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02019 Analysis of NEA C5MOX benchmark with computer code ‘COHINT’ based on interface current approach
05 Nuclear fuels (scientific, technical) order material temperature. Alternative scalings associated with the t w o - c o m p o n e n t limit characterized by a stronger coupling between the m a t e r i a l and the optically thin c o m p o n e n t were also discussed.
05•02016 An investigation of the effects of neutron energygroup structures and resonance treatment in a fusionfission hybrid reactor fuelling with Tho 2 Yildiz, K. Annals of Nuclear Energy, 2005, 32, (1), 101 118. In this work, the effects of neutron energy-group structures and resonance t r e a t m e n t s on the main integral neutronic p a r a m e t e r s are investigated in a fusion fission hybrid reactor, which has a fast and a t h e r m a l b l a n k e t fuelling with ThO2. A D T fusion n e u t r o n (14.1 MeV) is used as a neutron source. Fissile zone is cooled: (a) with light water for the m o d e r a t e d b l a n k e t and (b) with pressurized helium gas for the fast blanket. The neutronic p a r a m e t e r s have been evaluated with and w i t h o u t a resonance t r e a t m e n t for the same blanket compositions for the sake of a consistent comparison. The study has shown that neutron reactions above a threshold energy in fast neutron groups are less sensitive to resonance treatment, such as 7 Li(n,cm I )T and 23 7 Th(n,f). Neutron energy-group structures in the neutron libraries and description of fusion n e u t r o n source spectrum mainly affect these reactions. On the other hand, neutron reactions in the resonance and t h e r m a l e n e r ~ groups are sensitive to resonance treatment, such as 6Li(n,ct)T and ~2Th(n,g), d e p e n d i n g on the resonance structures. In the fast b l a n k e t calculations, resonance-based errors are lower and neutron source based errors are higher than in the m o d e r a t e d blanket. F u r t h e r m o r e , a correct description of the fusion neutron source spectrum over several neutron energy groups is essential to calculate fission reaction rates, fission heating density, fusile and fissile b r e e d i n g rates and n e u t r o n leakage accurately.
05•02017 Analysis and improvements of the DPN acceleration technique for the method of characteristics in unstructured meshes Santandrea, S. and Sanchez, R. Annals of Nuclear Energy, 2005, 32, (2), 163 193. A l g e b r a i c preconditioners, r e n u m b e r i n g techniques and a two-level algebraic multigrid m e t h o d have been i m p l e m e n t e d to speed up the Krylov iterations of the DPN equations used for the acceleration of the m e t h o d of characteristics in unstructured meshes. These algorithms were customized to take a d v a n t a g e of the cell-based structure of the DPN equations. Moreover, two techniques to speed up the solution of the m u l t i g r o u p eigenvalue M O C equations have been implemented. A solution of the m u l t i g r o u p eigenvalue DPN equation has been developed to provide a first guess for the external transport iterations. Next, a m u l t i g r o u p DPN acceleration m e t h o d has been developed to accelerate the thermal iterations. This latter development has been particularly useful because the standard m u l t i g r o u p rebalancing acceleration was counterproductive in the presence of heavy absorbents. All these acceleration techniques have been incorporated in the spectral code A P O L L O 2 . N u m e r i c a l examples and comparisons are given for the 6-group eigenvalue A t r i u m b e n c h m a r k problem. The best calculation, an initialized I L U 0 - p r e c o n d i t i o n e d DP1 scheme with thermal acceleration, was 7.7 times faster that the free iteration calculation, while the total n u m b e r of transport iterations was divided by 17.
flow domains inside and outside the c o n t a i n m e n t vessel, and heat and mass transfer models. Various key p a r a m e t e r s of the C O M M I X - 1 D results and corresponding AP-600 PCCS experimental data are compared and the agreement is good. Significant findings from this study are summarized.
05•02019 Analysis of NEA C5MOX benchmark with computer code 'COHINT' based on interface current approach M o h a n a k r i s h n a n , P. Progress in Nuclear Energy, 2004, 45, (2 4), 125 131. Interface current approach to solution of n e u t r o n transport equation has been earlier used for L W R lattice problems. The analysis of the C 5 M O X b e n c h m a r k is a opportunity to test its applicability to h e t e r o g e n e o u s reactor problem. C o m p u t e r code C O H I N T , which incorporates a routine for solution of neutron t r a n s p o r t equation in X-Y geometry by interface current approach was used for this analysis by representing the fuel rod as a square one. R e g i o n interface angular fluxes are r e p r e s e n t e d by a four-term expansion. It is found that the average pin power error is a b o u t 2.28% (peak pin error 4.1%) relative to reference calculations. F u r t h e r i m p r o v e m e n t is possible by introduction of the capability to r e p r e s e n t circular rods with in a square cell in C O H I N T .
05•02020 Application of two preconditioned generalized conjugate gradient methods to three-dimensional neutron and photon transport equations Chert, G. S. and Sheu, R. D. Progress in Nuclear Energy, 2004, 45, (1), 11 23. In this p a p e r the p r e c o n d i t i o n e d generalized conjugate gradient methods are applied to solve the linear system of equations that arise in t h r e e - d i m e n s i o n a l neutron and photon transport equations. These generalized conjugate gradient methods are the CGS (conjugate gradient square) algorithm and the B i - C G S T A B (bi-conjugate gradient stabilized) algorithm. Several subroutines are developed from these p r e c o n d i t i o n e d generalized conjugate gradient methods for use in t i m e - i n d e p e n d e n t multi-group t h r e e - d i m e n s i o n a l neutron and p h o t o n t r a n s p o r t equations. These subroutines are connected to the computer program T O R T . The reason for choosing the p r e c o n d i t i o n e d generalized conjugate gradient methods is that these m e t h o d s have good residual error control procedures during computation and have good convergence rates. A problem was rested which had an eight-set of matrix equations with 24255 u n k n o w n s each, in a personal computer with an A M D A t h l o n - X P 1 6 0 0 + central processing unit ( C P U ) and using M a n d r a k e Linux 6.3 as the o p e r a t i n g system. The point-wise incomplete L U factorization (ILU) and modified point-wise incomplete L U factorization ( M I L U ) are the preconditioning techniques used in the test problem. It was found that the p r e c o n d i t i o n e d CGS and Bi-CGSTAB methods with the preconditioner I L U are more efficient than with the preconditioner M I L U in the test problem. The n u m e r i c a l solution of flux by the p r e c o n d i t i o n e d Bi-CGSTAB and CGS methods produces the same results as those obtained by the successive over relaxation m e t h o d (SOR) in the T O R T program which is usually used for the calculation of radiation shielding in nuclear power plant and nuclear spent fuel storage.
05•02018 Analysis of large-scale tests for AP-600 passive containment cooling system Sha, W. T. et al. Nuclear Engineering and Design, 2004, 232, (2), 197 216. All next-generation light water reactors utilize passive systems to remove heat via natural circulation and are significantly different from past and current nuclear plant designs. One u n i q u e feature of the AP600 is its passive c o n t a i n m e n t cooling system (PCCS), which is designed to m a i n t a i n c o n t a i n m e n t pressure below the design limit for 72 h w i t h o u t action by the reactor operator. D u r i n g a design-basis accident (DBA), i.e. either a loss-of-coolant or a main-steam-line b r e a k accident, steam escapes and comes in contact with the much cooler c o n t a i n m e n t vessel wall. H e a t is transferred to the inside surface of the steel c o n t a i n m e n t wall by convection and condensation of steam and through the c o n t a i n m e n t steel wall by conduction. H e a t is then transferred from the outside of the c o n t a i n m e n t surface by heating and evaporation of a thin liquid film that is formed by applying water at the top of the c o n t a i n m e n t vessel dome. Air in the annular space is h e a t e d by both convection and injection of steam from the evaporating liquid film. The h e a t e d air and vapor rise as a result of natural circulation and exit the shield building through the outlets above the c o n t a i n m e n t shell. All of the analytical models that are developed for and used in the C O M M I X - 1 D code for predicting performance of the PCCS will be described. These models cover governing conservation equations for m u l t i - c o m p o n e n t s single-phase flow, t r a n s p o r t equations for the k two-equation turbulence model, auxiliary equations, liquid-film tracking model for b o t h inside (condensate) and outside (evaporating liquid film) surfaces of the containment vessel wall, thermal coupling between
300
Fuel and Energy Abstracts
September 2005
05•02021 Benchmark on deterministic 2-D MOX fuel assembly transport calculationswithout spatial homogenization Smith, M. A. et al. Progress in Nuclear Energy, 2004, 45, (2 4), 107 118. A n i m p o r t a n t issue of deterministic t r a n s p o r t methods for whole core calculations concerns the accuracy of h o m o g e n i z a t i o n techniques. A direct calculation for whole core h e t e r o g e n e o u s g e o m e t r i e s was not feasible in the past due to the limited capability of computers. With m o d e r n c o m p u t a t i o n a l abilities, direct whole core h e t e r o g e n e o u s calculations are b e c o m i n g feasible. This paper explores a recent O E C D / N E A b e n c h m a r k problem proposed to test the accuracy of m o d e r n deterministic t r a n s p o r t methods w h e n applied to reactor core problems without spatial homogenization. For this work a twod i m e n s i o n a l configuration was investigated and an accurate M o n t e Carlo reference solution was obtained. Twenty participants submitted solutions for the two-dimensional configuration and all of the participant solutions were c o m p a r e d to a reference M o n t e Carlo solution. Overall all the results submitted by the participants agreed well with the reference solution. A majority of the participants obtained solutions that were more than acceptable for typical reactor calculations and the r e m a i n i n g errors in the participant solutions can be attributed to the high order space-angle approximation necessary to solve this particular b e n c h m a r k problem. It is i m p o r t a n t to note that the high order space-angle approximation n e e d e d for this b e n c h m a r k is not necessary typical for all such whole-core h e t e r o g e n e o u s problems.
05•02016 An investigation of the effects of neutron energygroup structures and resonance treatment in a fusionfission hybrid reactor fuelling with Tho 2 Yildiz, K. Annals of Nuclear Energy, 2005, 32, (1), 101 118. In this work, the effects of neutron energy-group structures and resonance t r e a t m e n t s on the main integral neutronic p a r a m e t e r s are investigated in a fusion fission hybrid reactor, which has a fast and a t h e r m a l b l a n k e t fuelling with ThO2. A D T fusion n e u t r o n (14.1 MeV) is used as a neutron source. Fissile zone is cooled: (a) with light water for the m o d e r a t e d b l a n k e t and (b) with pressurized helium gas for the fast blanket. The neutronic p a r a m e t e r s have been evaluated with and w i t h o u t a resonance t r e a t m e n t for the same blanket compositions for the sake of a consistent comparison. The study has shown that neutron reactions above a threshold energy in fast neutron groups are less sensitive to resonance treatment, such as 7 Li(n,cm I )T and 23 7 Th(n,f). Neutron energy-group structures in the neutron libraries and description of fusion n e u t r o n source spectrum mainly affect these reactions. On the other hand, neutron reactions in the resonance and t h e r m a l e n e r ~ groups are sensitive to resonance treatment, such as 6Li(n,ct)T and ~2Th(n,g), d e p e n d i n g on the resonance structures. In the fast b l a n k e t calculations, resonance-based errors are lower and neutron source based errors are higher than in the m o d e r a t e d blanket. F u r t h e r m o r e , a correct description of the fusion neutron source spectrum over several neutron energy groups is essential to calculate fission reaction rates, fission heating density, fusile and fissile b r e e d i n g rates and n e u t r o n leakage accurately.
05•02017 Analysis and improvements of the DPN acceleration technique for the method of characteristics in unstructured meshes Santandrea, S. and Sanchez, R. Annals of Nuclear Energy, 2005, 32, (2), 163 193. A l g e b r a i c preconditioners, r e n u m b e r i n g techniques and a two-level algebraic multigrid m e t h o d have been i m p l e m e n t e d to speed up the Krylov iterations of the DPN equations used for the acceleration of the m e t h o d of characteristics in unstructured meshes. These algorithms were customized to take a d v a n t a g e of the cell-based structure of the DPN equations. Moreover, two techniques to speed up the solution of the m u l t i g r o u p eigenvalue M O C equations have been implemented. A solution of the m u l t i g r o u p eigenvalue DPN equation has been developed to provide a first guess for the external transport iterations. Next, a m u l t i g r o u p DPN acceleration m e t h o d has been developed to accelerate the thermal iterations. This latter development has been particularly useful because the standard m u l t i g r o u p rebalancing acceleration was counterproductive in the presence of heavy absorbents. All these acceleration techniques have been incorporated in the spectral code A P O L L O 2 . N u m e r i c a l examples and comparisons are given for the 6-group eigenvalue A t r i u m b e n c h m a r k problem. The best calculation, an initialized I L U 0 - p r e c o n d i t i o n e d DP1 scheme with thermal acceleration, was 7.7 times faster that the free iteration calculation, while the total n u m b e r of transport iterations was divided by 17.
flow domains inside and outside the c o n t a i n m e n t vessel, and heat and mass transfer models. Various key p a r a m e t e r s of the C O M M I X - 1 D results and corresponding AP-600 PCCS experimental data are compared and the agreement is good. Significant findings from this study are summarized.
05•02019 Analysis of NEA C5MOX benchmark with computer code 'COHINT' based on interface current approach M o h a n a k r i s h n a n , P. Progress in Nuclear Energy, 2004, 45, (2 4), 125 131. Interface current approach to solution of n e u t r o n transport equation has been earlier used for L W R lattice problems. The analysis of the C 5 M O X b e n c h m a r k is a opportunity to test its applicability to h e t e r o g e n e o u s reactor problem. C o m p u t e r code C O H I N T , which incorporates a routine for solution of neutron t r a n s p o r t equation in X-Y geometry by interface current approach was used for this analysis by representing the fuel rod as a square one. R e g i o n interface angular fluxes are r e p r e s e n t e d by a four-term expansion. It is found that the average pin power error is a b o u t 2.28% (peak pin error 4.1%) relative to reference calculations. F u r t h e r i m p r o v e m e n t is possible by introduction of the capability to r e p r e s e n t circular rods with in a square cell in C O H I N T .
05•02020 Application of two preconditioned generalized conjugate gradient methods to three-dimensional neutron and photon transport equations Chert, G. S. and Sheu, R. D. Progress in Nuclear Energy, 2004, 45, (1), 11 23. In this p a p e r the p r e c o n d i t i o n e d generalized conjugate gradient methods are applied to solve the linear system of equations that arise in t h r e e - d i m e n s i o n a l neutron and photon transport equations. These generalized conjugate gradient methods are the CGS (conjugate gradient square) algorithm and the B i - C G S T A B (bi-conjugate gradient stabilized) algorithm. Several subroutines are developed from these p r e c o n d i t i o n e d generalized conjugate gradient methods for use in t i m e - i n d e p e n d e n t multi-group t h r e e - d i m e n s i o n a l neutron and p h o t o n t r a n s p o r t equations. These subroutines are connected to the computer program T O R T . The reason for choosing the p r e c o n d i t i o n e d generalized conjugate gradient methods is that these m e t h o d s have good residual error control procedures during computation and have good convergence rates. A problem was rested which had an eight-set of matrix equations with 24255 u n k n o w n s each, in a personal computer with an A M D A t h l o n - X P 1 6 0 0 + central processing unit ( C P U ) and using M a n d r a k e Linux 6.3 as the o p e r a t i n g system. The point-wise incomplete L U factorization (ILU) and modified point-wise incomplete L U factorization ( M I L U ) are the preconditioning techniques used in the test problem. It was found that the p r e c o n d i t i o n e d CGS and Bi-CGSTAB methods with the preconditioner I L U are more efficient than with the preconditioner M I L U in the test problem. The n u m e r i c a l solution of flux by the p r e c o n d i t i o n e d Bi-CGSTAB and CGS methods produces the same results as those obtained by the successive over relaxation m e t h o d (SOR) in the T O R T program which is usually used for the calculation of radiation shielding in nuclear power plant and nuclear spent fuel storage.
05•02018 Analysis of large-scale tests for AP-600 passive containment cooling system Sha, W. T. et al. Nuclear Engineering and Design, 2004, 232, (2), 197 216. All next-generation light water reactors utilize passive systems to remove heat via natural circulation and are significantly different from past and current nuclear plant designs. One u n i q u e feature of the AP600 is its passive c o n t a i n m e n t cooling system (PCCS), which is designed to m a i n t a i n c o n t a i n m e n t pressure below the design limit for 72 h w i t h o u t action by the reactor operator. D u r i n g a design-basis accident (DBA), i.e. either a loss-of-coolant or a main-steam-line b r e a k accident, steam escapes and comes in contact with the much cooler c o n t a i n m e n t vessel wall. H e a t is transferred to the inside surface of the steel c o n t a i n m e n t wall by convection and condensation of steam and through the c o n t a i n m e n t steel wall by conduction. H e a t is then transferred from the outside of the c o n t a i n m e n t surface by heating and evaporation of a thin liquid film that is formed by applying water at the top of the c o n t a i n m e n t vessel dome. Air in the annular space is h e a t e d by both convection and injection of steam from the evaporating liquid film. The h e a t e d air and vapor rise as a result of natural circulation and exit the shield building through the outlets above the c o n t a i n m e n t shell. All of the analytical models that are developed for and used in the C O M M I X - 1 D code for predicting performance of the PCCS will be described. These models cover governing conservation equations for m u l t i - c o m p o n e n t s single-phase flow, t r a n s p o r t equations for the k two-equation turbulence model, auxiliary equations, liquid-film tracking model for b o t h inside (condensate) and outside (evaporating liquid film) surfaces of the containment vessel wall, thermal coupling between
300
Fuel and Energy Abstracts
September 2005
05•02021 Benchmark on deterministic 2-D MOX fuel assembly transport calculationswithout spatial homogenization Smith, M. A. et al. Progress in Nuclear Energy, 2004, 45, (2 4), 107 118. A n i m p o r t a n t issue of deterministic t r a n s p o r t methods for whole core calculations concerns the accuracy of h o m o g e n i z a t i o n techniques. A direct calculation for whole core h e t e r o g e n e o u s g e o m e t r i e s was not feasible in the past due to the limited capability of computers. With m o d e r n c o m p u t a t i o n a l abilities, direct whole core h e t e r o g e n e o u s calculations are b e c o m i n g feasible. This paper explores a recent O E C D / N E A b e n c h m a r k problem proposed to test the accuracy of m o d e r n deterministic t r a n s p o r t methods w h e n applied to reactor core problems without spatial homogenization. For this work a twod i m e n s i o n a l configuration was investigated and an accurate M o n t e Carlo reference solution was obtained. Twenty participants submitted solutions for the two-dimensional configuration and all of the participant solutions were c o m p a r e d to a reference M o n t e Carlo solution. Overall all the results submitted by the participants agreed well with the reference solution. A majority of the participants obtained solutions that were more than acceptable for typical reactor calculations and the r e m a i n i n g errors in the participant solutions can be attributed to the high order space-angle approximation necessary to solve this particular b e n c h m a r k problem. It is i m p o r t a n t to note that the high order space-angle approximation n e e d e d for this b e n c h m a r k is not necessary typical for all such whole-core h e t e r o g e n e o u s problems.