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Core design of a high breeding fast reactor cooled by supercritical pressure light water
Nuclear Engineering and Design 296 (2016) 30–37
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Core design of a high breeding fast reactor cooled by supercritical pressure light water Takayuki Someya ∗ , Akifumi Yamaji Cooperative Major in Nuclear Energy, Graduate School of Advanced Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjyuku-ku, Tokyo 169-8555, Japan
h i g h l i g h t s • • • •
Core design concept of supercritical light water cooled fast breeding reactor is developed. Compound system doubling time (CSDT) is applied for considering an appropriate target of breeding performance. Breeding performance is improved by reducing fuel rod diameter of the seed assembly. Core pressure loss is reduced by enlarging the coolant channel area of the seed assembly.
a r t i c l e
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Article history: Received 16 July 2015 Received in revised form 9 November 2015 Accepted 17 November 2015 Available online 3 December 2015
A high breeding fast reactor core concept, cooled by supercritical pressure light water has been developed with fully-coupled neutronics and thermal-hydraulics core calculations, which takes into account the influence of core pressure loss to the core neutronics characteristics. Design target of the breeding performance has been determined to be compound system doubling time (CSDT) of less than 50 years, by referring to the relationship of energy consumption and economic growth rate of advanced countries such as the G7 member countries. Based on the past design study of supercritical water cooled fast breeder reactor (Super FBR) with the concept of tightly packed fuel assembly (TPFA), further improvement of breeding performance and reduction of core pressure loss are investigated by considering different fuel rod diameters and coolant channel geometries. The sensitivities of CSDT and the core pressure loss with respect to major core design parameters have been clarified. The developed Super FBR design concept achieves fissile plutonium surviving ratio (FPSR) of 1.028, compound system doubling time (CSDT) of 38 years and pressure loss of 1.02 MPa with positive density reactivity (negative void reactivity). The short CSDT indicates high breeding performance, which may enable installation of the reactors at a rate comparable to energy growth rate of developed countries such as G7 member countries. © 2015 Elsevier B.V. All rights reserved.
1. Introduction For countries with advanced nuclear technologies, such as some of the G7 countries, establishing fast breeder reactor (FBR) fuel cycles may be an attractive option to secure sustainable source of energy, because FBRs can breed fissile 239 Pu from naturally abundant 238 U and can save consumption of the limited 235 U resources. One of the indices of breeding performance is the compound system doubling time (CSDT), which indicates required time to double energy output (i.e., total capacity) of the installed reactors by utilizing excess fissile materials gained from breeding (Waltar and
∗ Corresponding author. Tel.: +81 9072146047. E-mail address: [email protected] (T. Someya). http://dx.doi.org/10.1016/j.nucengdes.2015.11.007 0029-5493/© 2015 Elsevier B.V. All rights reserved.
Reynolds, 1981). It is evaluated by considering the following scenario. At first, some FBRs are operated, and excess fissile material (e.g., 239 Pu) is produced by breeding. The excess fissile materials are accumulated until the amount reaches the inventory required to startup another FBR reactor. At this point, the excess fissile materials are loaded into another FBR for operation. One way to consider an appropriate target of breeding performance of FBRs may be to consider CSDT with respect to growth rate of energy demand. The linear relationship between energy demand of a country and its Gross Domestic Product (GDP) is generally well acknowledged and is also supported by evidences (Soytas and Sari, 2003; Richmond et al., 2013). In the meanwhile, according to the economy outlook by Organization for Economic Co-operation and Development (OECD), average GDP growth rate of the G7 countries has been almost constant at around 1.4% per year for the past 30
T. Someya, A. Yamaji / Nuclear Engineering and Design 296 (2016) 30–37
Nomenclature D De E f g G K L Pfric Pform Pgrav Pacce Pcollapse Re t u z
fuel rod diameter equivalent hydraulic diameter Young’s modulus friction pressure loss coefficient gravitational acceleration mass flux form friction coefficient length of channel friction pressure loss form pressure loss gravity pressure loss acceleration pressure loss buckling pressure Reynolds number cladding thickness axial coolant velocity axial node width kinematic viscosity coefficient coolant density
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greatly reduced to favor breeding. As the result, the study showed that Super FBR with TPFA achieved CSDT of 47 years. However, the core pressure loss of Super FBR was high (1.48 MPa) and its influence (feedback) to the core neutronics was not considered in the previous study (Yoshida, 2014). Also, there is need to investigate ways of further reducing CSDT with the current core arrangement, which is yet to consider control rod designs. There may be different ways of modifications to the current core arrangement to accommodate control rod insertions, but such modifications may reduce breeding performance of the core and achieving the target CSDT of 50 years may be difficult with the current core arrangement. By considering the above all, this study aims to show Super FBR core design with TPFA concept by considering fully-coupled neutronics and thermal-hydraulics core calculations, which takes into account the influence of core pressure loss to the core neutronics characteristics. Moreover, further improvement of CSDT and reduction of core pressure loss of Super FBR is investigated by considering different fuel rod diameters and coolant channel geometries. 2. Design method 2.1. Design goals and criteria
years (Gurria and Padoan, 2012). These relationship and data indicate that average energy demand of the G7 countries has been growing at about 1.4% per year and may continue to grow at the same rate and double in the next 50 years (i.e., 1.01450 = 2.0). The role of nuclear power in such countries may be greatly enhanced if FBRs can be installed at similar rate to cope with the growing energy demand. In this study, CSDT of less than 50 years is considered to be a design target of FBRs. Among different types of FBR systems, large amount of effort have been devoted to development of sodium cooled FBRs, because of its high efficiency in breeding (USAEC Division of Technical Information, 1970; Srinivasan et al., 2006). However, there remain issues with handling of sodium and the high capital cost. On the other hand, light water reactors (LWRs) have been commercially used in many countries for decades with generally excellent reliabilities and high economic competitiveness against other technologies. However, current commercial LWRs are thermal reactors fueled with enriched uranium and sustainability of the fuel cycle is limited. Concepts of FBRs cooled by light water have been studied for many years, but most concepts are high conversion type reactors (Edlund, 1975; Oldekop et al., 1982). Few of the concepts show breeding ability, but generally, high breeding is difficult with LWRs, because light water acts as good moderator and softens the neutron spectrum, which disfavors breeding. For example, BWR type RMWR concept of JAEA is a breeder reactor. It adopts tight fuel rod lattice of triangular arrangement to reduce coolant (moderator) to fuel volume fraction (Vm /Vf ) to 0.17 and minimize neutron moderation (Iwamura et al., 2006). However, its CSDT is 245 years, which is far from achieving the above mentioned target of 50 years. In order to achieve short CSDT (high breeding performance) with light water cooling, the tightly packed fuel assembly (TPFA) concept with coolant to fuel volume ratio of less than 0.085 has been proposed and studied at Waseda University (Oka et al., 2013). The TPFA concept was then applied in core design of Super FBR, which is Waseda University concept of Supercritical Water Cooled Reactor (SCWR) for breeding 239 Pu with mixed oxide (MOX) fuel (Yoshida, 2014). In Super FBR, coolant temperature is not limited by the saturation temperature of water and its density can be reduced to around 0.36 g/cm3 . Moreover, fuel rods can be effectively cooled with narrow coolant channel by powerful pumps operating at supercritical pressure. Thus, coolant inventory in the core can be
Design goals and criteria are adopted from the studies of previous Super FBR and Super FR (Yoshida, 2014; Liu and Oka, 2013). They are summarized as following: The design goals (1) Fissile plutonium surviving ratio (FPSR) should be over 1.0. (2) Compound system doubling time (CSDT) should be shorter than 50 years. The design criteria (1) Positive water density (negative void) reactivity is achieved through a cycle. (2) Maximum linear heat generation rate (MLHGR) should be below 39 kW/m. (3) Maximum cladding surface temperature (MCST) should be below 650 ◦ C at normal condition. FPSR is an index of breeding for a reactor whose fission reactions are mainly from those of fissile plutonium (Pu) isotopes (such as 239 Pu and 241 Pu). FPSR of over 1.0 indicates that breeding of fissile Pu is achieved. The CSDT criterion of below 50 years is also adopted as described in the previous section. Definitions of these indices are provided in the following section. The design criterion of positive water density reactivity corresponds to the negative void reactivity of BWRs and is essential for assuring inherent safety of water cooled reactors. The design criteria of MLHGR and MCST are tentatively determined to ensure fuel integrities during abnormal transients for the purpose of conceptual development (Yamaji et al., 2003). Core pressure loss is not a design criterion, but high core pressure loss may influence coolant density distribution in the core and consequently influence its breeding performance (FPSR and CSDT). Hence, in this study, core pressure loss is evaluated and its influence on CSDT is evaluated through coupled neutronics and thermal hydraulics calculations as described in the following section. Another concern of high core pressure loss is channel stability and high pumping power requirement (Hetrick, 1993). Low core pressure loss is desirable from the viewpoints of these potential issues. One effective way to reduce core pressure loss is to enlarge coolant channel flow area, but this may influence the core breeding
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Fig. 1. Flow chart of coupled core calculation.
performance by softening neutron spectrum. Hence, in this study, influences of coolant channel geometries on core pressure loss and CSDT are investigated to find ways of reducing core pressure loss, while minimizing deterioration of CSDT. It should be noted that generally, channel stability can be improved by setting appropriate pressure loss at an entrance orifice. Emphasis of the present study is on conceptual development of high breeding core with supercritical water cooling, while pumping power and other engineering issues should also be addressed in future studies as the development of the concept makes further progress. 2.2. Analysis methods Core design in the present study is carried out by three dimensional diffusion calculation fully coupled with thermal hydraulic calculation, which also takes into account influence of pressure loss to core neutronics. It is the first time that the neutronic and thermalhydraulic calculations are fully coupled in the core design study of Super FBR, incorporating the influence of the large core pressure drop on core neutronics characteristics. The calculation flow chart is shown in Fig. 1. A neutronic calculation part is based on SRAC 2006 code system and JENDL-3.3 library developed by JAEA (Okumura et al., 2007). Unit cell and assembly depletion calculations are executed in SRAC-PIJ based on a collision probability method code and ASMBURN included in the SRAC system as an option code in order to prepare homogenized cross sections of fuel assemblies for core calculation. As stated above, cross sections are homogenized for each fuel assembly. Hence, in parallel to the assembly depletion calculation by ASMBURN, heterogeneous form factor (HFF) is also calculated to reconstruct pin-power distributions within each fuel assembly for a thermal hydraulic calculation. Core calculation is executed in auxiliary code COREBN which is a multi-dimensional core burn up calculation code including CITATION using a finite difference method and a function of interpolating cross sections by burn up and coolant density. Diffusion codes such as COREBN often introduce simplification in the z-direction. The code can be adopted to analyze this study’s core, because the core neutron spectrum is relatively uniform along the axial direction. As an example, neutron spectra at EOEC are shown for the lower part, middle part and upper part of a seed
Fig. 2. Neutron spectrum.
assembly in Fig. 2. The neutron spectra are almost the same at different elevations of the core, because the influence of the coolant density change is small due to its low inventory in TPFA. A thermal hydraulic calculation part is executed in SPROD code, which is based on axial heat transportation in single channel and radial heat transfer across fuel pellet, gap, cladding, and coolant (Han, 2011). The thermal hydraulics calculations are carried out with two single channel power distributions, obtained from the above mentioned pin-power reconstruction of each fuel assembly. One is the maximum power channel and the other is an average power channel. Coolant flow rate to each fuel assembly is determined by designing the corresponding inlet orifice pressure loss to satisfy the MCST design criterion and it is determined by the following calculations. At first, coolant flow rate is determined to satisfy the MCST criterion in the maximum power channel. The flow rate to each fuel assembly is given by determining inlet orifice pressure loss, and this flow fate is fixed through a cycle. In order to evaluate MCST, heat transfer coefficients at cladding surface of the maximum power channel is calculated with Watts’s correlation (Watts and Chou, 1982). Watts’s correlation shows good predictability for
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normal heat transfer condition with thermal hydraulic diameter of 4.4 mm (Shioiri et al., 2003) and is tentatively used in this study for the purpose of conceptual development. Validation of heat transfer correlation for the small thermal hydraulic diameter of TPFA (1.9 mm) is an issue for future study. Then, coolant density, temperature, and pressure loss is calculated with the determined flow rate in an average power channel. While coolant density and temperature are calculated from its enthalpy at each axial node as in previous studies (Yoshida, 2014). Core pressure loss is calculated by considering three kinds of pressure losses as described below (Duderstadt and Hamilton, 1976; Ozawa and Ami, 2013). As the Fanning friction factor, Blasius formula is used as shown in Eq. (2). When the total pressure loss is about 1.02 MPa for the core design adopting TPFA, friction pressure loss is the major contribution (about 90%), while contributions from gravity pressure loss (about 3%) and acceleration pressure loss (about 7%) are minor. (1) Friction pressure loss Pfric = f
L 1 2 u De 2
uL −0.25
f = 0.3164 Re−0.25 = 0.3164
(2)
(2) Gravity pressure loss Pgrav = gz
(3)
(3) Acceleration pressure loss Pacce =
G
Fig. 3. One pass with all upward flow scheme.
(1)
= u2
(4)
above definition indicates the sum of 239 Pu and 241 Pu. This definition is considered to well describe surviving ratio of fissile isotopes in the MOX fueled Super FBR core, which consists of enriched plutonium and depleted uranium (DU). In Super FBR core, contribution of 235 U may be negligible as it can only be found in DU and the total inventory is extremely small, compared with that of fissile plutonium. The definition of CSDT is shown below: CSDT =
(Reactor doubling time, RDT) (Operation rate)
× RDT =
(6)
(Excore factor) × ln 2 1 − (Rate of excore Puf decrease)
(Equilibrium loaded Puf inventory) × (Refueling batch) (Cycle length) × 365 (Puf inventory at EOEC) − (Puf inventory at BOEC)
(7)
(Cycle length) (Cycle length) + (Refueling and periodic inspection period)
(8)
Operation rate =
Excore factor = 1 +
These evaluated thermal hydraulic parameters are fed to the neutronic calculation and the two calculations are iterated to incorporate thermal hydraulic feedbacks to neutronics. Until both the burn up distribution from the neutronic calculation and the water density distribution from the thermal hydraulic calculation converge, these coupled calculations are iterated (Han, 2011).
(period of excore stay) (period of incore stay)
(9)
In order to calculate CSDT, the followings are assumed as in the previous study (Yoshida, 2014): period of ex-core stay by reprocessing and fuel fabrication is 5 years, half-life of 241 Pu is 14.4 years, and period of refueling and periodic inspection per cycle is 30 days. Thus, CSDT indicates required time to double energy output (i.e., total capacity) of the installed reactors by utilizing excess fissile materials gained from breeding. 3. Reference core design
2.3. Breeding evaluation 3.1. In-vessel coolant flow scheme For evaluating breeding performance of cores, breeding ratio and doubling time are often used, but these indices are used with various definitions depending on purposes and core properties. In the Super FBR studies, fissile plutonium surviving ratio (FPSR) and compound system doubling time (CSDT) are used as breeding ratio and doubling time, respectively. The definition of FPSR is shown below: FPSR =
(The total amount of fissile Pu at EOEC) (The total amount of fissile Pu at BOEC)
(5)
Except for plutonium, this definition does not include other fissile materials such as 235 U, and fissile plutonium calculated in the
In the Super FBR designs, the one pass with all upward flow is used as in-vessel flow scheme as shown in Fig. 3 (Liu and Oka, 2013). In this flow scheme, the inlet coolant is directed to the lower plenum via down comer, before flowing up the fuel channels. The flow rate to each fuel assembly is designed by applying different orifice pressure losses at the inlet of fuel assemblies to satisfy the MCST criterion. Compared with the previously studied two pass flow scheme, the one pass flow scheme is simpler and is similar to that of current PWRs, which is desirable from the viewpoint of simplifying the upper core structure, as well as to simplify refueling procedure (Liu and Oka, 2013).
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Fig. 4. Concept of TPFA and seed and blanket assembly without ZrH.
3.2. Fuel assembly design As described in Section 1, this study aims to develop Super FBR core design which achieves high breeding (CSDT < 50 years) with the TPFA concept. In the TPFA design, as illustrated in Fig. 4, the gap clearance between fuel rods is 0 mm, and a coolant channel is installed in the space made by three fuel rods touching each other in this TPFAs. In addition, some of this space is narrowed by being plugged with metal fitting (stainless steel) to minimize the coolant flow area. The ratio of coolant to fuel volume can be drastically decreased, and high breeding performance is expected. For example, the ratio is decreased to 0.0635 when fuel rod diameter is 12 mm. In this study, the above mentioned TPFA design is adopted for the following three types of fuel assemblies: Seed assemblies, in which MOX fuel rods are loaded, blanket assemblies, in which DU fuel rods are loaded, and blanket assemblies, in which some of the DU fuel rods are replaced with zirconium hydride (ZrH) rods. The ZrH rods act as solid moderators and are employed in some of blanket assemblies for achieving positive density reactivity (negative void reactivity) (Oka and Jevremovic, 1996). In some of the blanket assemblies, two rows of DU rods are replaced with ZrH rods as illustrated in Fig. 5. These blanket assemblies with ZrH solid moderators improve the coolant density reactivity by effectively capturing neutrons and introducing negative reactivity when coolant density is reduced (Oka and Jevremovic, 1996).
Fig. 5. Blanket assembly with ZrH.
Fig. 6. Loading pattern.
3.3. Core design The reference core is designed with the three types of TPFAs explained in the previous section. By referring to the past experience of Super FBR core design, this study adopts the same core loading pattern and axial constitution as those of the previous study. They are shown in Figs. 6 and 7, respectively (Yoshida, 2014). The loading pattern was designed from the viewpoint of maximizing breeding performance while maintaining positive density reactivity. Refueling is designed in 4 batches in the seed assemblies,
Fig. 7. Axial constitution.
T. Someya, A. Yamaji / Nuclear Engineering and Design 296 (2016) 30–37 Table 2 Summary of fuel assembly design parameters.
Table 1 Reference core design parameter. Thermal power [MW t] Operation pressure [MPa] Active height [m] Equivalent active diameter [m] Operation cycle length [day] Number of fuel batches (Seed/Blanket) Average Pu enrichment (seed) [wt.%] Average discharge burn up (Seed) [GWd/t] Density reactivity (BOEC/EOEC) [%k/k] Maximum cladding surface temperature (MCST) [◦ C] Maximum linear heat generation rate (MLHGR) [kW/m] Pressure loss [MPa] FPSR CSDT [year]
35
1372 30 2.0 4.17 550 4/1 29.9 54.5 0.29/0.58 650 35.43 1.83 1.026 40
and in 1 batch in the blanket assemblies. Also, the axial fuel zoning as illustrated in Fig. 7 was designed to minimize axial power peaking. Table 1 shows the reference core design parameters and evaluated core characteristics when fuel rod diameter of every assembly is 12 mm. CSDT has been improved from 47 years of the previous study to 40 years. However, CSDT may be deteriorated (increased) when control rods are designed. In Super FBR core design, cluster type control rods (similar to that of PWR) are being considered for reactivity control (Yoshida, 2014). Hence, to accommodate insertions of control rods, some space will need to be created in TPFA, which may deteriorate breeding performance of the core. Therefore, it is worth investigating whether CSDT can be further improved. The evaluated pressure loss of 1.48 MPa is remarkably high compared with those of current LWRs and may give rise to concerns of stability and pumping power requirement. Although the main scope of this study is on conceptual development of Super FBR core, it is important to address possibility of reducing pressure loss, which will reduce future challenges when detailed engineering issues will be addressed.
4. Sensitivity studies for design improvements In the Super FBR core design, three kinds of fuel assemblies are used, and their respective role is different as follows.
Fuel rod diameter [mm] Pellet diameter [mm] Gap clearance [mm] Cladding thickness [mm] Number of fuel rods Number of coolant paths Vm /Vf 1 Assembly pitch [cm] 1
12 10.4063 0.100 0.6968 397 792 0.063 24.66
11 9.5058 0.100 0.6471 469 936 0.064 24.66
10 8.6053 0.100 0.5974 547 1092 0.065 24.66
9.5 8.1850 0.085 0.5725 631 1260 0.064 24.66
Vm /Vf : The ratio of coolant (moderate) to fuel volume.
4.1. Sensitivity study of fuel rod diameter The design range of fuel rod diameter is determined from 12 mm used in the previous study to 9.5 mm used in current PWRs. For a given fuel rod diameter, cladding thickness is determined with a standard of the buckling. The equation for evaluating buckling pressure of an escalope hollow cylinder as follows: Pcollapse =
1 t × 2.2E 3 D−t
3
where, Pcollapse is determined to be 20.3 MPa by assuming external pressure of 25 MPa and internal pressure of 4.7 MPa (Ishiwatari, 2000). Gap clearance is tentatively determined referring to current BWRs and PWRs. Summary of the fuel rod design is shown in Table 2. TPFAs with the fixed pitch of 24.66 cm are designed with the above designed fuel rods. The assembly size is fixed and the gap between the inner surface of the channel box and the peripheral fuel rods are filled with stainless steel. From the definition of CSDT, it is expected that increase of thermal power is effective to improve CSDT. Hence, first, the influence of fuel rod diameter in seed assembly is studied while fuel rod diameter of the other assemblies is kept constant at 12 mm. As shown in Fig. 8, the core thermal power is increased by decreasing fuel rod diameter, because the number of fuel rods loaded into an assembly is increased. As a result, CSDT is monotonically improved by reducing fuel rod diameter. However, pressure loss is increased by reducing fuel rod diameter, because coolant channel area is reduced. By considering the above sensitivities, 11 mm is adopted as a design point of fuel rod diameter in the seed assemblies. Secondly, the influence of fuel rod diameter in the blanket assemblies without ZrH is investigated when fuel rod diameter of the other assemblies is fixed at 11 mm. In this case, reducing the rod
(1) Seed: Bearing most of the thermal power of the core. (2) Blanket without ZrH: Converting (breeding) from 238 U to 239 Pu or 241 Pu. (3) Blanket with ZrH: Contributing to positive density reactivity and converting (breeding).
Hence, it is expected that design of the seed assembly is influential to pressure loss, because of the high coolant mass flux to cool the high power seed assemblies. In the meantime, design of the blanket without ZrH is expected to be influential to CSDT, as it is the main part of the core, which is contributing to breeding. In the reference core design described in the previous section, fuel rod diameter and coolant channel shape was the same in all fuel assemblies. From the viewpoint of improving CSDT, the core power density should be maximized, but coolant channel area needs to be maximized to minimize pressure loss. Hence, in this study, improvement of CSDT and reduction of pressure loss are studied by changing fuel rod diameter and coolant channel shape with consideration of these different roles of the fuel assemblies.
(10)
Fig. 8. Sensitivities of fuel rod diameter in the seed assembly.
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Fig. 9. Sensitivities of fuel rod diameter in the blanket assembly without ZrH.
diameter has small influence on the core thermal power, because power of a DU rod is much smaller than that of a MOX rod. Hence, CSDT is not sensitive to the fuel rod diameter as shown in Fig. 9. However, density reactivity coefficient is influenced by the rod diameter. In particular, the results indicate that the rod diameter should not be around 10 mm from the viewpoint of assuring positive density reactivity. This is because the blanket fuel domain area is substantially reduced when the rod diameter is around 10 mm, due to alignment of the fuel rods in the assembly, whose size is fixed. 4.2. Reduction of pressure loss Three kinds of coolant channels are investigated as shown in Fig. 10. The coolant channel of Geometry A is used in the reference core design (Section 3). Also, in the sensitivity analysis of fuel rod diameter (Section 4.1), Geometry A is applied to all assemblies regardless of the difference of fuel rod diameter. As described in Section 3.2, a circular coolant channel is introduced between the contacting fuel rods and the remaining space is filled with the metal fitting. In order to investigate possibility of reducing core pressure loss, two other channel geometries are considered. In Geometry B, the coolant channel area is expanded and replaces most of the metal fitting domain. In contrast, in Geometry C, the coolant channel area is reduced and the metal fitting domain is enlarged. In this sensitivity study, Geometry B is employed in the seed assemblies where pressure loss is large. In this way, decrease of
pressure loss is expected, because equivalent hydraulic diameter (De ) is increased and axial coolant velocity (u) is decreased in Eqs. (1) and (2) (Section 2.2). However, the ratio of coolant to fuel volume in the seed assemblies is increased, which may deteriorate breeding performance of the reactor by softening the neutron spectrum. Thus, Geometry C is employed in the blanket assemblies without ZrH, where pressure loss is not large, in order to prevent the increase of the coolant to fuel volume ratio of the core. On the other hand, the coolant channel in the blanket assemblies with ZrH is not changed to Geometry C, but Geometry A is adopted. Because, the coolant mass flux in the blanket assemblies with ZrH is needed more than that in the blanket assemblies without ZrH due to large local power peaking affected by the ZrH layer, and hence pressure loss tends to be larger. The final core design with consideration of different fuel rod diameters and coolant channel geometries is compared with the reference core design in Table. 3. Compared with the reference core design, CSDT has been improved from 40 years to 38 years, while also improving core pressure loss from 1.83 MPa to 1.02 MPa. The improvements show that both CSDT and core pressure loss can be improved by considering roles of the different fuel assemblies in the core and designing fuel rod diameters and coolant channel geometries. In this study, pressure loss evaluation is integrated into fullycoupled neutronics and thermal-hydraulics core calculations for the first time in the conceptual development of Super FBR. In the previous study (Yoshida, 2014), influence of the core pressure loss was not taken into account in the neutronics calculations
Fig. 10. Coolant channel geometry.
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Table 3 Result of reducing pressure loss. Core
Reference core design
Final concept
Seed fuel rod diameter [mm]/coolant channel geometry Blanket without ZrH fuel rod diameter [mm]/coolant channel geometry Blanket with ZrH fuel rod diameter [mm]/coolant channel geometry Thermal power [MWt] Discharge burn up(Seed) [GWd/t] Density reactivity (BOEC/EOEC) [%k/k] Maximum cladding surface temperature [◦ C] Maximum linear heat generation rate [kW/m] Pressure loss [MPa] FPSR (EOEC/BOEC) CSDT [year]
12/A 12/A 12/A 1372 54.5 0.29/0.58 650 35.43 1.83 1.026 40
11/B 12/C 12/A 1598 64.6 1.38/0.83* (1.17/1.37) 650 35.40 (35.18) 1.02 (1.01) 1.028 38
*
The values in parentheses indicate the results with method of the previous study (Yoshida, 2014) (i.e., neutronics and thermal-hydraulic calculations are not fully coupled).
(i.e., water density is evaluated by assuming constant core pressure of 30 MPa throughout the core). Comparison between calculation method of this study and that of the previous study has been executed by using above final concept. Water density evaluated by this study’s method is 0.325 g/cm3 at the core outlet, while that by the previous study’s method is 0.220 g/cm3 at the outlet (i.e., water density is underestimated when core pressure loss is not considered). As shown in Table 3, most neutronics characteristics are not influenced because water inventory is very little in TPFA concept. However, density reactivity calculated by this study’s method is 1.38%k/k at BOEC and 0.83%k/k at EOEC, while that calculated by the previous study’s method is 1.17%k/k at BOEC and 1.37%k/k at EOEC. These differences are not negligible as they determine the most fundamental safety characteristics of water cooled reactors. Hence, it is necessary to integrate pressure loss evaluation into fully-coupled neutronics and thermal-hydraulics core calculations. 5. Conclusion Conceptual design of a Super FBR core with Tightly Packed Fuel Assembly (TPFA) has been developed with fully-coupled neutronics and thermal-hydraulics core calculations. The calculations take into account the influence of core pressure loss to the core neutronics characteristics for the first time in the development of Super FBR concept. It has been shown that the fully-coupled calculation is important for Super FBR core design as coolant density reactivity is influenced significantly. Furthermore, improvement of breeding performance (reduction of CSDT) and reduction of core pressure loss are shown by changing fuel rod diameter and coolant channel geometries. The concept achieves CSDT of 38 years, indicating high breeding performance, which may enable installation of the reactors at a rate comparable to energy growth rate of developed countries such as G7 member countries. It has been clarified that CSDT is sensitive to linear heat generation rate of seed assemblies, which bears most of the thermal power of the core. Hence, reducing fuel rod diameter of the seed assembly, while enlarging the coolant channel area has been shown to be effective to reduce CSDT and pressure loss simultaneously by increasing the power while maintaining cooling. In contrast, thermal power of blanket assemblies are low and coolant channel area can be reduced to achieve low coolant to fuel volume ratio for attaining high breeding. Optimization of the fuel rod diameter
and coolant channel geometry for each type of fuel assembly may be an issue for future studies. References Duderstadt, J.J., Hamilton, J.L., 1976. Nuclear Reactor Analysis. John Wiley & Sons Inc, New York, USA, Chapter 12. Edlund M.C., 1975. High conversion ratio plutonium recycle in pressurized water reactors. Ann. Nucl. Energy 2, 801–807. Gurria, A., Padoan, P.C., 2012. Economic outlook no. 92. In: Organisation for Economic Co-operation and Development (OECD). Press Conference in Paris, November 27, 2012, p. 2. Han, C., 2011. Improvement in code system for SWFR core design. In: Technical Report. University of Tokyo. Hetrick, D.L., 1993. Dynamics of nuclear reactors. Am. Nucl. Soc., Chapter 5 and 6. Ishiwatari, Y., 2000. Study of Breeding Performance of Super FR. University of Tokyo, Bachelor thesis. Iwamura, T., Uchikawa, S., Okubo, T., Kugo, T., Akie, H., Nakano, Y., Nakatsuka, T., 2006. Concept of innovative water reactor for flexible fuel cycle (FLWR). Nucl. Eng. Des. 236, 1599–1605. Liu, Q., Oka, Y., 2013. One pass core design of a super fast reactor. In: GLOBAL 2013, September 29–October 3, 2013, Salt Lake city, UT, USA. Oka, Y., Jevremovic, T., 1996. Negative void reactivity in large fast breeder reactors with hydrogeneous moderator layer. Ann. Nucl. Energy 23, 1105–1115. Oka, Y., Inoue, T., Yoshida, T., 2013. Plutonium breeding of light water cooled fast reactors. J. Nucl. Sci. Technol. 50 (1), 15–20. Okumura, K., Kugo, T., Kaneko, K., Tsuchihashi, K., 2007. SRAC2006: a comprehensive neutronics calculation code system. In: Technical Report. Japan Atomic Energy Agency (JAEA). Oldekop, W., Berger, H.D., Zeggel, W., 1982. General features of advanced pressurized water reactors with improved fuel utilization. Nucl. Technol. 59, 212–227. Ozawa, M., Ami, T., 2013. Design Handbook of Boilling Two-Phase Flow. Techno Systems, Inc, Chapter 3.2. Richmond, P., Mimkes, J., Hutzler, S., 2013. Econophysics and Physical Economics. Oxford, UK, pp. 174–175. Shioiri, A., Moriya, K., Oka, Y., Mori, H., Takahashi, H., 2003. Development of supercritical-water cooled power reactor conducted by a Japanese Joint Team. In: GENES4/ANP2003, Sep 15–19, 2003, Kyoto, Japan. Soytas, U., Sari, R., 2003. Energy consumption and GDP: causality relationship in G-7 countries and emerging markets. Energy Econ. 25 (1), 33–37. Srinivasan, G., Sureshkumar, K., Rajendran, B., Ramalingam, P., 2006. The fast breeder test reactor-design and operating experiences. Nucl. Eng. Des. 236, 796–811. USAEC Division of Technical Information, 1970. ANL-175—Nuclear Reactors Built, Being Built, or Planned in the United States as of June 30, 1970. TID-8200 (22nd Rev.). Waltar, A.E., Reynolds, A.B., 1981. Fast Breeder Reactors. Pergamon Press, New York, USA, Chapter 7-7. Watts, M.J., Chou, C.T., 1982. Mixed convection heat transfer to supercritical pressure water. In: Proc. Seventh Int. Heat Transfer Conf Vol. 3, Munchen, p. 495. Yamaji, A., Oka, Y., Koshizuka, S., 2003. Fuel design of high temperature reactors cooled and moderated by supercritical light water. In: GENES4/ANP2003, Sep 15–19, 2003, Kyoto, Japan. Yoshida, T., 2014. Core design of a Breeding Super FR. University of Waseda, Master’s thesis.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Core design of a high breeding fast reactor cooled by supercritical pressure light water Takayuki Someya ∗ , Akifumi Yamaji Cooperative Major in Nuclear Energy, Graduate School of Advanced Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjyuku-ku, Tokyo 169-8555, Japan
h i g h l i g h t s • • • •
Core design concept of supercritical light water cooled fast breeding reactor is developed. Compound system doubling time (CSDT) is applied for considering an appropriate target of breeding performance. Breeding performance is improved by reducing fuel rod diameter of the seed assembly. Core pressure loss is reduced by enlarging the coolant channel area of the seed assembly.
a r t i c l e
a b s t r a c t
i n f o
Article history: Received 16 July 2015 Received in revised form 9 November 2015 Accepted 17 November 2015 Available online 3 December 2015
A high breeding fast reactor core concept, cooled by supercritical pressure light water has been developed with fully-coupled neutronics and thermal-hydraulics core calculations, which takes into account the influence of core pressure loss to the core neutronics characteristics. Design target of the breeding performance has been determined to be compound system doubling time (CSDT) of less than 50 years, by referring to the relationship of energy consumption and economic growth rate of advanced countries such as the G7 member countries. Based on the past design study of supercritical water cooled fast breeder reactor (Super FBR) with the concept of tightly packed fuel assembly (TPFA), further improvement of breeding performance and reduction of core pressure loss are investigated by considering different fuel rod diameters and coolant channel geometries. The sensitivities of CSDT and the core pressure loss with respect to major core design parameters have been clarified. The developed Super FBR design concept achieves fissile plutonium surviving ratio (FPSR) of 1.028, compound system doubling time (CSDT) of 38 years and pressure loss of 1.02 MPa with positive density reactivity (negative void reactivity). The short CSDT indicates high breeding performance, which may enable installation of the reactors at a rate comparable to energy growth rate of developed countries such as G7 member countries. © 2015 Elsevier B.V. All rights reserved.
1. Introduction For countries with advanced nuclear technologies, such as some of the G7 countries, establishing fast breeder reactor (FBR) fuel cycles may be an attractive option to secure sustainable source of energy, because FBRs can breed fissile 239 Pu from naturally abundant 238 U and can save consumption of the limited 235 U resources. One of the indices of breeding performance is the compound system doubling time (CSDT), which indicates required time to double energy output (i.e., total capacity) of the installed reactors by utilizing excess fissile materials gained from breeding (Waltar and
∗ Corresponding author. Tel.: +81 9072146047. E-mail address: [email protected] (T. Someya). http://dx.doi.org/10.1016/j.nucengdes.2015.11.007 0029-5493/© 2015 Elsevier B.V. All rights reserved.
Reynolds, 1981). It is evaluated by considering the following scenario. At first, some FBRs are operated, and excess fissile material (e.g., 239 Pu) is produced by breeding. The excess fissile materials are accumulated until the amount reaches the inventory required to startup another FBR reactor. At this point, the excess fissile materials are loaded into another FBR for operation. One way to consider an appropriate target of breeding performance of FBRs may be to consider CSDT with respect to growth rate of energy demand. The linear relationship between energy demand of a country and its Gross Domestic Product (GDP) is generally well acknowledged and is also supported by evidences (Soytas and Sari, 2003; Richmond et al., 2013). In the meanwhile, according to the economy outlook by Organization for Economic Co-operation and Development (OECD), average GDP growth rate of the G7 countries has been almost constant at around 1.4% per year for the past 30
T. Someya, A. Yamaji / Nuclear Engineering and Design 296 (2016) 30–37
Nomenclature D De E f g G K L Pfric Pform Pgrav Pacce Pcollapse Re t u z
fuel rod diameter equivalent hydraulic diameter Young’s modulus friction pressure loss coefficient gravitational acceleration mass flux form friction coefficient length of channel friction pressure loss form pressure loss gravity pressure loss acceleration pressure loss buckling pressure Reynolds number cladding thickness axial coolant velocity axial node width kinematic viscosity coefficient coolant density
31
greatly reduced to favor breeding. As the result, the study showed that Super FBR with TPFA achieved CSDT of 47 years. However, the core pressure loss of Super FBR was high (1.48 MPa) and its influence (feedback) to the core neutronics was not considered in the previous study (Yoshida, 2014). Also, there is need to investigate ways of further reducing CSDT with the current core arrangement, which is yet to consider control rod designs. There may be different ways of modifications to the current core arrangement to accommodate control rod insertions, but such modifications may reduce breeding performance of the core and achieving the target CSDT of 50 years may be difficult with the current core arrangement. By considering the above all, this study aims to show Super FBR core design with TPFA concept by considering fully-coupled neutronics and thermal-hydraulics core calculations, which takes into account the influence of core pressure loss to the core neutronics characteristics. Moreover, further improvement of CSDT and reduction of core pressure loss of Super FBR is investigated by considering different fuel rod diameters and coolant channel geometries. 2. Design method 2.1. Design goals and criteria
years (Gurria and Padoan, 2012). These relationship and data indicate that average energy demand of the G7 countries has been growing at about 1.4% per year and may continue to grow at the same rate and double in the next 50 years (i.e., 1.01450 = 2.0). The role of nuclear power in such countries may be greatly enhanced if FBRs can be installed at similar rate to cope with the growing energy demand. In this study, CSDT of less than 50 years is considered to be a design target of FBRs. Among different types of FBR systems, large amount of effort have been devoted to development of sodium cooled FBRs, because of its high efficiency in breeding (USAEC Division of Technical Information, 1970; Srinivasan et al., 2006). However, there remain issues with handling of sodium and the high capital cost. On the other hand, light water reactors (LWRs) have been commercially used in many countries for decades with generally excellent reliabilities and high economic competitiveness against other technologies. However, current commercial LWRs are thermal reactors fueled with enriched uranium and sustainability of the fuel cycle is limited. Concepts of FBRs cooled by light water have been studied for many years, but most concepts are high conversion type reactors (Edlund, 1975; Oldekop et al., 1982). Few of the concepts show breeding ability, but generally, high breeding is difficult with LWRs, because light water acts as good moderator and softens the neutron spectrum, which disfavors breeding. For example, BWR type RMWR concept of JAEA is a breeder reactor. It adopts tight fuel rod lattice of triangular arrangement to reduce coolant (moderator) to fuel volume fraction (Vm /Vf ) to 0.17 and minimize neutron moderation (Iwamura et al., 2006). However, its CSDT is 245 years, which is far from achieving the above mentioned target of 50 years. In order to achieve short CSDT (high breeding performance) with light water cooling, the tightly packed fuel assembly (TPFA) concept with coolant to fuel volume ratio of less than 0.085 has been proposed and studied at Waseda University (Oka et al., 2013). The TPFA concept was then applied in core design of Super FBR, which is Waseda University concept of Supercritical Water Cooled Reactor (SCWR) for breeding 239 Pu with mixed oxide (MOX) fuel (Yoshida, 2014). In Super FBR, coolant temperature is not limited by the saturation temperature of water and its density can be reduced to around 0.36 g/cm3 . Moreover, fuel rods can be effectively cooled with narrow coolant channel by powerful pumps operating at supercritical pressure. Thus, coolant inventory in the core can be
Design goals and criteria are adopted from the studies of previous Super FBR and Super FR (Yoshida, 2014; Liu and Oka, 2013). They are summarized as following: The design goals (1) Fissile plutonium surviving ratio (FPSR) should be over 1.0. (2) Compound system doubling time (CSDT) should be shorter than 50 years. The design criteria (1) Positive water density (negative void) reactivity is achieved through a cycle. (2) Maximum linear heat generation rate (MLHGR) should be below 39 kW/m. (3) Maximum cladding surface temperature (MCST) should be below 650 ◦ C at normal condition. FPSR is an index of breeding for a reactor whose fission reactions are mainly from those of fissile plutonium (Pu) isotopes (such as 239 Pu and 241 Pu). FPSR of over 1.0 indicates that breeding of fissile Pu is achieved. The CSDT criterion of below 50 years is also adopted as described in the previous section. Definitions of these indices are provided in the following section. The design criterion of positive water density reactivity corresponds to the negative void reactivity of BWRs and is essential for assuring inherent safety of water cooled reactors. The design criteria of MLHGR and MCST are tentatively determined to ensure fuel integrities during abnormal transients for the purpose of conceptual development (Yamaji et al., 2003). Core pressure loss is not a design criterion, but high core pressure loss may influence coolant density distribution in the core and consequently influence its breeding performance (FPSR and CSDT). Hence, in this study, core pressure loss is evaluated and its influence on CSDT is evaluated through coupled neutronics and thermal hydraulics calculations as described in the following section. Another concern of high core pressure loss is channel stability and high pumping power requirement (Hetrick, 1993). Low core pressure loss is desirable from the viewpoints of these potential issues. One effective way to reduce core pressure loss is to enlarge coolant channel flow area, but this may influence the core breeding
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Fig. 1. Flow chart of coupled core calculation.
performance by softening neutron spectrum. Hence, in this study, influences of coolant channel geometries on core pressure loss and CSDT are investigated to find ways of reducing core pressure loss, while minimizing deterioration of CSDT. It should be noted that generally, channel stability can be improved by setting appropriate pressure loss at an entrance orifice. Emphasis of the present study is on conceptual development of high breeding core with supercritical water cooling, while pumping power and other engineering issues should also be addressed in future studies as the development of the concept makes further progress. 2.2. Analysis methods Core design in the present study is carried out by three dimensional diffusion calculation fully coupled with thermal hydraulic calculation, which also takes into account influence of pressure loss to core neutronics. It is the first time that the neutronic and thermalhydraulic calculations are fully coupled in the core design study of Super FBR, incorporating the influence of the large core pressure drop on core neutronics characteristics. The calculation flow chart is shown in Fig. 1. A neutronic calculation part is based on SRAC 2006 code system and JENDL-3.3 library developed by JAEA (Okumura et al., 2007). Unit cell and assembly depletion calculations are executed in SRAC-PIJ based on a collision probability method code and ASMBURN included in the SRAC system as an option code in order to prepare homogenized cross sections of fuel assemblies for core calculation. As stated above, cross sections are homogenized for each fuel assembly. Hence, in parallel to the assembly depletion calculation by ASMBURN, heterogeneous form factor (HFF) is also calculated to reconstruct pin-power distributions within each fuel assembly for a thermal hydraulic calculation. Core calculation is executed in auxiliary code COREBN which is a multi-dimensional core burn up calculation code including CITATION using a finite difference method and a function of interpolating cross sections by burn up and coolant density. Diffusion codes such as COREBN often introduce simplification in the z-direction. The code can be adopted to analyze this study’s core, because the core neutron spectrum is relatively uniform along the axial direction. As an example, neutron spectra at EOEC are shown for the lower part, middle part and upper part of a seed
Fig. 2. Neutron spectrum.
assembly in Fig. 2. The neutron spectra are almost the same at different elevations of the core, because the influence of the coolant density change is small due to its low inventory in TPFA. A thermal hydraulic calculation part is executed in SPROD code, which is based on axial heat transportation in single channel and radial heat transfer across fuel pellet, gap, cladding, and coolant (Han, 2011). The thermal hydraulics calculations are carried out with two single channel power distributions, obtained from the above mentioned pin-power reconstruction of each fuel assembly. One is the maximum power channel and the other is an average power channel. Coolant flow rate to each fuel assembly is determined by designing the corresponding inlet orifice pressure loss to satisfy the MCST design criterion and it is determined by the following calculations. At first, coolant flow rate is determined to satisfy the MCST criterion in the maximum power channel. The flow rate to each fuel assembly is given by determining inlet orifice pressure loss, and this flow fate is fixed through a cycle. In order to evaluate MCST, heat transfer coefficients at cladding surface of the maximum power channel is calculated with Watts’s correlation (Watts and Chou, 1982). Watts’s correlation shows good predictability for
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33
normal heat transfer condition with thermal hydraulic diameter of 4.4 mm (Shioiri et al., 2003) and is tentatively used in this study for the purpose of conceptual development. Validation of heat transfer correlation for the small thermal hydraulic diameter of TPFA (1.9 mm) is an issue for future study. Then, coolant density, temperature, and pressure loss is calculated with the determined flow rate in an average power channel. While coolant density and temperature are calculated from its enthalpy at each axial node as in previous studies (Yoshida, 2014). Core pressure loss is calculated by considering three kinds of pressure losses as described below (Duderstadt and Hamilton, 1976; Ozawa and Ami, 2013). As the Fanning friction factor, Blasius formula is used as shown in Eq. (2). When the total pressure loss is about 1.02 MPa for the core design adopting TPFA, friction pressure loss is the major contribution (about 90%), while contributions from gravity pressure loss (about 3%) and acceleration pressure loss (about 7%) are minor. (1) Friction pressure loss Pfric = f
L 1 2 u De 2
uL −0.25
f = 0.3164 Re−0.25 = 0.3164
(2)
(2) Gravity pressure loss Pgrav = gz
(3)
(3) Acceleration pressure loss Pacce =
G
Fig. 3. One pass with all upward flow scheme.
(1)
= u2
(4)
above definition indicates the sum of 239 Pu and 241 Pu. This definition is considered to well describe surviving ratio of fissile isotopes in the MOX fueled Super FBR core, which consists of enriched plutonium and depleted uranium (DU). In Super FBR core, contribution of 235 U may be negligible as it can only be found in DU and the total inventory is extremely small, compared with that of fissile plutonium. The definition of CSDT is shown below: CSDT =
(Reactor doubling time, RDT) (Operation rate)
× RDT =
(6)
(Excore factor) × ln 2 1 − (Rate of excore Puf decrease)
(Equilibrium loaded Puf inventory) × (Refueling batch) (Cycle length) × 365 (Puf inventory at EOEC) − (Puf inventory at BOEC)
(7)
(Cycle length) (Cycle length) + (Refueling and periodic inspection period)
(8)
Operation rate =
Excore factor = 1 +
These evaluated thermal hydraulic parameters are fed to the neutronic calculation and the two calculations are iterated to incorporate thermal hydraulic feedbacks to neutronics. Until both the burn up distribution from the neutronic calculation and the water density distribution from the thermal hydraulic calculation converge, these coupled calculations are iterated (Han, 2011).
(period of excore stay) (period of incore stay)
(9)
In order to calculate CSDT, the followings are assumed as in the previous study (Yoshida, 2014): period of ex-core stay by reprocessing and fuel fabrication is 5 years, half-life of 241 Pu is 14.4 years, and period of refueling and periodic inspection per cycle is 30 days. Thus, CSDT indicates required time to double energy output (i.e., total capacity) of the installed reactors by utilizing excess fissile materials gained from breeding. 3. Reference core design
2.3. Breeding evaluation 3.1. In-vessel coolant flow scheme For evaluating breeding performance of cores, breeding ratio and doubling time are often used, but these indices are used with various definitions depending on purposes and core properties. In the Super FBR studies, fissile plutonium surviving ratio (FPSR) and compound system doubling time (CSDT) are used as breeding ratio and doubling time, respectively. The definition of FPSR is shown below: FPSR =
(The total amount of fissile Pu at EOEC) (The total amount of fissile Pu at BOEC)
(5)
Except for plutonium, this definition does not include other fissile materials such as 235 U, and fissile plutonium calculated in the
In the Super FBR designs, the one pass with all upward flow is used as in-vessel flow scheme as shown in Fig. 3 (Liu and Oka, 2013). In this flow scheme, the inlet coolant is directed to the lower plenum via down comer, before flowing up the fuel channels. The flow rate to each fuel assembly is designed by applying different orifice pressure losses at the inlet of fuel assemblies to satisfy the MCST criterion. Compared with the previously studied two pass flow scheme, the one pass flow scheme is simpler and is similar to that of current PWRs, which is desirable from the viewpoint of simplifying the upper core structure, as well as to simplify refueling procedure (Liu and Oka, 2013).
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Fig. 4. Concept of TPFA and seed and blanket assembly without ZrH.
3.2. Fuel assembly design As described in Section 1, this study aims to develop Super FBR core design which achieves high breeding (CSDT < 50 years) with the TPFA concept. In the TPFA design, as illustrated in Fig. 4, the gap clearance between fuel rods is 0 mm, and a coolant channel is installed in the space made by three fuel rods touching each other in this TPFAs. In addition, some of this space is narrowed by being plugged with metal fitting (stainless steel) to minimize the coolant flow area. The ratio of coolant to fuel volume can be drastically decreased, and high breeding performance is expected. For example, the ratio is decreased to 0.0635 when fuel rod diameter is 12 mm. In this study, the above mentioned TPFA design is adopted for the following three types of fuel assemblies: Seed assemblies, in which MOX fuel rods are loaded, blanket assemblies, in which DU fuel rods are loaded, and blanket assemblies, in which some of the DU fuel rods are replaced with zirconium hydride (ZrH) rods. The ZrH rods act as solid moderators and are employed in some of blanket assemblies for achieving positive density reactivity (negative void reactivity) (Oka and Jevremovic, 1996). In some of the blanket assemblies, two rows of DU rods are replaced with ZrH rods as illustrated in Fig. 5. These blanket assemblies with ZrH solid moderators improve the coolant density reactivity by effectively capturing neutrons and introducing negative reactivity when coolant density is reduced (Oka and Jevremovic, 1996).
Fig. 5. Blanket assembly with ZrH.
Fig. 6. Loading pattern.
3.3. Core design The reference core is designed with the three types of TPFAs explained in the previous section. By referring to the past experience of Super FBR core design, this study adopts the same core loading pattern and axial constitution as those of the previous study. They are shown in Figs. 6 and 7, respectively (Yoshida, 2014). The loading pattern was designed from the viewpoint of maximizing breeding performance while maintaining positive density reactivity. Refueling is designed in 4 batches in the seed assemblies,
Fig. 7. Axial constitution.
T. Someya, A. Yamaji / Nuclear Engineering and Design 296 (2016) 30–37 Table 2 Summary of fuel assembly design parameters.
Table 1 Reference core design parameter. Thermal power [MW t] Operation pressure [MPa] Active height [m] Equivalent active diameter [m] Operation cycle length [day] Number of fuel batches (Seed/Blanket) Average Pu enrichment (seed) [wt.%] Average discharge burn up (Seed) [GWd/t] Density reactivity (BOEC/EOEC) [%k/k] Maximum cladding surface temperature (MCST) [◦ C] Maximum linear heat generation rate (MLHGR) [kW/m] Pressure loss [MPa] FPSR CSDT [year]
35
1372 30 2.0 4.17 550 4/1 29.9 54.5 0.29/0.58 650 35.43 1.83 1.026 40
and in 1 batch in the blanket assemblies. Also, the axial fuel zoning as illustrated in Fig. 7 was designed to minimize axial power peaking. Table 1 shows the reference core design parameters and evaluated core characteristics when fuel rod diameter of every assembly is 12 mm. CSDT has been improved from 47 years of the previous study to 40 years. However, CSDT may be deteriorated (increased) when control rods are designed. In Super FBR core design, cluster type control rods (similar to that of PWR) are being considered for reactivity control (Yoshida, 2014). Hence, to accommodate insertions of control rods, some space will need to be created in TPFA, which may deteriorate breeding performance of the core. Therefore, it is worth investigating whether CSDT can be further improved. The evaluated pressure loss of 1.48 MPa is remarkably high compared with those of current LWRs and may give rise to concerns of stability and pumping power requirement. Although the main scope of this study is on conceptual development of Super FBR core, it is important to address possibility of reducing pressure loss, which will reduce future challenges when detailed engineering issues will be addressed.
4. Sensitivity studies for design improvements In the Super FBR core design, three kinds of fuel assemblies are used, and their respective role is different as follows.
Fuel rod diameter [mm] Pellet diameter [mm] Gap clearance [mm] Cladding thickness [mm] Number of fuel rods Number of coolant paths Vm /Vf 1 Assembly pitch [cm] 1
12 10.4063 0.100 0.6968 397 792 0.063 24.66
11 9.5058 0.100 0.6471 469 936 0.064 24.66
10 8.6053 0.100 0.5974 547 1092 0.065 24.66
9.5 8.1850 0.085 0.5725 631 1260 0.064 24.66
Vm /Vf : The ratio of coolant (moderate) to fuel volume.
4.1. Sensitivity study of fuel rod diameter The design range of fuel rod diameter is determined from 12 mm used in the previous study to 9.5 mm used in current PWRs. For a given fuel rod diameter, cladding thickness is determined with a standard of the buckling. The equation for evaluating buckling pressure of an escalope hollow cylinder as follows: Pcollapse =
1 t × 2.2E 3 D−t
3
where, Pcollapse is determined to be 20.3 MPa by assuming external pressure of 25 MPa and internal pressure of 4.7 MPa (Ishiwatari, 2000). Gap clearance is tentatively determined referring to current BWRs and PWRs. Summary of the fuel rod design is shown in Table 2. TPFAs with the fixed pitch of 24.66 cm are designed with the above designed fuel rods. The assembly size is fixed and the gap between the inner surface of the channel box and the peripheral fuel rods are filled with stainless steel. From the definition of CSDT, it is expected that increase of thermal power is effective to improve CSDT. Hence, first, the influence of fuel rod diameter in seed assembly is studied while fuel rod diameter of the other assemblies is kept constant at 12 mm. As shown in Fig. 8, the core thermal power is increased by decreasing fuel rod diameter, because the number of fuel rods loaded into an assembly is increased. As a result, CSDT is monotonically improved by reducing fuel rod diameter. However, pressure loss is increased by reducing fuel rod diameter, because coolant channel area is reduced. By considering the above sensitivities, 11 mm is adopted as a design point of fuel rod diameter in the seed assemblies. Secondly, the influence of fuel rod diameter in the blanket assemblies without ZrH is investigated when fuel rod diameter of the other assemblies is fixed at 11 mm. In this case, reducing the rod
(1) Seed: Bearing most of the thermal power of the core. (2) Blanket without ZrH: Converting (breeding) from 238 U to 239 Pu or 241 Pu. (3) Blanket with ZrH: Contributing to positive density reactivity and converting (breeding).
Hence, it is expected that design of the seed assembly is influential to pressure loss, because of the high coolant mass flux to cool the high power seed assemblies. In the meantime, design of the blanket without ZrH is expected to be influential to CSDT, as it is the main part of the core, which is contributing to breeding. In the reference core design described in the previous section, fuel rod diameter and coolant channel shape was the same in all fuel assemblies. From the viewpoint of improving CSDT, the core power density should be maximized, but coolant channel area needs to be maximized to minimize pressure loss. Hence, in this study, improvement of CSDT and reduction of pressure loss are studied by changing fuel rod diameter and coolant channel shape with consideration of these different roles of the fuel assemblies.
(10)
Fig. 8. Sensitivities of fuel rod diameter in the seed assembly.
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Fig. 9. Sensitivities of fuel rod diameter in the blanket assembly without ZrH.
diameter has small influence on the core thermal power, because power of a DU rod is much smaller than that of a MOX rod. Hence, CSDT is not sensitive to the fuel rod diameter as shown in Fig. 9. However, density reactivity coefficient is influenced by the rod diameter. In particular, the results indicate that the rod diameter should not be around 10 mm from the viewpoint of assuring positive density reactivity. This is because the blanket fuel domain area is substantially reduced when the rod diameter is around 10 mm, due to alignment of the fuel rods in the assembly, whose size is fixed. 4.2. Reduction of pressure loss Three kinds of coolant channels are investigated as shown in Fig. 10. The coolant channel of Geometry A is used in the reference core design (Section 3). Also, in the sensitivity analysis of fuel rod diameter (Section 4.1), Geometry A is applied to all assemblies regardless of the difference of fuel rod diameter. As described in Section 3.2, a circular coolant channel is introduced between the contacting fuel rods and the remaining space is filled with the metal fitting. In order to investigate possibility of reducing core pressure loss, two other channel geometries are considered. In Geometry B, the coolant channel area is expanded and replaces most of the metal fitting domain. In contrast, in Geometry C, the coolant channel area is reduced and the metal fitting domain is enlarged. In this sensitivity study, Geometry B is employed in the seed assemblies where pressure loss is large. In this way, decrease of
pressure loss is expected, because equivalent hydraulic diameter (De ) is increased and axial coolant velocity (u) is decreased in Eqs. (1) and (2) (Section 2.2). However, the ratio of coolant to fuel volume in the seed assemblies is increased, which may deteriorate breeding performance of the reactor by softening the neutron spectrum. Thus, Geometry C is employed in the blanket assemblies without ZrH, where pressure loss is not large, in order to prevent the increase of the coolant to fuel volume ratio of the core. On the other hand, the coolant channel in the blanket assemblies with ZrH is not changed to Geometry C, but Geometry A is adopted. Because, the coolant mass flux in the blanket assemblies with ZrH is needed more than that in the blanket assemblies without ZrH due to large local power peaking affected by the ZrH layer, and hence pressure loss tends to be larger. The final core design with consideration of different fuel rod diameters and coolant channel geometries is compared with the reference core design in Table. 3. Compared with the reference core design, CSDT has been improved from 40 years to 38 years, while also improving core pressure loss from 1.83 MPa to 1.02 MPa. The improvements show that both CSDT and core pressure loss can be improved by considering roles of the different fuel assemblies in the core and designing fuel rod diameters and coolant channel geometries. In this study, pressure loss evaluation is integrated into fullycoupled neutronics and thermal-hydraulics core calculations for the first time in the conceptual development of Super FBR. In the previous study (Yoshida, 2014), influence of the core pressure loss was not taken into account in the neutronics calculations
Fig. 10. Coolant channel geometry.
T. Someya, A. Yamaji / Nuclear Engineering and Design 296 (2016) 30–37
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Table 3 Result of reducing pressure loss. Core
Reference core design
Final concept
Seed fuel rod diameter [mm]/coolant channel geometry Blanket without ZrH fuel rod diameter [mm]/coolant channel geometry Blanket with ZrH fuel rod diameter [mm]/coolant channel geometry Thermal power [MWt] Discharge burn up(Seed) [GWd/t] Density reactivity (BOEC/EOEC) [%k/k] Maximum cladding surface temperature [◦ C] Maximum linear heat generation rate [kW/m] Pressure loss [MPa] FPSR (EOEC/BOEC) CSDT [year]
12/A 12/A 12/A 1372 54.5 0.29/0.58 650 35.43 1.83 1.026 40
11/B 12/C 12/A 1598 64.6 1.38/0.83* (1.17/1.37) 650 35.40 (35.18) 1.02 (1.01) 1.028 38
*
The values in parentheses indicate the results with method of the previous study (Yoshida, 2014) (i.e., neutronics and thermal-hydraulic calculations are not fully coupled).
(i.e., water density is evaluated by assuming constant core pressure of 30 MPa throughout the core). Comparison between calculation method of this study and that of the previous study has been executed by using above final concept. Water density evaluated by this study’s method is 0.325 g/cm3 at the core outlet, while that by the previous study’s method is 0.220 g/cm3 at the outlet (i.e., water density is underestimated when core pressure loss is not considered). As shown in Table 3, most neutronics characteristics are not influenced because water inventory is very little in TPFA concept. However, density reactivity calculated by this study’s method is 1.38%k/k at BOEC and 0.83%k/k at EOEC, while that calculated by the previous study’s method is 1.17%k/k at BOEC and 1.37%k/k at EOEC. These differences are not negligible as they determine the most fundamental safety characteristics of water cooled reactors. Hence, it is necessary to integrate pressure loss evaluation into fully-coupled neutronics and thermal-hydraulics core calculations. 5. Conclusion Conceptual design of a Super FBR core with Tightly Packed Fuel Assembly (TPFA) has been developed with fully-coupled neutronics and thermal-hydraulics core calculations. The calculations take into account the influence of core pressure loss to the core neutronics characteristics for the first time in the development of Super FBR concept. It has been shown that the fully-coupled calculation is important for Super FBR core design as coolant density reactivity is influenced significantly. Furthermore, improvement of breeding performance (reduction of CSDT) and reduction of core pressure loss are shown by changing fuel rod diameter and coolant channel geometries. The concept achieves CSDT of 38 years, indicating high breeding performance, which may enable installation of the reactors at a rate comparable to energy growth rate of developed countries such as G7 member countries. It has been clarified that CSDT is sensitive to linear heat generation rate of seed assemblies, which bears most of the thermal power of the core. Hence, reducing fuel rod diameter of the seed assembly, while enlarging the coolant channel area has been shown to be effective to reduce CSDT and pressure loss simultaneously by increasing the power while maintaining cooling. In contrast, thermal power of blanket assemblies are low and coolant channel area can be reduced to achieve low coolant to fuel volume ratio for attaining high breeding. Optimization of the fuel rod diameter
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