Figure 1.
Two energy groups fluxes for a sphere made of 93% enriched U. Dotted line: Thermal flux, Dashed line: Fast flux, Solid line: Total fluxes.
Figure 1.
Two energy groups fluxes for a sphere made of 93% enriched U. Dotted line: Thermal flux, Dashed line: Fast flux, Solid line: Total fluxes.
Figure 2.
Two energy groups fluxes of a cylinder made of 93% enriched U. Dotted line: Thermal flux, Dashed line: Fast flux, Solid line: Total fluxes.
Figure 2.
Two energy groups fluxes of a cylinder made of 93% enriched U. Dotted line: Thermal flux, Dashed line: Fast flux, Solid line: Total fluxes.
Figure 3.
Two Energy Groups fluxes for an infinite Slab of 93% enriched U. Dotted line: Thermal flux, Dashed line: Fast flux, Solid line: Total fluxes.
Figure 3.
Two Energy Groups fluxes for an infinite Slab of 93% enriched U. Dotted line: Thermal flux, Dashed line: Fast flux, Solid line: Total fluxes.
Figure 4.
Four energy groups fluxes and total flux for a spherical reactor. Dotted-dotted dashed line: , Dotted line: , Dotted dashed line: , Dashed line: , Solid line: Total fluxes.
Figure 4.
Four energy groups fluxes and total flux for a spherical reactor. Dotted-dotted dashed line: , Dotted line: , Dotted dashed line: , Dashed line: , Solid line: Total fluxes.
Figure 5.
Four energy groups fluxes and total flux for a cylindrical reactor. Dotted-dotted dashed line: , Dotted line: , Dotted dashed line: , Dashed line: , Solid line: Total fluxes.
Figure 5.
Four energy groups fluxes and total flux for a cylindrical reactor. Dotted-dotted dashed line: , Dotted line: , Dotted dashed line: , Dashed line: , Solid line: Total fluxes.
Figure 6.
Four energy groups fluxes and total flux for a slab reactor. Dotted-dotted dashed line: , Dotted line: , Dotted dashed line: , Dashed line: , Solid line: Total fluxes.
Figure 6.
Four energy groups fluxes and total flux for a slab reactor. Dotted-dotted dashed line: , Dotted line: , Dotted dashed line: , Dashed line: , Solid line: Total fluxes.
Table 1.
Two Group Data.
Fast Energy Group |
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Thermal Energy Group |
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Table 2.
The values of the coefficients are calculated from Equation (3).
Table 2.
The values of the coefficients are calculated from Equation (3).
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Table 3.
The critical radius of a 93 % enriched Uranium spherical reactor.
Table 3.
The critical radius of a 93 % enriched Uranium spherical reactor.
BC | Classical Method | RPSM | Transport Theory |
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ZF | | | - |
EBC | | | 16.049836 |
Table 4.
The normalized thermal, fast and total fluxes in a spherical geometry.
Table 4.
The normalized thermal, fast and total fluxes in a spherical geometry.
Flux | Method | | | | | | |
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Fast | Classical | | | | | | |
| RPSM | | | | | | |
Thermal | Classical | | | | | | |
| RPSM | | | | | | |
Total | Classical | | | | | 1.3699 | 0.2498 |
| RPSM | | | | | 1.3699 | 0.2498 |
Table 5.
The cylindrical reactor critical radius for two boundary conditions
Table 5.
The cylindrical reactor critical radius for two boundary conditions
BC | Classical Method | RPSM |
---|
ZF | | |
EBC | | |
Table 6.
The normalized thermal, fast, and total fluxes values across a cylindrical geometry.
Table 6.
The normalized thermal, fast, and total fluxes values across a cylindrical geometry.
Flux | Method | | | | | | |
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Fast | Classical | | | | | | |
| RPSM | | | | | | |
Thermal | Classical | | | | | | |
| RPSM | | | | | | |
Total | Classical | | | | | 1.5340 | 0.3213 |
| RPSM | | | | | 1.5340 | 0.3213 |
Table 7.
The slab reactor critical radius for two boundary conditions.
Table 7.
The slab reactor critical radius for two boundary conditions.
BC | Classical Method | RPSM | Transport Theory |
---|
ZF | | | |
EBC | | | |
Table 8.
The normalized thermal, fast and total fluxes values across a slab geometry.
Table 8.
The normalized thermal, fast and total fluxes values across a slab geometry.
Flux | Method | | | | | | |
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Fast | Transport | | | | | | |
| Classical | | | | | | |
| RPSM | | | | | | |
Thermal | Transport | | | | | | |
| Classical | | | | | | |
| RPSM | | | | | | |
Total | Transport | | | | | | |
| Classical | | | | | | |
| RPSM | | | | | | |
Table 9.
Group data.
Group 1 (1.35 Mev – 10 Mev) |
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Group 2 (9.1 kev - 1.35 Mev) |
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Group 3 (0.4 ev – 9.1 kev) |
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Group 4 (0.0 ev – 0.4 ev) |
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Table 10.
The values of the coefficients.
Table 10.
The values of the coefficients.
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Table 11.
The spherical reactor critical radius .
Table 11.
The spherical reactor critical radius .
BC | Classical Method | RPSM |
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ZF | 8.770 | 8.770 |
EBC | 7.905 | 7.905 |
Table 12.
The four groups fluxes and total flux in spherical reactor geometry.
Table 12.
The four groups fluxes and total flux in spherical reactor geometry.
Flux | Method | | | | | | |
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Group 1 | Classical | | | | | | |
| RPSM | | | | | | |
Group 2 | Classical | | 4.1716 | | | | |
| RPSM | | 4.1716 | | | | |
Group 3 | Classical | | 2.7361 | | | | |
| RPSM | | 2.7361 | | | | |
Group 4 | Classical | | 3.0931 | | | | |
| RPSM | | 3.0931 | | | | |
Total | Classical | | 11.0008 | | | | |
| RPSM | | 11.0008 | | | | |
Table 13.
Cylindrical reactor critical radius for two boundary conditions.
Table 13.
Cylindrical reactor critical radius for two boundary conditions.
BC | Classical Method | RPSM |
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ZF | 6.71303 | 6.71303 |
EBC | 5.84763 | 5.84763 |
Table 14.
The four groups fluxes and total flux in cylindrical reactor geometry.
Table 14.
The four groups fluxes and total flux in cylindrical reactor geometry.
Flux | Method | | | | | | |
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Group 1 | Classical | | | 0.9326 | 0.743977 | 0.471824 | 0.169557 |
| RPSM | | | 0.9326 | 0.743977 | 0.471824 | 0.169557 |
Group 2 | Classical | | 4.1716 | 3.8904 | 3.10354 | 1.96824 | 0.707317 |
| RPSM | | 4.1716 | 3.8904 | 3.10354 | 1.96824 | 0.707317 |
Group 3 | Classical | | 2.7361 | 2.55169 | 2.0356 | 1.29096 | 0.463925 |
| RPSM | | 2.7361 | 2.55169 | 2.0356 | 1.29096 | 0.463925 |
Group 4 | Classical | | 3.0931 | 2.88465 | 2.30122 | 1.45941 | 0.524462 |
| RPSM | | 3.0931 | 2.88465 | 2.30122 | 1.45941 | 0.524462 |
Total | Classical | | 11.0008 | 10.2593 | 8.18434 | 5.19044 | 1.86526 |
| RPSM | | 11.0008 | 10.2593 | 8.18434 | 5.19044 | 1.86526 |
Table 15.
The slab reactor critical radius for both boundary conditions.
Table 15.
The slab reactor critical radius for both boundary conditions.
BC | Classical Method | RPSM |
---|
ZF | 4.38485 | 4.38485 |
EBC | 3.51945 | 3.51945 |
Table 16.
The four groups fluxes and total flux in slab reactor geometry.
Table 16.
The four groups fluxes and total flux in slab reactor geometry.
Flux | Method | | | | | | |
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Group 1 | Classical | | | 0.950736 | 0.807797 | 0.585267 | 0.305072 |
| RPSM | | | 0.950736 | 0.807797 | 0.585267 | 0.305072 |
Group 2 | Classical | | 4.1716 | 0.950736 | 0.807797 | 0.585267 | 0.305072 |
| RPSM | | 4.1716 | 0.950736 | 0.807797 | 0.585267 | 0.305072 |
Group 3 | Classical | | 2.7361 | 2.60131 | 2.21021 | 1.60135 | 0.834709 |
| RPSM | | 2.7361 | 2.60131 | 2.21021 | 1.60135 | 0.834709 |
Group 4 | Classical | | 3.0931 | 2.94075 | 2.49862 | 1.81031 | 0.943628 |
| RPSM | | 3.0931 | 2.94075 | 2.49862 | 1.81031 | 0.943628 |
Total | Classical | | 11.0008 | 10.4588 | 8.88641 | 6.4384 | 3.35604 |
| RPSM | | 11.0008 | 10.4588 | 8.88641 | 6.4384 | 3.35604 |
Table 17.
The value of the th-residual error ( for the results obtained by classical method.
Table 17.
The value of the th-residual error ( for the results obtained by classical method.
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Table 18.
The value of the th-residual error ( for the results obtained by RPSM.
Table 18.
The value of the th-residual error ( for the results obtained by RPSM.
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