The authors look for an attractive light water reactor (LWR) concept, which achieves high breeding performance with respect to the compound system doubling time (CSDT). In the preceding study, a high breeding fast reactor concept, cooled by supercritical pressure light water (Super FBR), was developed using tightly packed fuel assembly (TPFA) concept, in which fuel rods were arranged in a hexagonal lattice and packed by contacting each other. However, the designed concept had characteristics, which had to be improved, such as low power density (7.4 kW/m), large core pressure loss (1.02 MPa), low discharge burnup (core average: 8 GWd/t), and low coolant temperature rise in the core (38 °C). The aim of this study is to clarify the main issues associated with improvement of the Super FBR with respect to these design parameters and to show the improved design. The core design is carried out by fully coupled three-dimensional neutronics and single-channel thermal-hydraulic core calculations. The design criteria are negative void reactivity, maximum linear heat generation rate (MLHGR) of 39 kW/m, and maximum cladding surface temperature (MCST) of 650 °C for advanced stainless steel. The results show that significant improvement is possible with respect to the core thermal-hydraulic characteristics with minimal deterioration of CSDT by replacing TPFA with the commonly acknowledged hexagonal tight lattice fuel assembly (TLFA). Further design studies are necessary to improve the core enthalpy rise by reducing the radial power swing and power peaking.
In some countries with established nuclear power infrastructures, commercial use of fast breeder reactors (FBRs) is regarded as an attractive option to secure a sustainable source of energy. The intended scenarios often assume gradual replacement of the currently operating light water reactors (LWRs) and fossil-fired power plants. In such scenarios, the rate at which FBRs can be introduced is considered to be one of the influential factors, because sufficient fissile plutonium (Pu) inventory is required to startup the reactors while Pu supply is limited by the rate at which it can be produced in these reactors if there is not sufficient stock of Pu. Among several different definitions and parameters, the compound system doubling time (CSDT) is often referred in such context. In this study, the following CSDT definition is adopted: The time required for a system of identical breeder reactors to double the fissile material in the system, assuming that the number of reactors is increasing at a rate such that all of the fissile material is being utilized .
Hence, a large effort has been devoted to the development of sodium-cooled fast reactors (SFRs), which attain short CSDT such as 45 years . However, it seems that still more effort is required to overcome difficulties with handling of sodium as a coolant. In the meantime, extensive research has been conducted on development of fast spectrum light water reactors, which are based on commercially matured LWR technology. However, because of inevitable neutron moderation by the coolant (light water), many of the design concepts were high conversion type reactors [3,4] and few boiling water reactor type concepts aimed for breeding with light water cooling, but with poor CSDT performance of some 200–300 years . Similarly, in the development of supercritical water-cooled reactor, most countries are primarily focusing on development of the thermal spectrum reactor under the framework of Generation IV international Forum .
In the meantime, breeding with supercritical light water reactors has been studied by utilizing the low coolant density of supercritical water at elevated temperature (e.g., conceptual studies on Super FBR by Waseda University utilized the coolant above the pseudo-critical temperature, which is 385 °C at 25 MPa) [7,8]. In particular, the preceding core design study by Waseda University achieved CSDT, which was as short as 38 years, by adopting tightly packed fuel assembly (TPFA) concept with coolant to fuel volume ratio of less than 0.085 to minimize neutron moderation . However, the designed concept had characteristics which had to be improved, such as low core power density (linear heat generation rate of 7.4 kW/m), large core pressure loss (1.02 MPa), low discharge burnup (65 GWd/t in the seed region and only 8 GWd/t when averaged over the whole core region including blanket regions), and low coolant temperature rise in the core (38 °C). Regarding breeding performance of supercritical water-cooled fast reactors, some sensitivity analyses have been carried out with different assembly design parameters and core arrangements using MCNP4C Monte Carlo code without coupling with thermal-hydraulic calculations . However, the study adopted unique blanket assembly design, where blanket was cooled by coolant tubes. Moreover, since supercritical water exhibits large density change in the core, coupling of neutronics and thermal-hydraulic calculations is necessary to clarify the main issues associated with improvement of the Super FBR core design .
Hence, the aim of this study is to clarify the main issues associated with improvement of the Super FBR core design with respect to these design parameters and show the improved design concept. The desired characteristics of the design concept are high breeding, large discharge burnup, high power density, and large coolant enthalpy rise. Generally, there are trade-off relationships between these design parameters with the core design requirements, such as negative void reactivity, minimal peak power, effective core cooling, and low core pressure loss. In order to increase the core thermal power while reducing the core pressure loss with minimal deterioration in the breeding performance, impact of replacing the TPFA with the commonly acknowledged hexagonal tight lattice fuel assembly (TLFA) is investigated with fully coupled three-dimensional neutronics and single-channel thermal-hydraulic core calculations.
Design Targets and Criteria.
Thermal power of the preceding core design (1598 MW ) was effectively limited by use of TPFA, which was introduced to reduce coolant to fuel volume ratio (Vm/Vf) to around 0.06 for achieving high breeding performance. Due to the small hydraulic diameter of less than 2 mm, the use of TPFA introduced a problem of high core pressure loss, which was highly sensitive to the linear heat rate (i.e., small increase in the core power density, or power distribution led to large increase in the core pressure loss). Although core pressure loss may not be regarded as a design criterion for developing the core design concept, excessively high core pressure loss should be avoided from the viewpoint of minimizing loss of efficiency due to pumping the coolant and avoiding channel instability [8,11]. By referring to the preceding core design , it can be deduced that the core average power density and average linear heat generation rate (ALHGR) of the preceding design were 59 W/cm3 and 7.4 kW/m, respectively (including blanket fuel assemblies). The power density was similar to that of a typical boiling water reactor core. This study aims to increase the core power density to be greater than 100 W/cm3, which is similar to that of a typical pressurized water reactor core while reducing the core pressure loss compared with the preceding design by replacing TPFA with TLFA.
where BOEC and EOEC refer to the beginning of equilibrium cycle and end of equilibrium cycle, respectively. The fissile Pu isotopes considered in Puf refer to the sum of 239Pu and 241Pu and other fissile materials such as 235U are not included in the above expression.
In the above evaluations, the following are assumed as in the preceding study : Period of ex-core unloaded duration during reprocessing and fuel fabrication is 5 years, the half-life of 241Pu 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.
The average discharge burnup of the preceding design was low. It was about 65 GWd/t when averaged for mixed oxide fuel (MOX) fuels . However, when averaged over the whole core including blanket regions, it was as low as 8 GWd/t, because of excessive use of blanket assemblies. Generally, increasing the average discharge burnup improves operation rate of the reactor and reduces the fuel cycle cost. Hence, in this study, the target average discharge burnup (including blanket regions) was tentatively set to about 45 GWd/t, which is comparable to that of the current LWR.
While the previously mentioned design targets are considered, the following design criteria are tentatively determined for the purpose of conceptual development. First, negative void reactivity has to be attained throughout the cycle for assuring the inherent safety of the reactor. The use of highly enriched Pu fuel to attain high burnup tends to make the void reactivity more positive . Thus, this design criterion may limit the average discharge burnup of the core.
From the viewpoint of ensuring fuel integrities, the maximum linear heat generation rate (MLHGR) and the maximum cladding surface temperature (MCST) design criteria are considered. In LWR core designs, MLHGR of about 43–44 kW/m is generally given to prevent fuel rod failure by excessive pellet cladding mechanical interaction during abnormal transient (i.e., at power ramp, which initiates from MLHGR of about 43–44 kW/m). It is often related to the center melting of the fuel pellet during the transient (usually, for pressurized water reactor) because it leads to significant expansion of the fuel pellets. The same design principle applies to supercritical water-cooled reactor fuel design, but with consideration of higher coolant temperature and pressure. Thus, MLHGR of 39 kW/m (in normal operation) is tentatively determined as a design criterion . Similarly, a design criterion to ensure sufficient cooling of the fuel rod is necessary. Hence, 650 °C is tentatively used for a stainless steel cladding MCST design criterion with expectation of net temperature increase of 200 °C due to nonuniform coolant flow within a fuel assembly (which is not considered in the core design study) and core heat up during loss of core cooling transient .
In the current study, as mentioned earlier, the pressure loss is not considered as a design criterion for conceptual study. However, large pressure loss may lead to channel instability. Such instability can be suppressed by applying appropriate pressure loss at entrance orifices of the channels . However, this would further increase the total core pressure loss and may lead to large pumping power requirement. The core pressure loss in the preceding core design was about 1.0 MPa . Hence, although it is not considered as a design criterion, core pressure loss is evaluated in the current study with an intention to keep it as low as possible. Also, evaluation of the core pressure loss is important as it influences the core void reactivity due to its influence on the core coolant density distribution .
Thus, design targets and criteria have been determined to develop Super FBR concept with TLFA that attains high breeding performance with improved thermal-hydraulic characteristics (larger core power and reduced pressure loss) and larger discharge burnup compared with those of the preceding design study. These targets and criteria are summarized in Table 1.
Core Calculation Method.
The core calculation method is the same as the method adopted for the preceding study . The three-dimensional diffusion calculation is fully coupled with single-channel thermal-hydraulic calculations as shown in Fig. 1. For the neutronics calculations, SRAC 2006 code system  and JENDL-3.3 nuclear data library  developed at Japan Atomic Energy Agency are used. In the neutronics calculations, macrocross sections are prepared for representative fuel assemblies by unit cell and assembly burnup calculations with different coolant density, based on a collision probability method, and calculates productions and decays of major isotopes in the burnup chain. For each base-case burnup calculations, branch-off burnup calculations are also carried out to consider influences of instantaneous changes in the coolant density on the macrocross sections. When the cross sections are homogenized for each fuel assembly, the heterogeneous form factor is also calculated to obtain pinwise power distribution within each fuel assembly. The three-dimensional core burnup calculation then uses these macrocross sections based on finite difference method and interpolates the macrocross sections with burnups and coolant density.
For thermal-hydraulic calculations, in-house code (SPROD) is used. First, the radial heat transfer and conductance across fuel pellet, gap, cladding, and coolant in each of the axial calculation meshes are considered. Then, the axial heat transport is calculated, where energy and mass conservations are considered while the axial heat conductance is neglected . For each fuel assembly, the peak channel and average channel are identified. Coolant flow rate to each fuel assembly, which is kept constant throughout the cycle, is determined by setting the corresponding inlet orifice pressure loss to satisfy the MCST design criterion for the peak channel throughout the cycle. For evaluating the heat transfer coefficients at cladding surface, Watt's correlation is used  as often used by other design studies due to its relatively good predictability for normal heat transfer conditions . However, it should be noted that the hydraulic diameter of the TLFA design adopted in this study ranges from 1.7 to 3.1 mm while the Watt's correlation is obtained from experiments conducted with a hydraulic diameter of 4.4 mm. Development of heat transfer correlations for such small hydraulic diameter may be an issue for future study. Determination of the flow rate is done by iteration of the coolant flow rate evaluation and pressure loss evaluation based on the evaluated coolant density and temperature. The pressure loss is calculated with the determined flowrate in an average power channel by calculating friction loss, gravity loss, and acceleration loss as in the previous study . In the meantime, the coolant density and temperature at each elevation is calculated from its enthalpy and pressure at each axial node (each channel is divided into 20 axial nodes). These thermal-hydraulic parameters are then provided to the next time step of the core neutronics calculations to reflect changes in the coolant density distributions.
Thus, the neutronics calculations and thermal-hydraulic calculations are coupled. The fuel replacements are considered at the end of each cycle. Thus, neutronics and thermal-hydraulics calculated are iterated until convergences are obtained for both the core burnup distribution and coolant density distribution.
Fuel Assembly and Coolant Channel Designs.
Cross sections of the previously adopted TPFA  and the currently adopted TLFA designs are shown in Figs. 2 and 3, respectively. In the TPFA design, fuel rods are packed by contacting each other. The space between the fuel rods is filled with metal fitting, which accommodates either circular or triangular coolant channel. The preceding study showed that the core power density can be increased by about 16% to 59 W/cm3 by changing coolant channel geometry from circular to triangular in the seed assemblies while reducing the core pressure loss from 1.83 MPa to 1.02 MPa (note that CSDT was deteriorated from 38 years to 40 years). However, it seems difficult to further raise the core power density and/or reduce the core pressure loss with TPFA as there is no more space available to enlarge the coolant channel area. Hence, in this study, the TLFA design shown in Fig. 3 is adopted, which is more commonly used for fast reactor core designs.
As used in the preceding study , three different types of fuel assemblies are used in this study as shown in Fig. 4, namely, the seed assembly and two different types of blanket assemblies. The seed assembly consists of mixed oxide fuel (MOX) of enriched Pu, which bears most of thermal power of the core. The Pu composition is determined by referring to that of the reprocessed spent LWR fuel as shown in Table 2. The axial Pu enrichment zoning was determined from the viewpoint of reducing axial power peaking of the core.
The blanket assemblies, as are often used in other fast breeder reactor core designs, consist of depleted U (DU) for converting 238U to 239Pu. There is also another type of blanket assembly with ZrH rods used to replace some of the DU rods in the assembly. The ZrH rods act as solid moderators, which have the effect of attaining negative void reactivity characteristics. In the case of voided condition, ZrH moderates the fast neutrons and enhance resonance capture by the DU rods and reduces the coolant void reactivity effect . Good stability of ZrH at elevated temperature and under neutron irradiation condition has been demonstrated in the driver core of the German KNK-II reactor, which is an experimental liquid metal-cooled fast reactor . Stability of ZrH in supercritical water condition may need to be investigated in the future studies.
where E is Young's modulus, t is the cladding thickness, and D is the rod diameter. Specifications of the assemblies are summarized in Table 3.
In the current design, control rods are not considered, but a cluster type design as adopted by the preceding study  may be considered in the future study (i.e., similar to the design as adopted by the current pressurized water reactor). In the design, 18 fuel rod positions are replaced with control rod guide tubes for insertion of control rods from the top of the core. In order to avoid softening of neutron spectrum when control rods are withdrawn from the core, the control rods may be equipped with a follower structure, which displaces the coolant when the absorber rods are withdrawn from the core as adopted by some other light water-cooled fast reactor design .
Core Design Specifications and Fuel Loading Patterns.
Following the earlier considerations, the core design specifications have been determined. The average core power density of 128 W/cm3 and LHGR of 12.4 kW/m was determined by referring to the corresponding design targets (>100 W/cm3 and >12 kW/m). The active core height of 1.84 m (including upper and lower blanket regions) was determined from consideration of suppressing core pressure loss with the given inlet coolant pressure of 25 MPa, temperature of 385 °C and flow rate, which satisfies the MCST design criterion of 650 °C. Size of the core (the number of fuel assemblies) was then determined to satisfy the negative void reactivity design criterion. Thus, the basic core design specifications have been determined, which are summarized in Table 4.
The cycle length was tentatively determined as 600 days by referring to the average power density and target discharge burnup with considerations of refueling batches for the seed and blanket assemblies. The refueling patterns (considered for the 1/6 symmetric core) were designed separately for the seed assemblies and blanket assemblies without ZrH rods to minimize radial power peaking and fluctuations during the equilibrium cycle. For the seed fuel assemblies, the refueling scheme is based on an out-in refueling scheme, in which fresh fuels are gradually shuffled and moved toward the center of the core. For the blanket assemblies, it is based on an in-out refueling scheme (generally, reactivity of the blanket assemblies in this core design increases with burnup). One batch refueling is tentatively adopted for the blanket with ZrH rods from the viewpoint of reducing power peakings in the assembly. The designed core loading patterns and fuel shuffling scheme are shown in Fig. 5.
Core Characteristics and Needs for Further Improvements.
The equilibrium core, specified in Sec. 3.2, was modeled and its characteristics were evaluated using the neutronics and thermal-hydraulic core calculation method described in Sec. 2.2. The evaluated core characteristics are summarized in Table 5 and compared with those of the preceding design . The core thermal power has been increased from 1598 MW of the preceding design to 2296 MW. This increase is primarily due to the increase in the core power density from 59 to 128 W/cm3 (the corresponding increase in LHGR from 7.4 to 12.4 kW/m) while the core pressure loss has been decreased from 1.02 to 0.65 MPa because of the larger hydraulic diameter of the fuel channel.
The presented new design also shows large increase in the average discharge burnup, particularly for the whole core average (including the blanket regions) from 7.5 to 46.2 GWd/t. This large increase is primarily due to reduction in the number of blanket fuel assemblies. In the preceding study, about 63% of the assemblies were blanket assemblies. In contrast, the corresponding ratio in the number of blanket assemblies has been reduced to about 48% in the new design.
In the meantime, deterioration in the breeding performance was found to be relatively small. CSDT increased from 38 years of the preceding study to 59 years, but it is still much shorter than those of the past LWR study (200–300 years ) and comparable to that of SFR (45 years ) and the expected lifetime of the current and future LWR (60–80 years ). The main difference in CSDT of the two designs arises from the difference in reactor doubling time (RDT), which is 16 years and 52 years for the preceding design and the new design, respectively. The short reactor doubling time of the preceding study was mainly attributed to the small fuel batch number (the blanket was replaced with only one batch in the preceding study), as can be understood from Eq. (3) described in Sec. 2.1.
Thus, the improvements in the core characteristics with respect to the thermal power and pressure loss can be primarily attributed to modification of the fuel channel from TPFA to TLFA. In the meantime, the core average discharge burnup was significantly increased by reducing the number of blanket fuel assemblies. The trade-off relationships between improvements of these core characteristics with the breeding performance of the core (CSDT) have been shown quantitatively as summarized in Table 5, which may be valuable information for the future conceptual development.
The current study also shows that increasing the core enthalpy rise still remains an issue for the future design studies, although some improvement was shown for the average outlet temperature, which improved from 420 °C in the previous study to 458 °C in the current study. Figure 6 shows average outlet temperature of each fuel assembly at BOEC and EOEC for the 1/6 symmetric core. From Fig. 6, the fuel assemblies with low outlet temperature may be categorized to the following three groups. These features of the fuel assemblies all lead to reduction in the coolant outlet temperature because of mismatch in the power to flow rate ration.
Fuel assemblies with large power swing from BOEC to EOEC
Fuel assemblies with large radial power gradient (in the core periphery)
Fuel assemblies with large local power peaking
The power swing can be seen from the core radial power distribution, shown for BOEC and EOEC in Fig. 7. As can be seen from Figs. 5 and 7, the power swing is particularly large for the blanket fuel assemblies, because of Pu buildup from BOEC to EOEC, which leads to increase in the reactivity. Such power swing may be inevitable when blanket fuel assemblies are utilized as in the present core design. The large power gradient in within fuel assemblies in the core periphery can be also seen from Fig. 7. Such power gradient also leads to the power/flow mismatch and reduction in the outlet temperature.
The local power peaking is particularly large for the fuel assemblies marked in Fig. 6, which correspond to the blanket fuel assemblies with ZrH layers (as shown in Fig. 5). As an example, pin-power distributions for the central fuel assembly at EOEC are shown in Fig. 8. As can be seen from the figure, the large power peaking is found near the ZrH layer, where neutron spectrum is expected to be softer than the other parts and fission cross section of Pu is larger. As one solution to resolve this problem, a stainless steel reflector may be employed in the peripheral region of the blanket assembly to decrease power of (and hence, neutron flux coming from) the neighboring seed assemblies .
A new Super FBR core design has been shown with TLFA. Compared with the preceding design with TPFA, the new design achieved much higher core thermal power due to larger hydraulic diameter of the fuel channel, which enabled increase in the core power density while reducing the core pressure loss. The core average discharge burnup was increased by reducing the number of blanket assemblies. The trade-off relationships between improvements of these core characteristics with the breeding performance of the core CSDT have been shown. The CSDT has increased from 38 years in the preceding design to 59 years in the new design, which is still comparable to the CSDT of SFR and the expected lifetime of the current and the future LWRs. Further design studies are necessary to improve the core enthalpy rise by reducing the radial power swing and power peaking.
I would like to gratefully acknowledge for STTN-BATAN and Research and innovation in Science and Technology program (RISET-PRO) of Indonesia (Ministry of Research, Technology and Higher Education of the Republic of Indonesia), which have supported this study.
- ALHGR =
average linear heat generation rate, kW/m
- BOEC =
beginning of equilibrium cycle
- CSDT =
compound system doubling time, year
- DU =
- EOEC =
end of equilibrium cycle
- FBR =
fast breeder reactor
- FPSR =
fissile plutonium surviving ratio
- LWR =
light water reactor
- MCST =
maximum cladding surface temperature, °C
- MLHGR =
maximum linear heat generation rate, kW/m
- MOX =
mixed oxide fuel
- Puf =
- RDT =
reactor doubling time, year
- SFRs =
sodium-cooled fast reactors
- TLFA =
tight lattice fuel assembly
- TPFA =
tightly packed fuel assembly
- ZrH =