Appendix B. KAIST Benchmark
The location of the UOX-2 (CR) and the UOX-2 (BA16) fuel assemblies within the LWR reactor core are presented in
Figure A1.
Figure A1.
UOX-2 (CR) and UOX-2 (BA16) locations within the KAIST 1A LWR reactor core.
Figure A1.
UOX-2 (CR) and UOX-2 (BA16) locations within the KAIST 1A LWR reactor core.
The mass flux feedback value between fuel cells at the average axial node layer in both the UOX-2 (CR) and the UOX-2 (BA16) fuel assemblies is provided to show the similarities and differences between coupling values. All these values can be observed in
Figure A2.
Figure A2.
(a) UOX-2 (CR) mass flux feedback values, (b) UOX-2 (BA16) mass flux feedback values.
Figure A2.
(a) UOX-2 (CR) mass flux feedback values, (b) UOX-2 (BA16) mass flux feedback values.
Both FLOCAL and CTF derive the mass flux from the fluid density and fluid velocity, which are mainly obtained by solving the fluid mass and fluid momentum equations.
In both the DYN3D and the DYN3D and CTF couplings with or without burnable absorber pin and/or guide tube cells, the mass flux feedback value between fuel cells at the average axial node layer was observed to remain similar in all the tests in the UOX-2 (BA16) fuel assembly when compared to the UOX-2 (CR) fuel assembly. This mass flux feedback value near equivalence occurred due to mass conservation in the corresponding test.
In both the DYN3D and the DYN3D and CTF couplings with or without burnable absorber pin and/or guide tube cells, the mass flux feedback value between fuel cells at the average axial node layer was observed to decrease only with low flux when compared to the reference in both the UOX-2 (CR) and UOX-2 (BA16) fuel assemblies. This mass flux feedback value decrease occurred due to the lower inlet mass flow, which resulted in lower fluid densities as well as higher vapor and lower liquid velocities according to the fluid mass and fluid momentum equations. In both the DYN3D and the DYN3D and CTF couplings, the mass flux feedback value between fuel cells at the average axial node layer was observed to remain constant with high power, high temperature, low pressure, and low boron when compared to the reference in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies.
In the DYN3D coupling with burnable absorber pin and/or guide tube cells compared to without burnable absorber pin and/or guide tube cells, the mass flux feedback value between all fuel cells at the average axial node layer was observed to decrease in all the tests in the UOX-2 (CR) fuel assembly and increase in all the tests in the UOX-2 (BA16) fuel assembly. This mass flux feedback value decrease and increase occurred, in particular, due to either the absence of power in the guide tube cells or lower power in the burnable absorber pin cells as well as in general due to the lack of mass and momentum transfer between fuel cells, leading to higher mass flux in either the guide tube or burnable absorber pin cells, which resulted, in general, in higher fluid densities, lower vapor, and higher liquid velocities according to the fluid mass and fluid momentum equations.
In the DYN3D and CTF coupling with burnable absorber pin and/or guide tube cells compared to without burnable absorber pin and/or guide tube cells, the mass flux feedback value between fuel cells at the average axial node layer was observed to decrease in all the tests in the UOX-2 (CR) fuel assembly and increase in all the tests in the UOX-2 (BA16) fuel assembly. This mass flux feedback value decrease and increase occurred, in general, due to the presence of mass and momentum transfer between fuel cells, leading to homogeneous mass flux in both the guide tube and burnable absorber pin cells, which resulted, in general, in almost unchanged fluid densities, vapor, and liquid velocities according to the fluid mass and fluid momentum equations.
Between the DYN3D and the DYN3D and CTF couplings with or without burnable absorber pin and/or guide tube cells, the mass flux feedback values between fuel cells at the average axial node layer in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies were observed to be different. These mass flux feedback value differences occurred due to different terms in the fluid mass and fluid momentum equations including the evaporation, viscous stress as well as the crossflow and turbulent mixing models between fuel cells. According to the obtained mass flux feedback values between fuel cells at the average axial node layer in the UOX-2 (CR) fuel assembly, most variations can be regarded as compatible between both couplings while in the UOX-2 (BA16) fuel assembly, also most of the variations can be regarded as compatible between both couplings. Such variations can be regarded as compatible between couplings due to the similarity of the mass flux feedback values.
Axial mass flux feedback distributions for central, side, and corner fuel cells and average between fuel cells as well as transversal mass flux feedback distributions for all the fuel cells at the average axial node layer are provided for the UOX-2 (CR) fuel assembly compatible reference case to show the similarities and differences between both coupling distributions, as observed in
Figure A3,
Figure A4 and
Figure A5.
Figure A3.
Axial mass flux feedback distribution.
Figure A3.
Axial mass flux feedback distribution.
Figure A4.
DYN3D coupling transversal mass flux feedback distribution.
Figure A4.
DYN3D coupling transversal mass flux feedback distribution.
Figure A5.
DYN3D and CTF coupling transversal mass flux feedback distribution.
Figure A5.
DYN3D and CTF coupling transversal mass flux feedback distribution.
In both the DYN3D and the DYN3D and CTF couplings, the axial mass flux feedback distribution in the central, side, and corner fuel cells as well as the transversal mass flux feedback distribution for all fuel cells at the average axial node layer in the UOX-2 (CR) fuel assembly compatible reference case was observed to decrease more in the central than in the side or corner fuel cells. This axial and transversal mass flux feedback distribution decrease occurred in both couplings due to the fuel cell neighbours, leading to higher heat fluxes in the central fuel cells, which resulted in lower fluid densities, higher vapor, and lower liquid velocities according to the fluid mass and fluid momentum equations.
Between the DYN3D and the DYN3D and CTF couplings, the axial mass flux feedback distribution for the central, corner, and side fuel cells as well as the transversal mass flux feedback distribution for all the fuel cells at the average axial node layer in the UOX-2 (CR) fuel assembly compatible reference case were observed to be different. These axial and transversal mass flux feedback distribution differences occurred due to different terms in the fluid mass and fluid momentum equations including the evaporation, viscous stress as well as the crossflow and turbulent mixing models between fuel cells.
The void fraction feedback value between fuel cells at the top axial node layer in both the UOX-2 (CR) and the UOX-2 (BA16) fuel assemblies is provided to show the similarities and differences between coupling values. All these values can be observed in
Figure A6.
Figure A6.
(a) UOX-2 (CR) void fraction feedback values, (b) UOX-2 (BA16) void fraction feedback values.
Figure A6.
(a) UOX-2 (CR) void fraction feedback values, (b) UOX-2 (BA16) void fraction feedback values.
Both FLOCAL and CTF derive the void fraction from the fluid density, fluid velocity, and fluid enthalpy, which are mainly obtained by solving the fluid mass, fluid momentum, and fluid energy equations.
Only in the DYN3D coupling with or without burnable absorber pin and/or guide tube cells, the void fraction feedback value between fuel cells at the top axial node layer was observed to increase in all the tests in the UOX-2 (BA16) fuel assembly when compared to in the UOX-2 (CR) fuel assembly. This void fraction feedback value increase occurred due to lower powers in the burnable absorber pin cells, which resulted in higher powers in the fuel pin cells, leading to an equivalent total power as when there were equal powers in all the fuel pin cells, which resulted in lower fluid densities, higher vapor, and lower liquid velocities as well as higher fluid enthalpies according to the fluid mass, fluid momentum, and fluid energy equations.
In both the DYN3D and the DYN3D and CTF couplings with or without burnable absorber pin and/or guide tube cells, the void fraction feedback value between fuel cells at the top axial node layer was observed to increase with high power, high temperature, low-pressure, and low flux when compared to the reference in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies. This void fraction feedback value increase occurred due to different reasons: in the high-power variation, this occurred due to the higher volumetric wall heat transfer term, which resulted in lower fluid densities, higher vapor, and lower liquid velocities as well as higher fluid enthalpies according to the fluid energy equation. In the high temperature variation, this occurred due to higher inlet fluid enthalpy, which resulted in higher fluid enthalpies according to the fluid energy equation. In the low-pressure variation, this occurred due to the lower pressure force term, which resulted in lower fluid densities, higher vapor, and lower liquid velocities according to the fluid mass and fluid momentum equations. In the low mass flux variation, this occurred due to the lower inlet mass flow, which resulted in lower fluid densities, higher vapor, and lower liquid velocities as well as higher fluid enthalpies according to the fluid mass, fluid momentum, and fluid energy equations. Only in the DYN3D and CTF coupling with or without burnable absorber pin and/or guide tube cells was the void fraction feedback value between the fuel cells at the top axial node layer observed to decrease with low boron when compared to the reference in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies. This void fraction feedback value decrease occurred due to the full boron transport model in the DYN3D and CTF coupling, which resulted in higher liquid velocities according to the boron tracking and precipitation equations when compared to the simplified boron transport model in the DYN3D coupling, which resulted in almost constant liquid velocities according to the simplified boron transport equation.
In the DYN3D coupling with burnable absorber pin and guide tube cells compared to without burnable absorber pin and/or guide tube cells, the void fraction feedback value between fuel cells at the top axial node layer was observed to decrease in all the tests in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies. This void fraction feedback value decrease occurred, in particular, due to either the absence of power in the guide tube cells or lower power in the burnable absorber pin cells as well as in general due to the lack of mass, momentum, and energy transfer between fuel cells, leading to no vapor in the guide tube cells and low vapor in the burnable absorber pin cells, which resulted, in general, in higher fluid densities, lower vapor, and higher liquid velocities as well as higher fluid enthalpies according to the fluid mass, fluid momentum, and fluid energy equations.
In the DYN3D and CTF coupling with burnable absorber pin and guide tube cells compared to without burnable absorber pin and/or guide tube cells, the void fraction feedback value between fuel cells at the top axial node layer was observed to remain almost unchanged in all the tests in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies. This void fraction feedback value near equivalence occurred, in general, due to the presence of mass, momentum, and energy transfer between fuel cells, leading to homogeneous vapor in both the guide tube cells and burnable absorber pin cells, which resulted, in general, in unchanged fluid densities, vapor, and liquid velocities as well as higher fluid enthalpies according to the fluid mass, fluid momentum, and fluid energy equations.
Between the DYN3D and the DYN3D and CTF couplings with or without burnable absorber pin and/or guide tube cells, the void fraction feedback values between all fuel cells at the top axial node layer in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies were observed to be different. These void fraction feedback value differences occurred due to different terms in the fluid mass, fluid momentum, and fluid energy equations including the evaporation, viscous stress, nucleate boiling correlations as well as the crossflow and turbulent mixing models between fuel cells. According to the obtained void fraction feedback values between fuel cells at the top axial node layer in the UOX-2 (CR) fuel assembly, most variations can be regarded as compatible between both couplings, while in the UOX-2 (BA16) fuel assembly, almost none of the variations can be regarded as compatible between both couplings. Such variations can be regarded as compatible between couplings due to the similarity in the void fraction feedback values.
Axial void fraction feedback distributions for central, side, and corner fuel cells and average between fuel cells as well as transversal void fraction feedback distribution for all the fuel cells at the top axial node layer are provided for the UOX-2 (CR) fuel assembly compatible reference case to show the similarities and differences between both coupling distributions, as observed in
Figure A7,
Figure A8 and
Figure A9.
Figure A7.
Axial void fraction feedback distribution.
Figure A7.
Axial void fraction feedback distribution.
Figure A8.
DYN3D coupling transversal void fraction feedback distribution.
Figure A8.
DYN3D coupling transversal void fraction feedback distribution.
Figure A9.
DYN3D and CTF coupling transversal void fraction feedback distribution.
Figure A9.
DYN3D and CTF coupling transversal void fraction feedback distribution.
In both the DYN3D and the DYN3D and CTF couplings, the axial void fraction feedback distribution for the central, side, and corner fuel cells as well as the transversal void fraction feedback distribution for all fuel cells at the top axial node layer in the UOX-2 (CR) fuel assembly compatible reference case was observed to increase more in the central than in the side or corner fuel cells. This axial and transversal void fraction feedback distribution increase occurred in both couplings due to the fuel cell neighbours, leading to higher heat fluxes in the central fuel cells, which resulted, in general, in higher fluid densities, lower vapor, and higher liquid velocities as well as higher fluid enthalpies according to the fluid mass, fluid momentum, and fluid energy equations.
Between the DYN3D and the DYN3D and CTF couplings, the axial void fraction feedback distribution for the central, corner, and side fuel cells as well as the transversal void fraction feedback distribution for all the fuel cells at the top axial node layer for the UOX-2 (CR) fuel assembly compatible reference case was observed to be higher in the DYN3D coupling and lower in the DYN3D and CTF coupling. These axial and transversal void fraction feedback distribution differences occurred due to different terms in the fluid mass, fluid momentum, and fluid energy equations including the evaporation, viscous stress, nucleate boiling correlations as well as the crossflow and turbulent mixing models between fuel cells.
The relative departure from nucleate boiling feedback value between fuel pins at the top axial node layer in both the UOX-2 (CR) and the UOX-2 (BA16) fuel assemblies is provided to show the similarities and differences between coupling values. All these values can be observed in
Figure A10.
Figure A10.
(a) UOX-2 (CR) DNBR feedback values, (b) UOX-2 (BA16) DNBR feedback values.
Figure A10.
(a) UOX-2 (CR) DNBR feedback values, (b) UOX-2 (BA16) DNBR feedback values.
Both FLOCAL and CTF derive the relative departure from nucleate boiling from the heat flux, which is mainly obtained by solving the solid energy equation as well as the critical heat flux, which is obtained using different empirical departure from nucleate boiling correlations.
In both the DYN3D and the DYN3D and CTF couplings without burnable absorber pin and/or guide tube cells, the relative departure from nucleate boiling feedback value between fuel pins at the top axial node layer was observed to decrease in some tests in the UOX-2 (BA16) fuel assembly when compared to the UOX-2 (CR) fuel assembly. This relative departure from nucleate boiling feedback value decrease occurred due to lower powers in the burnable absorber pin cells, which resulted in higher powers in the fuel pin cells, leading to an equivalent total power as when there were equal powers in all the fuel pin cells, which resulted in higher heat fluxes according to the solid energy equation.
In both the DYN3D and the DYN3D and CTF couplings without burnable absorber pin and/or guide tube cells, the relative departure from nucleate boiling feedback value between fuel pins at the top axial node layer was observed to decrease with high power, high temperature, low-pressure, and low flux when compared to the reference in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies. This relative departure from the nucleate boiling feedback value decrease occurred due to different reasons: in the high-power variation, this occurred due to the higher volumetric wall heat transfer term, which resulted in higher heat fluxes according to the solid energy equation. In the high temperature variation, this occurred due to higher inlet fluid enthalpy, which resulted in higher critical heat fluxes according to the departure from nucleate boiling correlation. In the low-pressure variation, this occurred due to the lower pressure force term, which resulted in lower critical heat fluxes according to the critical heat flux correlation. In the low mass flux variation, this occurred due to the lower inlet mass flow, which resulted in lower critical heat fluxes according to the critical heat flux correlation. In both the DYN3D and the DYN3D and CTF couplings without burnable absorber pin and/or guide tube cells, the relative departure from nucleate boiling feedback value between fuel pins at the top axial node layer was observed to decrease with low boron when compared to the reference in the UOX-2 (BA16) fuel assembly. This relative departure from nucleate boiling feedback value increase in the low boron variation occurred due to the lower boric acid concentration term, which resulted in more heterogeneous heat fluxes according to the solid energy equation.
In both the DYN3D and the DYN3D and CTF couplings without burnable absorber pin and/or guide tube cells, the relative departure from nucleate boiling feedback value between all fuel pins at the top axial node layer was observed in all the tests in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies due to either the absence of power in the guide tube cells or lower power in the burnable absorber pin cells, which resulted in higher relative departure from nucleate boiling feedback value in both the guide tube cells and burnable absorber pin cells.
Between the DYN3D and the DYN3D and CTF couplings without burnable absorber pin and guide tube cells, the relative departure from nucleate boiling feedback values between fuel pins at the top axial node layer in both the UOX-2 (CR) and in the UOX-2 (BA16) fuel assemblies were observed to be different. These relative departure from nucleate boiling feedback value differences occurred due to different critical heat flux correlations. According to the obtained relative departure from nucleate boiling feedback values between fuel pins at the top axial node layer in the UOX-2 (CR) fuel assembly, most variations can be regarded as compatible between both couplings while in the UOX-2 (BA16) fuel assembly, also most of the variations can be regarded as compatible between both couplings. Such variations can be regarded as compatible between couplings due to the similarity of the relative departure from nucleate boiling feedback values.
Axial relative departure from nucleate boiling feedback distributions for central, side, and corner fuel pins and average between fuel pins as well as transversal relative departure from nucleate boiling feedback distributions for all the fuel pins at the top axial node layer is provided for the UOX-2 (CR) fuel assembly compatible reference case to show the similarities and differences between both coupling distributions, as observed in
Figure A11,
Figure A12 and
Figure A13.
Figure A11.
Axial DNBR feedback distribution.
Figure A11.
Axial DNBR feedback distribution.
Figure A12.
DYN3D coupling transversal DNBR feedback distribution.
Figure A12.
DYN3D coupling transversal DNBR feedback distribution.
Figure A13.
DYN3D and CTF coupling transversal DNBR feedback distribution.
Figure A13.
DYN3D and CTF coupling transversal DNBR feedback distribution.
In both the DYN3D and the DYN3D and CTF couplings, the axial relative departure from nucleate boiling feedback distribution for the central, corner, and side fuel pins as well as the transversal relative departure from nucleate boiling feedback distribution for all fuel pins at the top axial node layer in the UOX-2 (CR) fuel assembly compatible reference case was observed to decrease more for the central fuel pins than for the side or corner fuel pins. This axial and transversal relative departure from nucleate boiling feedback distribution decrease occurred in both couplings due to the fuel cell neighbours, leading to higher heat fluxes in the central fuel cells according to the solid energy equation.
Between the DYN3D and the DYN3D and CTF couplings, the axial relative departure from nucleate boiling feedback distribution for the central, corner, and side fuel pins as well as the transversal departure from nucleate boiling distribution for all the fuel pins at the top axial node layer in the UOX-2 (CR) fuel assembly compatible reference case were observed to be different. These axial and transversal relative departures from nucleate boiling feedback distribution differences occurred due to different critical heat flux correlations.