Inserted Control Rods Research Articles

High fidelity transient solver in STREAM based on multigroup coarse-mesh finite difference method

This study incorporates a high-fidelity transient analysis solver based on multigroup CMFD in the MOC code STREAM. Transport modeling with heterogeneous geometries of the reactor core increases computational cost in terms of memory and time, whereas the multigroup CMFD reduces the computational cost. The reactor condition does not change at every time step, which is a vital point for the utilization of CMFD. CMFD correction factors are updated from the transport solution whenever the reactor core condition changes, and the simulation continues until the end. The transport solution is adjusted once CMFD achieves the solution. The flux-weighted method is used for rod decusping to update the partially inserted control rod cell material, which maintains the solution's stability. A smaller time-step size is needed to obtain an accurate solution, which increases the computational cost. The adaptive step-size control algorithm is robust for controlling the time step size. This algorithm is based on local errors and has the potential capability to accept or reject the solution. Several numerical problems are selected to analyze the performance and numerical accuracy of parallel computing, rod decusping, and adaptive time step control. Lastly, a typical pressurized LWR was chosen to study the rod-ejection accident.

Development and verification of pin-by-pin homogenized simplified transport solver Tortin for PWR core analysis

Currently, the pin-by-pin homogenized solvers are a very active research field as they can, unlike the nodal codes, directly predict the local power, while requiring significantly less computational resources than the heterogeneous transport codes. This paper presents a recently developed pin-by-pin diffusion/SP3 solver Tortin, its spatial discretization method and the reflector treatment. Regarding the spatial discretization, it was observed that the finite difference method applied on pin-cell size mesh does not properly capture the big flux change between MOX and uranium fuel, while the nodal expansion method is more accurate but too slow. If the finite difference method is used with a finer mesh in the outer two pin rows of the fuel assembly, it increases the required computation time by only 50%, but decreases the pin power errors below 1% with respect to lattice code reference solutions. The paper further describes the coupling of Tortin with a microscopic depletion solver. Several verification tests show that the SP3 pin-by-pin solver can reproduce the heterogeneous transport solvers results with very good accuracy, even for fuel cycle depletion of very heterogeneous core employing MOX fuel or inserted control rods, while being two orders of magnitude faster.

A correction method for RAPID fission matrix calculations with control rod movement

The RAPID radiation transport code, based on a fission matrix combination method, was initially designed for spent fuel systems but has been applied on reactor core neutronics analysis. To improve the accuracy of the RAPID fission-matrix approach, a ratio correction method has been applied to the reflector region and for heterogeneous adjacent assembly types. The RAPID code has been tested on a modified BEAVRS benchmark at hot zero power condition without control rods, and reports accurate results (∼0.52% 2-D, pin-wise RMS error with ∼25 pcm keff difference compared to a Serpent 2 reference). In this paper, we apply the assembly correction to rodded assemblies on different control rod bank worth calculations, as well as separate ratios on different slices in order to solve for the partially inserted control rod problems. It is shown that RAPID is able to estimate the control rod worth for different banks (a maximum 37 pcm error and most within 20 pcm). RAPID can also perform calculations on a partially inserted control rod case, reporting a maximum control rod worth error of 17 pcm across some insertion levels of bank D. In addition, another type of correction ratio method is proposed, namely the “localized” ratio. It makes use of sets of four-assembly fission matrices from criticality calculations and allows the choice of any fission source in ratio generation. It greatly reduces the errors located near large source gradient locations, which was observed with the “multiplied” correction ratio since it always assumes a uniform source.

Preliminary control strategies of megawatt-class gas-cooled space nuclear reactor with different control rod configurations

A megawatt-class, gas-cooled fast reactor was designed to provide 2.2MWth power for space application. The reactor concept adopts 90% enriched annular UO2 rods as the fuel and He-Xe mixture as the coolant. The thermal power is converted into electric power through Brayton turbines. The neutron flux distributions of four selected reactor configurations with different control rod arrangement are calculated using Monte Carlo code. In addition, calculations with different combinations of inserted control rods are conducted to investigate their effects on the power profile. Results show that control rods arranged in the central region help reduce the neutron flux peak and the radial flux peaking factor. The outer control rods, however, show limited effects on the central power profile. Instead, they only affect the region of the control rod neighborhood. Besides, since the outer control rods will increase the radial peaking factor, they are better to be used as safety rods for emergency. Based on the calculation and analysis, three control strategy candidates are proposed considering power profile flattening and control flexibility.

Control Rod Calculation in Axially Heterogeneous Fast Reactors—II: Impact of Three-Dimensional Homogenization on Core Parameters

Advanced sodium-cooled fast reactors with improved safety features such as the French Advanced Sodium Technological Reactor for Industrial Demonstration (ASTRID) CFV (French acronym of Cœur à Faible effet de Vide sodium, meaning low sodium void effect core) core concept are characterized by an axial heterogeneous core that will present a challenge for the homogenization procedures used today, taking into account all the different axial material transitions. Reliable modeling of the control rod and accurate prediction of the control rod worth are essential to determining the shutdown margins and to ensuring safe operation.In this work (part II of two companion papers), two different homogenization schemes are compared. One is based on the traditional reactivity-equivalence procedure in two dimensions, and the other is a newly implemented three-dimensional (3-D) version of the reactivity-equivalence procedure, with approximations based on the results in the companion paper. The deterministic results are compared with a Monte Carlo reference.Both cross-section sets from the two homogenization schemes yielded results within the requested ±5% error margin in reactivity. The largest discrepancy was found for the classical procedure for the case with a slightly inserted control rod (normal operating conditions). Both cross-section sets yielded similar power profiles in the fuel subassembly neighboring the control rod within the 2σ Monte Carlo standard deviation. Neither of the cross-section sets was able to predict the large gradients in capture rates close to the internal control rod interfaces.The study showed that the traditional two-dimensional (2-D) reactivity-equivalence procedure produces homogenized cross sections that yield reliable results in a CFV-type core. One exception from this was found for slightly inserted control rods, where the effect of the follower-absorber interface could not be fully captured by the 2-D scheme, and for such cases, 3-D modeling is recommended.

Control Rod Calculation in Axially Heterogeneous Fast Reactors—II: Impact of Three-Dimensional Homogenization on Core Parameters

Advanced sodium-cooled fast reactors with improved safety features such as the French Advanced Sodium Technological Reactor for Industrial Demonstration (ASTRID) CFV (French acronym of Cœur à Faible effet de Vide sodium, meaning low sodium void effect core) core concept are characterized by an axial heterogeneous core that will present a challenge for the homogenization procedures used today, taking into account all the different axial material transitions. Reliable modeling of the control rod and accurate prediction of the control rod worth are essential to determining the shutdown margins and to ensuring safe operation.In this work (part II of two companion papers), two different homogenization schemes are compared. One is based on the traditional reactivity-equivalence procedure in two dimensions, and the other is a newly implemented three-dimensional (3-D) version of the reactivity-equivalence procedure, with approximations based on the results in the companion paper. The deterministic results are compared with a Monte Carlo reference.Both cross-section sets from the two homogenization schemes yielded results within the requested ±5% error margin in reactivity. The largest discrepancy was found for the classical procedure for the case with a slightly inserted control rod (normal operating conditions). Both cross-section sets yielded similar power profiles in the fuel subassembly neighboring the control rod within the 2σ Monte Carlo standard deviation. Neither of the cross-section sets was able to predict the large gradients in capture rates close to the internal control rod interfaces.The study showed that the traditional two-dimensional (2-D) reactivity-equivalence procedure produces homogenized cross sections that yield reliable results in a CFV-type core. One exception from this was found for slightly inserted control rods, where the effect of the follower-absorber interface could not be fully captured by the 2-D scheme, and for such cases, 3-D modeling is recommended.

Localized neutron flux assessment and verification studies using MCNPX PWR full core model

The existence of significant local intra-assembly and azimuthal neutron flux variations at or around PWR control rod fingers and which would eventually not be captured by lower order transport deterministic reactor analysis methods, was examined using simplified full-core Monte Carlo calculations. The locations of specific interest were the clad surfaces and absorber material zones around the tips of partially inserted control rods in controlled assemblies located at various core locations. A fixed-source option was adopted in order to reduce the modeling efforts and computational costs. However, the validity of the fixed-source approach for predictions of the local flux distributions was verified by comparisons against corresponding calculations performed in eigenmode and against deterministic CASMO/SIMULATE solutions. Noticeable azimuthal neutron flux variations up to ∼30% were observed but only for the thermal energy range. For the fast (>1MeV) neutron flux, the predicted azimuthal variations were found to be bounded by an upper value of about ∼10%. On the other hand, significant planar flux non-uniformities between individual control rods within a controlled assembly were seen for all energies. Hence, in addition of having allowed for a strengthened knowledge on the behavior of local flux variations around PWR control rods, these results also provide a first assessment of the likely uncertainty level in control rod tip fluence estimations based on lower resolution deterministic reactor analysis codes.

On the interpretation of the inverted kinetics equation and space-time calculations of the effectiveness of the VVER-1000 reactor scram system

In the present paper, an attempt is made to analyze the accuracy of calculating the effectiveness of the VVER-1000 reactor scram system by means of the inverted solution of the kinetics equation (ISKE). In the numerical studies in the intellectual ShIPR software system, the actuation of the reactor scram system with the possible jamming of one of the two most effective rods is simulated. First, the connection of functionals calculated in the space-time computation in different approximations with the kinetics equation is considered on the theoretical level. The formulas are presented in a manner facilitating their coding. Then, the results of processing of several such functions by the ISKE are presented. For estimating the effectiveness of the VVER-1000 reactor scram system, it is proposed to use the measured currents of ionization chambers (IC) jointly with calculated readings of IC imitators. In addition, the integral of the delayed neutron (DN) generation rate multiplied by the adjoint DN source over the volume of the reactor, calculated for the instant of time when insertion of safety rods ends, is used. This integral is necessary for taking into account the spatial reactivity effects. Reasonable agreement was attained for the considered example between the effectiveness of the scram system evaluated by this method and the values obtained by steady-state calculations as the difference of the reciprocal effective multiplication factors with withdrawn and inserted control rods. This agreement was attained with the use of eight-group DN parameters.

Experimental validation of control rod related perturbations of moderator regions in an SCWR-like fuel lattice

Two different types of perturbations of an SCWR-like fuel lattice have been investigated experimentally in the central test zone of the PROTEUS zero-power research reactor at the Paul Scherrer Institute in Switzerland. In each case, a campaign of high-resolution gamma-ray spectroscopy measurements was carried out on 34 fuel pins of the test lattice. In the first case, the test lattice was perturbed by inserting aluminum rods into the four central moderator regions, while in the second case, the perturbation was affected using steel absorber rods (instead of aluminum). The derived reaction rates are the capture rate in 238U ( C 8) and the total fission rate ( F tot), as also the reaction rate ratio C 8/ F tot. Each of these has been mapped on the lattice and compared to calculated results from whole-reactor Monte Carlo simulations with MCNPX. Excellent agreement has been obtained, for both perturbed lattices, between the calculated and experimental distributions of C 8, F tot and C 8/ F tot. Considering that control rods in an SCWR assembly are foreseen to be inserted into the central moderator regions, these results may be considered as generic validation of Monte Carlo simulations for the two different types of lattice perturbations which inserted control rods imply, viz. moderator displacement and strong neutron absorption. In a second step, calculated C 8, F tot and C 8/ F tot distributions for the two perturbed lattices (as well as for the unperturbed lattice) have been compared, at assembly level, between MCNPX and the deterministic LWR lattice code CASMO-4E. In the case of the unperturbed lattice, as well as for the lattice with steel rods, the agreement between the codes is found to be within ∼1% for all pins and each reaction rate. However, for the lattice with aluminum rods, i.e. the case with mainly just moderator displacement involved, CASMO overestimates the reaction rates in the vicinity of the perturbations by up to 2–3%, when employing the standard input options. The reason for this discrepancy has been found to be the leakage treatment, which uses the fundamental-mode buckling applied in a homogenized sense across the lattice. In this way, global leakage gradients get averaged out over the entire assembly. The optional input card BZ2 for CASMO resolves this problem, and the codes then agree within 1% even for the aluminum case.

Energy release distribution optimization in a RBMK core during operation

Refueling optimization is examined for RBMK. The optimal distribution of burnup and the number of inserted control rods is discussed. The possible effect of optimization is evaluated. Modeling shows that the economic effect of optimization of refueling at nuclear power plants can be comparable to strategic measures such as increasing fuel enrichment.

Computation accuracy and efficiency of a power series analytic method for two- and three- space-dependent transient problems

The establishment of solutions to large-scale three-dimensional (3-D) reactor benchmark problems is needed to serve as standards for the verification of design codes and for the detailed error analysis of calculational methods. A number of partially and fully inserted control rods, represented by absorber added to certain subassemblies, cause a strong nonseparable power distribution. In addition, the existence of a very large thermal flux peak in the reflector makes this a very difficult and challenging problem to solve. PWS code has been developed to include a numerical solution for the time-dependent neutron diffusion equations for the nuclear reactor analysis. The new technique employs a new parameter (α) which can reduce the rapid increase in magnitude of the power series coefficients. These coefficients, in turn, are determined by back substitutions in the non-linear canonical diffusion equations and treating terms of the same degree to obtain a modified recurrence relation which is valid for any type of the stiff non-linear kinetic diffusion equations. The validity of the algorithm was tested with three kinds of well-known two-group benchmark problems. The first one is the two-dimensional TWIGL seed-blanket reactor kinetics problem. The second is the two- and three-dimensional LAR BWR benchmark problem simulating a rod drop accident of a BWR core. The third is the three-dimensional LMW LRA transient problem which simulates an operational transient involving rod movements. The obtained results with the proposed PWS code are compared with those provided by other reference codes, indicating an overall agreement and excellent performance.

Reactivity worth of the control rods at the ET-RR-2 reactor core

Abstract Safety analysis of research reactors include a determination of control rod worth and kinetic parameters upon which the dynamic performance of the reactor depends. The core control of the ET-RR-2 reactor is accomplished through six Ag-In-Cd alloy-absorbing plates, which can be inserted into the core with a high velocity. In the present work, the fully and partially inserted control rod configuration in 3D reactor geometry and the effect of reactivity worth of the control rods on the reactor core is studied. The reactivity worth were calculated for each control rod and also for combinations of more than one rod. The total worth of all control rods in the reactor core is about 16.95% k/k from the core reactivity. Other neutronic parameters, i. e. the 3D neutron flux distribution and the change of the power peaking factor as a results of inserted and withdrawing the control rods were calculated.

Nuclear safety-related calculations for Ghana Research Reactor -1 core

Safety-related calculations were performed using lattice code Winfrith Improved Multigroup Scheme (WIMS) and diffusion code CITATION for Ghana Research Reactor-1 (GHARR-1) core with high-enriched uranium (HEU) fuel elements. Results are provided for power peaking factors with partially inserted control rods, kinet-ic parameters and isothermal reactivity coefficients. Comparisons of some computed values with results obtain-ed using other codes, which are in good agreement, are presented Journal of Applied Science and Technology (JAST) , Vol. 5, Nos. 1 & 2, 2000, pp. 32 - 38

Determination of PWR Control Rod Position by Core Physics and Neural Network Methods

A method is described by which the axial position of a control rod can be determined. The method is based on the influence of a partially inserted control rod on the axial flux profile. By measuring this flux profile, the control rod position can be in principle unfolded. One problem is however that the relationship between rod position and flux profile is rather implicit and cannot be explicitly inverted. Thus, it is suggested here to use neural network techniques to unfold the rod position from the measured flux profile. For training of the network, a large number of flux profiles are needed, corresponding to various known rod positions. These data can be generated by advanced core calculational codes. In this study, the Studsvik core master system SIMULATE was used. The method was tested with good results on both fully simulated data as well as on a measurement taken at the Swedish pressurized water reactor Ringhals 4.

Spatial Kinetics Studies in Liquid-Metal Fast Breeder Reactor Critical Assemblies

Recent measurements in the zero-power physics reactor have been used to study the effect of spatial decoupling in fast reactor critical assemblies of various sizes and compositions. Flux distributions in these assemblies had varying degrees of sensitivity to perturbations. Decoupling was investigated using rod-drop, boron-oscillator, and noise-coherence techniques, which emphasized different times following perturbations. Equilibrium flux distributions were also measured for subcritical configurations with inserted control rods. For most assemblies, accurate reactivity measurements were obtained by analyzing the power history from a single detector using inverse kinetics methods, assuming an instantaneous efficiency change for the detector. The instantaneous efficiency change assumption broke down, however, in assemblies with zones in which normal plutonium fuel was replaced by /sup 235/U fuel or fuel with a high /sup 240/Pu content. Flux redistributions caused by perturbations in these cores took several minutes to evolve.

Application of ‘natural coordinate system’ in the finite element solution of multigroup neutron diffusion equation

A simple method of generating stiffness matrices for the solution of multigroup diffusion equation by ‘natural coordinate system’ has been presented. A comparative study has been made using triangular elements with linear model, triangular elements with quadratic model and rectangular elements with bilinear model to demonstrate their relative efficiencies. The quadratic interpolation model has been shown to be superior to linear and bilinear models with respect to computing time, computer storage and relative error in K eff for a two group diffusion example. The flexibility of the finite element treatment has been demonstrated by the calculation of the reactivity of a partially inserted control rod. Good agreement has been obtained with a perturbation calculation.

Two Interesting Phenomena Observed in the Axial Power Distribution of a BWR

Two interesting phenomena were observed in the axial power distribution in the core of the Japan Power Demonstration Reactor. One is the control-rod and void coupled bump on the axial power shape; this is a kind of local power peaking produced by the interacted effect between the partially inserted control rod and the axial void changes in the moderator. The other may be termed a burnup oscillation of the axial power distribution''; this is a long-term, periodic change of the axial power distribution due to core exposure and to the withdrawal of the control rods. It is found that the upper and lower half-channel integrations of the local leakage of thermal neutrons are essential factors for the occurrence of those phenomena. 9 references. (auth)

Effects of Multiple Control Rods

In this paper is proposed a new method of calculation of the effects of multiple control rods. The reactor is divided into two parts—the uniform fuel region and the control rods. The sinks for both thermal and epithermal fluxes of the control rods are taken into account. This method overcomes such disadvantages of the conventional methods as limitations on the number, the properties, and on the locations of the inserted control rods, as well as the considerable calculating time required. The validity of the theory proposed in this paper was ascertained by comparisons with experiments in a natural U fueled, water moderated subcritical facility and with results obtained with the conventional method.

Effects of Multiple Control Rods

In this paper is proposed a new method of calculation of the effects of multiple control rods. The reactor is divided into two parts—the uniform fuel region and the control rods. The sinks for both thermal and epithermal fluxes of the control rods are taken into account. This method overcomes such disadvantages of the conventional methods as limitations on the number, the properties, and on the locations of the inserted control rods, as well as the considerable calculating time required. The validity of the theory proposed in this paper was ascertained by comparisons with experiments in a natural U fueled, water moderated subcritical facility and with results obtained with the conventional method.

On the efficiency of a concentric cut-off rod of a thermal reactor as a function of the inserted length of the rod

The problem considered is that of determining the efficiency of a partially inserted control rod of a thermal reactor by calculating the buckling. Since, according to one-group theory, this buckling is the smallest eigenvalue of the differential equation for the thermal neutron flux with the corresponding boundary conditions, it is derived from a classical variational problem.