Optimization of the upper plenum of a PBMR to enhance thermal performance in the reactor core

An upper plenum of a PBMR type gas cooled nuclear reactor has been optimized using three-dimensional Reynolds-averaged Navier–Stokes (RANS) analysis and surrogate modeling technique. Shear stress transport turbulence model is used as a turbulence closure. Two geometric design variables viz., ratio of height of upper plenum to diameter of rising channels, and ratio of height of the slot at inlet to that at outlet, are used as design variables for the optimization. Design points are selected by Latin-hypercube sampling. The objective function is defined as a linear combination of uniformity of temperature distribution in the core and pressure drop through the upper plenum. The optimal point is determined through surrogate-based optimization method which uses RANS derived calculations at design points. The results show that the optimization improves considerably both the temperature uniformity and the friction performance.     

Optimization of a nuclear fuel spacer grid spring using homology constraints

The springs in a spacer grid support the fuel rods in a nuclear fuel system. The spacer grid is part of the fuel assembly. Since the spring has repeated contact with the fuel rod, fretting wear occurs on the surface of the fuel rod. Design is usually performed to reduce the wear while the functions of the spring are maintained. The design process for the spring is defined by using the Independence Axiom of axiomatic design and the design is carried out based on the direction that the design matrix indicates. For a detailed design, an optimization problem is formulated. In optimization, a homologous design is employed to reduce the fretting wear. The deformation of a structure is called homologous if a given geometrical relationship holds for a certain number of structural points before, during, and after the deformation. In this case, the deformed shape of the spring should be the same as that of the fuel rod. This condition is transformed to a function and considered as a constraint in the optimization process. The fretting wear is expected to be reduced due to the homology constraint. The objective function is minimizing the maximum stress to allow local plastic deformation. Optimization results show that contact occurs in a wide range. The results are verified by non-linear finite element analysis.     

The optimum design of tight lattice reactor core with thin rod bundles

The fuel height, rod diameter, pitch, and the loading pattern are all important parameters in the reactor core design process. Based on the analysis of the core performance, optimization calculation is performed on the three objective functions of ABV-6M reactor, i.e., power density, coolant temperature difference between the inlet and outlet, and flow-induced vibration are proposed for optimization calculation. Then a multi-objective problem (MOP) model is applied and computed optimally by non-dominated sorting genetic algorithm (NSGA-II) with the aim of maximizing power density and temperature difference as well as minimizing the flow-induced vibration. The results of optimal designs called ‘Pareto-optimal solutions’ are a set of multiple optimum solutions, from which the final optimization can be chosen after sensitivity analysis is performed. On the basis of lattice parameters optimization, the radial one-dimensional fuel loading pattern was optimized for achieving the optimum fuel utilization. The typical optimum design considered to be safe in a verification check showed that tight lattice effectively improved the reactor performances and saved the fuel consumption.     

BWR fuel cycle optimization using neural networks

In nuclear fuel management activities for BWRs, four combinatorial optimization problems are solved: fuel lattice design, axial fuel bundle design, fuel reload design and control rod patterns design. Traditionally, these problems have been solved in separated ways due to their complexity and the required computational resources. In the specialized literature there are some attempts to solve fuel reloads and control rod patterns design or fuel lattice and axial fuel bundle design in a coupled way. In this paper, the system OCONN to solve all of these problems in a coupled way is shown. This system is based on an artificial recurrent neural network to find the best combination of partial solutions to each problem, in order to maximize a global objective function. The new system works with a fuel lattices’ stock, a fuel reloads’ stock and a control rod patterns’ stock, previously obtained with different heuristic techniques. The system was tested to design an equilibrium cycle with a cycle length of 18 months. Results show that the new system is able to find good combinations. Cycle length is reached and safety parameters are fulfilled.     

Loading pattern optimization of PWR reactors using Artificial Bee Colony

In this paper a core reloading technique using Artificial Bee Colony algorithm, ABC, is presented in the context of finding an optimal configuration of fuel assemblies. The proposed method can be used for in-core fuel management optimization problems in pressurized water reactors. To evaluate the proposed technique, the power flattening of a VVER-1000 core is considered as an objective function although other variables such as K_eff, power peaking factor, burn up and cycle length can also be taken into account. The proposed optimization method is applied to a core design optimization problem previously solved with Genetic and Particle Swarm Intelligence Algorithm. The results, convergence rate and reliability of the new method are quite promising and show that the ABC algorithm performs very well and is comparable to the canonical Genetic Algorithm and Particle Swarm Intelligence, hence demonstrating its potential for other optimization applications in nuclear engineering field as, for instance, the cascade problems.     

Turbulent flow simulation in a wire-wrap rod bundle of an LMFBR

The pressure drop and heat transfer characteristics of wire-wrapped 19-pin rod bundles in a nuclear reactor subassembly of liquid metal cooled fast breeder reactor (LMFBR) have been investigated through three-dimensional turbulent flow simulations. The predicted results of eddy viscosity based turbulence models (k-?, k-ω) and the Reynolds stress model are compared with those of experimental correlations for friction factor and Nusselt number. The Re is varied between 50,000 and 150,000 and the ratio of helical pitch of wire wrap to the rod diameter is varied from 15 to 45. All the three turbulence models considered yield similar results. The friction factor increases with reduction in the wire-wrap pitch while the heat transfer coefficient remains almost unaltered. However, reduction in the wire-wrap pitch also enhances the transverse flow velocity in the cross-sectional plane as well as the local turbulence intensity, thereby improving the thermal mixing of coolant. Consequently, the presence of wire wrap reduces temperature variation within each section of the subassembly. The associated reduction in differential thermal expansion of rods is expected to improve the structural integrity of the fuel subassembly.     

An optimization method based on combination of cellular automata and simulated annealing for VVER-1000 NPP loading pattern

This paper introduces a design methodology in the context of finding new and innovative design principles by means of optimization techniques. In this method cellular automata (CA) and simulated annealing (SA) were combined and used for solving the optimization problem. This method contains two principles that are neighboring concept from CA and accepting each displacement basis on decreasing of objective function and Boltzman distribution from SA that plays role of transition rule. Proposed method was used for solving fuel management optimization problem in VVER-1000 Russian reactor. Since the fuel management problem contains a huge amount of calculation for finding the best configuration for fuel assemblies in reactor core this method has been introduced for reducing the volume of calculation. In this study reducing of power peaking factor inside the reactor core of Bushehr NPP is considered as the objective function. The proposed optimization method is compared with Hopfield neural network procedure that was used for solving this problem and has been shown that the result, velocity and qualification of new method are comparable with that. Besides, the result is the optimum configuration, which is in agreement with the pattern proposed by the designer.     

Optimization of zigzag flow channels of a printed circuit heat exchanger for nuclear power plant application

Printed circuit heat exchanger (PCHE) is recently considered as a recuperator for the high-temperature gas cooled reactor. In this study, shape optimization of zigzag flow channels in a PCHE has been performed to enhance heat transfer performance and reduce the friction loss based on three-dimensional Reynolds-averaged Navier–Stokes analysis with the Shear Stress Transport Turbulence model. A multi-objective genetic algorithm is used for the multi-objective optimization. Two non-dimensional objective functions related to heat transfer performance and friction loss are employed. The shape of a flow channel is defined by two geometric design variables, viz. the cold channel angle and the ellipse aspect ratio of the cold channel. The experimental points within the design space are selected using Latin hypercube sampling as the design of the experiment. The response surface approximation model is used to approximate the Pareto-optimal front. Five optimal designs on the Pareto-optimal front have been selected using k-means clustering. The flow and heat transfer characteristics, as well as the objective function values, of these designs have been compared with those of the reference design.     

An experimental study and assessment of existing friction factor correlations for wire-wrapped fuel assemblies

The main objective of the present study is to perform a comparative study of five existing correlations that have been selected and identify the best performing correlations in the subchannel pressure drop analysis of a wire-wrapped fuel assembly by means of directly comparing with experimental data obtained in the present work. For this purpose, a series of water experiments have been performed using a helical wire-wrapped 19-pin fuel assembly for various combinations of test parameters. Four different test sections that have different pitch to rod diameter ratios (P/D) and wire lead length to rod diameter ratios (H/D) have been fabricated. A series of pressure drop measurements were made to obtain friction factors for these four test sections. A total of 293 data were obtained and the present along with existing data are used in the present comparative study of existing correlations. The results of this study show that both the original and the simplified Cheng and Todreas correlations give the best agreement with experimental data for all flow regions.     

Analysis of MOX fuel behavior in reduced-moderation water reactor by fuel performance code FEMAXI-RM

To assess the feasibility of the 31% Pu-MOX fuel rod design of reduced-moderation water reactor (RMWR) in terms of thermal and mechanical behaviors, a single rod assumed to be irradiated in the core of RMWR up to 106 GWd/tHM has been analyzed by a fuel performance code FEMAXI-RM which is an extended version of FEMAXI-6 code. In the analysis, design specifications of fuel rod and irradiation conditions have been input, and available models of both MOX fuel and UO₂ fuel have been used as appropriate. The results are: fission gas release is several tens of percent, rod internal pressure does not exceed the coolant pressure, and the highest fuel center temperature is 2400 K, while cladding diameter increase caused by pellet swelling is within 1% strain. These predictions suggest that the MOX fuel rod integrity will be held during irradiation in RMWR, though actual behavior of MOX pellet swelling and cladding oxidation require to be investigated in detail.     

3D finite element analysis of a nuclear fuel rod with gap elements between the pellet and the cladding

Nuclear fuel rods which comprises an important component of a nuclear power plant are composed of nuclear fuel and cladding. Simulating the nuclear fuel rod using a computer program is the universal method to verify its safety. The computer program used for this is called the fuel performance code. The main objective of this study is to simulate the nuclear fuel rod behavior considering the gap conductance using three-dimensional gap elements. Gap elements are used because, unlike other methods, this approach does not require special methods or other variables such as the Lagrange multiplier. In this work, a nuclear fuel rod has been simulated and the results are compared with the experimental results.     

PWR fuel management optimization using continuous particle swarm intelligence

The objective of nuclear fuel management is to minimize the cost of electrical energy generation subject to operational and safety constraints. In the present work, a core reload optimization package using continuous version of particle swarm optimization, CRCPSO, which is a combinatorial and discrete one has been developed and mapped on nuclear fuel loading pattern problems. This code is applicable to all types of PWR cores to optimize loading patterns. To evaluate the system, flattening of power inside a WWER-1000 core is considered as an objective function although other variables such as K_eff along power peaking factor, burn up and cycle length can be included. Optimization solutions, which improve the safety aspects of a nuclear reactor, may not lead to economical designs. The system performed well in comparison to the developed loading pattern optimizer using Hopfield along SA and GA.     

Fuel design study and optimization for PEACER development

In order to increase the transmutation capability for the Pb-Bi cooled burner, PEACER, metallic fuel rods (60U–30TRU–10Zr with Pb-bond in HT-9 clad) having a short (50 cm) active length with a large gas plenum have been designed with a peak design TRU burnup of 15%. A 17 × 17 square-lattice with relatively high pitch-to-diameter ratio was employed to reduce the actinide production and pumping load associated with the high-density coolant. Fuel rod failure modes are identified and fuel design criteria are established. A fuel rod design model, named as RODSIS, has been obtained by incorporating Pb properties and a cladding oxidation rate equation. A thermal analysis has been conducted for a fuel rod having peak-power based on a predicted power distribution and history during an equilibrium cycle. Taking into account the high coolant density, all fuel rods are fastened in the assembly using a stiff middle grid structure and softer end grids made of HT-9. Based on fuel rod thermal analysis results, a finite element analysis (FEA) has been conducted for both thermal and mechanical analyses of the middle grid structure. Furthermore, a fuel assembly static analysis has been conducted to determine the consequences of the axial loading caused by buoyancy and flow. The PEACER fuel system design was visualized by using a three-dimensional design and visualization software.     

Thermo-mechanical analysis of supercritical pressure light water-cooled fast reactor fuel rod by FEMAXI-6 code

Thermo-mechanical behaviors of supercritical pressure light water cooled fast reactor (SWFR) fuel rod and cladding have been investigated by FEMAXI-6 (Ver.1) code with high enriched MOX fuel at elevated operating condition of high coolant system pressure (25 MPa) and high temperature (500 °C in core average outlet temperature). Fuel rod failure modes and associated fuel rod design criteria that is expected to be limiting in SWFR operating condition have been investigated in this fuel rod design study. Fuel centerline temperature is evaluated to be 1853 °C and fission gas release fraction is about 45% including helium production. Cumulative damage fraction is evaluated by linear life fraction rule with time-to-rupture correlation of advanced austenitic stainless steel. In a viewpoint of mechanical strength of fuel cladding against creep rupture and cladding collapse at high operation temperature, currently available stainless steels or being developed has a potential for application to SWFR. Admissible design range in terms of initial gas plenum pressure and its volume ratio are suggested for fuel rod design The stress ranges suggested by this study could be used as a preliminary target value of cladding material development for SWFR application.     

Optimization of BWR fuel lattice enrichment and gadolinia distribution using genetic algorithms and knowledge

An optimization methodology based on the Genetic Algorithms (GA) method was developed for the design of radial enrichment and gadolinia distributions for boiling water reactor (BWR) fuel lattices. The optimization algorithm was linked to the HELIOS code to evaluate the neutronic parameters included in the objective function. The goal is to search for a fuel lattice with the lowest average enrichment, which satisfy a reactivity target, a local power peaking factor (PPF), lower than a limit value, and an average gadolinia concentration target. The methodology was applied to the design of a 10 × 10 fuel lattice, which can be used in fuel assemblies currently used in the two BWRs operating at Mexico. The optimization process showed an excellent performance because it found forty lattice designs in which the worst one has a better neutronic performance than the reference lattice design. The main contribution of this study is the development of an efficient procedure for BWR fuel lattice design, using GA with an objective function (OF) which saves computing time because it does not require lattice burnup calculations.     

Fuel loading and control rod patterns optimization in a BWR using tabu search

This paper presents the QuinalliBT system, a new approach to solve fuel loading and control rod patterns optimization problem in a coupled way. This system involves three different optimization stages; in the first one, a seed fuel loading using the Haling principle is designed. In the second stage, the corresponding control rod pattern for the previous fuel loading is obtained. Finally, in the last stage, a new fuel loading is created, starting from the previous fuel loading and using the corresponding set of optimized control rod patterns. For each stage, a different objective function is considered. In order to obtain the decision parameters used in those functions, the CM-PRESTO 3D steady-state reactor core simulator was used. Second and third stages are repeated until an appropriate fuel loading and its control rod pattern are obtained, or a stop criterion is achieved. In all stages, the tabu search optimization technique was used. The QuinalliBT system was tested and applied to a real BWR operation cycle. It was found that the value for k_eff obtained by QuinalliBT was 0.0024 Δk/k greater than that of the reference cycle.     

BWR control rod design using tabu search

An optimization system to get control rod patterns (CRP) has been generated. This system is based on the tabu search technique (TS) and the control cell core heuristic rules. The system uses the 3-D simulator code CM-PRESTO and it has as objective function to get a specific axial power profile while satisfying the operational and safety thermal limits. The CRP design system is tested on a fixed fuel loading pattern (LP) to yield a feasible CRP that removes the thermal margin and satisfies the power constraints. Its performance in facilitating a power operation for two different axial power profiles is also demonstrated. Our CRP system is combined with a previous LP optimization system also based on the TS to solve the combined LP-CRP optimization problem. Effectiveness of the combined system is shown, by analyzing an actual BWR operating cycle. The results presented clearly indicate the successful implementation of the combined LP-CRP system and it demonstrates its optimization features.     

AXIAL: a system for boiling water reactor fuel assembly axial optimization using genetic algorithms

A system named AXIAL is developed based on the genetic algorithms (GA) optimization method, using the 3D steady state simulator code Core-Master-PRESTO (CM-PRESTO) to evaluate the objective function. The feasibility of this methodology is investigated for a typical boiling water reactor (BWR) fuel assembly (FA). The axial location of different fuel compositions is found in order to minimize the FA mean enrichment needed to obtain the cycle length under the safety constraints. Thermal limits are evaluated at the end of cycle using the Haling calculation; the hot excess reactivity and the shutdown margin at the beginning of cycle are also evaluated. The implemented objective function is very flexible and complete, incorporating all the thermal and reactivity limits imposed during fuel design analysis; furthermore, additional constraints can be easily introduced in order to obtain an improved solution. The results show a small improvement in the FA average enrichment obtained with the system related to the reference case that has been studied. The results show that the system converge to an optimal solution, it is observed that the mean fuel enrichment decreases while all the constraints are satisfied. A comparison was also performed using one-point and two-points crossover operator and the results of a sensitivity study for different mutation percentage are also showed.     

Analysis of fuel rod behavior under normal operating conditions in Super Fast Reactor

A Super Fast Reactor is a pressure-vessel type, fast spectrum supercritical water-cooled reactor (SCWR) that is presently researched in a Japanese project. A preliminary core has been designed with 1.59E+06 W/m³ of power density [1]. In order to ensure the fuel rod integrity, the fuel rod behaviors under the normal operating conditions are analyzed using FEMAXI-6 code. Three types of the limiting fuel rods, with the maximum cladding surface temperature (MCST), maximum power peak (MPP) and maximum discharge burnup (MDB), are chosen to cover all the fuel rods in the core. The power histories of these fuel rods are taken from the neutronics calculation results in the core design. The available design range of the fuel rod design parameters, such as the initial gas plenum pressure, gas plenum length, grain size and pellet-cladding gap size, are found out in order to satisfy the following design criteria: (1) Maximum fuel centerline temperature should be less than 1900 °C. (2) Maximum cladding stress in circumstance direction should be less than 100 MPa. (3) Pressure difference on the cladding should be less than 1/3 of buckling collapse pressure. (4) Compressive stress to yield strength ratio should be less than 0.2. (5) Cumulative damage fraction (CDF) on the cladding should be less than 1.0. Finally the improved fuel rod design is proposed.