Author Affiliations
1School of Nuclear Science and Technology, University of South China, Hengyang 421001, China2Hunan Engineering and Technology Research Center for Virtual Nuclear Reactor, University of South China, Hengyang 421001, Chinashow less
Fig. 1. Main technical principle of core intelligent optimization method
Fig. 2. Comparison of two sampling results
Fig. 3. Flow diagram of SEUMRE spatial search algorithm
Fig. 4. Realization flowchart of DOPPLER
Fig. 5. SPARLER-4 structure diagram
Fig. 6. URANUS structure diagram
Fig. 7. Comparison of Keff, burnup predicted by Kriging surrogate model and RMC calculated value
Fig. 8. Iterative graph of fuel loading optimization for SPALLER-4
Fig. 9. Comparison of Keff, burnup predicted by Kriging surrogate model and RMC calculated value
Fig. 10. Iterative graph of fuel loading optimization for URANUS
| correlation function | expression | | exponential function | ${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\exp(-{\theta }_{k}{d}_{k})$ | | Gaussian function | ${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\exp(-{\theta }_{k}{d}_{k}^{2})$ | | linear function | $ {R}_{k}\left({\theta }_{k},{d}_{k}\right)=\mathrm{m}\mathrm{a}\mathrm{x}\{\mathrm{0,1}-{\theta }_{k}{d}_{k}\} $ | | cubic spline function | ${R}_{k}\left({\theta }_{k},{d}_{k}\right)=\left\{\begin{array}{l}1-15{\zeta }_{k}+30{\zeta }_{k}^{3},\quad 0\leqslant {\zeta }_{k}\leqslant 0.2\\ 1.25{(1-15{\zeta }_{k})}^{3},\quad 0.2 < {\zeta }_{k} < 1\\ 0,\quad{\zeta }_{k}\geqslant 1,{\zeta }_{k}={\theta }_{k}{d}_{k}\end{array}\right.$ |
|
Table 1. Commonly used related functions of Kriging surrogate model and their expressions
| design
scheme
| thermal
power/MW
| fuel
loading/kg
| equivalent
diameter
of active
region/cm
| height of
active
area/cm
| average volume
power density
of active
region/(W·cm−3)
| fuel (mass
fraction
of Pu)/%
| coolant
and
reflector
| shielding
layer
| | SPALLER-4 | 4 | 577.89 | 95.4 | 80 | 6.99 | PuN-ThN (31/48) | 208Pb-Bi(90)
| B4C(126)
| | URANUS | 100 | 17580 | 97.02 | 180 | 19.18 | UO2(9.55/17.09)
| 208Pb-Bi(27.11 cm)
| B4C(15 cm)
| | | design
scheme
| solid
moderator
(thickness/cm)
| gate
diameter
ratio
| fuel rod
core
radius/cm
| air gap
of fuel rod
(thickness/cm)
| cladding of
fuel rod
(thickness/cm)
| upper/lower
end plug
of fuel
rod (height/cm)
| gas cavity/
spring area
of fuel rod
(height/cm)
| top/bottom
insulation
of fuel
rod (height/cm)
| | SPALLER-4 | BeO (3.5) | 1.20 | 0.60 | He (0.015) | TH-9(0.06) | TH-9(3/3) | He(48/14) | He(1/1) | | URANUS | — | 1.35 | 0.72 | He (0.010) | TH-9(0.06) | TH-9(30/30) | He(130/30) | — |
|
Table 2. Materials used for the design parameters of SPALLER-4 and the interval value of optimization variables
| contrast
group
| thickness
of solid
moderator/cm
| mass fraction
of Pu in
fuel/%
| fuel rod
core
radius/cm
| height of
core active
zone/cm
| grid
diameter
ratio
| third-year Keff | | burnup/(MW·d·kg−1)
| | prediction
by KSM
| calculation
by RMC
| relative
error/%
| prediction
by KSM
| calculation
by RMC
| relative
error/%
| | 1 | 4.6555 | 47.2024 | 0.2911 | 112.1659 | 1.3710 | 1.0502 | 1.0503 | −0.0154 | | 22.9477 | 22.7960 | 0.6654 | | 2 | 4.8222 | 45.4101 | 0.2776 | 115.2353 | 1.3773 | 1.0352 | 1.0352 | 0.0006 | | 24.6610 | 24.4460 | 0.8794 | | 3 | 4.9908 | 48.9315 | 0.2608 | 118.1860 | 1.4117 | 1.0325 | 1.0334 | −0.0846 | | 26.8646 | 26.8940 | 0.1093 | | 4 | 4.5899 | 48.8228 | 0.2117 | 103.6606 | 1.3534 | 1.0164 | 1.0174 | −0.0987 | | 46.3528 | 46.5440 | 0.4108 | | 5 | 4.7828 | 46.6647 | 0.2173 | 116.5918 | 1.3548 | 1.0244 | 1.0234 | 0.0994 | | 39.1589 | 39.3960 | 0.6019 |
|
Table 3. Accuracy verification results of Kriging surrogate model for predicting Keff and burnup
| thickness
of solid
moderator/cm
| mass fraction
of Pu in
fuel/%
| fuel rod
core
radius/cm
| height of
core active
zone/cm
| grid
diameter
ratio
| third-year Keff | | burnup/(MW·d·kg−1)
| | prediction
by KSM
| calculation
by RMC
| relative
error/%
| prediction
by KSM
| calculation
by RMC
| relative
error/%
| | 4.5732 | 49.8686 | 0.2003 | 100.0818 | 1.3131 | 1.0057 | 1.0052 | 0.0550 | | 53.7021 | 53.7990 | −0.0018 |
|
Table 4. Optimization results of SPALLER-4 core design scheme
| contrast
group
| fuel rod
core
radius/cm
| height of
core active
zone/cm
| grid diameter
ratio
| twentieth-year Keff | | burnup/(MW·d·kg−1)
| | prediction
by KSM
| calculation
by RMC
| relative
error/%
| prediction
by KSM
| calculation
by RMC
| relative
error/%
| | 1 | 0.7287 | 164.3119 | 1.3207 | 1.0010 | 1.0018 | −0.0809 | | 44.0797 | 44.4100 | −0.7438 | | 2 | 0.7373 | 157.4453 | 1.3208 | 1.0004 | 1.0007 | −0.0338 | | 45.2746 | 45.2710 | 0.0080 | | 3 | 0.7388 | 156.9933 | 1.3211 | 1.0005 | 1.0009 | −0.0409 | | 45.2266 | 45.2130 | 0.0301 | | 4 | 0.7410 | 153.9331 | 1.3205 | 0.9994 | 0.9999 | −0.0585 | | 43.5830 | 43.5540 | 0.0666 | | 5 | 0.7374 | 157.4387 | 1.3203 | 1.0006 | 1.0003 | 0.0297 | | 45.2645 | 45.2560 | 0.0187 |
|
Table 5. Accuracy verification results of Kriging surrogate model for predicting Keff and burnup
| URANUS
core
| fuel rod
core
radius/cm
| height of
core active
zone/cm
| grid
diameter
ratio
| initial
Keff | twentieth-year Keff | | burnup/(MW·d·kg−1)
| | prediction
by KSM
| calculation
by RMC
| relative
error/%
| prediction
by KSM
| calculation
by RMC
| relative
error/%
| | initial | 0.7200 | 180.0000 | 1.3500 | 1.0289 | — | 1.0031 | — | | — | 41.5240 | — | | optimization | 0.7314 | 155.5838 | 1.2893 | 1.0307 | 1.0007 | 1.0010 | −0.0229 | | 46.5773 | 46.5530 | 0.0523 |
|
Table 6. Optimization results of design parameters for URANUS core
| URANUS
core
| refueling
interval/
EFPY
| fuel
loading/kg
| total mass
of core
(including
reflector)/kg
| volume of
the active
area/m3 | average volume
power density
of the active
area/(W·cm−3)
| total volume
of core
(including
reflector)/m3 | maximum
temperature
of fuel
cladding/K
| maximum
temperature
of fuel
core/K
| | initial | 20 | 17580.0925 | 175459.3633 | 5.2138 | 19.1800 | 8.5734 | 600.6219 | 770.3892 | | optimization | 20 | 15681.0697 | 155309.9496 | 4.2697 | 23.4208 | 7.1059 | 604.1702 | 796.0589 |
|
Table 6. [in Chinese]
