leakage flows throughout the primary circuit) still need to be investigated by additional sensitivity calculations.
This benchmark exercise has focused on establishment of natural convection (experimental data limited to 900 s). It would be interesting to pursue this assessment work for long term behaviour.
7.5. KIT (GERMANY)/KYUSHU UNIVERSITY (JAPAN) 7.5.1. Geometry/discretization
All the reactor components were taken into account for creating the 2-D R-Z SIMMER-III v.3E [30] model. Unavoidable approximations were introduced for modelling the reactor outlet ‘Z-Pipe’ and the sodium inlet pipes. In FIG. 82 the SIMMER-III r-z model for SHRT-17 (full tank model) is shown. Values for select model parameters are compared against the benchmark specification values in TABLE 6. As indicated in TABLE 6, the chosen axial meshes reasonably represent the relative positions of the components.
FIG. 82. SIMMER-III EBR-II r-z model (SHRT-17).
TABLE 6. SIMMER-III SHRT-17 R-Z MODEL PARAMETERS
Components Reference (m.) SIMMER-III Model (m.)
Total height 7.988 7.988
External radius 3.962 3.962
Sodium free surface level 6.941 6.941
Upper plenum upper boundary (zsup) 3.816 3.816 Upper plenum radial boundary (rext) 1.1555 1.1555 Upper plenum lower boundary (zinf) 2.975 2.999
Radial position, IHX centre 2.95 2.95
Radial position, pump centre 3.251 3.22
Z-Pipe at upper plenum exit 3.57 3.421
The zones outside of the core were modelled in the same way for the two tests. However, in order to take into account the different core layout and control rod axial positions for the two tests, the core zone was modelled using one discretization for SHRT-17 (18 radial mesh cells) and a different one for SHRT-45R (34 radial mesh cells). In total, the SHTR-17 model
consists of 30 radial and 50 axial fluid-dynamic mesh cells. The SHRT-45R model has, instead, 49 radial and 52 axial fluid-dynamic mesh cells. In order to assess the ring-wise model, the subassemblies (SAs) were grouped according to their location and to their type.
TABLE 7 shows some examples for some special SA types.
TABLE 7. DISTANCE FROM THE CORE CENTRE OF SAFETY ROD, HW-CR, XX10, AND XX09
Distance from the centre (m) SA type HEX-Z model R-Z SIMMER model
SHRT-17 R-Z SIMMER model
SHRT-45R
Safety Rod 0.118 0.116 0.116
XX09 0.204 0.215 0.192
HW-CR 0.224 0.225 0.221
XX10 0.236 0.235 0.197
7.5.2. Nuclear and thermo-physical data/correlations
For the EBR-II benchmark, the standard SIMMER-III version was modified by Kyushu University (KU) in order to take into account the thermodynamic properties for the U-5%Fs (Fissium) alloy.
In the SIMMER codes, the thermodynamic properties of reactor core materials in solid, liquid and vapour phases are calculated by using an analytical equation of state (EOS) model ([82], [83], [84]) expressed as polynomial fits for temperature (T) and specific volume (υ) as a function of specific internal energy (e). For the EBR-II transients, only solid properties of metal fuel were considered, introducing six fitting coefficients for temperature and six for the specific volume in order to take into account the two solid-solid phase transitions. A comparison with the data provided in the benchmark specifications (Section 4) was performed, as indicated in FIG. 83. Good agreement was obtained also for thermal conductivity.
From the neutronics point of view, SIMMER-III is a deterministic code with separated cell and flux calculations [85]. In each cell the self-shielded macroscopic cross-sections are calculated inside the code from a set of infinite diluted cross-sections and self-shielding factors tabulated as a function of temperature and updated at every timestep of the reactivity calculation [86]. Neutron flux calculations are performed through a SN transport code (TWODANT or PARTISN-based) using a diffusion synthetic acceleration scheme [50].
For SHRT-17, only the fluid dynamics modules of SIMMER were applied, and its neutronics module was deactivated. The reasons for choosing this option are: 1) no details on fuel compositions for SHRT-17, and 2) the lack of a gamma heating model in the neutronics model of SIMMER. The power was provided externally as input data and was adjusted to match the power given in the benchmark specifications (see FIG. 84).
(a) (b)
FIG. 83. Comparison of SIMMER EOS analytical model and input data: (a) density-temperature correlation; (b) specific heat-temperature correlation.
For SHRT-45R, coupled neutronics and thermal hydraulics calculations were carried out [87].
Both the TWODANT module of SIMMER [50] and the new KIT development [88] based on the PARTISN code were employed. For the transient calculations, cases were run with a S8
approximation and 11 energy groups [89] assuming the transport approximation for the treatment of the anisotropy of neutron scattering. A finer (compared to the thermal hydraulic mesh) neutronics mesh was applied for the overall core zone (including blankets). In total, 118 radial and 138 axial neutronics mesh cells were considered. The SIMMER code does not need to use pre-calculated reactivity feedback coefficients. In addition to feedbacks related to fuel, coolant, steel and control material density variations and Doppler effect, core thermal expansion effects were also recently introduced at KIT ([90], [91], [92]). The standard SIMMER version was used for the blind SHRT-45R calculation, while the extended version was used for the final results.
(a) (b)
FIG. 84. SHRT-17: comparison of the power per ring between input data and SIMMER results (steady state).
7.5.3. Thermal hydraulics methods and models 7.5.3.1. Code(s) used
For the transient calculations, the SIMMER-III code was used. For SHRT-17, oriented to
For the transient calculations, the SIMMER-III code was used. For SHRT-17, oriented to