2.1. The Truly-Optimized PWR Lattice
Figure 1 depicts the typical 17×17 PWR FA and its detailed dimensions and specifications are given in Table I [9]. The average coolant and fuel temperatures are taken from typical PWR designs. It should be noted that the HTU ratio is about 4.1. It is mentioned that other commercial FA designs such as Korean APR1400 [10] have a similar HTU ratio.
Based on the typical FA design, there are two ways to enhance the HTU ratio to improve the neutron economy. The first one is to reduce the fuel rod diameter or the number of fuel rod per FA while preserving the FA and active core size. However, fuel inventory per FA can be reduced significantly in this case, consequently the cycle length may be reduced unacceptable, which outweighs the improved neutron economy due to enhanced moderation [6]. In addition, a new fuel pellet needs to be developed in the case of the reduced fuel diameter. On the other hand, the second way is to enlarge the pin pitch while preserving the fuel rod dimension. Thus, the FA and active core sizes become slightly bigger in the radial direction. In this paper, the modification on the pin pitch is concerned to assess the TOP design, as thermal and mechanical performances of the standard fuel rod are rather well validated under the standard PWR conditions. Moreover, for the existing PWRs, the first approach is possible as the core size is fixed. Meanwhile, for the new reactor design like ATOM, both of the two options are possible. However, the second way is adopted to minimize the fuel rod design changes.
In order to select a TOP design for an SBF SMR, several objectives must be taken into account:
- Maximization of the neutron economy
- Sufficiently & appropriately negative MTC and fuel temperature coefficient (FTC)
- Minimization of the temperature defect for improved CR worth margin
- Maintenance of the clad-to-coolant heat transfer characteristics
- Acceptable size of FA
To find an optimal pitch for the typical FA design, a parametric study has been performed for a 2-dimensional infinite array of the FA using the Serpent code. The pin pitch is adjusted to obtain various HTU ratios and Fig. 2 shows the infinite multiplication factor (kinf) with respect to the HTU ratio at zero burnup for two fuel enrichments and boron concentrations. In the Serpent calculations, 300 active and 100 inactive cycles are used with 100,000 histories per cycle, resulting in about 5.0 pcm uncertainty of the kinf values.
One can clearly notice in Fig. 2 that the typical FA design is quite under-moderated due to the soluble-boron and the neutron economy is far from the optimal condition for the two commercial enrichment regardless of the boron. For the 5.0 w/o case, the optimal HTU ratio is about 9.0. Consequently, the kinf value can be increased quite substantially by increasing the HTU value in an SBF core. In the commercial PWRs, the fuel lattice is quite under-moderated mainly due to potentially positive MTC at hot-zero-power (HZP)-BOC condition requiring a high boron concentration [10]. In the TOP approach, the HTU value should be determined such that the MTC should be sufficiently and appropriately negative over the whole cycle with an acceptable FA size, and the fuel utilization should be enhanced. It is important to recall that the HTU ratio should not be too close to the optimal condition in Fig. 2 since the MTC will be quite small or close to zero.
To quantify benefit of the TOP design in terms of fuel burnup, non-poisonous FA with 4.95 w/o U was depleted using Serpent and the burnup-dependent kinfvalues are plotted in Fig. 3 for a few HTU values. One standard deviation of the kinf values in Fig. 3 is about 10 pcm. In the FA depletion, specific power density of the ATOM core is used, i.e., 26 W/gU [5]. One can notice that the BOC kinf clearly increases when HTU increases from 4.1 to 7.0. However, after a certain burnup, the behavior of kinfis inversed, which is due to smaller buildup of Pu-239 and higher fission product poisoning in a softer spectrum.
In order to investigate the cycle length and discharge burnup for a two-batch fuel management (FM), a linear reactivity model [11] is used and the results are given in Table II, in which it is assumed that neutron leakage is 7,000 pcm. One can see that the cycle length and discharge burnup increase noticeably with a slight increase in the HTU ratio from the reference one. It should be noted that the fuel burnup is rather maximized with the HTU ratio of ~5.7, about 3% higher than the reference case, and then it even decreases with further increasing HTU ratio beyond 5.7. One also observed that the FA size increases by about 10% for HTU=5.7, which will lead to a ~10% bigger core size. Therefore, the HTU can be increased up to ~5.7 for the TOP design if the 10% larger FA is acceptable in the core design.
Figure 4 shows a neutron spectrum comparison for several HTU ratios at two burnup points. It can be seen that the spectrum becomes softened with bigger HTU ratio. In particular, the spectrum is much softer with HTU=7.0 and this enhances fission product poisoning leading to a lower fuel burnup. In addition, it is important to note that 100% mixed-oxide (MOX) core is likely to be feasible as the significantly softer spectrum of the TOP design, an enhanced-moderation design, can resolve problems caused by the spectrum hardening due to Pu isotopes [12] [13] [14].
In Fig. 5, power peaking factor (PPF) in the FAs for various HTU values is plotted as a function of burnup. One can notice that PPF decreases with burnup for all cases and the maximum value is about 1.08 at 0 GWd/tU. It is also observed that a larger HTU ratio results in a similar or slightly smaller PPK than that of the reference one regardless of burnup. It is because the impact of water-filled guide tube on PPF is less significant as the neutron spectrum becomes softer with a higher HTU ratio. The associated uncertainty of the PPF is about 0.5% in this analysis.
The most important parameters for the inherent safety of the core are temperature coefficients, FTC and MTC, which must be always negative at any condition. Nevertheless, too much negative temperature coefficients are not always preferable, such as a strongly negative MTC at EOC condition (e. g., -63 pcm/K) results in a large control worth requirement [5]. In addition, a less negative FTC reduces the deviation of inlet coolant during an autonomous operation [15]. It is recommended that the MTC should be around -30.0 pcm/K and the FTC should be about -2.0 pcm/K for a successful passive frequency operation [15]. The FTC and MTC values for various HTU ratios at HFP condition are listed in Table III. One can notice that temperature coefficients become less negative with increased HTU ratio due to the softener neutron spectrum, while they are more negative with burnup due to Pu-239 and fission poisoning buildups. The optimal HTU ratio for autonomous operation is around 5.7 as the FTC is about -2 pcm/K and the MTC is around -30 pcm/K. The associated uncertainties of FTC and MTC are 0.14 pcm/K and 0.8 pcm/K, respectively. It is assumed that temperature coefficients are linear functions of temperature in this evaluation.
The reactivity difference between HFP and CZP conditions is defined as temperature defect, which is compensated by CR insertion to obtain CZP condition. Temperature defects from HZP to HFP for various HTU ratios and fuel burnups are tabulated in Table IV. As expected, it decreases significantly with increased HTU ratio since temperature coefficients are smaller with a higher HTU ratio as shown in Table III. It is advantageous that a smaller shutdown rod worth is required for a larger HTU ratio. In addition, CR radius can be enlarged with a higher HTU ratio to enhance the CR worth further. The associated uncertainty of the temperature defect is about 12 pcm.
Overall, an optimal HTU ratio to meet aforementioned TOP goals is about 5.7. The use of TOP lattice maximizes the cycle length, reduces the temperature defect for an enhanced cold shutdown margin, and provides sufficient temperature coefficients for an autonomous operation, while assuring the inherent safety of the core. The pin pitch corresponding to 5.7 HTU ratio is 1.40 cm, which is then adopted in the two-batch ATOM core. One should note that the equivalent diameter of the TOP-based ATOM core is 224 cm, which is about 10% higher than that with the standard ATOM design [5].
In the selected HTU ratio for the TOP design, the coolant flow area is increased by ~30% and it should affect thermal-hydraulics designs of the fuel assembly and its impacts are dependent on design choice among several options. Since this work is largely concerned with the neutronic attributes of the TOP concept, it is assumed that the average coolant speed remains unchanged and the coolant inlet temperature is appropriately increased for a given coolant temperature rise. In this case, the FA thermal-hydraulics will be quite similar to the conventional one, while the balance of the plant design should be accordingly modified. Meanwhile, the coolant speed can be reduced significantly in the TOP design if the same coolant temperature rise is adopted, and the core pressure drop should decrease a lot. However, in this approach, the thermal-hydraulics will be quite different due to a slower coolant flow, e.g., the critical heat flux can be lowered if other design measures are not introduced. Therefore, the thermal-hydraulic design for the TOP lattice needs to be optimized for the given plant system.
2.2. Innovative Burnable Absorbers for the TOP ATOM Core
To obtain a very small excess reactivity in the SBF ATOM core without compromising the core performances, a new innovative 3-D BA design, centrally-shielded burnable absorber (CSBA), is utilized [5]. In the CSBA design, gadolinia (Gd2O3) is loaded into the central region of the fuel pellet in the spherical form, which provides the strongest self-shielding effect of the BA, resulting in slow gadolinium depletion. .
A recent 3-D multi-physics study [16] demonstrated that the effective stress at the interface between CSBA balls and fuel is very acceptable, while the maximum temperature of the CSBA-loaded fuel pellet is comparable to that of the conventional one. In addition, the effect of asymmetric power distribution due to neighboring effect on the fuel temperature is relatively small, about 15K in terms of peak temperature and subsequent thermal expansion and stress are hardly changed. Moreover, the material and experimental studies for the CSBA-loaded fuel are currently under-investigation and several preliminary outcomes are available at references [17] [18].
Gadolinia is an effective and well-proven BA material in the nuclear technology. However, it is disadvantageous in that the residual gadolinium isotopes, e. g., Gd-158 and Gd-160, result in noticeable reactivity penalty. In addition, a simple 1-ball CSBA design is more favorable than 2-ball and 3-ball designs in terms of fabrication and quality control. Therefore, for a more flexible reactivity control, B4C is additionally used as the second BA material to reduce the residual gadolinium for enhanced neutron economy. In this work, B4C is used in the form of disk-type burnable absorber (DiBA), which was recently proposed [19]. A combination of the two BA designs is shown in Fig. 6. The B4C disk is cladded with Zr-4 with axial cladding thickness of 0.04 mm, while the outer diameter of radial cladding is the same as pellet diameter. The number of DiBA is identical to the number of fuel pellets per fuel rod, so-called 1P1D (1 pellet 1 DiBA) option.
Advantage of DiBA is that the self-shielding effect can be flexibly adjusted by controlling both the height-to-diameter (H-to-D) ratio and the volume of the BA disk as shown in Fig. 7, in which neutronic calculations of 17x17 lattice are performed with the Serpent 2 code. The number of active and inactive cycles are 200 and 100, respectively, with 100,000 histories. One should note that the amount of B4C should be limited so that the internal rod pressure due to fission gas and helium gas from B-10 depletion should not exceed the upper limit. In this study, the B4C volume is adjusted so that B-10 loading should be 0.09 mg B-10 per mm pellet, which is typical of the conventional IFBA design [20]. A 90% enriched B-10 is utilized to minimize the DiBA volume.
Figure 7b compares the kinf value for B4C DiBA designs and ZrB2 112-IFBA design [9]. The kinf values of the DiBA case with 0.016 cm3 B4C (BA volume =0.8 V) and the IFBA case at the fresh condition are adjusted to be the same for a consistent neutronic comparison. It can be seen clearly that the kinf of IFBA design increases significantly after Xenon equilibrium. It is because boron in the IFBA design quickly burns out as the ZrB2 coating layer exposes largely to the neutron flux. The kinf of the IFBA design decreases linearly and follows the no-BA case once boron depletes completely at 20 GWd/tU. On the other hand, boron in the DiBA case depletes rather slow as the kinf stays around 1.05 until 30 GWd/tU. It is due to the H-to-D ratio close to 1.0, which minimizes the exposure of the BA to neutron flux. However, the reactivity penalty of the DiBA design is higher than that of the IFBA as a large amount of BA is necessary to hold down the excess reactivity throughout the cycle.