CITATION Codes Research Articles

Analysis of core life-time and neutronic parameters for HEU and potential LEU/MEU fuels in a typical MNSR

For the standard HEU and various potential LEU and MEU cores of MNSR systems, a comparative neutronic study has been carried out using the cluster option in the WIMS-D/4 and RZ-model in the CITATION code. For the HEU core, the computed values of excess reactivity, control rod worth, shutdown margin and the value of equilibrium xenon worth are in good agreement with the corresponding values found in literature. The 235U enrichment required for the LEU UO2–Zr core found as 12.5% is in good agreement with the 12.6% found in literature. Compared with 1100g total uranium loading for the HEU core, the corresponding requirement for UO2, U3Si–Al, U3Si2–Al and U–9Mo–Al cores have been found as 10733.5, 6319, 5515 and 7549g respectively. For the HEU core, the computed 18.98mk value of the total worth of top Be shim plates is in good agreement with the corresponding experimental value of 18.5mk reported in FSAR. The corresponding computed values for LEU and MEU cores are 17.28mk for UO2–Zr fuel, 17.47mk for UO2–Al, 18.37mk for U3Si2–Al. Compared with 21.2year value for the HEU core, 30.6years cycle length for UO2–Zr LEU core has been found.

Benchmark analysis of SPERT IV reactor

Benchmark calculations have been performed for SPERT IV D-12/25 core. Experimental data of the core was provided by International Atomic Energy Agency (IAEA). Combination of WIMS/D4 and CITATION codes has been used for performing the neutronic analysis of the reactor. Lattice calculations have been performed through WIMS/D4 while 3-dimensional reactor core has been modeled in CITATION. Ten energy groups were considered for these calculations. Energy wise microscopic cross-sections were generated for fuel, control absorber, control follower, guide tube, grid plate, reflector and structural regions separately of the core using WIMS/D4. Thermal neutron flux profiles at different axial and radial locations of the core were evaluated. Critical position of the control rods, excess reactivity, shut down margin, control rod worth, reactivity feed back coefficients and kinetic parameters of the core were estimated. Reasonable agreement has been found between experimentally determined and the calculated parameters.

Kinetic parameters evaluation of PWRs using static cell and core calculation codes

In this paper, evaluation of the kinetic parameters (effective delayed neutron fraction and prompt neutron lifetime) in PWRs, using static cell and core calculation codes, is reported. A new software has been developed to link the WIMS, BORGES and CITATION codes in Visual C# computer programming language. Using the WIMS cell calculation code, multigroup microscopic cross-sections and number densities of different materials can be generated in a binary file. By the use of BORGES code, these binary-form cross-sections and number densities are converted to a format readable by the CITATION core calculation code, by which the kinetic parameters can be finally obtained. This software is used for calculation of the kinetic parameters in a typical VVER-1000 and NOK Beznau reactor. The ratios ( β eff ) i ( β eff ) core , which are the important input data for the reactivity accident analysis, are also calculated. Benchmarking of the results against the final safety analysis report (FSAR) of the aforementioned reactors shows very good agreements with these published documents.

Investigation of burnable poisons effects in reactor core design

Burnable absorber rods (BAR) and chemical shim are the main control poisons that are used in the core for improving the reactor behavior and satisfying the safety criteria during the core life time. These poisons have several constraints, criteria, advantages and also disadvantages from the safety and operation points of view; and these characteristics depend on the concentration and distribution of mentioned poisons in the reactor core. Therefore, understanding their effects on the reactor core behavior, especially the mutual interaction between them, is a crucial issue in reactor core design procedure. In this study, the influences of the burnable poisons on the main parameters of the reactor such as multiplication factor, burnup, soluble poison concentration, moderator temperature coefficient and power peaking factor over the reactor life time are investigated. The VVER-1000 reactor was selected for this investigation. The reactor core was modeled by WIMS and CITATION codes. Several different loading patterns based on different distributions and concentrations of BARs were defined. Subsequently, the main parameters of the core for each pattern were calculated by the core model and were investigated to analyze the effects of BAR concentration and distribution on the reactor behavior. The presented results made it possible to analyze and understand the BAR and chemical shims effects on the behavior of the nuclear reactor core.

Effects of various spacer grid modeling on the neutronic parameters of the VVER-1000 reactor

The main objective of this paper is to study the effects of various spacer grid models on the neutronic parameters of a VVER-1000 reactor. Specifically, the data of the nuclear power plant at the Bushehr site, which is of a VVER-1000 type, will be studied. Three models, representing the spacer grids along the fuel assemblies are presented. These three models are the homogeneous and the heterogeneous local spacer grid models and the shroud spacer grid model. In the homogeneous and the heterogeneous models, the spacer grids are considered at their actual locations in the axial direction. The only difference between the two models is that in the homogeneous model, the spacer grids are homogenized with the coolant while in the heterogeneous model, the spacer grids are modeled around the fuel cells at their exact axial positions. In the shroud model, the spacer grids are modeled in the shroud region containing the coolant and are not necessarily placed at their appropriate axial positions. The aforementioned models and the core geometry are modeled in 3-D hexagonal geometry and solved by the CITATION code. The required cross sections are obtained from the WIMS code using the associated ENDF/B-7 based library. The visual FORTRAN programming 90 is used for analysis of the whole calculation process and provides a sophisticated link between the WIMS and the CITATION codes during core cycle burnup. The core excess reactivity and the critical boron concentration of the reactor are calculated at normal operating state. In addition, the changes in the critical boron concentration and power peaking factors during the first core cycle, for the homogeneous and shroud models are also predicted. The core calculation analysis is done for the core with fully withdrawn control rods. As will be shown, the heterogeneous model, which is a close representation of the actual case, provides a more accurate result than the homogeneous and the shroud models. However, the heterogeneous model is complicated as compared to the other two models. Therefore, the choice of which model to use depends on the accuracy required by the user.

Time dependent burn-up and fission products inventory calculations in the discharged fuel of the Syrian MNSR

The Syrian Miniature Neutron Source Reactor (MNSR), a 30 kW, 89.8% HEU fueled (U-Al), went critical in March, 1996. By operating the reactor at nominal power for 2.5 h/day, the estimated core life is 10 years. This paper presents the results of fuel burn-up and depletion analysis of the MNSR fuel lattice using the ORIGEN 2 code. A one-group cross-section data base for the ORIGEN 2 computer code was developed for the Syrian MNSR research reactor. The ORIGEN 2 predicted burn-up dependent actinide compositions of MNSR spent fuel using the newly developed data base show a good agreement with the published results in the literature. In addition, the burn-up characteristics of MNSR spent fuel was analyzed with the new data base. Finally, to study the effect of burn-up on the reactivity, the microscopic cross-sections of the fission products calculated by the WlMS code (using the number densities of fission products generated by the ORIGEN 2 code as a function of burn-up time), were used as an input for the CITATION code calculations. The results contained in this paper could be used in performing criticality safety analysis and shielding calculations for the design of a spent fuel storage cask for the MNSR core.

Design and implementation of a relational database of macroscopic cross-sections for steady-state and transient analysis in a medium sized PWR

This paper deals with the design and implementation of a relational database of macroscopic cross-sections as well as validation and its usage as a component in steady-state and transient analysis. These types of analysis are definitely designated as data-driven processes in which their behavior is changed based on data. The data in this manner can be the variation of fuel composition density as well as the fuel temperature during the reactor operation or in some accidents. In order to gain the accurate results in transient analysis, applying these variations is inevitable. Therefore, for each changing in fuel behavior, the new set of macroscopic cross-sections must be reproduced by performing the lattice calculations at run-time. During recent years some approaches have been done in both academic and commercial areas to take advantage of already calculated cross-sections instead of recalculate them by lattice codes during the analysis. Using this approach leverages the computation performance by reducing the floating point operations which can decrease the CPU load as well as the calculation time. Although this approach delivers a good performance in terms of time and computation, when a large number of fuel or reactor core circumstances are subjected to be analyzed the accuracy is became an important point. In this situation the cross-sections for all expected conditions must be already calculated. This cause the large number of cross-section data which must be stored and managed somehow. The system applied in this study to store and manage these cross-section data sets is a relational database management system (RDBMS) which is based on Microsoft SQL Server 2008 Management System. The node wise macroscopic cross-sections for each nominal and off-nominal of a typical medium sized PWR reactor core conditions which are calculated by WIMS-D5 and CITATION codes are tabulated in this system and can be retrieved by structured query language extremely rapid on demand.

A spatial kinetic model for simulating VVER-1000 start-up transient

An accurate prediction of reactor core behavior in transients depends on how much it could be possible to exactly determine the thermal feedbacks of the core elements such as fuel, clad and coolant. In short time transients, results of these feedbacks directly affect the reactor power and determine the reactor response. Such transients are commonly happened during the start-up process which makes it necessary to carefully evaluate the detail of process. Hence this research evaluates a short time transient occurring during the start up of VVER-1000 reactor. The reactor power was tracked using the point kinetic equations from HZP state (100 W) to 612 kW. Final power (612 kW) was achieved by withdrawing control rods and resultant excess reactivity was set into dynamic equations to calculate the reactor power. Since reactivity is the most important part in the point kinetic equations, using a Lumped Parameter (LP) approximation, energy balance equations were solved in different zones of the core. After determining temperature and total reactivity related to feedbacks in each time step, the exact value of reactivity is obtained and is inserted into point kinetic equations. In reactor core each zone has a specific temperature and its corresponding thermal feedback. To decrease the effects of point kinetic approximations, these partial feedbacks in different zones are superposed to show an accurate model of reactor core dynamics. In this manner the reactor point kinetic can be extended to the whole reactor core which means “Reactor spatial kinetic”. All required group constants in calculations are prepared using the WIMS code. In addition CITATION code was used to calculate the flux, power distribution and core reactivity inside the core. To update the last change in group constants and resultant reactivity in point kinetic equations, these neutronic codes were coupled with a developed dynamic program. This study is applied on a typical VVER-1000 reactor core to show the reactor response in short time transients caused during start-up procedure.

Effect of mesh grid size on the accuracy of deterministic VVER-1000 core calculations

Numerical solutions based on finite-difference method require the domain in the problem to be divided into a number of nodes in the form of triangles, rectangular, and so on. To apply the finite-difference method in reactor physics for solving the diffusion equation with satisfactory accuracy, the distance between adjacent mesh-points should be small in comparison with a neutron mean free path. In this regard the effect of number of mesh points on the accuracy and computation time have been investigated using the VVER-1000 reactor of Bushehr NPP as an example, and utilizing WIMS and CITATION codes. The best results obtained in this study belong to meshing models with higher numbers of mesh-points in both radial and axial directions of the reactor core.

Dependence of control rod worth on fuel burnup

One important parameter in the design and the analysis of a nuclear reactor core is the reactivity worth of the control rods, i.e. their efficiency to absorb excess reactivity. The control rod worth is affected by parameters such as the fuel burnup in the rod vicinity, the Xe concentration in the core, the operational time of the rod and its position in the core. In the present work, two different computational approaches, a deterministic and a stochastic one, were used for the determination of the rods worth dependence on the fuel burnup level and the Xe concentration level in a conceptual, symmetric reactor core, based on the MTR fuel assemblies used in the Greek Research Reactor (GRR-1). For the deterministic approach the neutronics code system composed by the SCALE modules NITAWL and XSDRN and the diffusion code CITATION was used, while for the stochastic one the Monte Carlo code TRIPOLI was applied. The study showed that when Xe is present in the core, the rods worth is significantly reduced, while the rod worth variation with increasing burnup depends on the rods position in the core grid. The rod worth obtained with the use of the Monte Carlo code is higher than the one obtained from the deterministic code.

Neutronic Analysis of Generic Heavy Water Research Reactor Core Parameters to Use Standard Hydride Fuel

This research presents neutronic calculations for heavy water research reactor core substituting hydride fuel for uranium dioxide fuel. The aim of this research is feasibility analysis of reactor utilization with its original design using a new proposed fuel and changing the coolant and moderator circuit to light water. The required group constants for the CITATION code will be calculated using WIMSD-4 code. Neutronic calculations such as multiplication factors, radial and axial power peaking factor and fuel burn-up calculations are carried out by the CITATION code.

Comparison between triangular and hexagonal modeling of a hexagonal-structured reactor core using box method

A hexagonal-structured reactor core (e.g. VVER-type) is mostly modeled by structured triangular and hexagonal mesh zones. Although both the triangular and hexagonal models give good approximations over the neutronic calculation of the core, there are some differences between them that seem necessary to be clarified. For this purpose, the neutronic calculations of a hexagonal-structured reactor core have to be performed using the structured triangular and hexagonal meshes based on box method of discretisation and then the results of two models should be benchmarked in different cases. In this paper, the box method of discretisation is derived for triangular and hexagonal meshes. Then, two 2-D 2-group static simulators for triangular and hexagonal geometries (called TRIDIF-2 and HEXDIF-2, respectively) are developed using the box method. The results are benchmarked against the well-known CITATION computer code in case of a VVER-1000 reactor core. Furthermore, the relative powers calculated by the TRIDIF-2 and HEXDIF-2 along with the ones obtained by the CITATION code are compared with the verified results which have been presented in the Final Safety Analysis Report (FSAR) of the aforementioned reactor. Different benchmark cases revealed the reliability of the box method in contrast with the CITATION code. Furthermore, it is shown that the triangular modeling of the core is more acceptable compared with the hexagonal one.

Introducing and validating a new method for coupling neutronic and thermal-hydraulic calculations

In this study, a new and innovative method is introduced for analyzing neutronic and thermal-hydraulic calculation. For this aim, VVR-S research reactor was selected, and the calculation procedure was performed for it. WIMS, CITATION and COBRA-EN codes were used for investigation. Calculation model consists of two sub-models: neutronic and thermo-hydraulic. The neutronic model uses WIMS and CITATION codes for neutronic simulation of the reactor core and calculating flux and power distribution over it. WIMS code simulates the fuel assemblies and CITATION models the core. The thermal-hydraulic model uses COBRA-EN code for performing the relative calculation. In this study, FORTRAN 90 program is used for linking two sub-models and performing the calculation. The proposed procedure is performed for VVR-S analysis and finally, the obtained results are compared with the experimental results that show good agreement with it.

Fuel management optimization based on power profile by Cellular Automata

Fuel management in PWR nuclear reactors is comprised of a collection of principles and practices required for the planning, scheduling, refueling, and safe operation of nuclear power plants to minimize the total plant and system energy costs to the extent possible. Despite remarkable advancements in optimization procedures, inherent complexities in nuclear reactor structure and strong inter-dependency among the fundamental parameters of the core make it necessary to evaluate the most efficient arrangement of the core. Several patterns have been presented so far to determine the best configuration of fuels in the reactor core by emphasis on minimizing the local power peaking factor ( P q ). In this research, a new strategy for optimizing the fuel arrangements in a VVER-1000 reactor core is developed while lowering the P q is considered as the main target. For this purpose, a Fuel Quality Factor, Z( r), served to depict the reactor core pattern. Mapping to ideal pattern is tracked over the optimization procedure in which the ideal pattern is prepared with considering the Z( r) constraints and their effects on flux and P q uniformity. For finding the best configuration corresponding to the desired pattern, Cellular Automata (CA) is applied as a powerful and reliable tool on optimization procedure. To obtain the Z( r) constraints, the MCNP code was used and core calculations were performed by WIMS and CITATION codes. The results are compared with the predictions of a Neural Network as a smart optimization method, and the Final Safety Analysis Report (FSAR) as a reference proposed by the designer.

Experimental and operational validation of burn-up calculations for the Syrian MNSR

The calculation of the uranium-235 burn-up in the Syrian Miniature Research Reactor was conducted in this paper using the WIMS-D/4 and CITATION codes. The uranium-235 burn-up was measured experimentally using the measured photoneutron flux in the Be reflector of MNSR subcritical state as well. Good agreements were obtained between the calculated and measured results. The results of the CITATION code were more accurate compared with the results of WIMS-D/4 code. The maximum relative difference between the WIMS-D/4 code and experimental results was 28%, while the maximum relative difference between the CITATION code and measured results was 5%.

SHTV, as a technique for core calculation using spatial homogenization and temperature variation

The accuracy of static neutronic parameters in the nuclear reactors depends upon the determination of group constants of the diffusion equation in the desired geometry. Although several methods have been proposed for calculating these parameters, there is still the need for more reliable methods. In this paper a powerful and innovative method based on Spatial Homogenization and Temperature Variation (SHTV) of physical properties of a WWER-1000 nuclear reactor core for calculating the relative power distribution of Fuel Assemblies (FA) and the hot fuel rod, is presented. The method is based on replacing the heterogeneous lattices of materials with different properties by an equivalent homogeneous mixture of these material for determining the few group constants, while the effect of temperature variation in the fuel and coolant density along the axial core direction is considered. All calculations are performed using WIMS and CITATION codes. The obtained results are compared with the results of Final Safety Analysis Report (FSAR) prepared by the designer, and good agreement between the two results is shown.

The use of WIMS and CITATION codes in fuel loading required for the conversion of HEU MNSR core to LEU

The Nigerian Research Reactor-1 (NIRR-1) falls in the category of Miniature Neutron Source Reactors (MNSR) using a fuel of 90% HEU. It is therefore desirable to convert it from this enrichment to LEU (less than 20%) in conformity with the new global trend of making research reactor fuel as unattractive as possible to groups that may be interested in using such highly enriched cores for non-peaceful purposes. In this work, we have developed a computational scheme based on WIMS and CITATION that would theoretically achieve this objective as easily as possible. The scheme systematically reduces the enrichment from 90% (or any other initial values) to less than 20% in steps of 5% or any desired percentage variation. Two fuel types (UAl 4 and UO 2) are considered in here, while maintaining the size and geometry of the core as well as the excess reactivity (between 3.5 and 4 mk). Our results show that the U-235 loading increases sharply as enrichment decreases. It has also been noticed that at 5% enrichment the fuel loading for both types is 2505 g. However, at 90% enrichment, the loading drops sharply to 998 g for UAl 4 fuel and 946 g for UO 2 fuel. Below the enrichment of 5%, the operation of NIRR-1 with both fuel types can be considered unrealistic as this requires structural adjustment which the work tries to maintain constant.

Xenon transient simulation of the VVER-1000 nuclear reactor using adiabatic approximation

The neutronic behavior of very slow transients like fuel burn up and xenon studies can be performed with the sequence of instantaneous criticality calculations. Such a scheme is known as the adiabatic approximation. 135Xe as a fission product has an enormous thermal absorption cross section, on the order of a million barns, therefore the study of xenon poisoning and its effect on flux and power distribution is very important in thermal reactors. In this work xenon transient analysis of the VVER-1000 nuclear reactor and its effect on the flux and power distribution from reactor start up to xenon saturation and the change of power from nominal to 25% of nominal is carried out using WIMS and CITATION codes. We used the WIMS cell calculation code and found some relations between xenon concentration and group constants of different FA (Fuel Assemblies); in this way we bypassed the WIMS running at each time step. Also, the CITATION code is used as a core calculation code to find the effective multiplication factor as well as flux and power distributions. In order to link WIMS and CITATION codes and facilitate numerous executions, a VISUAL BASIC program has been developed. The results have a good agreement with the safety analysis report of the reference plant such that the relative differences in most cases are less than 10%.

Modified COBRA-EN code to investigate thermal-hydraulic analysis of the Iranian VVER-1000 core

Thermal-hydraulic analysis of a typical VVER-1000 core at steady-state condition, using COBRA-EN code, is presented herein. Required power distribution was computed by the WIMS-D4 and CITATION codes based on the neutronic calculations. Maximum and average fuel temperature, enthalpy, void fraction, coolant temperature and density, coolant mass flow rate and pressure drop are calculated using EPRI model. Thermal-hydraulic calculations of the most rated channel which is determined based on neutronic calculations results in temperature, enthalpy, critical heat flux and minimum DNBR (MDNBR) of the core hottest channel are investigated. The COBRA-EN code is modified in order to make a thermal-hydraulic analysis for the VVER reactor, and this is the main objective of the present article. Our results are compared with analytical approaches and the reactor FSAR.

Properties of the United States Code Citation Network

The United States Code (Code) is an important source of Federal law that is produced by the interactions of many heterogeneous actors in a complex, dynamic space. The Code can be represented as the union of a hierarchical network and a citation network over the vertices representing the language of the Code. In this paper, we investigate the properties of the Code’s citation network by examining the directed degree distributions of the network. We find that the power-law model is a plausible fit for the outdegree distribution but not for the indegree distribution. In order to better understand this result, we construct a model with the assumption that the probability of citation is a per-word rate. We calculate the adjusted degree of each vertex under this model and study the directed adjusted degree distributions. These adjusted degree distributions indicate that both the adjusted indegree and outdegree distributions seems to follow a log-normal form, not a power-law form. Our findings indicate that the power-law is not generally applicable to degree distributions within the United States Code but that the distribution of degree per word is well-described by a log-normal model.