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.     

Neutronics Experiments of D-T Fast Neutrons by Application of Associated Particle Method

A probabilistic method is proposed that will permit in the design stage to estimate quantitatively the likelihood with which any or all design criteria applicable to a nuclear reactor are actually satisfied after its construction. The method is trially applied to the core reactivity balance problem of the experimental Very High Temperature Reactor, and calculations are performed on the probability with which a design study core will, upon construction, satisfy design criteria concerning (a) one rod stuck and (b) startup margin. The method should prove useful in making engineering judgments before approving reactor core design.     

Direct deterministic method for neutronics analysis and computation of asymptotic burnup distribution in a recirculating pebble-bed reactor

A new deterministic method has been developed for the neutronics analysis of a pebble-bed reactor (PBR). The method accounts for the flow of pebbles explicitly and couples the flow to the neutronics. The method allows modeling of once-through cycles as well as cycles in which pebbles are recirculated through the core an arbitrary number of times. This new work is distinguished from older methods by the systematically semi-analytical approach it takes. In particular, whereas older methods use the finite-difference approach (or an equivalent one) for the discretization and the solution of the burnup equation, the present work integrates the relevant differential equation analytically in discrete and complementary sub-domains of the reactor. Like some of the finite-difference codes, the new method obtains the asymptotic fuel-loading pattern directly, without modeling any intermediate loading pattern. This is a significant advantage for the design and optimization of the asymptotic fuel-loading pattern. The new method is capable of modeling directly both the once-through-then-out fuel cycle and the pebble recirculating fuel cycle. Although it currently includes a finite-difference neutronics solver, the new method has been implemented into a modular code that incorporates the framework for the future coupling to an efficient solver such as a nodal method and to modern cross section preparation capabilities. In its current state, the deterministic method presented here is capable of quick and efficient design and optimization calculations for the in-core PBR fuel cycle. The method can also be used as a practical “scoping” tool. It could, for example, be applied to determine the potential of the PBR for resisting nuclear-weapons proliferation and to optimize proliferation-resistant features. However, the purpose of this paper is to show that the method itself is viable. Refinements to the code are under way, with the objective of producing a powerful reactor physics analysis tool for PBRs.     

Development of a Method for Evaluation of Pin-wise Power Distribution in Fuel Assemblies of Fast Reactors

In the design of fast reactor core with higher burnup and higher linear power, prediction accuracy of burnup history of fuel pin should be upgraded so as to assure fuel integrity without extra design margin under increased neutron fluence and burnup. A method is studied to predict fuel pin-wise power and its burnup history in fast reactors accurately based on an analytic solution of diffusion theory equation on hexagonal geometry with boundary condition from core calculation by finite-differenced diffusion calculation code. The present method is applied to a fast reactor core model, and its accuracy in predicting fuel pin power is tested. The result is compared with the reference solution by the finite difference calculation with very fine mesh. It is found that the present method predicts the power peaking factors in fuel assemblies accurately. The fuel pin-wise nuclide depletion calculation is also done using neutron fluxes for each fuel pin. The result shows that the fuel pin-wise depletion calculation is very important in predicting the burnup history of the fuel assembly in detail.     

Efficient code system of core characteristics for small cylindrical thermal reactor

A new code system for the overall neutronic calculation of a thermal reactor by a simple and effective way is presented. The code covers microscopic library compilation, macroscopic constant generation, cell calculations by multi-group treatment for neutron transport equation and core calculations over three zones for fuel and one zone for moderator. The Dancoff correction factor required in the interpolation of the self-shielding factors of resonance nuclides is automatically calculated by the installed collision probability routines. The burn-up calculation and Garrison and Ross model of fission product have been included. Also the effect of control rod on the reactivity of the reactor with special treatment for the control rod based on the homogenization technique has been included. Making a comparison with SRAC95 code system has checked the adopted code.     

Calculation of fuel burnup and radionuclide inventory in the Syrian miniature neutron source reactor using the GETERA code

Calculations of the fuel burnup and radionuclide inventory in the Syrian miniature neutron source reactor (MNSR) after 10 years (the reactor core expected life) of the reactor operation time are presented in this paper using the GETERA code. The code is used to calculate the fuel group constants and the infinite multiplication factor versus the reactor operating time for 10, 20, and 30 kW operating power levels. The amounts of uranium burntup and plutonium produced in the reactor core, the concentrations and radionuclides of the most important fission products and actinide radionuclides accumulated in the reactor core, and the total radioactivity of the reactor core were calculated using the GETERA code as well. It is found that the GETERA code is better than the WIMSD4 code for the fuel burnup calculation in the MNSR reactor since it is newer, has a bigger library of isotopes, and is more accurate.     

Experimental examinations of the 2D-thermal-hydraulic code FRECON for single phase natural convection flows in complex structures

An experimental program for the verification of the 2D-thermal-hydraulic code FRECON is being carried out. This code serves for the simulation of single phase natural convective flows in complex structures. As a special application it has already been used in the analyses of severe LWR accidents. For this, the code has been coupled with the KESS code system describing the core behaviour during such an accident. While strong improvements have been reached meanwhile concerning the FRECON code itself as well as its application to the reactor problem, experimental verification has not yet been performed. Such a verification is strongly required because of the basic assumption of a quasi-continuum approach for the solid structures in FRECON and the problem of describing local characteristic properties of the structures within this approach.In contrast to integral experiments aiming to simulate the real reactor situation as closely as possible, the present experiments aim to check specific structures and aspects in detail. Thus, in a first step, natural convective flows in a rod bundle with imposed solid temperature profiles are being analysed. In addition to temperature measurements in the solid as well as in the gas, the flow patterns are visualized by means of light-weight glass spheres as tracers, illuminated with a laser-light-sheet. After recording the tracers by a video system the analysis of the flow patterns is made either directly at the TV-monitor or by using the digital image processing technique PIDV (Particle Image Displacement Velocimetry). First comparisons between code calculations and experimental results support the code development in general, but need further refinement.     

Finite element spherical harmonics (PN) solutions of the three-dimensional Takeda benchmark problems

A set of multi-group eigenvalue (K_eff) benchmark problems in three-dimensional homogenised reactor core configurations have been solved using the deterministic finite element transport theory code EVENT and the Monte Carlo code MCNP4C. The principal aim of this work is to qualify numerical methods and algorithms implemented in EVENT. The benchmark problems were compiled and published by the Nuclear Data Agency (OECD/NEACRP) and represent three-dimensional realistic reactor cores which provide a framework in which computer codes employing different numerical methods can be tested. This is an important step that ought to be taken (in our view) before any code system can be confidently applied to sensitive problems in nuclear criticality and reactor core calculations. This paper presents EVENT diffusion theory (P₁) approximation to the neutron transport equation and spherical harmonics transport theory solutions (P₃–P₉) to three benchmark problems with comparison against the widely used and accepted Monte Carlo code MCNP4C. In most cases, discrete ordinates transport theory (S_N) solutions which are already available and published have also been presented. The effective multiplication factors (K_eff) obtained from transport theory EVENT calculations using an adequate spatial mesh and spherical harmonics approximation to represent the angular flux for all benchmark problems have been estimated within 0.1% (100 pcm) of the MCNP4C predictions. All EVENT predictions were within the three standard deviation uncertainty of the MCNP4C predictions. Regionwise and pointwise multi-group neutron scalar fluxes have also been calculated using the EVENT code and compared against MCNP4C predictions with satisfactory agreements. As a result of this study, it is shown that multi-group reactor core/criticality problems can be accurately solved using the three-dimensional deterministic finite element spherical harmonics code EVENT.     

Simulation of MCCI with the TOLBIAC-ICB code based on the phase segregation model

In the event of a severe accident in a pressurized water reactor, corium, a mixture of molten materials issued from the fuel, cladding and structural elements, appears in the reactor core. In some circumstances, corium is likely to melt through the reactor pressure vessel and spread over the concrete basemat of the reactor pit. Molten core concrete interaction (MCCI) then occurs. The main question that has to be addressed in this scenario is whether and when the corium will make its way through the basemat. For some years, CEA is developing a numerical code named TOLBIAC-ICB in order to simulate molten core concrete interaction in reactor case. The general approach used in this code is based on the phase segregation model developed by CEA. The solid phase is supposed to be located at the corium pool boundaries as a solid crust composed of refractory oxides, whereas the corium pool contains no solid. The interfacial temperature between the crust and the pool is the liquidus temperature calculated with the composition of the pool. The interaction between thermalhydraulics (mass and energy balances) and physico-chemistry (liquidus temperature, crust composition, chemical reaction) is modelled through a coupling between TOLBIAC-ICB and the GEMINI code for the determination of the physico-chemistry variables. The main purpose of this paper is to present the modelling used in TOLBIAC-ICB and some validation calculations using the data of experiments available in the literature.     

DERMAGA – An alternative tool to generate random patterned-channel-age in CANDU fuel management analyses part I: Method development

In any reactor physics analysis, the instantaneous power distribution in the reactor core of any power reactor, including CANDU-type reactor, can be calculated when the actual bundle-wise burnup distribution is known. Considering the fact that CANDU utilizes the on-power refuelling to compensate for the reduction in reactivity due to fuel burnup, in the CANDU fuel management analysis, snapshots of power and burnup distributions can be obtained by simulating and tracking reactor operation over an extended period using various tools such as the *SIMULATE module of the reactor fuelling simulation program (RFSP) code. However, for some studies, such as an evaluation of a conceptual design of a next generation CANDU reactor, the preferred approach to obtain a snapshot of the power distribution in the core is based on the patterned-channel-age model implemented in the *INSTANTAN module of the RFSP code. The objective of this approach is to obtain a representative snapshot of core conditions quickly. Presently such patterns could be generated by a program called RANDIS which is implemented within the *INSTANTAN module. Presented in this paper is an alternative approach to derive the patterned-channel-age model where an optimization algorithm is utilized to find patterns which produce representative power distributions in the core. In the present analysis, the genetic algorithm (GA) technique has been successfully utilized to find a quasi-optimal patterned-channel-age. This paper is Part I of a two-part paper which highlights the development of this alternative method for generating patterned-channel-ages.     

New genetic algorithms (GA) to optimize PWR reactors: Part III: The Haling power depletion method for in-core fuel management analysis

The Haling Power Distribution (HPD) has been applied in a unique process to greatly accelerate the in-core fuel management optimization calculations. These calculations involve; the arrangement of fuel assemblies (FAs) and the placement of Burnable Poisons (BPs) in the fresh FAs. The HPD deals only with the arrangement of FAs. The purpose of this paper is to describe past uses of the HPD, provide an example selected from many similar calculations to explain why and how it can be used, and also to show its effectiveness as a filter in the GARCO GA code. The GARCO (Genetic Algorithm Reactor Core Optimization) is an innovative GA code that was developed by modifying the classical representation of the genotype and GA operators. A reactor physics code evaluates the LPs in the population using the HPD Method, which rapidly depletes the core in a single depletion step with a constant power distribution. The HPD is used basically in GARCO as a filter to eliminate invalid LPs created by the genetic operators, to choose a reference LP for BP optimization, and to create an initial population for simultaneous optimization of the LP and BP placement into the core. The accurate depletion calculation of the LP with BPs is done with the coupled lattice and reactor physics CASMO-4/SIMULATE3 package. However, the fact that these codes validate safety of the core with the added BP placement design also validates the use of the HPD method. The calculations are applied to the TMI-1 core as an example PWR providing concrete results.     

Contributions to the neutronic analysis of a gas-cooled fast reactor

In this work the Monte Carlo codes MCNPX and TRIPOLI-4 were used to perform the criticality calculations of the fuel assembly and the core configuration of a gas-cooled fast reactor (GFR) concept, currently in development. The objective is to make contributions to the neutronic analysis of a gas-cooled fast reactor. In this study the fuel assembly is based on a hexagonal lattice of fuel-pins. The materials used are uranium and plutonium carbide as fuel, silicon carbide as cladding, and helium gas as coolant. Criticality calculations were done for a fuel assembly where the axial reflector thickness was varied in order to find the optimal thickness. In order to determine the best material to be used as a reflector, in the reactor core with neutrons of high energy spectrum, criticality calculations were done for three reflector materials: zirconium carbide, silicon carbide and natural uranium. It was found that the zirconium carbide provides the best neutron reflection. Criticality calculations using different active heights were done to determine the optimal height, and the reflector thickness was adjusted. Core criticality calculations were performed with different radius sizes to determine the active radial dimension of the core. A negative temperature coefficient of reactivity was verified for the fuel. The effect on reactivity produced by changes in the coolant density was also evaluated. We present the main neutronic characteristics of a preliminary fuel and core designs for the GFR concept. ENDF-VI cross-sections libraries were used in both the MCNPX and TRIPOLI-4 codes, and we verified that the obtained results are very similar.     

Qualification of the CFD code Trio_U for full scale reactor applications

The article presents a procedure to qualify the Trio_U code for the prediction of the boron concentration at the core inlet of a French 900 MWe pressurized water reactor under accidental conditions (inherent dilution problem).¹ The objective of this procedure is to ensure that the validation calculations are performed with the same modelling hypotheses as the full scale reactor analysis, for which usually no experimental data are available. A density driven ROCOM experiment as well as an UPTF Tram-C3 experiment have been used for the qualification of the Trio_U code. Both experiments present similar thermal hydraulic conditions as the reactor case. The predicted boron concentration at the core inlet of the reactor shows that the potential return to criticality might not be excluded in the case of a small break LOCA. Further neutronic calculations are necessary to confirm this result.     

Comprehensive Analysis of Mechanical and Thermohydraulic Processes in the Graphite Masonry of Channel Rectors during an Accidental Rupture of a Fuel Channel

A methodology and preliminary results of a computational analysis of the processes occurring in the graphite masonry in RBMK channel reactors during the rupture of a fuel channel as a result of accidental overheating are presented. The methodology for the computational analysis is implemented using the U_STACK code, simulating the thermohydraulic and mechanical processes occurring in masonry with varying geometry in continuous coupling with the processes in the circulation loop and accident containment system. The deformation and rupture of a pipe in the damaged channel and coolant efflux are calculated using the prescribed accident scenario. After channel rupture, the parameters of the medium, the displacement of graphite blocks, and the sagging of channel pipes in the entire volume of the core are calculated. As a result, the additional force loads on neighboring fuel channels in the rupture zone, the reactor case, and the top and bottom plates are estimated. The objective of the calculations performed with the U_STACK code are assessment of the integrity of the components of the reactor core and substantiation of the impossibility of multiple ruptures occurring in the reactor fuel channels.     

Monte Carlo simulation of the Greek Research Reactor neutron irradiation facilities

A Monte Carlo simulation of the Greek Research Reactor was carried out using MCNP-4C2 code and continuous energy cross-section data from ENDF/B-VI library. A detailed model of the reactor core was employed including standard and control fuel assemblies, reflectors and irradiation devices. The model predicted neutron flux distributions within the core in good agreement with calculations performed using the deterministic code CITATION and measurements using activation foils. The model is used for the prediction of the neutron field characteristics at the reactor irradiation devices and enables the design and evaluation of experiments involving material irradiations.     

Containment venting as a mitigation technique for BWR MARK I plant ATWS

Containment venting is studied as a mitigation strategy for preventing or delaying severe fuel damage following hypothetical BWR Anticipated Transient Without Scram (ATWS) accidents initiated by MSIV-closure, and compounded by failure of the Standby Liquid Control (SLC) system injection of sodium pentaborate solution and by the failure of manually initiated control rod insertion. The venting of primary containment after reaching 75 psia (0.52 MPa) is found to result in the release of the vented steam inside the reactor building, and to result in inadequate Net Positive Suction Head (NPSH) for any system pumping from the pressure suppression pool. CONTAIN code calculations show that personnel access to large portions of the reactor building would be lost soon after the initiation of venting and that the temperatures reached would be likely to result in independent equipment failures. It is concluded that containment venting would be more likely to cause or to hasten the onset of severe fuel damage than to prevent or to delay it.Two alternative strategies that do not require containment venting, but that could delay or prevent severe fuel damage, are analyzed. BWR-LTAS code results are presented for a successful mitigation strategy in which the reactor vessel is depressurized, and for one in which the reactor vessel remains at pressure. For both cases the operators are assumed to take action to intentionally restrict injected flow such that fuel in the upper part of the core would be steam cooled. Resulting fuel temperatures are estimated with an off-line calculation and found to be acceptable.     

3D neutron diffusion computational code based on GFEM with unstructured tetrahedron elements: A comparative study for linear and quadratic approximations

In the present study, the comparison between the results obtained from the linear and quadratic approximations of the Galerkin Finite Element Method (GFEM) for neutronic reactor core calculation was reported. The sensitivity analysis of the calculated neutron multiplication factor, neutron flux and power distributions in the reactor core vs. the number of the unstructured tetrahedron elements and order of the considered shape function was performed. The cost of the performed calculation using linear and quadratic approximation was compared through the calculation of the FOM. The neutronic core calculation was performed for both rectangular and hexagonal geometries. Both the criticality and fixed source calculations were done using the developed GFEM-3D computational code. An acceptable accuracy with low computational cost is the main advantage of applying the unstructured tetrahedron elements. The generated unstructured tetrahedron elements with Gambit software were used in the GFEM-3D computational code via a developed interface. The criticality calculation was benchmarked against the valid data for IAEA-3D and VVER-1000 benchmark problems. Also, the neutron fixed source calculation was validated through the comparison with the similar computational code. The results show that the accuracy of the calculation for the both linear and quadratic approximations improves vs. the number of elements. Quadratic approximation gives acceptable results for almost all considered number of the elements, while the results obtained from the linear approximation have good accuracy for only high number of the elements.     

Heat transfer from a totally blocked fuel subassembly of a liquid metal fast breeder reactor: II. Numerical simulation

Fast breeder nuclear reactors used for power generation, have fuel subassemblies in the form of rod bundles enclosed inside tall hexagonal cavities. Each subassembly can be considered as a porous medium with internal heat generation. A three-dimensional analysis is carried out here to estimate the heat transfer due to natural convection, in such an anisotropic, partially heat generating porous medium, which corresponds to the typical case of blocked flow in a fuel subassembly inside the reactor core. Using the finite volume technique, the temperatures at various locations inside hexagonal cavity are obtained. The simulations by the three-dimensional code developed are compared with the results of experiments [Suresh, Ch.S.Y., Sateesh, G., Das, Sarit K., Venkateshan, S.P., Rajan, M., 2004. Heat transfer from a totally blocked fuel subassembly of a liquid metalfast breeder reactor. Part 1: Experimental investigation. Nucl. Eng. Design, present issue] conducted using liquid sodium as the heat transfer fluid. Further, the code is used to predict the maximum temperature in typical liquid metal fast breeder reactors to find the power level where the liquid sodium starts boiling. It helps to decide the power level for initiation of monitoring the temperature for the purpose of reactor control.