Chapter 2. Background
2.1.3 Step Size
As the finite difference diffusion theory-based code CITATION is used for the global core calculations of the PARR-2 HEU core, the reactor model developed for the HEU core was used as a benchmark for neutronic calculations of LEU-fuelled cores. Table 7.3 shows the criticality position and keff values at different positions of the control rod for HEU and LEU fuels. It can be seen that the criticality position and shutdown margins are lower for core 2 and core 3 due to the higher density of uranium in the fuel material and spectrum hardening in the LEU fuel. In the LEU fuel, spectrum hardening causes a decrease in the thermal neutron flux at the central control rod position, and hence the absorption cross-section of the control rod decreases. Therefore, use of the same control rod as in the HEU core results in a decreased control rod worth for the LEU-fuelled core. In order to enhance the shutdown margin and control rod worth, the thickness of the neutron absorber control rod is increased in core 4. Therefore core 4 represents about the same value of control rod worth as for the operating HEU core.
TABLE 7.3. COMPARISON OF CORE REACTIVITY
Core Fuel material/
enrichment U density (g/cm3)
Amount of U235 in core
(g)
Criticality position
(cm)
Excess reactivity
(mk)
Shutdown margin
(mk)
Control rod worth
(mk) 1 UAl alloy/
90.2% 0.92 995 9 4.046 –2.344 –6.39
2 UO2 fuel/
12.6% 9.35 1353 7 4.007 –1.43 –5.437
3 UO2 fuel/
12.3% 9.35 1264 7 4.16 –1.498 –5.658
4 UO2 fuel/
12.46% 9.35 1339 8.5 4.012 –2.375 –6.387
Originally, ten energy group calculations are performed through CITATION. For comparison of flux levels, ten group fluxes are condensed to three group (thermal, epithermal, fast) fluxes at a nominal reactor power of 30 kW. A power level of 30 kW results in lower thermal flux values at the irradiation sites and fission chambers for LEU UO2 fuel as compared to HEU fuel, as shown in Tables 7.4 and 7.5.
TABLE 7.4. FLUX AT INNER IRRADIATION SITES AND FISSION CHAMBERS
Core Fuel material Reactor power (kW)
Flux at inner sites (cm-2s-1) Flux at fission chambers (cm-2s-1) Fast
(0.821 MeV–
10 MeV)
Epithermal (0.625 eV–
0.821 MeV)
T hermal (0 eV–
0.625 eV)
Fast (0.821 MeV–
10 MeV)
Epithermal (0.625 eV–
0.821 MeV)
T hermal (0 eV–
0.625 eV) 1 UAl alloy pin diameter
5.5 mm/ 90.2% 30 1.40 × 1011 5.72 × 1011 1.02 × 1012 1.46 × 1011 6.67 × 1011 1.09 × 1012
2 UO2 fuel pin diameter 5.5 mm/ 12.6%
30 1.35 × 1011 5.58 × 1011 9.36 × 1011 1.40 × 1011 6.50 × 1011 9.96 × 1011 33 1.48 × 1011 6.14 × 1011 1.03 × 1012 1.54 × 1011 7.15 × 1011 1.10 × 1012
3 UO2 fuel pin diameter 5.1 mm/ 12.3%
30 1.33 × 1011 5.49 × 1011 9.41 × 1011 1.39 × 1011 6.40 × 1011 1.00 × 1012 33 1.47 × 1011 6.04 × 1011 1.04 × 1012 1.52 × 1011 7.04 × 1011 1.10 × 1012
4 UO2fuel pin diameter 5.5 mm/ 12.46%
30 1.24 × 1011 5.16 × 1011 9.16 × 1011 1.37 × 1011 6.36 × 1011 9.81 × 1011 33 1.36 × 1011 5.68 × 1011 1.01 × 1012 1.51 × 1011 6.99 × 1011 1.08 × 1012
179 TABLE 7.5. FLUX AT OUTER IRRADIATION SITES
Core Fuel material
Reactor power (kW)
Flux at three small outer sites (cm-2s-1) Flux at two large outer sites (cm-2s-1) Fast
(0.821 MeV–
10 MeV)
Epithermal (0.625 eV–
0.821 MeV)
T hermal (0 eV–0.625 eV)
Fast (0.821 MeV–
10 MeV)
Epithermal (0.625 eV–
0.821 MeV)
T hermal (0 eV–0.625
eV) 1 UAl alloy pin diameter
5.5 mm/ 90.2% 30 3.20 × 1010 1.22 × 1011 5.30 × 1011 2.88 × 1010 1.08 × 1011 4.75 × 1011
2 UO2 fuel pin diameter 5.5 mm/ 12.6%
30 3.08 × 1010 1.18 × 1011 4.98 × 1011 2.77 × 1010 1.05 × 1011 4.47 × 1011 33 3.38 × 1010 1.30 × 1011 5.48 × 1011 3.05 × 1010 1.16 × 1011 4.92 × 1011
3 UO2 fuel pin diameter 5.1 mm/ 12.3%
30 3.05 × 1010 1.17 × 1011 4.96 × 1011 2.74 × 1010 1.04 × 1011 4.45 × 1011 33 3.35 × 1010 1.28 × 1011 5.46 × 1011 3.02 × 1010 1.14 × 1011 4.90 × 1011
4 UO2 pin
diameter5.5/ mm12.46%
30 2.95 × 1010 1.12 × 1011 4.82 × 1011 2.71 × 1010 1.03 × 1011 4.36 × 1011 33 3.25 × 1010 1.23 × 1011 5.30 × 1011 2.98 × 1010 1.13 × 1011 4.79 × 1011
However at a power level of 33 kW, these flux levels match the values for HEU fuel.
The fast and epithermal flux values at the irradiation sites and fission chambers also exhibit similar behaviour. The axial flux profiles for HEU and LEU fuel are shown in Figs 7.5—7.10.
The height of the irradiation site is 19 cm, and the origin is assumed to be the bottom of the channel. It is obvious that the flux level drops along the axial distance of the core.
FIG. 7.5. Axial neutron flux profile at inner irradiation sites of PARR-2 (HEU fuel) (Courtesy of Pakistan Institute of Nuclear Science and Technology (PINSTECH), Pakistan).
1.00E+08 1.00E+09 1.00E+10 1.00E+11 1.00E+12 1.00E+13
0 10 20 30 40 50
Flux (/cm2-sec)
Distance from Bottom of Site (cm)
Fast Epithermal Thermal
FIG. 7.6. Axial neutron flux profile at fission chambers of PARR-2 (HEU fuel) (Courtesy of Pakistan Institute of Nuclear Science and Technology (PINSTECH), Pakistan).
FIG. 7.7. Axial neutron flux profile at outer irradiation sites of PARR-2 (HEU fuel) (Courtesy of Pakistan Institute of Nuclear Science and Technology (PINSTECH), Pakistan).
1.00E+08 1.00E+09 1.00E+10 1.00E+11 1.00E+12 1.00E+13
0 10 20 30 40 50
Flux (/cm2-sec)
Distance from Bottom of Site (cm)
Fast Epithermal Thermal
1.00E+08 1.00E+09 1.00E+10 1.00E+11 1.00E+12 1.00E+13
0 10 20 30 40 50
Flux (/cm2-sec)
Distance from Bottom of Site (cm)
Fast Epithermal Thermal
181
FIG. 7.8. Axial neutron flux profile at inner irradiation sites of PARR-2 (LEU fuel) (Courtesy of Pakistan Institute of Nuclear Science and Technology (PINSTECH), Pakistan).
FIG. 7.9. Axial neutron flux profile at fission chamber of PARR-2 (LEU fuel) (Courtesy of Pakistan Institute of Nuclear Science and Technology (PINSTECH), Pakistan).
1.00E+08 1.00E+09 1.00E+10 1.00E+11 1.00E+12 1.00E+13
0 10 20 30 40 50
Flux (/cm2-sec)
Distance from Bottom of Site (cm)
Fast Epithermal Thermal
1.00E+08 1.00E+09 1.00E+10 1.00E+11 1.00E+12 1.00E+13
0 10 20 30 40 50
Flux (/cm2-sec)
Distance from Bottom of Site (cm)
Fast Epithermal Thermal
FIG. 7.10. Axial neutron flux profile at outer irradiation sites of PARR-2 (LEU fuel) (Courtesy of Pakistan Institute of Nuclear Science and Technology (PINSTECH), Pakistan).
Average values of reactivity coefficients are shown in Table 7.6. Due to increased content of 238U in LEU fuel, the Doppler coefficient increases about ten times for LEU UO2
fuel compared to HEU fuel. There is also some increment in the void coefficient, but the moderator temperature coefficient decreases for LEU fuel compared to HEU fuel. Peaking factors increase slightly for LEU fuel, as shown in Table 7.7. The reactivity worth of the top beryllium shim plate was also calculated and compared with quoted data in the Final SAR [7.2]. Comparison of these calculations in Fig. 7.11 indicates the HEU fuel reactivity worth of the top beryllium shim plate is higher than its value for LEU fuel.
1.00E+08 1.00E+09 1.00E+10 1.00E+11 1.00E+12 1.00E+13
0 10 20 30 40 50
Flux (/cm2-sec)
Distance from Bottom of Site (cm)
Fast Epithermal Thermal
183 TABLE 7.6. AVERAGE VALUES OF REACTIVITY COEFFICIENTS
Core Fuel Parameter Temperature
range (°C) Average value
1 HEU (UAl4–Al) 90.2 % enriched
Moderator temperature coefficient (pcm/°C) 20—100 –6.5291 Doppler coefficient (pcm/°C) 20—400 –0.1397 Void coefficient (pcm/%void) 20—100 –337.67
2
LEU (UO2) pin diameter
5.5 mm 12.6 % enriched
Moderator temperature coefficient (pcm/°C) 20—100 –3.9659 Doppler coefficient (pcm/°C) 20—400 –1.3951 Void coefficient (pcm/%void) 20—100 –356.22
3
LEU (UO2) pin diameter
5.1 mm 12.3 % enriched
Moderator temperature coefficient (pcm/°C) 20—100 –4.1985 Doppler coefficient (pcm/°C) 20—400 –1.34239 Void coefficient (pcm/%void) 20—100 –348.355
4
LEU (UO2) pin diameter
5.5 mm 12.46% enriched
Moderator temperature coefficient (pcm/°C) 20—100 –3.86149 Doppler coefficient (pcm/°C) 20—400 –1.39316 Void coefficient (pcm/%void) 20—100 –344.014
TABLE 7.7. PEAKING FACTOR CALCULATIONS
Parameter Core 1 Core 2 Core 3 Core 4
Max. power density (W/cm3) 4.1159 4.16728 4.21557 4.66630 Average power density along hot channel (W/cm3) 3.6518 3.67685 3.70154 3.49493 Average power density of core (W/cm3) 3.2505 3.25052 3.25052 3.24977
Axial peaking factor 1.1271 1.13338 1.13887 1.33516
Radial peaking factor 1.1234 1.13116 1.13875 1.07544
Total peaking 1.2662 1.28203 1.29689 1.43589
FIG. 7.11. Comparison of reactivity worth of top beryllium shim for HEU and LEU fuel of PARR -2 (Courtesy of Pakistan Institute of Nuclear Science and Technology (PINSTECH), Pakistan).