- Email: [email protected]
Neutronic simulation of China Experimental Fast Reactor start-up tests. Part I: SARAX code deterministic calculation
Annals of Nuclear Energy 136 (2020) 107046
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Neutronic simulation of China Experimental Fast Reactor start-up tests. Part I: SARAX code deterministic calculation Xianan Du, Jiwon Choe, Tuan Quoc Tran, Deokjung Lee ⇑ Department of Nuclear Engineering, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Republic of Korea
a r t i c l e
i n f o
Article history: Received 7 June 2019 Received in revised form 24 July 2019 Accepted 7 September 2019
Keywords: CEFR Start-up tests SARAX code system Validation Measurement data
a b s t r a c t As one of participants of recent coordinated research project proposed by International Atomic Energy Agency and China Institute of Atomic Energy, the computational reactor physics and experiment laboratory of Ulsan National Institute of Science and Technology, Republic of Korea, is currently focused on a study involving the neutronic simulation of the China Experimental Fast Reactor (CEFR) start-up tests. The CEFR start-up tests include obtaining measurements of the criticality, control rod worth, sodium void reactivity, temperature reactivity, and subassembly swap reactivity. The fast reactor neutronic analysis code SARAX is selected for performing such simulations for additional validation. The obtained numerical results are compared with measurement data. In addition, the differences in the expected results of the heterogeneous and homogeneous models are quantified in this study. According to the simulation, the calculated results agreed well with the measured values in the case of the majority of the neutronic characteristics. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Fast reactors (FRs) are important as next-generation advanced nuclear reactor systems owing to their abundant neutrons and hard spectrum. The utilization of uranium resources can be increased while the accumulation of high-level waste can be reduced by implementing the FR technique as soon as possible. According to the report of International Atomic Energy Agency, extensive research and development work has been conducted on this subject in recent decades (IAEA, 2012). Extensive experience of operating FRs has been gained from the operation of more than 20 experimental reactor cores, such as CEFR and BN-600. In this context, identifying biases in the measurement data is useful for improving the accuracy of current methodologies. Therefore, the measurement data of several experimental reactors have been published—for instance, control rod withdrawal tests performed during Phenix end-of-life experiments (IAEA, 2014). Recently, a 4-year coordinated research project (CRP) was launched from February 2018, which was proposed by the China Institute of Atomic Energy and was focused on the neutronics benchmarks analysis of CEFR start-up tests (Huo et al., 2018). The CEFR is a sodium-cooled fast reactor loaded with PuO2–UO2 fuel. However, only UO2 fuel was loaded in the first loading. The ⇑ Corresponding author. E-mail address: [email protected] (D. Lee). https://doi.org/10.1016/j.anucene.2019.107046 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
start-up tests of the CEFR were performed in China from 2010 to 2011. In the benchmarks, the evaluation of the criticality, control rod worth, reactivity effects, and neutron spectral characteristics are included. According to the plan of the CRP, each participant is required to perform a blind neutronics calculation independently at first. After the experimental data is released, each participant can perform a comparison of the simulation results and improve their physical models and simulation codes. As one of the participants of the CRP, the computational reactor physics and experiment (CORE) laboratory of Ulsan National Institute of Science and Technology (UNIST) started the work related with FRs in 2013 (Tak et al., 2013, 2014, 2015). At that time, several studies were focused on core design to obtain a better understanding of neutron behavior and core performance. It is beneficial to use the Monte Carlo method to perform this work with a high accuracy; however, the efficiency of the Monte Carlo calculation is low. Therefore, the development of a deterministic code is necessary to improve the efficiency of the FR design. The STREAM/ RAST-K (Choe et al., 2019; Choi et al., 2017) code system was to be used for the FR neutronic analysis, and the initial work was performed in a recent study (Du et al., 2019). In addition, the SARAX (Zheng et al., 2018a,b, 2018b) code and MC2-3 (Lee and Yang, 2017)/REBUS (Toppel, 1983) code are used for gathering knowledge regarding the simulation modeling and methodology. In this paper, the numerical simulation was performed based on the SARAX deterministic code of the CEFR start-up tests. The
2
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
obtained results were compared with the published measurement data. The results of the in-house Monte Carlo simulation (MCS) (Jang et al., 2018) are introduced in a subsequent paper. In the previous study (Zheng et al., 2018b), the SARAX code was validated based on JOYO MK-I experiments (Yokoyama et al., 2006) and several assembly layouts of zero power physics reactor series experiments (Ikegami et al., 2006). In comparison with the experiment benchmarks, the fuel assembly pitch of the CEFR core was 6.1 cm, which is the smallest value obtained. In addition, the active core height is 45 cm. Such a small core results in a high neutron leakage and makes the deterministic calculation a challenge. Therefore, the aims of the current study are as follows: 1. To quantify the difference in reactivity and safety related parameters between the heterogeneous and homogeneous modeling of the CEFR core; 2. To perform an additional validation of the SARAX code system in such a high leakage system. The remainder of this paper is organized as follows. Section 2 presents the general description of the CEFR start-up tests. In section 3, SARAX code is briefly introduced, and a sensitivity test is performed based on operation loading. This section demonstrates the convergence to the keff value when various calculation conditions are selected. Section 4 summarizes all the expected results of the CRP. In this section, the criticality, control rod worth, sodium void worth, temperature reactivity, and assembly swap reactivity are calculated. The conclusions of this study are presented in Section 5. 2. Description of CEFR start-up tests The CEFR core is the first FR of China, which reached its first criticality in 2010. It is a 65 MWth pool-type sodium-cooled FR. The uranium dioxide fuel with the enrichment of 235U at 64.4% was used in the first loading. The main design parameters are listed in Table 1. The core of the first loading consists of 79 fuel subassemblies (SA), eight control rod (CR) SAs, one neutron source (NS) SA, 338 stainless steel (SS) SAs, and 230 boron shielding. Three control rod types are considered in the operation: two regulating (RE1/2) CR SAs; three shim (SH-1/2/3) CR SAs; and three safety (SA1/2/3) SAs. Fig. 1 shows the layout of only the active core region, including all the control SAs. The axially material distribution and height of each SA is shown in Fig. 2. Note that the real geometry is much more complicated. For example, the lower structure of the fuel SA contains several parts, such as gas plenum, lower con-
Table 1 Main design parameter of CEFR. Parameters
Value
Thermal/Electric power, MW Designed life, year Maximum burn-up, MWd/t Maximum neutron flux, cm-2 s1 Refueling period, day Diameter/Height of main vessel, m Covering gas pressure, MPa Core inlet/outlet temperature, °C Equivalent diameter/height of active core, cm Subassembly lattice pitch, mm Enrichment of 235U of fuel, % Number of fuel SAs Total mass of UO2/U in fuel, kg Total mass of UO2/U in blanket, kg Total mass of B4C in control SAs, kg Total mass of B4C in boron shielding SA2, kg
65/20 30 60,000 3.2e15 80 8.0/12.2 0.005 360/530 60/45 61 64.4 79 417/367 356/313 6.9 552
nector, and bottom end plug. To simplify the deterministic simulation, the axial distribution is simplified based on the volume of each part. In the active part, the fuel assembly contains 61 fuel rods, and the rod lattice pitch is 6.95 mm. The outer diameters of the fuel pellet and cladding are 5.4 mm and 6.0 mm, respectively. In the center of the fuel pellet, a hole of 1.6-mm diameter is designed to deal with the swelling. There is a wrapper of 1.2-mm thickness outside the fuel assembly and the outer/inner flat-to-flat dimensions are 59.0/56.6 mm. The eight CR SAs have the same geometry description. Each CR SA contains seven absorber pellets with a 12.2-mm outer diameter. The outer diameter of the cladding is 14.9 mm. Between the absorber pellet and cladding, there is a 0.7-mm thick sodium bond. These seven absorber rods are stuck together using a 2-mm thick stainless steel circle. Further detailed information can be found in reference (Huo et al., 2018). During the start-up tests, the fuel loading and criticality, control rod worth, sodium void reactivity, temperature reactivity, and subassembly swap reactivity are measured. The condition and state of the core during the measurements are summarized in the following sections with the numerical results.
3. Simulation code and sensitivity test As mentioned previously, the CEFR is a small core with a high leakage. Therefore, it is necessary to perform a sensitivity test to determine the calculation condition before we simulate the startup tests. In this section, the SARAX code is briefly introduced, and the sensitivity test is performed based on the first loading of the CEFR. 3.1. SARAX code SARAX is developed at Xi’an Jiaotong University and is used for FR neutronic analysis. The objectives of the code are to achieve a good accuracy while using advanced methods and modeling schemes with few data adjustments. For the steady-state calculation, the TULIP (Du et al., 2018), Hydra (Xu et al., 2017), and LAVENDER (Zhou et al., 2014) modules are used. Fig. 3 shows the computational flow chart for the steady-state calculation performed using SARAX code. The TULIP code generates 1968-group self-shielded cross sections in a homogeneous or 1D heterogeneous problem based on ENDF/B-VII.0 (Steven and Marck, 2006) point-wise cross sections. After generating the cross sections for each material zone, a 2D R-Z homogeneous core problem is developed, and the neutron flux is solved using the SN difference method. With the obtained spatially dependent neutron flux, the 1968-group cross sections are collapsed into 33 groups, which are used in the 3D SN nodal calculation. The final keff value and power distribution are obtained using LAVENDER code. The 1968-/33-group structures are the same as those of the ECCO (Rimpault, 1995) code. In order to properly generate accurate cross sections of control rod assembly, 1-D supercell model and the SPH method are applied. The detailed information can be found in reference. (Zheng, et al., 2018a) 3.2. Sensitivity test For performing the sensitivity test, the CEFR core based on the first loading is used. For this state, the temperature of all the materials is 250 °C, which is called the cold state. During the operation, all the safety rods are outside the core. The rod position of three shim rods is 330 mm, which is the distance from the bottom of
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
3
Fig. 1. CEFR layout of active core region.
Fuel SA
CR SA
SS(NS) SA
Upper Shielding 500 mm
Handling head
Upper Structure 590 mm
Upper Structure 90 mm
Shielding SA
Upper Structure 500 mm
Connecting Sector 90mm
Upper Blanket 100 mm
Absorber 510 mm Reflector (Neutron Source) 800 mm
Fuel 450 mm
Lower Blanket 250 mm
CR follower
Lower Structure 500 mm
Lower Structure 500 mm
Boron shielding 800 mm
Fig. 3. The computational flow chart of SARAX steady-state calculation. Lower Structure 500 mm
Fig. 2. Axially configuration of each SA.
Lower Structure 500 mm
the active region to the end of the control rod. Two regulating rods have the same rod position of 250 mm. The self-shielded cross sections of the fuel, blanket, and absorber region are prepared using the heterogeneous model. The homogeneous model is used for the other material zones. The
4
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
S8P5 approximation is used when performing the 2D Hydra calculation. In the 3D core modeling, each SA is divided into six triangles, and the height of each node is approximately 50 mm. Owing to the high neutron leakage, the neutron flux becomes more anisotropic. Therefore, the sensitivity test is focused on the SNPN approximation during the 3D core calculation. Table 2 summarizes the keff results of the CEFR first loading state under different approximations. The discretization of the angles is from S4 to S8, and the expansion of the scattering transfer matrices is from P1 to P5. In addition, the outflow transport correction is applied in the S6 calculation. Obviously, a large variance exists between the keff value of the outflow transport correction and P1 approximation. On increasing the order of the scattering matrices to P3, the keff value still exhibits a difference of over 300 pcm. When a more rigorous P5 approximation is applied, the keff value changes slightly. In the LAVENDER code, the 60° symmetric quadrature (Lu, 2007) is used. The number of total angular directions is 12 N, where N is the SN order. Therefore, the keff value does not change significantly for different SN orders. Based on this sensitivity test, the simulations in the following section comprise the use of the S6P3 approximation for obtaining the converged keff value. 4. Numerical results of CEFR start-up tests In this section, the criticality, control rod worth, sodium void reactivity, temperature reactivity, and subassembly swap reactivity of the CEFR start-up tests are calculated using SARAX code. For each calculation, both the homogeneous and heterogeneous models are used to quantify the difference of those parameters. In the homogeneous model, all the SAs are smeared according to the volume fraction. In contrast, only the fuel, blanket, and absorber parts are considered in the heterogeneous model. The cross sections are prepared using the 1D equivalent cylindrical assembly model. 4.1. Criticality Prior to the start-up of the reactor, the core was preliminarily loaded with 81 mock-up fuel SAs in the fuel positions. In the mock-up fuel SA, the fuel region is replaced by a filter that contains only sodium and stainless steel. The volume fraction of sodium is 87.1%. In the lower and upper parts, the fraction of the sodium reduces to 40.9%. A greater amount of stainless steel makes causes these parts to act as the shielding.
Table 2 keff value obtained under different approximation.
Out-flow P1 P3 P5
S4
S6
S8
/ 1.01054 1.01391
1.01613 1.01064 1.01415 1.01414
/ 1.01068 1.01420 1.01421
The reactor reached first criticality on replacing the mock-up fuel SAs with the real fuel SAs in a step-by-step manner. After the loading of the 40th fuel SA, two SS SAs are loaded. According to the measurement obtained, the core eventually reached criticality with 72 fuel SAs loaded, with the RE-2 control rod inserted at the position of 70 mm. In order to simulate the process of reacting the criticality, calculations are performed for several cases, and the core state of each case is listed in Table 3. The layouts of the loading core of 71 and 72 fuel SAs are presented in Figs. 4 and 5, respectively. The results of the SARAX calculation are summarized in Table 4. As the heterogeneous model is applied, the obtained results are closer to the measurement. When only 71 fuel SAs are loaded, the core is under the sub-critical state. The reactivity increases significantly after an additional fuel SA is loaded in the core. The reactivity continues to decrease owing to the insertion of the RE-2 control rod. At the end of this step, the final reactivity is approximately 25 pcm. As compared with heterogeneous model, the homogeneous model underestimated the keff value and reactivity. A difference of approximately 300 pcm can be found between the two models. Owing to the spatial self-shielding effect, the absorption of 238U decreases in the heterogeneous model. In addition, the wrapper reflects more neutrons into the fuel pellets such that the fission reaction rate increases. These two effects cause the homogeneous model to underestimate the keff value. 4.2. Control rod worth The measurement of the control rod worth is an essential part of the reactor start-up test. From this measurement, the data for the reactor operation and safety can be provided. The operation layout, which comprises 79 fuel SAs and 2 SS SAs, was carried out for the control rod worth measurement. The experiment was supposed to be performed in the cold state, while the measured sodium temperature was approximately 245 °C. The eight control rod SAs are divided into two shutdown systems according to the safety regulation. Three shim rod SAs and two regulating rod SAs are included in the first shutdown system while the other three safety rod SAs are included in the second shutdown system. During the experiment, the worth of each control rod and shutdown system is measured. In addition, the shutdown margin should be sufficient when one rod of the largest worth is stuck out of the core, and thus, such situations were taken into consideration as well. In the SARAX calculation, the control rod worth is calculated based on the reactivity changes before and after the rod drop. The position of each rod in the case of each measurement is listed in Table 5. Both the keff value and control rod worth of each case are calculated. The results are summarized in Table 6. The measurement data in Table 6 are obtained from reference (Chen et al., 2013). However, the results of two regulating rods and the uncertainty of the measurement are not provided in that reference. According to the simulation results, the control rod worth calculated using the heterogeneous model is always less than that
Table 3 Description of core state to reach criticality. Case No.
1 2 3 4 5
Number of fuel SAs loaded
71 72 72 72 72
Rod position
Core state
RE-2, mm
Others
Out of the core 190 170 151 70
Out of the core
End of sub-critical Super-critical (1) Super-critical (2) Super-critical (3) Critical
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
5
Fig. 4. Layout of 71 fuel SAs loading core.
of the homogeneous model. In the previous study (Guo et al., 2019), a similar study was conducted, and the same conclusions were obtained. Owing to the spatial self-shielding effect, the neutrons are easily absorbed by the surface of the absorber rod. Few neutrons can reach the center of the absorber rods. However, when the infinite homogeneous absorber medium is considered, the possibility of a neutron being absorbed by the absorber is identical at any position. Therefore, the homogeneous model overestimates the absorption reaction rate and obtains a higher control rod worth. The keff value obtained with homogeneous control rod model is smaller than that of heterogeneous model. In addition, it should be noted that the heterogeneity effects between the un-rodded and rodded cases are quite different. In the criticality simulation, the heterogeneity effect is approximately 300 pcm. In that calculation, only one regulating control rod is inserted. However, when all the rods are inserted in the core, the heterogeneity effect is more than 1000 pcm. Therefore, the total heterogeneity effect is contributed by both the fuel SAs and control rod SAs. In the rodded case, the contribution of the control rod SAs is much higher than that of the fuel SAs. This means that the modeling of the control rod SAs is important, especially in the rodded case. In the CEFR core design, the shim and safety rods comprise 90% enriched B4C as the absorber material. However, the enrichment of 10 B of the regulating rods is only 20%. Therefore, the regulating rods show the smallest control rod worth. The SARAX code shows simulation results that are in good agreement with the measurement data, especially in the case of the use of the heterogeneous model. For the case of 1st shutdown system with SH-1 stuck, the error is 11.4%, which is larger than 10%. On the one hand, the uncertainties of measurement data were not provided in the refer-
ence paper. On the other hand, this overestimation indicates that the RE-1 and RE-2 control rod worth were also overestimated. 4.3. Sodium void reactivity In the sodium-cooled FR, the reactivity changes due to sodium void or boiling is one of the most important reactivity feedbacks. The measurement of this reactivity is of vital importance to the verification of the safety features of the reactor. The sodium void reactivity is measured by replacing one fuel SA with a voided SA in combination with the measurement of the change in the critical control rod position. A total of five different fuel SA locations were measured. The location of each voided SA is presented in Fig. 6. The geometry of the voided SA is similar to the normal fuel SA but without the sodium from the bottom to the top of the entire assembly. During the experiment, the shim rods and safety rods were kept unchanged. The position of the three shim rods was 239 mm, while the position of the three safety rods was 499 mm. The rod position of the regulating rods is shown in Table 7. In the SARAX calculation, the keff value of the original and voided case can be obtained by changing the control rod position. The reactivity difference between the voided and original cases is contributed by the control rod worth and sodium void reactivity. Therefore, the final sodium void reactivity is calculated using the following equation.
Dqsodium ¼ ðqv oided qoriginal Þ DqCR
ð1Þ
To obtain the reactivity change due to the control rod movement (DqCR ), the averaged differential worth of the regulating rods is used. Based on the control rod worth calculation, the averaged
6
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
Fig. 5. Layout of 72 fuel SAs loading core.
Table 4 SARAX keff results of CEFR criticality simulation. Case No.
Hetero. Model
Reactivity, pcm
Homo. Model
Reactivity, pcm
1 2 3 4 5
0.99685 1.00016 1.00008 1.00001 0.99975
316 16 8 1 25
0.99404 0.99727 0.99717 0.99710 0.99682
599 274 284 291 320
worth of the two regulating rods is listed in Table 8. The SARAX simulation results are summarized in Table 9. The measurement data in the table are obtained from reference (Zhou et al., 2013), and corrections of the temperature and composition are applied. During the sodium void, the harden spectrum introduces a positive contribution of the reactivity feedback, while the neutron leakage introduces a negative contribution. As shown in Table 9, the sodium void reactivity of each location is negative owing to the high leakage of the core. From the center to the outside of the core, the reactivity exhibits a trend of becoming positive. As few neutrons are concentrated at the outside of the core, the contribution of the neutron leakage is reduced. In the heterogeneous model, the neutrons leak out of the reactor more readily from the axial direction when the sodium is voided. Therefore, in the comparison of the void reactivity between the two models, the heterogeneous model obtains a more negative value than the homogeneous model, although the difference is small. To validate the accuracy of the code, the SARAX code shows results that are very close to the measurement data. For each case, the error is
always smaller than the measurement uncertainty, which is around 13%. 4.4. Temperature reactivity The temperature effect is another important reactivity feedback in the sodium-cooled FR. This measurement was conducted at different temperature levels by increasing the temperature from 250 °C to 300 °C. The basic layout of the core is based on operation loading with 79 fuel SAs. In the actual measurement, the reactivity changes are still obtained by changing the control rod position under different temperature states to reach the criticality. Owing to the small temperature reactivity in the FR, in the SARAX simulation the control rod position is fixed to make sure the simulation results only have a dependency on temperature. On considering that a difference of only 50 °C exists during the measurement, only the fuel temperature and sodium density are changed. The thermal expansion of the geometry is neglected. The sodium density is calculated using the following equation (Huo et al., 2018).
7
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046 Table 5 Control rod position for control rod worth measurement. Object
Rod or rod group
Regulating rod worth
RE-1 RE-2
Shim rod worth
SH-1 SH-2 SH-3
Safety rod worth
SA-1 SA-2 SA-3
1st shutdown system
3*SH + 2*RE
1st shutdown system with SH-1 stuck
SH-2/3 + 2*RE
2nd shutdown system
3*SA
2nd shutdown system with SA3 stuck
SA-1/2
All control rods
2*RE + 3*SH + 3*SA
All control rods with SH-1 stuck
2*RE + SH-2/3 + 3*SA
Control rod positions, mm
Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After
RE-1
RE-2
SH-1
SH-2
SH-3
SA-1
SA-2
SA-3
501 1 106 106 240 240 239 239 240 240 240 240 240 240 240 240 247 0 247 2 247 247 247 247 247 0 248 2
106 106 499 5 240 240 240 240 239 239 239 239 240 239 239 239 247 5 248 2 249 249 248 248 248 3 248 2
240 240 240 240 501 4 151 151 148 148 240 240 240 240 240 240 239 1 501 501 240 240 240 240 240 2 500 500
240 240 240 240 141 141 498 1 150 150 240 240 240 240 240 240 240 1 141 3 240 240 240 240 240 2 141 3
239 239 239 239 141 141 151 151 498 7 241 241 240 240 240 240 239 7 141 16 240 240 240 240 240 0 141 7
498 498 498 498 498 498 498 498 498 498 498 46 498 498 498 498 498 498 498 498 498 46 498 45 499 45 498 45
500 500 500 500 499 499 500 500 500 500 499 499 499 55 499 499 500 500 500 500 500 56 500 54 500 56 500 55
500 500 500 500 499 499 500 500 500 500 499 499 499 499 499 40 499 499 499 499 499 40 500 500 500 40 499 40
Table 6 SARAX simulation results of control rod worth. Rod or rod group
SARAX simulation
Measurement worth, pcm
Hetero. Model
RE-1 RE-2 SH-1 SH-2 SH-3 SA-1 SA-2 SA-3 3*SH + 2*RE SH-2/3 + 2*RE 3*SA SA-1/2 2*RE + 3*SH + 3*SA 2*RE + SH-2/3 + 3*SA
Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After
Homo. Model
keff
worth, pcm
1.00333 1.00176 1.00066 0.99912 0.99957 0.98057 1.00005 0.98152 0.99989 0.98145 1.00048 0.99145 1.00044 0.99154 1.00043 0.99091 1.00040 0.97080 0.99963 0.98992 1.00051 0.97226 1.00052 0.98233 1.00052 0.94314 0.99963 0.96181
156
Error, %
153 1939
4.0
1888
2.7
1879
0.5
910
7.8
897
6.9
960
2.1
3048
6.0
981
11.4
2904
6.7
1851
9.4
6081
2.1
3935
2.4
q ¼ 950:0483 0:2298 T 14:6045 106 T 2 þ 5:6377 109 T 3 ð2Þ
where T is in centigrade. The SARAX simulation results are shown in Table 10. However, the measurement data of the temperature reactivity is not pub-
keff
worth, pcm
Error, %
0.99820 0.99649 0.99529 0.99363 0.99409 0.97336 0.99459 0.97437 0.99442 0.97429 0.99510 0.98516 0.99505 0.98523 0.99504 0.98454 0.99501 0.96257 0.99416 0.98341 0.99513 0.96388 0.99514 0.97506 0.99515 0.93208 0.99416 0.95236
171
/
168
/
2142
6.1
2019
2087
13.5
1839
2077
10.0
1889
1014
2.7
987
1001
4.0
963
1073
9.3
981
3388
17.7
2877
1099
24.8
881
3258
4.7
3112
2069
1.3
2042
6799
9.5
6210
4415
9.6
4030
lished. In the table, TRC stands for temperature reactivity coefficient. The 250 °C temperature point is the reference point for calculating the TRC. In addition, the Doppler reactivity coefficient (DRC) is calculated by only changing the fuel temperature. The temperatures of 250 °C and 300 °C are used to obtain the DRC. As the temperature increases, the TRC decreases slightly. As the
8
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
Fig. 6. The location of sodium voided fuel SA in the measurement.
Table 7 Control rod position of sodium void reactivity measurement. Measurement position in core
(2–4) (3–7) (4–9) (5–11) (6–13)
Original Voided Original Voided Original Voided Original Voided Original Voided
Control rod position, mm RE-1
RE-2
277 336 278 337 277 338 278 338 278 338
277 336 277 337 277 337 276 337 276 338
Table 8 Averaged differential worth of two regulating rods, unit in pcm/mm.
RE-1 RE-2
Hetero. model
Homo. model
0.347 0.341
0.381 0.374
results show, the DRC is small as compared with the typical light water reactor. An increase in the fuel temperature of 500 °C introduces a negative reactivity of less than 130 pcm. This is not conducive to the reactivity control of the core. Owing to the design of such a small core, the high neutron leakage causes the negative contribution to defeat the positive contribution of the harden spec-
trum when the sodium density decreases. Therefore, the TRC is more negative and is approximately 1.1 pcm/°C. At the same time, the TRC results of the homogeneous model are slightly higher than those of the heterogeneous model. In contrast to the results shown in Table 9, only the fuel and blanket region showed a changed sodium density in the temperature reactivity simulation. Therefore, the neutron leakage is underestimated when the temperature increases in Table 10. However, DRC of the heterogeneous and homogeneous models still exhibits an obvious difference. The utilization of a more negative reactivity coefficient results in an overestimation of the reactor safety, especially during the transient simulation. Therefore, the use of the heterogeneous model is suggested for the calculation of safety-related parameters to obtain more reliable results. 4.5. Subassembly swap reactivity The subassembly swap measurement is used to simulate the possible accident of a fuel loading error. In the measurement, seven SAs were selected, among which, five were fuel SAs and the other two were SS SAs. The position and SA loading of the subassembly swap reactivity measurement can be observed in Fig. 7 and Table 11. It should be noted that for the (7–31) and (5–19) cases, one of the SS SA is replaced by a fuel SA. To prevent the insertion of a large positive reactivity, one of the fuel SAs is replaced by an SS SA at the same time. The measurement of the control rod movement was performed, which is similar to the previous measurements. The reactivity changes between the original and swapped cases
9
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046 Table 9 Sodium void reactivity simulation results and comparison. Measurement position in core
(2–4) (3–7) (4–9) (5–11) (6–13)
Original Voided Original Voided Original Voided Original Voided Original Voided
SARAX simulation results
Measurement, pcm
Hetero. Model
Homo. model
keff
Void reactivity, pcm
Error, %
keff
Void reactivity, pcm
Error, %
1.00064 1.00065 1.00064 1.00065 1.00064 1.00067 1.00064 1.00069 1.00064 1.00071
39.6
8.2
38.2
11.4
43.1 ± 5.8
40.4
6.8
40.0
7.7
43.3 ± 5.6
39.1
7.4
38.5
5.8
36.4 ± 5.4
37.3
6.7
36.9
7.7
40.0 ± 5.2
35.4
3.8
0.99529 0.99535 0.99529 0.99534 0.99529 0.99536 0.99529 0.99537 0.99529 0.99539
35.2
4.2
36.8 ± 5.6
Table 10 Temperature reactivity coefficient simulation results. Temperature, °C
Hetero. model
Homo. model
keff 250 260 270 280 290 300 DRC, pcm/°C
1.01415 1.01404 1.01393 1.01383 1.01372 1.01362 0.220
TRC, pcm/°C
keff
TRC, pcm/°C
1.089 1.075 1.066 1.064 1.060
1.00991 1.00980 1.00969 1.00958 1.00947 1.00936 0.240
1.110 1.113 1.113 1.108 1.104
RE-1 ------7-11 F ------6-10 F ------6-12 F ------6-13 F ------6-14 F ------6-15 F ------6-16
SA-3 ------5-13
F ------6-17
F ------4-11
F ------5-15
F ------6-19
F ------4-12
F ------5-16
F ------6-20
F ------3-8
SH-2 ------3-9
F ------4-13
F ------5-17
F ------2-5
F ------3-10
F ------4-14
F ------5-18
F ------2-6
F ------4-15
SS ------5-19
F F ------------6-22 6-23 RE-2 ------7-27
F ------3-11
F ------4-16
F ------5-20
F ------6-24
SA-2 ------5-21
F ------6-25
F ------6-2
F ------5-1
F ------5-24
F ------5-23
F ------5-22
F ------6-3
F ------5-2
F ------4-1
F ------4-18
F ------4-17
F ------6-4
F ------5-3
F ------4-2
SH-1 ------3-1
F ------3-12
F ------6-5
F ------5-4
F ------4-3
F ------3-2
F ------2-1
F ------6-6
SA-1 ------5-5
F ------4-4
F ------3-3
F ------2-2
NS ------1-1
F ------6-7
F ------5-6
F ------4-5
F ------3-4
F ------2-3
F ------2-4
F ------6-8
SS ------5-7
F ------4-6
SH-3 ------3-5
F ------3-6
F ------3-7
F ------6-9
F ------5-8
F ------4-7
F ------4-8
F ------4-9
F ------4-10
F ------5-14
F ------6-18
F ------5-10
F ------5-11
F ------5-12
F ------5-9
Type ------Index
F ------6-30
F ------6-29
F ------6-28
F ------6-27
F ------6-26 SS ------7-31
Fig. 7. Position of swapped SAs during subassembly swap reactivity measurement.
10
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
Table 11 The SA loading of measurement. Position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Type of SA loaded (2–6)
(3–11)
(4–17)
(5–23)
(6–29)
(7–31)
(5–19)
SS Fuel Fuel Fuel Fuel Fuel Fuel
Fuel SS Fuel Fuel Fuel Fuel Fuel
Fuel Fuel SS Fuel Fuel Fuel Fuel
Fuel Fuel Fuel SS Fuel Fuel SS
Fuel Fuel Fuel Fuel SS SS Fuel
SS SS SS SS SS Fuel SS
SS SS SS SS SS SS Fuel
Table 12 Control rod position for single rod measurement. Measurement position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Rod position, mm
Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped
RE-1
RE-2
SH-1
SH-2
SH-3
268 239 258 259 258 258 258 258 257 299 258 257 257 258
268 238 258 258 257 258 258 257 260 298 258 257 257 257
287 287 267 267 267 268 265 265 267 267 262 262 262 262
286 286 267 267 267 268 266 266 266 267 263 262 262 263
151 342 189 353 188 334 193 303 190 300 198 285 285 248
RE-1
RE-2
SH-1
SH-2
SH-3
267 327 258 258 259 257 258 293 259 318 258 295 295 295
267 325 257 260 257 258 257 293 259 317 260 295 295 295
241 298 242 293 242 288 241 276 241 278 241 268 268 255
242 297 242 293 242 289 241 275 242 277 241 267 267 255
241 299 242 295 241 289 241 275 242 279 242 269 269 256
Table 13 Control rod position for multiple rods measurement. Measurement position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Rod position, mm
Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped
contributed to the control rod movement and swap reactivity. During the experiment, the three shim rods and two regulating rods were used. For each case, the swap reactivity was measured twice—by using a single rod and multiple rods. The measurements of the control rod positions of the single rod and multiple rods are listed in Tables 12 and 13. The three safety rods are outside the core during the entire measurement. The averaged differential control rod worth of those five control rods is shown in Table 14. The SARAX simulation results are summarized in Tables 15 and 16. As in the temperature reactivity measurement, the measurement data of the swap reactivity is not published. Only the discussion regarding the SARAX results is presented. As the measurements proceed one by one, and the swap reactivity is changed from a large negative value to nearly zero. For the fuel SA swap measurement, the results are reasonable because the inner fuel SA has a large contribution to the core reactivity. After
replacement of the inner fuel SA, the reactivity is reduced by a large value. For the (7–31) case, the core layout can be treated as the (6–29) case with one more fuel SA. The positive reactivity is introduced into the core system. Therefore, the (7–31) case has a smaller absolute value with a negative sign. The same situation can be observed in the (5–19) case. The core layout is similar as
Table 14 Averaged differential worth of shim and regulating rods, unit in pcm/mm.
RE-1 RE-2 SH-1 SH-2 SH-3
Hetero. model
Homo. model
0.347 0.341 4.308 4.196 4.176
0.381 0.374 4.761 4.637 4.616
11
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046 Table 15 SARAX simulation results of single rod measurement. Measurement position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Hetero. model
Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped
Homo. model
keff
Swap reactivity, pcm
keff
Swap reactivity, pcm
1.00104 1.00159 1.00077 1.00097 1.00072 1.00133 1.00080 1.00091 1.00077 1.00290 1.00071 1.00324 1.00530 1.00329
720.3
0.99571 0.99710 0.99538 0.99626 0.99533 0.99659 0.99540 0.99598 0.99538 0.99802 0.99531 0.99825 1.00031 0.99810
716.4
665.9 551.4 446.9 272.9 111.2 45.7
669.9 550.4 447.7 270.8 105.1 51.0
Table 16 SARAX simulation results of multiple rods measurement. Measurement position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Hetero. model
Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped
Homo. model
keff
Swap reactivity, pcm
keff
Swap reactivity, pcm
1.00087 1.00121 1.00091 1.00102 1.00086 1.00133 1.00076 1.00102 1.00087 1.00331 1.00082 1.00329 1.00535 1.00321
721.2
0.99554 0.99662 0.99555 0.99636 0.99551 0.99664 0.99540 0.99615 0.99551 0.99851 0.99546 0.99829 1.00034 0.99802
725.4
649.5 551.0 431.3 255.9 113.4 53.2
that in the (5–23) case with one more fuel SA loaded in the fifth ring. Therefore, the difference in the swap reactivity between the (5–19) and (5–23) cases is approximately 400 pcm. Compared with two measurement methods, the single rod and multiple rods measurements provide identical results. In addition, the results obtained with the heterogeneous and homogenous models are also identical. As only the core layout is changed, and the control rod movement is small, the heterogeneity effect is almost the same, such that the final swap reactivity should be similar. The results obtained with the SARAX code have less than a 10-pcm difference between the heterogeneous and homogeneous models. This proves that the SARAX code is capable of obtaining stable results irrespective of whether the layout is changed. 5. Conclusion In this paper, the CEFR start-up tests were simulated to perform an additional validation of the SARAX deterministic FR analysis code. The criticality, control rod worth, sodium void reactivity, temperature reactivity, and subassembly swap reactivity were calculated, and the obtained results were compared with the measurement data. During the calculation, the differences between the heterogeneous and homogeneous models of the numerical calculation were also quantified. Before the simulation, a sensitivity test was performed to determine the convergence of the keff value by using different approximations of numerical methods. As the CEFR is a small core, the
648.9 546.3 428.6 249.4 112.7 57.1
neutron leakage is large, such that the neutron flux is more anisotropic. To address this, the S6P3 approximation shows its precision in obtaining a converged keff value. The following calculations were then based on that approximation. A comparison between the SARAX results and measurement data was performed for the criticality, control rod worth, and sodium void reactivity calculation. Owing to the lack of published measurement data of the temperature reactivity and subassembly swap reactivity, the SARAX results were discussed for those two cases. According to the numerical results, the SARAX code underestimated the criticality by only 25 pcm. In the case of the control rod worth and sodium void reactivity calculation, the differences are also small as compared with the measurement data. The temperature reactivity and subassembly swap reactivity calculation showed reasonable and reliable results. The comparison between the heterogeneous and homogeneous models showed that the heterogeneity effect exists in both the fuel assembly and control rod assembly. For the rodded case, the contribution of the control rod assembly to the heterogeneity effect is large. In addition, an obvious difference could be observed in both the sodium void reactivity and temperature reactivity calculation. This indicates that the heterogenous model is necessary, especially for safety-related parameter calculations. In general, the results presented in this study demonstrate the good prediction capability of the SARAX calculation. In a future study, the MCS will be used to perform such calculations for the validation. At the same time, the modeling of a spacer wire will be discussed.
12
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT). (No. NRF-2017M2A8A2018595)
References Chen, Y.Y., Yang, Y., Gang, Z., et al., 2013. Measurement and analysis of CEFR safety and shim rod worth. At. Energy Sci. Technol. 47 (Suppl.), 92–94 (In Chinese). Choe, J.W., Choi, S., Zhang, P., Park, J.S., Kim, W.K., Shin, H.C., Lee, H.S., Jung, J.E., Lee, D., 2019. Verification and validation of STREAM/RAST-K for PWR analysis. Nucl. Eng. Technol. 51 (2), 356–368. Choi, S., Lee, C.H., Lee, D., 2017. Resonance treatment using pin-based pointwise energy slowing-down method. J. Comput. Phys. 330, 134–155. Du, X.N., Cao, L.Z., Zheng, Y.Q., Wu, H.C., 2018. A hybrid method to generate fewgroup cross sections for fast reactor analysis. J. Nucl. Sci. Technol. 55 (8), 931– 944. Du, X.N., Choe, J.W., Choi, S., et al., 2019. Application of TULIP/STREAM code in 2-D fast reactor core neutronic analysis. The International Congress on Advances in Nuclear Power Plants (ICAPP) 2019, 2019 May 12-15, JUAN-LES-PINS, France. Guo, H., Garcia, E., Faure, B., et al., 2019. Advanced method for neutronic simulation of control rods in sodium fast reactors: numerical and experimental validation. Ann. Nucl. Energy 129, 90–100. Huo, X.K., Hu, Y., Chen, X.L., et al., 2018. Technical Specifications for Neutronics Benchmark of CEFR Start-up Tests, CRP-I31032. CIAE. IAEA, 2012. Status of Fast Reactor Research and Technology Development, IAEATECDOC-1691. IAEA. IAEA, 2014. Benchmark Analyses on the Control Rod Withdrawal Tests Performed during the PHENIX End-of-Life Experiments, IAEA-TECDOC-1742. IAEA. Ikegami, T., Ishikawa, M., Lell, R.M., et al., 2006. ZPPR-9 Experiment: A 650 MWeClass Sodium-Cooled MOX-Fueled FBR Core Mock-Up Critical Experiment With Clean Core of Two Homogeneous Zones, ZPPR-LMFR-EXP-002, NEA/NSC/Doc (2006). OECD/NEA. Jang, J.R., Kim, W.Y., Jeong, S.G., Jeong, E., Park, J.S., Lemaire, M., Lee, H.S., Jo, Y.M., Zhang, P., Lee, D., 2018. Validation of UNIST Monte Carlo code MCS for criticality
safety analysis of pwr spent fuel pool and storage cask. Ann. Nucl. Energy 114, 495–509. Lee, C.H., Yang, W.S., 2017. MC2-3: multigroup cross section generation code for fast reactor analysis. Nucl. Sci. Eng. 187, 268–290. Lu H.L., 2007. Nodal Methods for the Neutron Diffusion and Transport Equations in Triangular Meshes, Ph.D thesis, Xi’an Jiaotong University, July 2007 (in Chinese). G. Rimpault, Algorithmic features of the ECCO cell code for treating heterogeneous fast reactor subassemblies, Proceedings of the International Topical Meeting on Reactor Physics and Computations; 1995 May 1–5; Portland (OR), USA. Steven, C., Marck, V.D., 2006. Benchmarking ENDF/B-VII.0. Nucl. Data Sheets 107, 3061–3118. Tak, T.W., Lee, D., Kim, T.K., 2013. Design of ultra-long cycle fast reactor employing breed-and-burn strategy. Nucl. Technol. 183 (3), 427–435. Tak, T.W., Lee, D., Kim, T.K., Hong, S.G., 2014. Optimization study for ultra-long cycle fast reactor core concept. Ann. Nucl. Energy 73, 145–161. Tak, T.W., Choe, J.W., Jeong, Y.J., Lee, D., Kim, T.K., Hong, S.G., 2015. Feasibility study on ultralong-cycle operation and material performance for compact liquid metal-cooled fast reactors: a review work. Int. J. Energy Res. 39 (14), 1859– 1878. Toppel, B.J., 1983. User’s Guide for the REBUS-3 Fuel Cycle Analysis Capability, ANL83-2. Argonne National Lab. Xu, L.F., Cao, L.Z., Zheng, Y.Q., et al., 2017. Development of a new parallel SN code for neutron-photon transport calculation in 3-D cylindrical geometry. Prog. Nucl. Energy 1, 1–21. Yokoyama, K., Shono, A., Sanda, T., et al., 2006. Japan’s Experimental Fast Reactor JOYO MKI Core: Sodium-Cooled Uranium-Plutonium Mixed Oxide Fueled Fast Core Surrounded by UO2 blanket, JOYO-LMFR-RSR-001, NEA/NSC/Doc(2006). OECD/NEA. Zheng, Y.Q., Qiao, L., Zhai, Z.A., Du, X.N., Xu, Z.T., 2018b. SARAX: a new code for fast reactor analysis part II: verification, validation and uncertainty quantification. Nucl. Eng. Des. 331, 41–53. Zheng, Y.Q., Du, X.N., Xu, Z.T., Zhou, S.C., Liu, Y., Wan, C.H., Xu, L.F., 2018a. SARAX: a new code for fast reactor analysis part I: methods. Nucl. Eng. Des. 340, 421–430. Zhou, S.C., Wu, H.C., Cao, L.Z., et al., 2014. LAVENDER: a steady-state core analysis code for design studies of accelerator driven subcritical reactors. Nucl. Eng. Des. 278, 434–444. Zhou, K.Y., Yu, H., Hu, Y., et al., 2013. The measurement and analysis of CEFR sodium void reactivity effect. Proceedings of the 2013 21st International Conference on Nuclear Engineering, 2013 July 29 – August 2, Chengdu, China.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Neutronic simulation of China Experimental Fast Reactor start-up tests. Part I: SARAX code deterministic calculation Xianan Du, Jiwon Choe, Tuan Quoc Tran, Deokjung Lee ⇑ Department of Nuclear Engineering, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulsan 44919, Republic of Korea
a r t i c l e
i n f o
Article history: Received 7 June 2019 Received in revised form 24 July 2019 Accepted 7 September 2019
Keywords: CEFR Start-up tests SARAX code system Validation Measurement data
a b s t r a c t As one of participants of recent coordinated research project proposed by International Atomic Energy Agency and China Institute of Atomic Energy, the computational reactor physics and experiment laboratory of Ulsan National Institute of Science and Technology, Republic of Korea, is currently focused on a study involving the neutronic simulation of the China Experimental Fast Reactor (CEFR) start-up tests. The CEFR start-up tests include obtaining measurements of the criticality, control rod worth, sodium void reactivity, temperature reactivity, and subassembly swap reactivity. The fast reactor neutronic analysis code SARAX is selected for performing such simulations for additional validation. The obtained numerical results are compared with measurement data. In addition, the differences in the expected results of the heterogeneous and homogeneous models are quantified in this study. According to the simulation, the calculated results agreed well with the measured values in the case of the majority of the neutronic characteristics. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Fast reactors (FRs) are important as next-generation advanced nuclear reactor systems owing to their abundant neutrons and hard spectrum. The utilization of uranium resources can be increased while the accumulation of high-level waste can be reduced by implementing the FR technique as soon as possible. According to the report of International Atomic Energy Agency, extensive research and development work has been conducted on this subject in recent decades (IAEA, 2012). Extensive experience of operating FRs has been gained from the operation of more than 20 experimental reactor cores, such as CEFR and BN-600. In this context, identifying biases in the measurement data is useful for improving the accuracy of current methodologies. Therefore, the measurement data of several experimental reactors have been published—for instance, control rod withdrawal tests performed during Phenix end-of-life experiments (IAEA, 2014). Recently, a 4-year coordinated research project (CRP) was launched from February 2018, which was proposed by the China Institute of Atomic Energy and was focused on the neutronics benchmarks analysis of CEFR start-up tests (Huo et al., 2018). The CEFR is a sodium-cooled fast reactor loaded with PuO2–UO2 fuel. However, only UO2 fuel was loaded in the first loading. The ⇑ Corresponding author. E-mail address: [email protected] (D. Lee). https://doi.org/10.1016/j.anucene.2019.107046 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
start-up tests of the CEFR were performed in China from 2010 to 2011. In the benchmarks, the evaluation of the criticality, control rod worth, reactivity effects, and neutron spectral characteristics are included. According to the plan of the CRP, each participant is required to perform a blind neutronics calculation independently at first. After the experimental data is released, each participant can perform a comparison of the simulation results and improve their physical models and simulation codes. As one of the participants of the CRP, the computational reactor physics and experiment (CORE) laboratory of Ulsan National Institute of Science and Technology (UNIST) started the work related with FRs in 2013 (Tak et al., 2013, 2014, 2015). At that time, several studies were focused on core design to obtain a better understanding of neutron behavior and core performance. It is beneficial to use the Monte Carlo method to perform this work with a high accuracy; however, the efficiency of the Monte Carlo calculation is low. Therefore, the development of a deterministic code is necessary to improve the efficiency of the FR design. The STREAM/ RAST-K (Choe et al., 2019; Choi et al., 2017) code system was to be used for the FR neutronic analysis, and the initial work was performed in a recent study (Du et al., 2019). In addition, the SARAX (Zheng et al., 2018a,b, 2018b) code and MC2-3 (Lee and Yang, 2017)/REBUS (Toppel, 1983) code are used for gathering knowledge regarding the simulation modeling and methodology. In this paper, the numerical simulation was performed based on the SARAX deterministic code of the CEFR start-up tests. The
2
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
obtained results were compared with the published measurement data. The results of the in-house Monte Carlo simulation (MCS) (Jang et al., 2018) are introduced in a subsequent paper. In the previous study (Zheng et al., 2018b), the SARAX code was validated based on JOYO MK-I experiments (Yokoyama et al., 2006) and several assembly layouts of zero power physics reactor series experiments (Ikegami et al., 2006). In comparison with the experiment benchmarks, the fuel assembly pitch of the CEFR core was 6.1 cm, which is the smallest value obtained. In addition, the active core height is 45 cm. Such a small core results in a high neutron leakage and makes the deterministic calculation a challenge. Therefore, the aims of the current study are as follows: 1. To quantify the difference in reactivity and safety related parameters between the heterogeneous and homogeneous modeling of the CEFR core; 2. To perform an additional validation of the SARAX code system in such a high leakage system. The remainder of this paper is organized as follows. Section 2 presents the general description of the CEFR start-up tests. In section 3, SARAX code is briefly introduced, and a sensitivity test is performed based on operation loading. This section demonstrates the convergence to the keff value when various calculation conditions are selected. Section 4 summarizes all the expected results of the CRP. In this section, the criticality, control rod worth, sodium void worth, temperature reactivity, and assembly swap reactivity are calculated. The conclusions of this study are presented in Section 5. 2. Description of CEFR start-up tests The CEFR core is the first FR of China, which reached its first criticality in 2010. It is a 65 MWth pool-type sodium-cooled FR. The uranium dioxide fuel with the enrichment of 235U at 64.4% was used in the first loading. The main design parameters are listed in Table 1. The core of the first loading consists of 79 fuel subassemblies (SA), eight control rod (CR) SAs, one neutron source (NS) SA, 338 stainless steel (SS) SAs, and 230 boron shielding. Three control rod types are considered in the operation: two regulating (RE1/2) CR SAs; three shim (SH-1/2/3) CR SAs; and three safety (SA1/2/3) SAs. Fig. 1 shows the layout of only the active core region, including all the control SAs. The axially material distribution and height of each SA is shown in Fig. 2. Note that the real geometry is much more complicated. For example, the lower structure of the fuel SA contains several parts, such as gas plenum, lower con-
Table 1 Main design parameter of CEFR. Parameters
Value
Thermal/Electric power, MW Designed life, year Maximum burn-up, MWd/t Maximum neutron flux, cm-2 s1 Refueling period, day Diameter/Height of main vessel, m Covering gas pressure, MPa Core inlet/outlet temperature, °C Equivalent diameter/height of active core, cm Subassembly lattice pitch, mm Enrichment of 235U of fuel, % Number of fuel SAs Total mass of UO2/U in fuel, kg Total mass of UO2/U in blanket, kg Total mass of B4C in control SAs, kg Total mass of B4C in boron shielding SA2, kg
65/20 30 60,000 3.2e15 80 8.0/12.2 0.005 360/530 60/45 61 64.4 79 417/367 356/313 6.9 552
nector, and bottom end plug. To simplify the deterministic simulation, the axial distribution is simplified based on the volume of each part. In the active part, the fuel assembly contains 61 fuel rods, and the rod lattice pitch is 6.95 mm. The outer diameters of the fuel pellet and cladding are 5.4 mm and 6.0 mm, respectively. In the center of the fuel pellet, a hole of 1.6-mm diameter is designed to deal with the swelling. There is a wrapper of 1.2-mm thickness outside the fuel assembly and the outer/inner flat-to-flat dimensions are 59.0/56.6 mm. The eight CR SAs have the same geometry description. Each CR SA contains seven absorber pellets with a 12.2-mm outer diameter. The outer diameter of the cladding is 14.9 mm. Between the absorber pellet and cladding, there is a 0.7-mm thick sodium bond. These seven absorber rods are stuck together using a 2-mm thick stainless steel circle. Further detailed information can be found in reference (Huo et al., 2018). During the start-up tests, the fuel loading and criticality, control rod worth, sodium void reactivity, temperature reactivity, and subassembly swap reactivity are measured. The condition and state of the core during the measurements are summarized in the following sections with the numerical results.
3. Simulation code and sensitivity test As mentioned previously, the CEFR is a small core with a high leakage. Therefore, it is necessary to perform a sensitivity test to determine the calculation condition before we simulate the startup tests. In this section, the SARAX code is briefly introduced, and the sensitivity test is performed based on the first loading of the CEFR. 3.1. SARAX code SARAX is developed at Xi’an Jiaotong University and is used for FR neutronic analysis. The objectives of the code are to achieve a good accuracy while using advanced methods and modeling schemes with few data adjustments. For the steady-state calculation, the TULIP (Du et al., 2018), Hydra (Xu et al., 2017), and LAVENDER (Zhou et al., 2014) modules are used. Fig. 3 shows the computational flow chart for the steady-state calculation performed using SARAX code. The TULIP code generates 1968-group self-shielded cross sections in a homogeneous or 1D heterogeneous problem based on ENDF/B-VII.0 (Steven and Marck, 2006) point-wise cross sections. After generating the cross sections for each material zone, a 2D R-Z homogeneous core problem is developed, and the neutron flux is solved using the SN difference method. With the obtained spatially dependent neutron flux, the 1968-group cross sections are collapsed into 33 groups, which are used in the 3D SN nodal calculation. The final keff value and power distribution are obtained using LAVENDER code. The 1968-/33-group structures are the same as those of the ECCO (Rimpault, 1995) code. In order to properly generate accurate cross sections of control rod assembly, 1-D supercell model and the SPH method are applied. The detailed information can be found in reference. (Zheng, et al., 2018a) 3.2. Sensitivity test For performing the sensitivity test, the CEFR core based on the first loading is used. For this state, the temperature of all the materials is 250 °C, which is called the cold state. During the operation, all the safety rods are outside the core. The rod position of three shim rods is 330 mm, which is the distance from the bottom of
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
3
Fig. 1. CEFR layout of active core region.
Fuel SA
CR SA
SS(NS) SA
Upper Shielding 500 mm
Handling head
Upper Structure 590 mm
Upper Structure 90 mm
Shielding SA
Upper Structure 500 mm
Connecting Sector 90mm
Upper Blanket 100 mm
Absorber 510 mm Reflector (Neutron Source) 800 mm
Fuel 450 mm
Lower Blanket 250 mm
CR follower
Lower Structure 500 mm
Lower Structure 500 mm
Boron shielding 800 mm
Fig. 3. The computational flow chart of SARAX steady-state calculation. Lower Structure 500 mm
Fig. 2. Axially configuration of each SA.
Lower Structure 500 mm
the active region to the end of the control rod. Two regulating rods have the same rod position of 250 mm. The self-shielded cross sections of the fuel, blanket, and absorber region are prepared using the heterogeneous model. The homogeneous model is used for the other material zones. The
4
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
S8P5 approximation is used when performing the 2D Hydra calculation. In the 3D core modeling, each SA is divided into six triangles, and the height of each node is approximately 50 mm. Owing to the high neutron leakage, the neutron flux becomes more anisotropic. Therefore, the sensitivity test is focused on the SNPN approximation during the 3D core calculation. Table 2 summarizes the keff results of the CEFR first loading state under different approximations. The discretization of the angles is from S4 to S8, and the expansion of the scattering transfer matrices is from P1 to P5. In addition, the outflow transport correction is applied in the S6 calculation. Obviously, a large variance exists between the keff value of the outflow transport correction and P1 approximation. On increasing the order of the scattering matrices to P3, the keff value still exhibits a difference of over 300 pcm. When a more rigorous P5 approximation is applied, the keff value changes slightly. In the LAVENDER code, the 60° symmetric quadrature (Lu, 2007) is used. The number of total angular directions is 12 N, where N is the SN order. Therefore, the keff value does not change significantly for different SN orders. Based on this sensitivity test, the simulations in the following section comprise the use of the S6P3 approximation for obtaining the converged keff value. 4. Numerical results of CEFR start-up tests In this section, the criticality, control rod worth, sodium void reactivity, temperature reactivity, and subassembly swap reactivity of the CEFR start-up tests are calculated using SARAX code. For each calculation, both the homogeneous and heterogeneous models are used to quantify the difference of those parameters. In the homogeneous model, all the SAs are smeared according to the volume fraction. In contrast, only the fuel, blanket, and absorber parts are considered in the heterogeneous model. The cross sections are prepared using the 1D equivalent cylindrical assembly model. 4.1. Criticality Prior to the start-up of the reactor, the core was preliminarily loaded with 81 mock-up fuel SAs in the fuel positions. In the mock-up fuel SA, the fuel region is replaced by a filter that contains only sodium and stainless steel. The volume fraction of sodium is 87.1%. In the lower and upper parts, the fraction of the sodium reduces to 40.9%. A greater amount of stainless steel makes causes these parts to act as the shielding.
Table 2 keff value obtained under different approximation.
Out-flow P1 P3 P5
S4
S6
S8
/ 1.01054 1.01391
1.01613 1.01064 1.01415 1.01414
/ 1.01068 1.01420 1.01421
The reactor reached first criticality on replacing the mock-up fuel SAs with the real fuel SAs in a step-by-step manner. After the loading of the 40th fuel SA, two SS SAs are loaded. According to the measurement obtained, the core eventually reached criticality with 72 fuel SAs loaded, with the RE-2 control rod inserted at the position of 70 mm. In order to simulate the process of reacting the criticality, calculations are performed for several cases, and the core state of each case is listed in Table 3. The layouts of the loading core of 71 and 72 fuel SAs are presented in Figs. 4 and 5, respectively. The results of the SARAX calculation are summarized in Table 4. As the heterogeneous model is applied, the obtained results are closer to the measurement. When only 71 fuel SAs are loaded, the core is under the sub-critical state. The reactivity increases significantly after an additional fuel SA is loaded in the core. The reactivity continues to decrease owing to the insertion of the RE-2 control rod. At the end of this step, the final reactivity is approximately 25 pcm. As compared with heterogeneous model, the homogeneous model underestimated the keff value and reactivity. A difference of approximately 300 pcm can be found between the two models. Owing to the spatial self-shielding effect, the absorption of 238U decreases in the heterogeneous model. In addition, the wrapper reflects more neutrons into the fuel pellets such that the fission reaction rate increases. These two effects cause the homogeneous model to underestimate the keff value. 4.2. Control rod worth The measurement of the control rod worth is an essential part of the reactor start-up test. From this measurement, the data for the reactor operation and safety can be provided. The operation layout, which comprises 79 fuel SAs and 2 SS SAs, was carried out for the control rod worth measurement. The experiment was supposed to be performed in the cold state, while the measured sodium temperature was approximately 245 °C. The eight control rod SAs are divided into two shutdown systems according to the safety regulation. Three shim rod SAs and two regulating rod SAs are included in the first shutdown system while the other three safety rod SAs are included in the second shutdown system. During the experiment, the worth of each control rod and shutdown system is measured. In addition, the shutdown margin should be sufficient when one rod of the largest worth is stuck out of the core, and thus, such situations were taken into consideration as well. In the SARAX calculation, the control rod worth is calculated based on the reactivity changes before and after the rod drop. The position of each rod in the case of each measurement is listed in Table 5. Both the keff value and control rod worth of each case are calculated. The results are summarized in Table 6. The measurement data in Table 6 are obtained from reference (Chen et al., 2013). However, the results of two regulating rods and the uncertainty of the measurement are not provided in that reference. According to the simulation results, the control rod worth calculated using the heterogeneous model is always less than that
Table 3 Description of core state to reach criticality. Case No.
1 2 3 4 5
Number of fuel SAs loaded
71 72 72 72 72
Rod position
Core state
RE-2, mm
Others
Out of the core 190 170 151 70
Out of the core
End of sub-critical Super-critical (1) Super-critical (2) Super-critical (3) Critical
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
5
Fig. 4. Layout of 71 fuel SAs loading core.
of the homogeneous model. In the previous study (Guo et al., 2019), a similar study was conducted, and the same conclusions were obtained. Owing to the spatial self-shielding effect, the neutrons are easily absorbed by the surface of the absorber rod. Few neutrons can reach the center of the absorber rods. However, when the infinite homogeneous absorber medium is considered, the possibility of a neutron being absorbed by the absorber is identical at any position. Therefore, the homogeneous model overestimates the absorption reaction rate and obtains a higher control rod worth. The keff value obtained with homogeneous control rod model is smaller than that of heterogeneous model. In addition, it should be noted that the heterogeneity effects between the un-rodded and rodded cases are quite different. In the criticality simulation, the heterogeneity effect is approximately 300 pcm. In that calculation, only one regulating control rod is inserted. However, when all the rods are inserted in the core, the heterogeneity effect is more than 1000 pcm. Therefore, the total heterogeneity effect is contributed by both the fuel SAs and control rod SAs. In the rodded case, the contribution of the control rod SAs is much higher than that of the fuel SAs. This means that the modeling of the control rod SAs is important, especially in the rodded case. In the CEFR core design, the shim and safety rods comprise 90% enriched B4C as the absorber material. However, the enrichment of 10 B of the regulating rods is only 20%. Therefore, the regulating rods show the smallest control rod worth. The SARAX code shows simulation results that are in good agreement with the measurement data, especially in the case of the use of the heterogeneous model. For the case of 1st shutdown system with SH-1 stuck, the error is 11.4%, which is larger than 10%. On the one hand, the uncertainties of measurement data were not provided in the refer-
ence paper. On the other hand, this overestimation indicates that the RE-1 and RE-2 control rod worth were also overestimated. 4.3. Sodium void reactivity In the sodium-cooled FR, the reactivity changes due to sodium void or boiling is one of the most important reactivity feedbacks. The measurement of this reactivity is of vital importance to the verification of the safety features of the reactor. The sodium void reactivity is measured by replacing one fuel SA with a voided SA in combination with the measurement of the change in the critical control rod position. A total of five different fuel SA locations were measured. The location of each voided SA is presented in Fig. 6. The geometry of the voided SA is similar to the normal fuel SA but without the sodium from the bottom to the top of the entire assembly. During the experiment, the shim rods and safety rods were kept unchanged. The position of the three shim rods was 239 mm, while the position of the three safety rods was 499 mm. The rod position of the regulating rods is shown in Table 7. In the SARAX calculation, the keff value of the original and voided case can be obtained by changing the control rod position. The reactivity difference between the voided and original cases is contributed by the control rod worth and sodium void reactivity. Therefore, the final sodium void reactivity is calculated using the following equation.
Dqsodium ¼ ðqv oided qoriginal Þ DqCR
ð1Þ
To obtain the reactivity change due to the control rod movement (DqCR ), the averaged differential worth of the regulating rods is used. Based on the control rod worth calculation, the averaged
6
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
Fig. 5. Layout of 72 fuel SAs loading core.
Table 4 SARAX keff results of CEFR criticality simulation. Case No.
Hetero. Model
Reactivity, pcm
Homo. Model
Reactivity, pcm
1 2 3 4 5
0.99685 1.00016 1.00008 1.00001 0.99975
316 16 8 1 25
0.99404 0.99727 0.99717 0.99710 0.99682
599 274 284 291 320
worth of the two regulating rods is listed in Table 8. The SARAX simulation results are summarized in Table 9. The measurement data in the table are obtained from reference (Zhou et al., 2013), and corrections of the temperature and composition are applied. During the sodium void, the harden spectrum introduces a positive contribution of the reactivity feedback, while the neutron leakage introduces a negative contribution. As shown in Table 9, the sodium void reactivity of each location is negative owing to the high leakage of the core. From the center to the outside of the core, the reactivity exhibits a trend of becoming positive. As few neutrons are concentrated at the outside of the core, the contribution of the neutron leakage is reduced. In the heterogeneous model, the neutrons leak out of the reactor more readily from the axial direction when the sodium is voided. Therefore, in the comparison of the void reactivity between the two models, the heterogeneous model obtains a more negative value than the homogeneous model, although the difference is small. To validate the accuracy of the code, the SARAX code shows results that are very close to the measurement data. For each case, the error is
always smaller than the measurement uncertainty, which is around 13%. 4.4. Temperature reactivity The temperature effect is another important reactivity feedback in the sodium-cooled FR. This measurement was conducted at different temperature levels by increasing the temperature from 250 °C to 300 °C. The basic layout of the core is based on operation loading with 79 fuel SAs. In the actual measurement, the reactivity changes are still obtained by changing the control rod position under different temperature states to reach the criticality. Owing to the small temperature reactivity in the FR, in the SARAX simulation the control rod position is fixed to make sure the simulation results only have a dependency on temperature. On considering that a difference of only 50 °C exists during the measurement, only the fuel temperature and sodium density are changed. The thermal expansion of the geometry is neglected. The sodium density is calculated using the following equation (Huo et al., 2018).
7
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046 Table 5 Control rod position for control rod worth measurement. Object
Rod or rod group
Regulating rod worth
RE-1 RE-2
Shim rod worth
SH-1 SH-2 SH-3
Safety rod worth
SA-1 SA-2 SA-3
1st shutdown system
3*SH + 2*RE
1st shutdown system with SH-1 stuck
SH-2/3 + 2*RE
2nd shutdown system
3*SA
2nd shutdown system with SA3 stuck
SA-1/2
All control rods
2*RE + 3*SH + 3*SA
All control rods with SH-1 stuck
2*RE + SH-2/3 + 3*SA
Control rod positions, mm
Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After
RE-1
RE-2
SH-1
SH-2
SH-3
SA-1
SA-2
SA-3
501 1 106 106 240 240 239 239 240 240 240 240 240 240 240 240 247 0 247 2 247 247 247 247 247 0 248 2
106 106 499 5 240 240 240 240 239 239 239 239 240 239 239 239 247 5 248 2 249 249 248 248 248 3 248 2
240 240 240 240 501 4 151 151 148 148 240 240 240 240 240 240 239 1 501 501 240 240 240 240 240 2 500 500
240 240 240 240 141 141 498 1 150 150 240 240 240 240 240 240 240 1 141 3 240 240 240 240 240 2 141 3
239 239 239 239 141 141 151 151 498 7 241 241 240 240 240 240 239 7 141 16 240 240 240 240 240 0 141 7
498 498 498 498 498 498 498 498 498 498 498 46 498 498 498 498 498 498 498 498 498 46 498 45 499 45 498 45
500 500 500 500 499 499 500 500 500 500 499 499 499 55 499 499 500 500 500 500 500 56 500 54 500 56 500 55
500 500 500 500 499 499 500 500 500 500 499 499 499 499 499 40 499 499 499 499 499 40 500 500 500 40 499 40
Table 6 SARAX simulation results of control rod worth. Rod or rod group
SARAX simulation
Measurement worth, pcm
Hetero. Model
RE-1 RE-2 SH-1 SH-2 SH-3 SA-1 SA-2 SA-3 3*SH + 2*RE SH-2/3 + 2*RE 3*SA SA-1/2 2*RE + 3*SH + 3*SA 2*RE + SH-2/3 + 3*SA
Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After Before After
Homo. Model
keff
worth, pcm
1.00333 1.00176 1.00066 0.99912 0.99957 0.98057 1.00005 0.98152 0.99989 0.98145 1.00048 0.99145 1.00044 0.99154 1.00043 0.99091 1.00040 0.97080 0.99963 0.98992 1.00051 0.97226 1.00052 0.98233 1.00052 0.94314 0.99963 0.96181
156
Error, %
153 1939
4.0
1888
2.7
1879
0.5
910
7.8
897
6.9
960
2.1
3048
6.0
981
11.4
2904
6.7
1851
9.4
6081
2.1
3935
2.4
q ¼ 950:0483 0:2298 T 14:6045 106 T 2 þ 5:6377 109 T 3 ð2Þ
where T is in centigrade. The SARAX simulation results are shown in Table 10. However, the measurement data of the temperature reactivity is not pub-
keff
worth, pcm
Error, %
0.99820 0.99649 0.99529 0.99363 0.99409 0.97336 0.99459 0.97437 0.99442 0.97429 0.99510 0.98516 0.99505 0.98523 0.99504 0.98454 0.99501 0.96257 0.99416 0.98341 0.99513 0.96388 0.99514 0.97506 0.99515 0.93208 0.99416 0.95236
171
/
168
/
2142
6.1
2019
2087
13.5
1839
2077
10.0
1889
1014
2.7
987
1001
4.0
963
1073
9.3
981
3388
17.7
2877
1099
24.8
881
3258
4.7
3112
2069
1.3
2042
6799
9.5
6210
4415
9.6
4030
lished. In the table, TRC stands for temperature reactivity coefficient. The 250 °C temperature point is the reference point for calculating the TRC. In addition, the Doppler reactivity coefficient (DRC) is calculated by only changing the fuel temperature. The temperatures of 250 °C and 300 °C are used to obtain the DRC. As the temperature increases, the TRC decreases slightly. As the
8
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
Fig. 6. The location of sodium voided fuel SA in the measurement.
Table 7 Control rod position of sodium void reactivity measurement. Measurement position in core
(2–4) (3–7) (4–9) (5–11) (6–13)
Original Voided Original Voided Original Voided Original Voided Original Voided
Control rod position, mm RE-1
RE-2
277 336 278 337 277 338 278 338 278 338
277 336 277 337 277 337 276 337 276 338
Table 8 Averaged differential worth of two regulating rods, unit in pcm/mm.
RE-1 RE-2
Hetero. model
Homo. model
0.347 0.341
0.381 0.374
results show, the DRC is small as compared with the typical light water reactor. An increase in the fuel temperature of 500 °C introduces a negative reactivity of less than 130 pcm. This is not conducive to the reactivity control of the core. Owing to the design of such a small core, the high neutron leakage causes the negative contribution to defeat the positive contribution of the harden spec-
trum when the sodium density decreases. Therefore, the TRC is more negative and is approximately 1.1 pcm/°C. At the same time, the TRC results of the homogeneous model are slightly higher than those of the heterogeneous model. In contrast to the results shown in Table 9, only the fuel and blanket region showed a changed sodium density in the temperature reactivity simulation. Therefore, the neutron leakage is underestimated when the temperature increases in Table 10. However, DRC of the heterogeneous and homogeneous models still exhibits an obvious difference. The utilization of a more negative reactivity coefficient results in an overestimation of the reactor safety, especially during the transient simulation. Therefore, the use of the heterogeneous model is suggested for the calculation of safety-related parameters to obtain more reliable results. 4.5. Subassembly swap reactivity The subassembly swap measurement is used to simulate the possible accident of a fuel loading error. In the measurement, seven SAs were selected, among which, five were fuel SAs and the other two were SS SAs. The position and SA loading of the subassembly swap reactivity measurement can be observed in Fig. 7 and Table 11. It should be noted that for the (7–31) and (5–19) cases, one of the SS SA is replaced by a fuel SA. To prevent the insertion of a large positive reactivity, one of the fuel SAs is replaced by an SS SA at the same time. The measurement of the control rod movement was performed, which is similar to the previous measurements. The reactivity changes between the original and swapped cases
9
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046 Table 9 Sodium void reactivity simulation results and comparison. Measurement position in core
(2–4) (3–7) (4–9) (5–11) (6–13)
Original Voided Original Voided Original Voided Original Voided Original Voided
SARAX simulation results
Measurement, pcm
Hetero. Model
Homo. model
keff
Void reactivity, pcm
Error, %
keff
Void reactivity, pcm
Error, %
1.00064 1.00065 1.00064 1.00065 1.00064 1.00067 1.00064 1.00069 1.00064 1.00071
39.6
8.2
38.2
11.4
43.1 ± 5.8
40.4
6.8
40.0
7.7
43.3 ± 5.6
39.1
7.4
38.5
5.8
36.4 ± 5.4
37.3
6.7
36.9
7.7
40.0 ± 5.2
35.4
3.8
0.99529 0.99535 0.99529 0.99534 0.99529 0.99536 0.99529 0.99537 0.99529 0.99539
35.2
4.2
36.8 ± 5.6
Table 10 Temperature reactivity coefficient simulation results. Temperature, °C
Hetero. model
Homo. model
keff 250 260 270 280 290 300 DRC, pcm/°C
1.01415 1.01404 1.01393 1.01383 1.01372 1.01362 0.220
TRC, pcm/°C
keff
TRC, pcm/°C
1.089 1.075 1.066 1.064 1.060
1.00991 1.00980 1.00969 1.00958 1.00947 1.00936 0.240
1.110 1.113 1.113 1.108 1.104
RE-1 ------7-11 F ------6-10 F ------6-12 F ------6-13 F ------6-14 F ------6-15 F ------6-16
SA-3 ------5-13
F ------6-17
F ------4-11
F ------5-15
F ------6-19
F ------4-12
F ------5-16
F ------6-20
F ------3-8
SH-2 ------3-9
F ------4-13
F ------5-17
F ------2-5
F ------3-10
F ------4-14
F ------5-18
F ------2-6
F ------4-15
SS ------5-19
F F ------------6-22 6-23 RE-2 ------7-27
F ------3-11
F ------4-16
F ------5-20
F ------6-24
SA-2 ------5-21
F ------6-25
F ------6-2
F ------5-1
F ------5-24
F ------5-23
F ------5-22
F ------6-3
F ------5-2
F ------4-1
F ------4-18
F ------4-17
F ------6-4
F ------5-3
F ------4-2
SH-1 ------3-1
F ------3-12
F ------6-5
F ------5-4
F ------4-3
F ------3-2
F ------2-1
F ------6-6
SA-1 ------5-5
F ------4-4
F ------3-3
F ------2-2
NS ------1-1
F ------6-7
F ------5-6
F ------4-5
F ------3-4
F ------2-3
F ------2-4
F ------6-8
SS ------5-7
F ------4-6
SH-3 ------3-5
F ------3-6
F ------3-7
F ------6-9
F ------5-8
F ------4-7
F ------4-8
F ------4-9
F ------4-10
F ------5-14
F ------6-18
F ------5-10
F ------5-11
F ------5-12
F ------5-9
Type ------Index
F ------6-30
F ------6-29
F ------6-28
F ------6-27
F ------6-26 SS ------7-31
Fig. 7. Position of swapped SAs during subassembly swap reactivity measurement.
10
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
Table 11 The SA loading of measurement. Position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Type of SA loaded (2–6)
(3–11)
(4–17)
(5–23)
(6–29)
(7–31)
(5–19)
SS Fuel Fuel Fuel Fuel Fuel Fuel
Fuel SS Fuel Fuel Fuel Fuel Fuel
Fuel Fuel SS Fuel Fuel Fuel Fuel
Fuel Fuel Fuel SS Fuel Fuel SS
Fuel Fuel Fuel Fuel SS SS Fuel
SS SS SS SS SS Fuel SS
SS SS SS SS SS SS Fuel
Table 12 Control rod position for single rod measurement. Measurement position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Rod position, mm
Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped
RE-1
RE-2
SH-1
SH-2
SH-3
268 239 258 259 258 258 258 258 257 299 258 257 257 258
268 238 258 258 257 258 258 257 260 298 258 257 257 257
287 287 267 267 267 268 265 265 267 267 262 262 262 262
286 286 267 267 267 268 266 266 266 267 263 262 262 263
151 342 189 353 188 334 193 303 190 300 198 285 285 248
RE-1
RE-2
SH-1
SH-2
SH-3
267 327 258 258 259 257 258 293 259 318 258 295 295 295
267 325 257 260 257 258 257 293 259 317 260 295 295 295
241 298 242 293 242 288 241 276 241 278 241 268 268 255
242 297 242 293 242 289 241 275 242 277 241 267 267 255
241 299 242 295 241 289 241 275 242 279 242 269 269 256
Table 13 Control rod position for multiple rods measurement. Measurement position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Rod position, mm
Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped
contributed to the control rod movement and swap reactivity. During the experiment, the three shim rods and two regulating rods were used. For each case, the swap reactivity was measured twice—by using a single rod and multiple rods. The measurements of the control rod positions of the single rod and multiple rods are listed in Tables 12 and 13. The three safety rods are outside the core during the entire measurement. The averaged differential control rod worth of those five control rods is shown in Table 14. The SARAX simulation results are summarized in Tables 15 and 16. As in the temperature reactivity measurement, the measurement data of the swap reactivity is not published. Only the discussion regarding the SARAX results is presented. As the measurements proceed one by one, and the swap reactivity is changed from a large negative value to nearly zero. For the fuel SA swap measurement, the results are reasonable because the inner fuel SA has a large contribution to the core reactivity. After
replacement of the inner fuel SA, the reactivity is reduced by a large value. For the (7–31) case, the core layout can be treated as the (6–29) case with one more fuel SA. The positive reactivity is introduced into the core system. Therefore, the (7–31) case has a smaller absolute value with a negative sign. The same situation can be observed in the (5–19) case. The core layout is similar as
Table 14 Averaged differential worth of shim and regulating rods, unit in pcm/mm.
RE-1 RE-2 SH-1 SH-2 SH-3
Hetero. model
Homo. model
0.347 0.341 4.308 4.196 4.176
0.381 0.374 4.761 4.637 4.616
11
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046 Table 15 SARAX simulation results of single rod measurement. Measurement position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Hetero. model
Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped
Homo. model
keff
Swap reactivity, pcm
keff
Swap reactivity, pcm
1.00104 1.00159 1.00077 1.00097 1.00072 1.00133 1.00080 1.00091 1.00077 1.00290 1.00071 1.00324 1.00530 1.00329
720.3
0.99571 0.99710 0.99538 0.99626 0.99533 0.99659 0.99540 0.99598 0.99538 0.99802 0.99531 0.99825 1.00031 0.99810
716.4
665.9 551.4 446.9 272.9 111.2 45.7
669.9 550.4 447.7 270.8 105.1 51.0
Table 16 SARAX simulation results of multiple rods measurement. Measurement position
(2–6) (3–11) (4–17) (5–23) (6–29) (7–31) (5–19)
Hetero. model
Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped Original Swapped
Homo. model
keff
Swap reactivity, pcm
keff
Swap reactivity, pcm
1.00087 1.00121 1.00091 1.00102 1.00086 1.00133 1.00076 1.00102 1.00087 1.00331 1.00082 1.00329 1.00535 1.00321
721.2
0.99554 0.99662 0.99555 0.99636 0.99551 0.99664 0.99540 0.99615 0.99551 0.99851 0.99546 0.99829 1.00034 0.99802
725.4
649.5 551.0 431.3 255.9 113.4 53.2
that in the (5–23) case with one more fuel SA loaded in the fifth ring. Therefore, the difference in the swap reactivity between the (5–19) and (5–23) cases is approximately 400 pcm. Compared with two measurement methods, the single rod and multiple rods measurements provide identical results. In addition, the results obtained with the heterogeneous and homogenous models are also identical. As only the core layout is changed, and the control rod movement is small, the heterogeneity effect is almost the same, such that the final swap reactivity should be similar. The results obtained with the SARAX code have less than a 10-pcm difference between the heterogeneous and homogeneous models. This proves that the SARAX code is capable of obtaining stable results irrespective of whether the layout is changed. 5. Conclusion In this paper, the CEFR start-up tests were simulated to perform an additional validation of the SARAX deterministic FR analysis code. The criticality, control rod worth, sodium void reactivity, temperature reactivity, and subassembly swap reactivity were calculated, and the obtained results were compared with the measurement data. During the calculation, the differences between the heterogeneous and homogeneous models of the numerical calculation were also quantified. Before the simulation, a sensitivity test was performed to determine the convergence of the keff value by using different approximations of numerical methods. As the CEFR is a small core, the
648.9 546.3 428.6 249.4 112.7 57.1
neutron leakage is large, such that the neutron flux is more anisotropic. To address this, the S6P3 approximation shows its precision in obtaining a converged keff value. The following calculations were then based on that approximation. A comparison between the SARAX results and measurement data was performed for the criticality, control rod worth, and sodium void reactivity calculation. Owing to the lack of published measurement data of the temperature reactivity and subassembly swap reactivity, the SARAX results were discussed for those two cases. According to the numerical results, the SARAX code underestimated the criticality by only 25 pcm. In the case of the control rod worth and sodium void reactivity calculation, the differences are also small as compared with the measurement data. The temperature reactivity and subassembly swap reactivity calculation showed reasonable and reliable results. The comparison between the heterogeneous and homogeneous models showed that the heterogeneity effect exists in both the fuel assembly and control rod assembly. For the rodded case, the contribution of the control rod assembly to the heterogeneity effect is large. In addition, an obvious difference could be observed in both the sodium void reactivity and temperature reactivity calculation. This indicates that the heterogenous model is necessary, especially for safety-related parameter calculations. In general, the results presented in this study demonstrate the good prediction capability of the SARAX calculation. In a future study, the MCS will be used to perform such calculations for the validation. At the same time, the modeling of a spacer wire will be discussed.
12
X. Du et al. / Annals of Nuclear Energy 136 (2020) 107046
Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT). (No. NRF-2017M2A8A2018595)
References Chen, Y.Y., Yang, Y., Gang, Z., et al., 2013. Measurement and analysis of CEFR safety and shim rod worth. At. Energy Sci. Technol. 47 (Suppl.), 92–94 (In Chinese). Choe, J.W., Choi, S., Zhang, P., Park, J.S., Kim, W.K., Shin, H.C., Lee, H.S., Jung, J.E., Lee, D., 2019. Verification and validation of STREAM/RAST-K for PWR analysis. Nucl. Eng. Technol. 51 (2), 356–368. Choi, S., Lee, C.H., Lee, D., 2017. Resonance treatment using pin-based pointwise energy slowing-down method. J. Comput. Phys. 330, 134–155. Du, X.N., Cao, L.Z., Zheng, Y.Q., Wu, H.C., 2018. A hybrid method to generate fewgroup cross sections for fast reactor analysis. J. Nucl. Sci. Technol. 55 (8), 931– 944. Du, X.N., Choe, J.W., Choi, S., et al., 2019. Application of TULIP/STREAM code in 2-D fast reactor core neutronic analysis. The International Congress on Advances in Nuclear Power Plants (ICAPP) 2019, 2019 May 12-15, JUAN-LES-PINS, France. Guo, H., Garcia, E., Faure, B., et al., 2019. Advanced method for neutronic simulation of control rods in sodium fast reactors: numerical and experimental validation. Ann. Nucl. Energy 129, 90–100. Huo, X.K., Hu, Y., Chen, X.L., et al., 2018. Technical Specifications for Neutronics Benchmark of CEFR Start-up Tests, CRP-I31032. CIAE. IAEA, 2012. Status of Fast Reactor Research and Technology Development, IAEATECDOC-1691. IAEA. IAEA, 2014. Benchmark Analyses on the Control Rod Withdrawal Tests Performed during the PHENIX End-of-Life Experiments, IAEA-TECDOC-1742. IAEA. Ikegami, T., Ishikawa, M., Lell, R.M., et al., 2006. ZPPR-9 Experiment: A 650 MWeClass Sodium-Cooled MOX-Fueled FBR Core Mock-Up Critical Experiment With Clean Core of Two Homogeneous Zones, ZPPR-LMFR-EXP-002, NEA/NSC/Doc (2006). OECD/NEA. Jang, J.R., Kim, W.Y., Jeong, S.G., Jeong, E., Park, J.S., Lemaire, M., Lee, H.S., Jo, Y.M., Zhang, P., Lee, D., 2018. Validation of UNIST Monte Carlo code MCS for criticality
safety analysis of pwr spent fuel pool and storage cask. Ann. Nucl. Energy 114, 495–509. Lee, C.H., Yang, W.S., 2017. MC2-3: multigroup cross section generation code for fast reactor analysis. Nucl. Sci. Eng. 187, 268–290. Lu H.L., 2007. Nodal Methods for the Neutron Diffusion and Transport Equations in Triangular Meshes, Ph.D thesis, Xi’an Jiaotong University, July 2007 (in Chinese). G. Rimpault, Algorithmic features of the ECCO cell code for treating heterogeneous fast reactor subassemblies, Proceedings of the International Topical Meeting on Reactor Physics and Computations; 1995 May 1–5; Portland (OR), USA. Steven, C., Marck, V.D., 2006. Benchmarking ENDF/B-VII.0. Nucl. Data Sheets 107, 3061–3118. Tak, T.W., Lee, D., Kim, T.K., 2013. Design of ultra-long cycle fast reactor employing breed-and-burn strategy. Nucl. Technol. 183 (3), 427–435. Tak, T.W., Lee, D., Kim, T.K., Hong, S.G., 2014. Optimization study for ultra-long cycle fast reactor core concept. Ann. Nucl. Energy 73, 145–161. Tak, T.W., Choe, J.W., Jeong, Y.J., Lee, D., Kim, T.K., Hong, S.G., 2015. Feasibility study on ultralong-cycle operation and material performance for compact liquid metal-cooled fast reactors: a review work. Int. J. Energy Res. 39 (14), 1859– 1878. Toppel, B.J., 1983. User’s Guide for the REBUS-3 Fuel Cycle Analysis Capability, ANL83-2. Argonne National Lab. Xu, L.F., Cao, L.Z., Zheng, Y.Q., et al., 2017. Development of a new parallel SN code for neutron-photon transport calculation in 3-D cylindrical geometry. Prog. Nucl. Energy 1, 1–21. Yokoyama, K., Shono, A., Sanda, T., et al., 2006. Japan’s Experimental Fast Reactor JOYO MKI Core: Sodium-Cooled Uranium-Plutonium Mixed Oxide Fueled Fast Core Surrounded by UO2 blanket, JOYO-LMFR-RSR-001, NEA/NSC/Doc(2006). OECD/NEA. Zheng, Y.Q., Qiao, L., Zhai, Z.A., Du, X.N., Xu, Z.T., 2018b. SARAX: a new code for fast reactor analysis part II: verification, validation and uncertainty quantification. Nucl. Eng. Des. 331, 41–53. Zheng, Y.Q., Du, X.N., Xu, Z.T., Zhou, S.C., Liu, Y., Wan, C.H., Xu, L.F., 2018a. SARAX: a new code for fast reactor analysis part I: methods. Nucl. Eng. Des. 340, 421–430. Zhou, S.C., Wu, H.C., Cao, L.Z., et al., 2014. LAVENDER: a steady-state core analysis code for design studies of accelerator driven subcritical reactors. Nucl. Eng. Des. 278, 434–444. Zhou, K.Y., Yu, H., Hu, Y., et al., 2013. The measurement and analysis of CEFR sodium void reactivity effect. Proceedings of the 2013 21st International Conference on Nuclear Engineering, 2013 July 29 – August 2, Chengdu, China.