5.1 Depletion analysis for unit cell models
In order to analyze the effect of different cladding materials on the assembly neutronics, a PWR pin cell geometry shown in Figure (2) was modeled with MCNPX code. The pin cell is composed of 4.9% enriched UO2 fuel pellet with density of 10.468 g/cm3. There is Helium gap of density 0.001625 g/cm3 between fuel pellet and cladding .Water is used as a coolant and moderator. The pin cell with Zircaloy clad was selected as reference case. The burnup calculations are carried out at a constant power of 38.33 MW per metric ton of Uranium (MTU) for a discharge burnup value 60 GWd/ton which corresponds to 1565 effective full power days. Four models were simulated by MCNPX code. These models have the same parameters and dimensions except for the cladding material type. The cladding materials are SiC, Zircaloy, FeCrAl and SS-310. The composition of clads used for calculations is summarized in Table (1).
Figure (4) shows the variation of K-infinity (infinite multiplication factor) with time for 4 different cladding materials. When compared with the reference case, the highest decrease in k-infinity occurs for 310 stainless-steel cladding case. The increase in plutonium inventory on the unit cell level of this proposed cladding design (SS-310) is the cause of this K-infinity reduction. Only increase in k-infinity occurs for SiC cladding case due to reduction in neutron absorption, since the absorption cross section of SiC is 0.086 barn (10-24 cm2) compared to 0.20 barn of Zircaloy.
For validation, the infinite multiplication factor of the four pin cell models is obtained firstly by MCNPX code using ENDF/B-VII.1 nuclear data library. Then the same models are simulated by WIMS-d5 code using WLUP-69.bib library. The K-inf results of the two codes are compared with each other. The results in figure (5) show that there is a good agreement between the two code results for all the candidate claddings.
According to the analysis of Table (4), SiC cladding provides the highest end of life (EOL) burnup among the other cladding materials. On the other hand, SS-310 cladding has the lowest EOL burnup. This means that that length of the fuel cycle decreases when Zircaloy cladding is replaced with either 310 stainless-steel (26.5% reduction) or FeCrAl (21.3% reduction), but increases when it is replaced by SiC (2.23% increase).
Table (4): Calculated discharge burnup of proposed models
Cladding Material
|
Discharge Burnup (GWd/ton)
|
Effective Full Power Days
|
SiC
|
44.666707
|
1165.316
|
Zircaloy
|
43.666699
|
1139.228
|
FeCrAl
|
36.000004
|
939.212
|
SS-310
|
32.083330
|
837.029
|
The remarkable drop in K-infinity values found for SS-310 and FeCrAl corresponds to a significant reduction in operational cycle length. As depicted in Figure (6), the absolute value of k-infinity difference for those two cladding materials decreases throughout the cycle. This is attributed to the increased plutonium content throughout the cycle in the presence of a harder neutron spectrum. The reactivity penalty at 60 GWd/ton for SS-310 were found to be nearly 5.933% k-infinity difference, while the ferritic alloy (FeCrAl) was slightly less negative at 4.123%. The less absorbing SiC cladding produced a positive 0.555% k-infinity difference at end of life (EOL).
This part concludes that the replacement of Zircaloy cladding with SiC will provide K-inf and penalty benefits. Meanwhile, the penalty associated with the other candidate claddings (SS-310 and FeCrAl) necessarily shortens the core life, which is undesirable to our design objective of achieving a long-life advanced PWR core.
5.2 Analysis of self-shielding on the radial power distribution
The self-shielding effect of the fuel rod causes a non-uniform radial power distribution. This is caused by the strong absorption of U-238 near the surface of the fuel rod. This in turn effects on the plutonium production and burnup at this position. Therefore, it is important to analyze the rim effect when considering the four cladding materials under investigation. The fuel region is divided into 10 rings of equal volumes, while the gap and cladding are located outside with their same dimensions. Figures 7, 8 and 9 illustrate the fission power in MW across the fuel pellet at BOL, MOL and end-of-life (EOL) for all candidate claddings for UO2 fuel (4.9% U-235). All figures show that the power is largest in the region next to cladding material (at fuel rod surface) and smallest at the center of the fuel rod due to spatial self-shielding as stated before. Because of the significant differences between the capture cross sections of different clads, the fission power values are higher for SiC model and lower for SS-310.
Figure (10) compares the microscopic capture cross sections of the 4 cladding materials. As one can see, in the thermal region (E < 0.625 eV), the capture cross sections of FeCrAl and SS-310 are higher than those of Zr and SiC. The high absorption cross section of both FeCrAl and SS-310 is mainly due to the fact that these materials contain at least 52% iron, a material that has an absorption cross section in the thermal groups of the order of 10 barns. Owing to the capture cross section of nickel-59, (SS-310) has the highest thermal neutron absorption among the candidate claddings. Nuclei having magic numbers of neutrons (90 Zr40) or a doubly semi-magic number (28 Si 14) are characterized by their low tendency in capturing neutrons.
For Zr and SiC claddings in figure 10, the graphs are linear and decreasing until about 10-6 MeV to Zircaloy and 0.01 MeV to SiC. It is clear that the SiC has a neutron absorption cross section lower than the Zircaloy, explaining the higher neutron multiplication for the SiC compared to Zircaloy.
The fission power behavior obtained by the self-shielding effect can be explained by Pu-239 atom density at MOL and EOL as a function of pellet radius. Because of the large contribution of Pu-239 to fission after U-235, Pu-239 is chosen for this analysis. Figure (11) shows the buildup of Pu-239 in the fuel pellets with burnup. The Pu-239 concentration increases differently with burnup stages for the 4 different claddings. As expected, the build-up of Pu-239 is higher in SS-310 model and lower in SiC model.
The increased concentration of Pu-239 with burnup (from MOL to EOL) is owing to the spatial self-shielding of neutrons, where thermalized neutrons are captured in the outer region and thus blocked from the center of the fuel. The higher Pu-239 production at the pellet periphery results in very high burnup in the rim region and greater local fission gas release, which is responsible for the formation of porosity in this region.
In figures 12 and 13, the buildup of Pu-239 on the periphery of the fuel pellet is significantly greater than in the center due to strong epithermal U-238 resonance absorption at this location. Furthermore, the MOL and EOL Pu-239 inventories are higher for FeCrAl and SS-310 with higher thermal capture cross-sections due to spectral hardening, unlike SiC and Zr. FeCrAl and SS-310 claddings absorb more thermal neutrons than Zr or SiC cladding, thereby decreasing the fast neutron in the later. This in turn increases the resonance capture in U-238, hence more Pu-239 breeding is observed throughout the cycle for the Fe- and steel-based cladding fuels.
5.3 U-235 enrichment and Cladding thickness matching cycle length requirements
In this section, the necessary enrichment and cladding thickness to match the fuel cycle length of the reference case (Zirconium model) were calculated for the candidate claddings. For U-235 enrichment, many trials are conducted by MCNPX code for reaching the suitable enrichment that achieve the same EOL burnup value of Zirconium case (43.66 GWd/ton). The cladding thicknesses for the SiC and Zircaloy cases were kept at 571.5 Μm, which represents a typical thickness for a Westinghouse PWR fuel rod. Meanwhile, the thickness of FeCrAl and SS-310 has to be reduced to 200 Μm. The fuel radius (0.409575 cm), fuel pitch (1.326) and Helium gap thickness were kept constant in all simulations.
Table (5): U-235 enrichment required for achieving the same EOL burnup of Zirconium model
End of burnup value (GWd/ton)
|
Cladding material
|
enrichment
|
clad radius
|
required thickness
|
43.66
|
SiC
|
4.83%
|
0.466725
|
571.5 μm
|
43.66
|
Zirconium
|
4.90%
|
0.466725
|
571.5 μm
|
43.66
|
FeCrAl
|
5.06%
|
0.429575
|
200 μm
|
43.66
|
SS-310
|
5.22%
|
0.429575
|
200 μm
|
The results in Table 5 reveal that SS-310 requires highest U-235 enrichment (5.22%) at the same thickness of FeCrAl (200 μm). This is expected due to the high capture cross section of SS-310 compared to FeCrAl. For SiC and Zr, SiC needs lower enrichment (4.83%) at the same thickness of Zirconium (571.5 μm). This is attributed to the high absorption cross section of Zr compared to SiC. The second part of this section investigated the suitable thickness of SS-310, FeCrAl and SiC that can achieve the EOL burnup value as in Zirconium case. The simulation was performed at constant enrichment, fuel radius, fuel pitch and helium gap but the cladding thickness was varied according to its type.
Table (6): Cladding thickness required for achieving the same EOL burnup of Zirconium model
End of burnup value (GWd/ton)
|
Cladding material
|
enrichment
|
clad radius
|
required thickness
|
43.66
|
SiC
|
4.90%
|
0.486575
|
770 μm
|
43.66
|
Zirconium
|
4.90%
|
0.466725
|
571.5 μm
|
43.66
|
FeCrAl
|
4.90%
|
0.424075
|
145 μm
|
43.66
|
SS-310
|
4.90%
|
0.420075
|
105 μm
|
As mentioned previously, SS-310 and FeCrAl contain elements with higher neutron absorption than Zircaloy. Therefore, a great heavy metal loading is required to achieve the EOL burnup value of Zircaloy at the constancy of fuel enrichment. This is conducted by using a thinner cladding while maintaining a constant fuel pitch. This means that the increased levels of U-235 enrichment via reducing the cladding thickness also could serve in obtaining the cycle length achieved by Zircaloy. In other words, the required thickness for SiC and SS-310 for obtaining the same cycle length of Zirconium is 770 μm and 105 μm respectively as in Table (6).
5.4 Spectral hardening in the assembly model
Spectral hardening was analyzed for the SS-310, FeCrAl, Zircaloy and SiC cladding materials under consideration. For this study, the neutron flux in (n/cm2.sec) was calculated by MCNPX code across a homogeneous cell of fuel, cladding, and moderator. Then, this flux was plotted against the neutron energy in MeV (figure 14). The cross section library used by MCNPX is ENDF/B-VII.1. Analysis of the thermal peaks in figure 14.a indicates that SS-310 and FeCeAl presents a lower thermal flux values at the beginning of life. This is because both of the two materials absorb thermal neutrons and this results in increasing the fraction of fast neutrons. Thus, the thermal peaks shown in figure 14.a are lower for SS-310 and FeCeAl compared to those of Zircaloy and SiC.
In the same time, the fast peaks at 1.225 MeV (figure 14.b) are higher for SS-310 and lower for Zircaloy and SiC. The combination between the two effects results in a hardening of the spectrum. This is attributed to the depletion of overall fissile material and, in turn, an increased accumulation of fission products and actinides in the system. This part concludes that SiC cladding is the least absorbing material among the four claddings, consequently it has the highest inventory of thermal neutrons .This results in a softening of neutron spectrum which improves neutron economy and discharge burnup. In contrast, FeCrAl and SS-310 contain more absorbing materials, more thermal neutrons are absorbed in these claddings, resulting in an increase in the fast neutrons fraction in the system compared to the Zr and SiC cladding cases.
5.5 Fuel temperature coefficient
It is important to evaluate the effect of SiC, FeCrAl and SS-310 claddings on the fuel temperature coefficient to compare their feedback response with that of the reference Zr cladding. For maintaining the safety standards of advanced PWRs, it is necessary that each cladding material produces negative fuel temperature coefficients especially at the earlier stages of fuel irradiation. For estimating the FTC, the temperature of moderator and clad was fixed at 600 K but the fuel temperature is increased from 900 K (operational temperature) to 1200 K i.e., temperature change is 300 K.
Table (7): The FTC in pcm/K at BOL for the 4 claddings for a 300 K change in fuel temperature
Cladding material
|
FTC (pcm/K)
|
SiC
|
-1.704
|
Zr
|
-1.708
|
FeCrAl
|
-1.82
|
SS-310
|
-1.87
|
As can be noted in figure (15), the FTC values for all cases are less negative at the BOL (0 GWd/ton) and more negative as the burnup increases to about 15 GWd/ton due to the changes in isotopic composition and the increased variety of isotopes present. Table (7) shows that the BOL FTC values are negative for all the candidate claddings. It is also observed that there is slight variation in FTC values owing to the differences of capture cross sections of these materials. The SS-310 and FeCrAl claddings exhibit marginally more negative FTC value compared to SiC and Zr at BOL. This is attributed to the Doppler broadening of fertile absorption. This can be explained via the variation of U-238 concentration with burnup. As shown in figure 16, the concentration of U-238 is higher for SiC and Zr compared to FeCrAl and SS-310 at all burnup stages. In other words, For the SiC case, there is a strongly negative feedback coefficient throughout the burnup progress. The SS-310 case has the weakest value. The lower absolute value of FTC is a result of the influence of Pu-239 and Pu-241 and the contribution of the reduced resonance absorption.
The fuel temperature coefficients of SiC, FeCrAl and SS-310 claddings are negative till 55, 50 and 48 GWd/ton respectively. This means that SiC case contributes more negative FTC values at longer periods and this is a very important safety aspect because the reactor stabilizes as an increase of the fuel temperature. The negative fuel temperature reactivity coefficient is fundamental because in this case occurs the broadening of resonances and an increase in the neutrons absorption, reducing the thermal flux and thus reactivity and temperature
5.6 Moderator temperature coefficient
Table (8) depicts that the MTC values at BOL are negative for all the cladding materials. The SS-310 and FeCrAl have more negative MTC values than those of Zr and SiC. The slight variations in MTC for the candidate claddings are due to differences in total capture cross section of fuel and cladding. This is indicative of the extent to which resonance capture plays a role, and the resultant impact on MTC. Figure (9) confirms that SS-310 and FeCrAl exhibit resonant behavior in the range 0.01–100eV and thereby provide lower (more negative) MTC values compared to the Zr and SiC cases. The reason for more negativity of MTC of SS-310 and FeCrAl claddings is the presence of Mo and Ni, and Mo isotopes.
Table (8): The MTC in pcm/K at BOL for the 4 claddings for a 300 K change in fuel temperature
Cladding material
|
MTC (pcm/K)
|
SiC
|
-7.54
|
Zr
|
-7.85
|
FeCrAl
|
-7.93
|
SS-310
|
-8.20
|
Figure (17) depicts the moderator temperature coefficient versus burnup for the candidate claddings. This parameter is evaluated when the temperatures of fuel and clad are fixed at 900 K and 600 K respectively. Meanwhile, the moderator temperature is lowered from 600 K to 300 K resulting in a temperature change 300 K. Then, using the equation = , the MTC can be calculated in pcm/K. where is the temperature coefficient, is the reactivity difference, and stands for temperature difference which is equal to 300 K.
According to figure (17), MCNPX simulation predicts that SiC, FeCrAl and SS-310 show negative MTC till 50, 44 and 42 GWd/ton. There is no a clear difference in the early stage. In the intermediate stages, the Zr case has a more strongly negative coefficient than the other cases. Conversely, the SS-310 case has the weakest negative coefficient.
The fuel and moderator temperature coefficients are the two most important elements of the reactor feedback coefficient. Figure 18 combines these two temperature coefficients into one total feedback coefficient. Throughout all the burnup stages, the Zr case has the most strongly negative coefficient. The SS-310 and FeCrAl cases have weaker negative feedback coefficients than the Zr case.
To briefly summarize the temperature feedback coefficient results, SS-310 and FeCrAl have the lowest values of fuel and moderator temperature coefficients. The SiC case has more negative FTCs and less negative MTCs compared to Zr case. This results in higher total temperature coefficient values for Zr case compared to SiC case. At the end of life burnup value (60 GWd/ton), the most strongly positive coefficient is observed in the SS-310 and FeCrAl cases.
5.7 Void Reactivity coefficient
For evaluating the void reactivity coefficient, the infinite multiplication factor is calculated at two different void cases. The first one is at 0% void (Density of water = 0.7199 g/cm3) and the other is at 40% void (Density of water = 0.4471 g/cm3). The void reactivity coefficient (VRC) is defined as the difference in reactivity over the void difference according to the following equation VRC (pcm/%) =
where, ρ40% is the reactivity at 40% void, is the reactivity at 0% void and VRC is the void reactivity coefficient in units of pcm/%. At the beginning of life as shown in Table (9), The SS-310 and FeCrAl have the highest negative values of VRC among the four cladding materials.
Table (9): The VRC in pcm/K at BOL for the 4 claddings
Cladding material
|
VRC (pcm/%)
|
SiC
|
-127.46
|
Zr
|
-133.06
|
FeCrAl
|
-135.10
|
SS-310
|
-139.54
|
From figure (19), the Zr and SiC fuel combination maintain the more negativity of VRC values at all the burnup steps. This guarantees the safe operation of the nuclear reactor.
5.8 Peaking factor
The pin peaking factor is defined as the maximum pin power divided by the average assembly power. It also describes maximum energy generated in the fuel rod on the assembly level. It is used to prevent fuel from reaching a melting point during operation.
Figure (20) illustrates the pin power peaking factor versus burnup stages for the 4 fuel-clad combinations. Zr and SiC claddings have almost the same peaking factor values through the fuel burnup. The peaking factor values for the case of SS-310 and FeCrAl cladding are larger than the other cases (Zr and Sic). Therefore, the use of SS-310 and FeCrAl cladding may lead to smaller shutdown margins which in turn reduces the safety of reactor operation. This means that the use of Zr or SiC are favorable claddings from the side of reducing the peaking factor throughout the burnup stages.
5.9 The thermal neutron fraction
As can be seen in figure (21), the thermal neutron fraction decreases with burnup for all cases till 20 GWd/ton. This is a result of the depletion of U-235 as the burnup proceeds. After 20 GWd/ton, the thermal neutron fraction increases with time till 60 GWd/ton. This is attributed to decreasing the macroscopic fission cross sections as the burnup proceeds. This causes increasing the thermal flux with burnup at a constant specific power assumed for each fuel-clad type. It is noticed that the thermal neutron fraction is lower for SS-310. This is because a large fraction of the neutrons will be in the fast and epithermal range and hence captured by U-238. On the other hand, SiC case has the highest values of thermal neutron fraction among the other cases.
5.10 The effect of candidate claddings on the fission products and actinides
As stated before, the calculated normalized flux over fuel, cladding and moderator mixtures can be differentiated in the thermal region. The absorbing materials of high capture cross sections allow fewer thermal neutrons to reach the fuel. For this reason, thermal peaks are arranged (higher for SiC, Zr, FeCrAl then SS-310), while fast peaks may appear superimposed. Lowering the thermal flux in the assembly leads to increasing the fast neutron fraction which in turn causes hardening of neutron flux spectrum. This spectral hardening was found at every depletion step in fuel, cladding and moderator mixtures. Consequently, in the case of spectral hardening, there is less accumulation of actinides and fission products as Ru-106 inventory in figure 22 and Xe-135 in figure 23.
5.11 Calculation the delayed neutron fraction ( at the BOL for the suggested models
The presence of delayed neutrons plays a significant role in reactor control due to its impact on reactor power change rate. Without delayed neutrons, a reactor would increase in power to such a magnitude and in such a short time period that a significant damage would result. The delayed neutron fraction for each of the 4 suggested models was calculated by using MCNPX code. The calculations are carried out at 10000 neutrons, 100 skipped cycles and 1000 active cycles resulting in a standard deviation ranging from 0.00018 to 0.00019. It can clear that of SiC and Zr models is higher than that of FeCrAl and SS-310 ones. This is because SiC and Zr have low capture cross sections that result in the availability of more fission reactions to occur. Consequently, there will be increasing in the delayed neutron. This ensures the more safety of reactor operation in case of Zr and SiC clads. Table (10) depicts the delayed neutron fraction for the four candidate claddings.
Table (10): Delayed neutron fraction for the candidate claddings.
|
SiC model
|
Zr-model
|
FeCrAl model
|
SS-310 model
|
K-eff
|
1.43893 0.00019
|
1.41187 0.00019
|
1.36419 0.00019
|
1.3229 0.00018
|
K-prompt
|
1.42912 0.00019
|
1.40177 0.00019
|
1.35503 0.00019
|
1.3142 0.00018
|
|
0.00682
|
0.00715
|
0.00671
|
0.00657
|