PHISICS is a reactor analysis toolkit developed over

the last 3 years at the Idaho National Laboratory. It has

been coupled with the reactor safety analysis code

RELAP5-3D. PHISICS is aimed at providing an optimal

trade off between needed computational resources (in the

range of 10~100 computer processors) and accuracy. In

fact, this range has been identified as the next 5 to 10

years average computational capability available to

nuclear reactor design and optimization nuclear reactor

cores.

Detailed information about the individual modules of

PHISICS can be found in [1]. An overview of the

modules used in this study is given in the next subsection.

Lately, the Idaho National Laboratory gained access plant

data for the first cycle of a PWR, including Hot Zero

Power (HZP) and Hot Full Power (HFP).

This data provides the opportunity to validate the

transport solver, the interpolation capability for mixed

macro and micro cross section and the criticality search

option of the PHISICS pack

A., Epiney

ALFONSI, ANDREA

C., Rabiti

F., Lodi

M., Sumini

English

PHISICS is a reactor analysis toolkit developed in the last 3 years at the Idaho National Laboratory that has been also coupled with the thermo-hydraulic plant simulator RELAP5-3D. PHISICS is aimed to provide an optimal trade off between needed computational resources and accuracy in the range of 10~100 cores. In fact this range has been identified as the next 5 to 10 years average computational capability available to nuclear engineer designing and optimizing nuclear reactor cores. Different publication has been already presented [1] showing test of the single modules composing the PHISICS package. Lately the Idaho National Laboratory had the opportunity to access to plant data for the first cycle of a PWR including Hot Zero Power (HZP) and Hot Full Power (HFP). This data provided the opportunity to validate the transport solver, the interpolation capability for mixed macro and micro cross section and the criticality search option of the PHISICS package. In the following we will firstly recall briefly the structure of the different PHISICS modules and then we will illustrate the modeling process and some preliminary results

Lodi, F.

Rabiti, C.

Alfonsi, A.

Epiney, A.

Sumini, M.

UNT Digital Library

  This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint should not be cited or reproduced without permission of the author. This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, or any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for any third party’s use, or the results of such use, of any information, apparatus, product or process disclosed in this report, or represents that its use by such third party would not infringe privately owned rights. The views expressed in this paper are not necessarily those of the United States Government or the sponsoring agency. INL/CON-13-28359PREPRINTHot Zero and Full Power Validation of PHISICS RELAP-5 Coupling  ANS Annual Meeting  F. Lodi C. Rabiti A. Alfonsi A. Epiney M. Sumini  June 2013  Hot Zero and Full Power Validation of PHISICS RELAP-5 Coupling  F. Lodi*, C. Rabiti**, A. Alfonsi**, A. Epiney**, M. Sumini*  *University of Bologna Dept. Of Industrial Engineering: Via dei Colli, 16 40136 Bologna Italy  **Idaho National Laboratory, 2525 North Fremont Street, Idaho Falls (ID) francesco.lodi2@studio.unibo.it   INTRODUCTION  PHISICS is a reactor analysis toolkit developed over the last 3 years at the Idaho National Laboratory (INL). Its goal is to provide state of the art simulation capability to reactor designers, especially for the simulation of advanced reactors such as Generation IV systems. It has been coupled with the thermo-hydraulic plant simulator RELAP5-3D. PHISICS is aimed to provide an optimal trade off between needed computational resources (in the range of 10~100 computer cores) and accuracy. In fact, this range has been identified as the next 5 to 10 years average computational capability available to nuclear engineers designing and optimizing nuclear reactor cores. The sought of an optimal trade off between flexibility, accuracy, and speed, in the above mentioned computational resource range, and the need to provide to INL a flexible tool capable to deal with several different reactor designs are the key differentiating factors that supported the development of this tool  The software is built in a modular approach in order to simplify the independent development of modules by different teams and future maintenance. Detailed information about the individual modules of PHISICS can be found in [1]. An overview of the modules used in this study is given in the next subsection. Lately, the INL gained access to plant data for the first cycle of a PWR, including Hot Zero Power (HZP) and Hot Full Power (HFP). This data provides the opportunity to validate the transport solver, the interpolation capability for mixed macro and micro cross section and the criticality search option of the PHISICS package. The current paper will first briefly recall the structure of the different PHISICS modules used, then illustrate the modeling process for the PWR HZP/HFP and finally present some preliminary results.  THE PHISICS MODULES USED FOR THE MODELLING  The following sections present the PHSICS toolkit involved in this simulation and a brief description of its capabilities and modules.  INSTANT  INSTANT [2] is the neutron transport solver. It is based on the spherical harmonics approximation of the angular dependence of the neutron flux. Currently the following nodal spatial meshes are available: Cartesian, hexagonal, and extruded triangle.  MIXER  The MIXER is tasked to perform the interpolation of the microscopic or macroscopic cross sections. It also generates the macroscopic cross sections used by INSTANT. PHISICS possesses a noticeable flexibility in the treatment of cross sections, since both microscopic and macroscopic cross sections can be combined together in the same simulation. Macroscopic cross sections are treated in the same way than microscopic ones with the atomic density equal to one. Cross sections can be tabulated for an unbounded number of parameters and having an unbounded number of tabulation points for each parameter. The interpolation of the cross sections within the parameter grid is linear.  Criticality Search Module  The Criticality Search (CS) adjusts isotope densities (user defined) for a specified location in the geometry until a prescribed value of keff is reached (or the densities would be outside user specified boundaries). A classical usage of this module is to search for critical boron concentration, fissile enrichment or control rod positioning. To speed up the process, the user can also specify if in case the concentration of an isotope is also a tabulation parameter, to use just a first order approximation, i.e. the user can specify that a) only the variation in density of the specific isotope impacts the macroscopic cross sections or b) the isotopes (user provided information) need to be re-evaluated to account for the change in the tabulation coordinate.  RELAP5 coupling  The coupling between RELAP5 and PHISICS allows for thermal-hydraulic feedbacks such as water density, fuel temperature, poisons and control rods. A good modeling of water density neutronic response is often crucial for acceptable and realistic results. The possible calculation paths resulting by combining PHISICS and RELAP5 are manifold. THE MODELLING APPROACH Microscopic Cross Section Library GenerationFigure 1 shows the core layout indicating the different assembly types (enrichment and burnable poison). Starting from that layout, a set of 30 libraries has been generated in order to account not only for assembly type but also for neighboring effects. Figure 2 shows the library correspondence to the 2D octant core. The chosen energy structure involves 8 groups with the followingupper bounds: 2.0E+07, 2.2313E+06, 8.2085E+05, 9.11884E+03, 1.3007E+02, 3.9279E+00, 6.2506E-01 and1.4572E-01 eV. Each fuel library has ~300 isotopes (only 200 are tracked) while each reflector library contains 24 isotopes (all tracked). Table 1 reports the tabulation parameters, the number of points and the values for each parameter and the total number of points. The burn-up has been added as an additional tabulation dimension for the HFP only, sincefor HFP, following the first and second depletion cycle ispart of the benchmark (second part). Figure 1: Core overview  Figure 2: Material placement  Table 1: HZP TabulationLibrary Type HZP HFPBoron Tabulation (ppm) 1700,1150, 1000, 1.0E-06 11501000 1.0E-06 Fuel Temperature (°C) 286.66, 291.66 300,  800,  1300 Moderator Density (kg/m3) 752.705, 733.36  752.705, 733.36 Burn-up (GWd) -- 0.150, 15.0 Total Number of Tabulation points 16 108 Description of the Boron Modeling The presence of boron both, as burnable poison and in the coolant to control the reactivity swing requiredsome modeling effort, especially due to the direct usage of microscopic cross sections in the simulation. In fact, the boron in the water is not burnable and its density follows both, the water density and the ppm of soluble boron maintained in the water by the plant control system while the boron in the poison locations is burnable. Correct prediction of the critical soluble boron concentration in the water (as a function of moderator temperate and burn-up) is a key value for reactor control.  In order to properly take into account this features in the PHISICS framework, we have generated two cross section sets for the boron in the water and in the burnable absorbers with HELIOS 2. Care needs to be taken since the cross sections generated in this way are normalized with respect the average flux in the water and in the burnable absorbers, while when used in the nodal simulation of the core, the reaction rates are computed using the average assembly fluxes. To eliminate this discrepancy the cross sections have been rescaled using the following formula:               ⎟⎟⎠⎞⎜⎜⎝⎛=regtotsubregrisoriso φφσσ  Where r is the reaction type index, iso is the isotope index and the fluxes are representative of (subreg) the sub-region where the homogenization has been made and (regtot) the whole region (usually the one used in the full core calculation for the reactor being considered). Another problem, connected to the soluble boron modeling that had to be addressed, was the water density feedback on its number density. In fact, the atomic density of the born in the water is not only linked to the ppm value but also to the density of the water itself. The macroscopic cross section of the coolant (water + boron) could be written as: ΣWr = NB (ρH2O, ppm)σ Br + NH2O (ρH2O )σ H2Or , where the density of the Boron ( NB ) is a linear function of the ppm value and water density ρH2O . Given that none of this two isotopes will be depleted and that the water density and ppm are already tabulation parameters, it is more convenient to use directly the ΣWr  with unitary densities. In this way, the variation of density of the water computed by RELAP5 and given as a feedback to PHISICS  will directly impact the amount of soluble Boron present in the core. The criticality searching, used to find the critical value of the Boron, is then performed on a dummy isotope with ‘zero’ cross sections while ΣWr  is the only isotope for which the values of the cross section are recomputed at each iteration of the CS.   SPH Factors Calculation         To further improve results, the Super-homogenization technique (SPH) [3] can be implemented in order to have reaction rates of the lattice calculation equal to the ones obtained in a 2D nodal representation of the core. SPH could be applied at different levels of resolution; in the present case, SPH factors by assembly and by energy group are used. Generally speaking, the SPH is a non-linear methodology where the unknowns are a) the average fluxes in each assembly computed by the nodal core simulator and b) the cross sections to be used in the nodal simulation. The average assembly core fluxes are provided by the INSTANT solver for a given set of homogenized cross-sections. These values have to be scaled by an unknown common scaling factor. In standard calculation this scaling factor is provided by the power normalization. In the case of the SPH set of equations, this normalization does not provide an additional constraint. In fact, this is equivalent to imposing the sum of all fission rates (volume weighted) to be equal between the lattice and the nodal simulation. This is a linear combination of a part of the second set of equations that are used in the SPH methodology, where all the reaction rates are forced to be the same between the lattice calculation and the nodal core calculation. The additional constraint we decided to use, is given by forcing the neutronic population given by the nodal solution to be equal to the one in the lattice solution. The solution of the non-linear system of equations (nodal core P1 equation, neutron population and reaction rates) is performed using a simple fixed-point scheme described in the following: 1. An initial set of homogenized cross section is used to compute the average assembly fluxes by PHISICS. 2. Normalization of the average fluxes of the core calculation to the ones of the lattice. ϕgnorm,i =ϕgiϕgi,latticeVii∑g∑ϕgiVii∑g∑⎛⎝⎜⎜⎜⎞⎠⎟⎟⎟ Where i is the region index and g the macro energy group index while V is the region volume. The lattice index identifies the flux of the lattice calculation. 3. Use the new flux to calculate the SPH correction factors α.  αgi =ϕgi,latticeϕgnorm,i⎛⎝⎜⎜⎞⎠⎟⎟  This can be proved to be equivalent to force the macro reaction rate to be the same in the lattice and core calculation when the cross section are scaled by the factor αgi . 4. Correct the cross sections by the factor α.  σ g,isoi,r ←αgiσ g,isoi,rσ s0,g→g ',isoi,r ←αgiσ s0,g→g ',isoi,r where the tilde indicates the corrected cross sections, iso is the particular isotope and s0 the zero order of the scattering cross section. Steps 1 to 4 are repeated until convergence is achieved in the correction factors. Special care needs to be taken in dealing with the corrective factors to be applied to the transport cross sections. In fact, the transport cross-section adjustment tries to preserve the assembly leakage rather then a reaction rate. In this case, the right weighting function is not anymore the average scalar flux but one over its gradient cross the assembly. Using the gradient in the 2D plane will lead to a correction coefficient for the transport cross-section that is directional dependent. In the present case, PHISICS (which is based on a coherent spherical harmonics approximation) does not use the transport cross-sections but the effect is emulated by altering the within group anisotropic scattering cross section as suggested in [4]. As a result the SPH factor for the σ s1,g→g,isoi  is computed as it follows: • Point 3 in the above iteration scheme is replaced by: iggsigTigiggsigigT →→ −=− ,1,,1,~1σσασβσ where this formula implicitly defines the SPH correction factor igβ  for the P1 scattering cross section. • Point 4 in the above iteration scheme is replaced by: iggsigiisoggs →→ ← ,1,,1~ σβσ  where σ T ,gi  is the total cross-section. Currently, the out-scattering anisotropic cross-sections are left unchanged. Even if this approach is convergent and gives satisfactory results using the P1 approximation in the core simulation, the correction on the border assemblies and especially in the reflector can become significant because of the simplification used in the preservation of the leakage that is a dominant effect in these regions. Besides that, the general accuracy of the calculation can be considerably increased.  RESULTS  The SPH correction has been performed for only one tabulation point and then applied to the whole library. The approximation is acceptable if for different points of the tabulation the relative magnitude of the fluxes in space and energy are reasonably preserved.        The final corrective factors averaged over energy for the HZP and HFP conditions are shown in Table 2.        The reaction rate relative errors averaged over energies are shown in Table 3. As can be seen from the errors, acceptable convergence can be reached with a reasonable amount of iterations (between 10 and 20).      Table 2: Corrective factor energy averaged  Material HZP HFP 1 0.94361 0.93266 2 0.91596 0.90558 3 0.92790 0.91873 4 0.91999 0.91254 5 0.90693 0.89993 6 0.92096 0.91640 7 0.90775 0.90336 8 0.92601 0.92361 9 0.91644 0.91497 10 0.94211 0.94568 11 0.92309 0.92333 12 0.93664 0.94043 13 0.93858 0.94734 14 0.99478 1.01220 15 0.95501 0.95933 16 0.96671 0.97303 17 0.96837 0.97675 18 0.97240 0.98753 19 0.95972 0.97865 20 1.07209 1.09028 21 0.99968 1.01190 22 0.96904 0.97928 23 0.99895 1.01304 24 1.05531 1.06646 25 1.13983 1.14627 26 1.19367 1.19248 27 1.14728 1.14730 28 1.15148 1.15189 29 1.24804 1.23865 Reflector 1.80192 1.67313 Table 3: Averaged relative errors Material HZP HFP 1 1.4676E-02 1.5996E-02 2 1.4745E-02 1.5869E-02 3 1.4676E-02 1.5855E-02 4 1.4811E-02 1.5924E-02 5 1.4810E-02 1.5924E-02 6 1.4858E-02 1.6028E-02 7 1.4885E-02 1.6106E-02 8 1.4934E-02 1.6159E-02 9 1.5178E-02 1.6235E-02 10 1.5404E-02 1.6249E-02 11 1.5162E-02 1.6323E-02 12 1.5307E-02 1.6386E-02 13 1.5767E-02 1.6628E-02 14 1.6194E-02 1.6509E-02 15 1.5604E-02 1.6438E-02 16 1.5524E-02 1.6475E-02 17 1.5797E-02 1.6575E-02 18 1.5956E-02 1.6653E-02 19 1.6489E-02 1.6588E-02 20 1.6747E-02 1.6465E-02 21 1.6330E-02 1.6645E-02 22 1.6376E-02 1.6610E-02 23 1.6252E-02 1.5996E-02 24 1.6379E-02 1.5869E-02 25 1.6160E-02 1.5855E-02 26 1.5873E-02 1.5924E-02 27 1.6452E-02 1.5924E-02 28 1.6499E-02 1.6028E-02 29 1.5950E-02 1.6106E-02 Reflector 1.4449E-02 1.6159E-02      The corresponding power distributions are shown in Figures 3 and 4.  Figure  3: HZP power distribution after SPH correction  Figure  4: HFP power distribution after SPH correction    Table 4 summarizes the differences between the nodal core simulation versus the 2D lattice calculation and experimental results for keff and the critical boron concentration. For the 3D calculation, a total of 64 libraries have been used. Besides the 30 libraries already described we added other 30 identical to the previous ones but located in a plane with grid spacers, while the remaining 4 are for the axial reflectors (top and bottom).The same SPH technique has been applied to the grid spacer planes libraries while for the axial reflector the same factors for the radial one have been used. Table 4: difference in 2D (code to code) and 3D (experimental to code) Reference PHISICS (PHISICS-Reference) Critical Boron (ppm) Keff (pcm) 2D HELIOS (HZP) Not calculated 127 3D Experimental (HZP) 22 250 3D Experimental (HFP) RELAP off 14 168 RELAP on 1.78 21.4 This initial attempt to model a realistic PWR core with the PHISICS package reveals a good robustness of the code and its flexibility for multiple usages. The criticality searching and mixer modules strategically combined togheter can improved the modeling, especially if combined with the RELAP5 feedbacks, thanks to their flexibility was in fact possible to realistically simulate the presence of soluble boron. Results compare in a satisfactory way with experimental results and further improvements are possible and considered for the second part of the benchmark when two cycles of the core will be simulated. ENDNOTES This work is supported by the U.S. Department of Energy, under DOE Idaho Operations Office Contract DE-AC07-05ID14517. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. This work was also supported by the University of Bologna thanks to its collaboration with INL for further developing the PHISICS modules capabilities. REFERENCES  1. C. RABITI, Y. WANG, G. PALMIOTTI, H. HIRUTA,J. COGLIATI, A. ALFONSI, A. EPINEY, T. GRIMMET “PHISICS: New Features and Advancements”, 2011 Annual Winter Meeting, Washington, D. C., USA, October 30-November 3 (2011). 2.    A. EPINEY, C. RABITI, A. ALFONSI, Y WANG, J.   COGLIATI, G. STRYDOM “PHISICS multi-group  transport neutronic capabilities for RELAP5”, Proc.  2012 ICAPP’12, Chicago, Illinois, USA, June 24-28,  (2012). 3.   A. HEBERT “A Consistent Technique for the Pin-by-  Pin Homogenisation of a Pressurized Water Reactor Assembly”, Nucl. Sci. Eng., 113, 227 (1993)4.   U. GRUNDMANN, S. MITTAG “Super-    homogenisation factors in pinwise calculations by the   reactor dynamics code DYN3D”, Annals of Nuclear     Energy, Volume 38, Issue 10, October 2011, Pages      2111–2119 (2011).  

Hot Zero and Full Power Validation of PHISICS RELAP-5 Coupling

LODI, FRANCESCO

SUMINI, MARCO

C. Rabiti

A. Alfonsi

A. Epiney

Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna

PHISICS is a reactor analysis toolkit developed over
the last 3 years at the Idaho National Laboratory. It has
been coupled with the reactor safety analysis code
RELAP5-3D. PHISICS is aimed at providing an optimal
trade off between needed computational resources (in the
range of 10~100 computer processors) and accuracy. In
fact, this range has been identified as the next 5 to 10
years average computational capability available to
nuclear reactor design and optimization nuclear reactor
cores.
Detailed information about the individual modules of
PHISICS can be found in [1]. An overview of the
modules used in this study is given in the next subsection.
Lately, the Idaho National Laboratory gained access plant
data for the first cycle of a PWR, including Hot Zero
Power (HZP) and Hot Full Power (HFP).
This data provides the opportunity to validate the
transport solver, the interpolation capability for mixed
macro and micro cross section and the criticality search
option of the PHISICS pack

F. Lodi

M. Sumini

Archivio della ricerca- Università di Roma La Sapienza

Hot Zero and Full Power Validation of PHISICS RELAP-5 Coupling  F. Lodi*, C. Rabiti**, A. Alfonsi**, A. Epiney**, M. Sumini*  *University of Bologna Dept. Of Industrial Engineering: Via dei Colli, 16 40136 Bologna Italy  **Idaho National Laboratory, 2525 North Fremont Street, Idaho Falls (ID) francesco.lodi2@studio.unibo.it   INTRODUCTION  PHISICS is a reactor analysis toolkit developed over the last 3 years at the Idaho National Laboratory. It has been coupled with the reactor safety analysis code RELAP5-3D. PHISICS is aimed at providing an optimal trade off between needed computational resources (in the range of 10~100 computer processors) and accuracy. In fact, this range has been identified as the next 5 to 10 years average computational capability available to nuclear reactor design and optimization nuclear reactor cores. Detailed information about the individual modules of PHISICS can be found in [1]. An overview of the modules used in this study is given in the next subsection. Lately, the Idaho National Laboratory gained access plant data for the first cycle of a PWR, including Hot Zero Power (HZP) and Hot Full Power (HFP). This data provides the opportunity to validate the transport solver, the interpolation capability for mixed macro and micro cross section and the criticality search option of the PHISICS package. The current paper will first briefly recall the structure of the different PHISICS modules used, then illustrate the modeling process for the PWR HZP/HFP and finally present some preliminary results of this validation effort.  THE PHISICS MODULES USED FOR THE MODELLING  The following sections present the PHSICS toolkit involved in this simulation and a brief description of its capabilities and modules. INSTANT INSTANT [2] is the neutron transport solver. It is based on the spherical harmonics approximation of the angular dependence of the neutron flux. Currently the following nodal spatial meshes are available: Cartesian, hexagonal, and extruded triangle. MIXER The MIXER is tasked to perform the interpolation of the microscopic or macroscopic cross sections. It also generates the macroscopic cross sections used by INSTANT. PHISICS offer a noticeable flexibility in the treatment of cross sections, since both microscopic and macroscopic cross sections can be combined together in the same simulation. Macroscopic cross sections are treated as microscopic ones with the atomic density equal to one. Cross sections can be tabulated for an unbounded number of parameters and an unbounded number of tabulation points for each parameter. The interpolation of the cross sections within the parameter grid is linear. Criticality Search Module The Criticality Search (CS) adjusts isotope densities (user defined) for a specified location in the geometry until a prescribed value of keff is reached (or the densities would be outside user specified boundaries). A classical usage of this module is to search for critical boron concentration, fissile enrichment, or control rod positioning. To speed up the process, the user can also specify whether (in case the concentration of an isotope is also a tabulation parameter) to use just a first order approximation, i.e. the user can specify that a) only the variation in density of the specific isotope impacts the macroscopic cross sections or b) the isotopes (user provided information) need to be re-evaluated to account for the change in the tabulation coordinate. RELAP5 coupling The coupling between RELAP5 and PHISICS allows for thermal-hydraulic feedbacks such as water density, fuel temperature, soluble poisons concentration and control rods positioning.   THE MODELLING APPROACH  Microscopic Cross Section Library Generation Figure 1 shows the core layout indicating the different assembly types (enrichment is given in the legend while the number on each assembly indicates the number of fuel rods with burnable poison). Starting from that layout, a set of 30 libraries has been generated in order to account not only for assembly type but also for neighboring effects. Figure 2 shows the library correspondence to the 2D octant core (circle indicates presence of instrumentation channels). The chosen energy structure involves 8 groups with the following upper bounds: 2.0E+07, 2.2313E+06, 8.2085E+05, 9.11884E+03, 1.3007E+02, 3.9279E+00, 6.2506E-01 and 1.4572E-01 eV. Each fuel library has ~300 isotopes (only 200 are tracked) while each reflector library contains 24 isotopes (all tracked). For the 3D full core analysis, to compare with experimental results, a total of 64 libraries have been used. Other 30 are identical to the ones described but located in a plane with grid spacers, while the remaining 4 are for the axial reflectors (top and bottom). Table 1 reports the tabulation parameters, the number of points and the values for each parameter and the total number of points. The burn-up has been added as an additional tabulation dimension for the HFP only, since for HFP, following the first and second depletion cycle is part of the benchmark (second part).  Figure 1: Core overview  Figure 2: Material placement   Table 1: HZP Tabulation Library Type HZP HFP Boron Tabulation (ppm) 1700, 1150, 1000, 1.0E-06 1150,1000,  1.0E-06 Fuel Temperature (°C) 286.66, 291.66 300,  800, 1300 Moderator Density (kg/m3) 752.705, 733.36  752.705, 733.36 Burn-up (GWd) -- 0.150, 15.0 Tabulation points 16 108 Description of the Boron Modeling The presence of boron both, as burnable poison and in the coolant to control the reactivity swing required some modeling effort, especially due to the direct usage of microscopic cross sections in the simulation. In fact, the boron in the water is not depleted and its density follows both, the water density and the ppm of soluble boron maintained in the water by the plant control system while the boron in the poison locations is burnable. Correct prediction of the critical soluble boron concentration in the water (as a function of moderator temperate and burn-up) is a key value for reactor control.  In order to properly take into account this features in the PHISICS framework, we have generated two cross section sets for the boron in the water and in the burnable absorbers with HELIOS 2. Care needs to be taken since the cross sections generated in this way are normalized with respect the average flux in the water and in the burnable absorbers, while when used in the nodal simulation of the core, the reaction rates are computed using the average assembly fluxes. To eliminate this discrepancy the cross sections have been rescaled using the following formula:               regtotsubregrisoriso  Where r is the reaction type index, iso is the isotope index and the fluxes are representative of (subreg) the sub-region where the homogenization has been made and (regtot) the whole region (usually the one used in the full core calculation for the reactor being considered). Another problem, connected to the soluble boron modeling that had to be addressed, was the water density feedback on its number density. In fact, the atomic density of the born in the water is not only linked to the ppm value but also to the density of the water itself. The macroscopic cross section of the coolant (water + boron) could be written as: SWr = NB(rH2O, ppm)s Br +NH2O(rH2O)sH2Or, where the density of the Boron ( NB ) is a linear function of the ppm value and water density rH2O . Given that none of this two components will be depleted and that the water density and ppm are already tabulation parameters, it is more convenient to use directly the SWr  with unitary densities. In this way, the water density variation computed by RELAP5, given as a feedback to PHISICS, directly impact the effective amount of soluble boron present in the core. The criticality searching, used to find the critical value of the Boron, is then performed on a dummy isotope with ‘zero’ cross sections while SWr  is the only isotope for which the values of the cross section are recomputed at each iteration of the CS.   SPH Factors Calculation        To further improve results, the super-homogenization technique (SPH) [3] can be implemented in order to have reaction rates of the lattice calculation equal to the ones obtained in a 2D nodal representation of the core. SPH could be applied at different levels of resolution; in the present case, SPH factors by assembly and by energy group are used. Generally speaking, the SPH is a non-linear methodology where the unknowns are a) the average fluxes in each assembly computed by the nodal core simulator and b) the cross sections to be used in the nodal simulation. The average assembly core fluxes are provided by the INSTANT solver for a given set of homogenized cross-sections. These values have to be scaled by an unknown common scaling factor. In standard calculation this scaling factor is provided by the power normalization. In the case of the SPH set of equations, this normalization does not provide an additional constraint. In fact, this is equivalent to imposing the sum of all fission rates (volume weighted) to be equal between the lattice and the nodal simulation. This is a linear combination of a part of the second set of equations that are used in the SPH methodology, where all the reaction rates are forced to be the same between the lattice calculation and the nodal core calculation. The additional constraint we decided to use, is given by forcing the neutronic population given by the nodal solution to be equal to the one in the lattice solution. The solution of the non-linear system of equations (nodal core P1 equation, neutron population and reaction rates) is performed using a simple fixed-point scheme described in the following: 1. An initial set of homogenized cross section is used to compute the average assembly fluxes by PHISICS. 2. Normalization of the average fluxes of the core calculation to the ones of the lattice. jgnorm,i =jgijgi,latticeViiågåjgiViiågåæèçççöø÷÷÷ Where i is the region index and g the macro energy group index while V is the region volume. The lattice index identifies the flux of the lattice calculation. 3. Use the new flux to calculate the correction factors α.  agi =jgi,latticejgnorm,iæèççöø÷÷ This can be proved to be equivalent to force the macro reaction rate to be the same in the lattice and core calculation when the cross section are scaled by the factor agi. 4. Correct the cross sections by the factor .  s g,isoi,r ¬agis g,isoi,rs s0,g®g ',isoi,r ¬agis s0,g®g ',isoi,r where the tilde indicates the corrected cross sections, iso is the particular isotope and s0 the zero order of the scattering cross section. Steps 1 to 4 are repeated until convergence is achieved in the correction factors. Special care needs to be taken in dealing with the corrective factors to be applied to the transport cross sections. In fact, the transport cross-section adjustment tries to preserve the assembly leakage rather then a reaction rate. In this case, the right weighting function is not anymore the average scalar flux but one over its gradient cross the assembly. Using the gradient in the 2D plane will lead to a correction coefficient for the transport cross-section that is directional dependent. In the present case, PHISICS (which is based on a coherent spherical harmonics approximation) does not use the transport cross sections but the effect is emulated by altering the within group anisotropic scattering cross section as suggested in [4]. As a result the SPH factor for the s s1,g®g,isoi  is computed as follows:  Point 3 in the above iteration scheme is replaced by: iggsigTigiggsigigT   ,1,,1,~1 where this formula implicitly defines the correction factor.  Point 4 in the above iteration scheme is replaced by: iggsigiisoggs   ,1,,1~   where s T ,gi is the total cross section. Currently, the out-scattering anisotropic cross sections are left unchanged. Even if this approach converges and gives satisfactory results using the P1 approximation in the core simulation, the correction on the border assemblies and especially in the reflector can become significant because of the simplification used in the preservation of the leakage that is a dominant effect in these regions. Besides that, the general accuracy of the calculation can be considerably increased by using the SPH factors.   RESULTS  The SPH correction has been performed for only one tabulation point and then applied to the whole library. The approximation is acceptable if for different points of the tabulation the relative magnitude of the fluxes in space and energy are reasonably preserved. The final corrective factors averaged over energy for the HZP and HFP conditions are shown in Table 2 with also the reaction rate relative errors averaged over energies are shown in Table 3. As can be seen from the errors, acceptable convergence can be reached with a reasonable amount of iterations (between 10 and 20).      Table 2: SPH factors energy averaged and relative error  Material  Factors Error HZP HFP HZP HFP 1 0.94361 0.93266 1.4676E-02 1.5996E-02 2 0.91596 0.90558 1.4745E-02 1.5869E-02 3 0.92790 0.91873 1.4676E-02 1.5855E-02 4 0.91999 0.91254 1.4811E-02 1.5924E-02 5 0.90693 0.89993 1.4810E-02 1.5924E-02 6 0.92096 0.91640 1.4858E-02 1.6028E-02 7 0.90775 0.90336 1.4885E-02 1.6106E-02 8 0.92601 0.92361 1.4934E-02 1.6159E-02 9 0.91644 0.91497 1.5178E-02 1.6235E-02 10 0.94211 0.94568 1.5404E-02 1.6249E-02 11 0.92309 0.92333 1.5162E-02 1.6323E-02 12 0.93664 0.94043 1.5307E-02 1.6386E-02 13 0.93858 0.94734 1.5767E-02 1.6628E-02 14 0.99478 1.01220 1.6194E-02 1.6509E-02 15 0.95501 0.95933 1.5604E-02 1.6438E-02 16 0.96671 0.97303 1.5524E-02 1.6475E-02 17 0.96837 0.97675 1.5797E-02 1.6575E-02 18 0.97240 0.98753 1.5956E-02 1.6653E-02 19 0.95972 0.97865 1.6489E-02 1.6588E-02 20 1.07209 1.09028 1.6747E-02 1.6465E-02 21 0.99968 1.01190 1.6330E-02 1.6645E-02 22 0.96904 0.97928 1.6376E-02 1.6610E-02 23 0.99895 1.01304 1.6252E-02 1.5996E-02 24 1.05531 1.06646 1.6379E-02 1.5869E-02 25 1.13983 1.14627 1.6160E-02 1.5855E-02 26 1.19367 1.19248 1.5873E-02 1.5924E-02 27 1.14728 1.14730 1.6452E-02 1.5924E-02 28 1.15148 1.15189 1.6499E-02 1.6028E-02 29 1.24804 1.23865 1.5950E-02 1.6106E-02 Reflector 1.80192 1.67313 1.4449E-02 1.6159E-02      The corresponding power distributions are shown in Figures 3 and 4.      The same SPH technique has been applied to the grid spacer planes libraries while for the axial reflector the same factors for the radial one have been used.      Table 3 summarizes the differences between the nodal core simulation versus the 2D lattice calculation and experimental results for keff and the critical boron concentration. For the 3D calculation, a total of 64 libraries have been used. The same SPH technique has been applied to the grid spacer planes libraries while for the axial reflector the same factors for the radial one have been used.  Table 3: difference in 2D (code to code) and 3D (experimental to code) Reference PHISICS (PHISICS-Reference) Critical Boron (ppm) Keff (pcm) 2D HELIOS (HZP) Not calculated 127 3D Experimental (HZP) 34 406 3D Experimental (HFP) 30 355 Figure  3: HZP power distribution after SPH correction  Figure  4: HFP power distribution after SPH correction    This initial attempt to model a realistic PWR core with the PHISICS package reveals a good robustness of the code and its flexibility for multiple usages. Results compare in a satisfactory way with experimental results and further improvements are possible and considered for the second part of the benchmark, when the simulation and comparison with operational data will be performed over two reactor cycles.  ENDNOTES This work is supported by the U.S. Department of Energy, under DOE Idaho Operations Office Contract DE-AC07-05ID14517. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. This work was also supported by the University of Bologna thanks to its collaboration with INL for further developing the PHISICS modules capabilities.    REFERENCES   1. C. RABITI, Y. WANG, G. PALMIOTTI, H. HIRUTA,J. COGLIATI, A. ALFONSI, A. EPINEY, T. GRIMMET “PHISICS: New Features and Advancements”, 2011 Annual Winter Meeting, Washington, D. C., USA, October 30-November 3 (2011). 2.    A. EPINEY, C. RABITI, A. ALFONSI, Y WANG, J.        COGLIATI, G. STRYDOM “PHISICS multi-group         transport neutronic capabilities for RELAP5”, Proc.        2012 ICAPP’12, Chicago, Illinois, USA, June 24-28,         (2012). 3.   A. HEBERT “A Consistent Technique for the Pin-by-       Pin Homogenisation of a Pressurized Water Reactor       Assembly”, Nucl. Sci. Eng., 113, 227 (1993) 4.   U. GRUNDMANN, S. MITTAG “Super-         homogenisation factors in pinwise calculations by the        reactor dynamics code DYN3D”, Annals of Nuclear       Energy, Volume 38, Issue 10, October 2011, Pages          2111–2119 (2011).      

https://iris.uniroma1.it/bitstream/11573/541750/1/Lodi_Hot_2013.pdf

Hot Zero and Full Power Validation of PHISICS RELAP-5 Coupling

Abstract

Similar works

Full text

Available Versions

UNT Digital Library

Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna

Archivio della ricerca- Università di Roma La Sapienza