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• System level LBE thermal-hydraulics analysis code is developed. • Coupling effect of LBE oxidation corrosion and thermal-hydraulics is considered. • Influence of oxidation layer on heat transfer characteristics of LBE reactor is conducted. For Lead-Bismuth Eutectic (LBE) alloy cooled reactor, oxidation corrosion is very important and would affect the thermal hydraulic characteristics of the reactor. In this paper, based on LETHAC code developed by Xi'an Jiaotong University (XJTU) for system level thermal hydraulic analysis LBE reactor, a simulation module for oxidation corrosion is developed and added. The influence of oxidation layer on the heat transfer characteristics of the reactor is conducted. Based on LESMOR reactor designed by XJTU, a simulation calculation is carried out under the long-term operation conditions of the reactor considering the growth of oxidation layer. The distribution of the oxide layer in the reactor, the change of temperature appreciation caused by the oxide layer over time and the distribution in the reactor are obtained. The presence of oxide layer will affect the fluid temperature and wall temperature of reactor. The longer the run time, the greater the impact. This paper could provide solid analysis methodology reference for the design of LBE reactor. [ABSTRACT FROM AUTHOR]

• A theoretical optimization method for the combined cycle -coupled to HTGRs and VHTRs is proposed based on total differential model. • Multivariable combined-cycle efficiency was determined to be a function of the reactor outlet temperature and main steam pressure. • The optimization method provides guidance for the design of the combined cycle-coupled VHTRs. Very high-temperature gas-cooled reactors (VHTRs) have attracted worldwide attention because of their multiple uses, which include hydrogen production and high-efficiency power generation. Efficient power conversion is a key to improving the competitiveness of VHTRs. The combined cycle is a cyclic form of energy cascade utilization that makes full use of the high-temperature heat source of VHTRs. In this paper, a theoretical optimization method of combined-cycle efficiency is proposed for combined cycle-coupled high-temperature gas-cooled reactors (HTGRs) and VHTRs without considering specific engineering constraints. Based on a total differential analysis combined with a numerical analysis, the multi-variable combined-cycle efficiency was reduced to a function of two key parameters: the reactor outlet temperature and the main steam pressure. The remaining parameters can be determined by optimization within the defined domain. The theoretical optimization method proposed in this paper is conceptually clear and solves the problems presented by the many variables involved in combined cycle-coupled HTGRs without a clear variable optimization strategy. The results of this study provide guidance for the theoretical analysis and parameter design of combined cycle-coupled VHTRs. [ABSTRACT FROM AUTHOR]

• A new class of non-linear acceleration methods has been created (SVRM). • The stability of SVRM is shown through a spectral radius and Fourier analysis. • The simplified numerical benchmark indicates a significant effectiveness advantage. In this paper we propose a new non-linear technique for accelerating the source iterations of the discrete-ordinates transport equation. The acceleration method, called Spatially Variant Rebalancing Method (SVRM), is based on the computation of the zeroth and first order spatial variation of the neutron balance equation. The non-linear acceleration is applied to the method of characteristics (MOC) with a step-approximation of the source. The new acceleration is meant to catch the high-order variation of the neutron flux within the spatial mesh. The paper proposes a numerical analysis of the technique based on the explicit computation of the Jacobian. The latter is analyzed with both spectral and Fourier analysis (Hong et al., 2010). Also, a comparison of the new method against CMFD (Smith, 1983), DSA (Larsen, 1982), and BPA (Adams et al., 1988) has been done for a parametrized heterogeneous problem, in order to study the performance of SVRM in different transport regimes. The analysis of SVRM has been constrained to plane geometries. [ABSTRACT FROM AUTHOR]

• A diamond-like carbon coated capacitance wire-mesh sensor (WMS) is designed for gas–liquid metal two-phase measurement. • Numerical model based on COMSOL of the coated WMS is established. • Effect of bubble position and structure parameters on the electric field and measurement accuracy of coated WMS is investigated. • Feasibility of the coated WMS is demonstrated and geometric structure is optimized. The detection of liquid metal-gas two-phase distribution in lead-cooled fast reactor once steam generator tube rupture occurs is vital to the security assessment of the reactor core. In this paper, considering the high temperature, corrosiveness and high conductivity of the liquid metal, a diamond-like carbon coated capacitance wire-mesh sensor is proposed to detect the two-phase distribution in liquid metal. Based on the software COMSOL, a numerical model is firstly established that is quantificationally verified by experiment to study and optimize the performance of the coated WMS. The measurement accuracy of the sensor is investigated by ranging the AC excitation frequency and structure parameters of the system. The results show that the liquid metal has blocking effect on the small bubbles and the sensor has great measurement accuracy when the transverse and vertical interval are 2 mm while the exitation frequecy, coat thickness and electrode diameter show little effect. This research could guide the measurement in liquid metal-gas two-phase flow. [ABSTRACT FROM AUTHOR]

The present paper is based on the work carried out in the framework of the European FP7 project MAXSIMA, in which MYRRHA safety studies are performed. MYRRHA is a pool-type 100 MWth system with MOX fuel designed to operate both in ADS and critical modes. It uses lead-bismuth eutectic (LBE) as primary coolant. The MOX fuel has almost the same density as the LBE coolant. In case of pin failure fuel pellets may break into chunks and particles carried by the coolant upwards and redistributed in the reactor pool. The transmutation group at IKET/KIT mainly with the numerical analysis tool is involved for studying severe accidents for MYRRHA reactor design. The highlight of the current work is that 3D simulations with explicit modelling on the gaps between fuel assemblies and 3D macroscopic pin bundle models are performed for the first time using a reactor safety analysis code, SIMMER-IV, with 3D geometry. In this paper, the numerical analyses are conducted for a single fuel assembly blockage and 19 pin-rods on basis of an LBE coolant experiment. The 3D analysis has been applied with both scales namely fuel assembly scale and pin bundle scale. For the fuel assembly scale, the evaluation of a single fuel assembly blockage using non-axisymmetric geometry configuration in the subcritical mode is addressed. For the pin bundle scale, the 3D pin bundle simulations show a good agreement from the experiment conducted at KALLA liquid metal laboratory. Note that this is the only code applied by now for blockage analyses after pin failure in MYRRHA. The current work has formed a solid basis for the safety analysis for MYRRHA in the future. [ABSTRACT FROM AUTHOR]

The paper describes the development and validation of a coupling methodology between the best-estimate system thermal-hydraulic code RELAP5-3D and the CFD code FLUENT, conceived for high fidelity plant-scale safety analyses of pool-type reactors. The computational tool is developed to assess the impact of three-dimensional phenomena occurring in accidental transients such as loss of flow (LOF) in the research reactor MYRRHA, currently in the design phase at the Belgian Nuclear Research Centre, SCK•CEN. A partitioned, implicit domain decomposition coupling algorithm is implemented, in which the coupled domains exchange thermal-hydraulics variables at coupling boundary interfaces. Numerical stability and interface convergence rates are improved by a novel interface Quasi-Newton algorithm, which is compared in this paper with previously tested numerical schemes. The developed computational method has been assessed for validation purposes against the experiment performed at the test facility TALL-3D, operated by the Royal Institute of Technology (KTH) in Sweden. This paper details the results of the simulation of a loss of forced convection test, showing the capability of the developed methodology to predict transients influenced by local three-dimensional phenomena. [ABSTRACT FROM AUTHOR]

The Variational Nodal Method (VNM) is generalized for heterogeneous nodes and applied to four kinds of problems including Molten Salt Reactor (MSR) core problem with continuous cross section profile, Pressurized Water Reactor (PWR) control rod cusping effect problem, PWR whole-core pin-by-pin problem, and heterogeneous PWR core problem without fuel-coolant homogenization in each pin cell. Two approaches have been investigated for the treatment of the nodal heterogeneity in this paper. To concentrate on spatial heterogeneity, diffusion approximation was adopted for the angular variable in neutron transport equation. To provide demonstrative numerical results, the codes in this paper were developed in slab geometry. The first method, named as function expansion (FE) method, expands nodal flux by orthogonal polynomials and the nodal cross sections are also expressed as spatial depended functions. The second path, named as finite sub-element (FS) method, takes advantage of the finite-element method by dividing each node into numbers of homogeneous sub-elements and expanding nodal flux into the combination of linear sub-element trial functions. Numerical tests have been carried out to evaluate the ability of the two nodal (coarse-mesh) heterogeneous VNMs by comparing with the fine-mesh homogeneous VNM. It has been demonstrated that both heterogeneous approaches can handle heterogeneous nodes. The FE method is good at continuous-changing heterogeneity as in the MSR core problem, while the FS method is good at discontinuous-changing heterogeneity such as the PWR pin-by-pin problem and heterogeneous PWR core problem. For problems with only one or two discontinuity points such as the PWR control rod cusping effect problem, both of the two methods can catch the effect with high efficiency. [ABSTRACT FROM AUTHOR]

• Detailed numerical analysis of a 2.5 MW LBE spallation target planned for CiADS was carried out. • Effect of geometric parameters on the target performances was investigated by single-factor analysis. • Multiple factors and multiple levels were objectively and reasonably optimized by multi-factor analysis. • Variation coefficient method was used to integrate multiple indexes into one index that can reflect the overall situation. In an Accelerator Driven System (ADS), the spallation target typically has a power of several megawatts or above. As high-power targets are challenging to design, the targets studied in the past generally had a power of 2 MW or less. For the China initiative Accelerator Driven System (CiADS) under construction, a 2.5 MW lead–bismuth eutectic (LBE) target is planned. In this paper, thermal–hydraulic and structural analyses were performed to optimize the design of the LBE spallation target. As a first step, given other conditions being fixed, the influence of a single parameter on the target performances, i.e., the outlet size, the diameter of the guide tube, the angle of the transition section, and the vertical distance from the origin of the beam window (BW) hemisphere to the upper end of the transition section, were investigated. Subsequently, the multi-factor analysis was conducted by adopting a four-factor and four-level orthogonal test. Results indicated that the target optimized by the multi-factor analysis, performed much better than the original design and that obtained by the single-factor analysis, providing a new approach for the parameter optimization of spallation target. Moreover, detailed analyses showed that the improved target met the thermal–hydraulic and mechanical design requirements. [ABSTRACT FROM AUTHOR]

This paper presents the development of a numerical tool meant at modelling the effect of stationary fluctuations in nuclear cores for systems cooled with either liquid water or boiling water. The originating fluctuations are defined for the variables describing the boundary conditions of the system, i.e. inlet velocity, inlet enthalpy, and outlet pressure. The tool then determines in the frequency domain the three-dimensional distributions within the core of the corresponding fluctuations in neutron flux, coolant density, coolant velocity, coolant enthalpy, and fuel temperature. The tool is thus based on the simultaneous modelling of neutron transport, fluid dynamics, and heat transfer in a truly integrated and fully coupled manner. The modelling of neutron transport relies on the two-group diffusion approximation and a spatial discretization based on finite differences. The modelling of fluid dynamics is performed using the Homogeneous Equilibrium Model, with a void fraction correction based on a pre-computed distribution of the static slip ratio (when two-phase flow conditions are encountered). Heat conduction in the fuel pins is also accounted for, and the heat transfer between the fuel pins and the coolant is modelled also using a pre-computed distribution of the heat transfer coefficient. The spatial discretization of the fluid dynamic and heat transfer problems is carried out using finite volumes. The tool, currently entirely Matlab based, requires minimal input data, mostly in form of the three-dimensional distributions of the macroscopic cross-sections and their relative dependence on coolant density and fuel temperature, the point-kinetic parameters of the core, as well as the three-dimensional distribution of the slip ratio (in case of two-phase flow conditions) and of the heat transfer coefficient. Such data can be provided by any static core simulator that thus needs to be run prior to using the present tool. In addition to briefly summarizing the different test cases used to verify the code, the paper also presents the results of simulations performed for a typical Pressurized Water Reactor and for a typical Boiling Water Reactor, as illustrations of the capabilities of the tool. [ABSTRACT FROM AUTHOR]

The advanced numerical simulation of a realistic physical system typically involves multi-physics problem. For example, analysis of a LWR core involves the intricate simulation of neutron production and transport, heat transfer throughout the structures of the system and the flowing, possibly two-phase, coolant. Such analysis involves the dynamic coupling of multiple simulation codes, each one devoted to the solving of one of the coupled physics. Multiple temporal coupling methods exist, yet the accuracy of such coupling is generally driven by the least accurate numerical scheme. The goal of this paper is to review in detail the approaches and numerical methods that can be used for the multi-physics temporal coupling, including a comprehensive discussion of the issues associated with the temporal coupling, and define approaches that can be used to perform multi-physics analysis. The paper is not limited to any particular multi-physics process or situation, but is intended to provide a generic description of multi-physics temporal coupling schemes for any development stage of the individual (single-physics) tools and methods. This includes a wide spectrum of situation, where the individual (single-physics) solvers are based on pre-existing computation codes embedded as individual components, or a new development where the temporal coupling can be developed and implemented as a part of code development. The discussed coupling methods are demonstrated in the framework of LWR core analysis. [ABSTRACT FROM AUTHOR]

• The mechanical friction force during the control rod drop is treated as a time-variant uncertainty for uncertainty analysis; • The interval process model is used to describe the time-variant uncertain mechanical friction during the CR drop; • The uncertainty analysis of CR drop considering various uncertain parameters is conducted; • A novel and general computational framework for uncertainty analysis of CR drop, UA-CRD, is proposed. Due to the influence of multiple factors, the control rod drop involves some uncertain parameters. The mechanical friction on the control rod is a time-variant uncertain parameter and is related to the position of the control rod. For the first time, this paper adopts the interval process model, which accurately describes the uncertainty parameters by using small-scale samples, to describe the uncertain mechanical friction on the control rod. The numerical experimental results demonstrate that the interval process model can describe the mechanical friction with high accuracy, even when employing small-scale samples. Furthermore, it is found that the uncertainty analysis can be considered as solving the extremal problem of a black-box model. Based on it, we propose a novel and general calculation framework for uncertainty analysis of control rod drop, UA-CRD. Through the analysis of numerical examples, it is verified that UA-CRD can accurately and efficiently conduct the uncertainty analysis of control rod drop. [ABSTRACT FROM AUTHOR]

Highlights • A preconditioning method is developed for MC modified power method simulation. • The preconditioning resolves the stability issue for practical application of MC MPM. • The accumulation of transfer matrix is adopted for stable performance. • BEAVRS benchmark results demonstrate MC MPM for large practical eigenvalue problems. Abstract The authors developed the modified power method (MPM) in previous publications to obtain multiple eigenmodes of an eigenvalue problem at the same time by employing a generalized eigenvalue problem (GEP) of the form of WX = VXK. Special attention has been paid to the Monte Carlo (MC) implementation of the MPM because it always suffers from the inherent statistical noises. In this paper, a preconditioning method for the GEP has been developed for the MC MPM, so that the performance is more stable and robust to the MC statistical noises. This preconditioning method is crucial for MC solving of problems with degenerated eigenmodes, which requires the accumulation of a so-called transfer matrix and the division of the system space into multiple sub-regions, the number of sub-regions being greater than the number of eigenmodes to be solved. The preconditioning method solves the issues arising from the mismatch between the number of sub-regions and the target number of eigenmodes to be calculated. The numerical results for a model cube problem and BEAVRS whole core neutron transport eigenvalue problem successfully demonstrate the validity of the preconditioning method and the extended applicability of the MC MPM for practical problems. [ABSTRACT FROM AUTHOR]

Highlights • The elastic-plastic dynamic responses of nuclear structure in excitation of strong earthquake sequences are focused. • Parametric analyses of upping to 112 computational cases is in detail investigated to show the dynamic behaviours of the nuclear structure under earthquake sequences. • Structural dynamic responses are greatly changed in strong aftershocks. • Damage aggravating effect induced by strong aftershocks can cause severe damage of structural members and it is found the greater the magnitude of aftershocks, the severer the aggravation effect. Abstract This paper studies dynamic responses of AP1000 nuclear island structure in strong earthquake sequences. A numerical model to simulate nuclear structural behaviors in earthquake is validated by comparison with data from a previous study on a nonlinear dynamic analysis of a reinforced concrete shield building. The validated numerical model is then used to carry out a series of parametric analyses with 112 computational cases so as to determine influence of strong aftershocks on structural elastic-plastic behavior considering input of three-dimensional ground motions. The results indicate that the influence of aftershocks on structural horizontal/vertical dynamic responses is very small in design basis earthquake sequences. However, the influence must be considered seriously in beyond-design basis earthquake sequences as values of RMVs (Ratio of Mean Value) deviating IPRs (Input Peak Ratio) obviously, which means structural dynamic responses are greatly changed in strong aftershocks. Damage aggravating effect induced by strong aftershocks can cause severe damage of structural members and it is found the greater the magnitude of aftershocks, the severer the aggravation effect. Although earthquake input energy is mostly dissipated by damping energy, plastic damage energy plays considerable role in strong aftershocks as it shares beyond 8 percent of the total input energy, which is 10 times more compared to design basis earthquake sequences. [ABSTRACT FROM AUTHOR]

• Thermal-hydraulics of LBE is studied and an experiment is carried out. • A new empirical correlation of LBE is developed, and validated by XJTU 7-rod bundle, KIT 19-rod bundle, and ENEA 37-rod bundle. • Detailed CFD is carried out to analyze the characteristics of flow and heat transfer of LBE. • Turbulent heat transfer model of LBE is discussed and verified. Lead-bismuth eutectic (LBE) is a liquid with low Prandtl number and high thermal conductivity, generally used as the coolant in lead-cooled fast reactors of Generation-IV. The traditional Reynolds analogy is not appropriate for LBE, hence the theoretical analysis and experimental measurements are studied to interpret the flow and heat transfer of LBE in this article. In this way, a single-rod experiment on flow and heat transfer for LBE is performed and a new empirical correlation is fitted. To analyze the behavior of flow and heat transfer for low Prandtl number fluids, and also to validate the turbulence model and new correlation in the hexagonal rod bundles. The CFD simulations are performed for the XJTU 7-rod bundle, the KIT 19-rod bundle, and the ENEA 37-rod bundle based on ANSYS Fluent. The convective heat transfer coefficient of LBE, the temperature of heating wall at different sub-channels, and the temperature non-uniformity are investigated in this paper, to reveal the flow and heat transfer characteristics of LBE. The results show that the deviations of the section averaged Nusselt number are in 25%, and the deviations of the local temperature of LBE and heating wall are in 10℃. Grid spacers will result in a 30% rise in the section averaged Nusselt number, which will improve the turbulent intensity and heat transfer. Temperature non-uniformity is reduced as the Peclet number is increased. The validations demonstrate that the new empirical correlation provides accurate convective heat transfer coefficient predictions for LBE flow and heat transfer in hexagonal rod bundles with a relative derivation in 20%, which can be used as a reference for additional LBE simulations and experiments. [ABSTRACT FROM AUTHOR]

This paper proposes an optimized design for the Heat Pipe ThermoElectric Generator (HPTEG) principle prototype based on the design of the NUSTER system. The numerical analysis platform has been established and verified. It is used to analyze the steady-state and transient (start-up and shutdown conditions) thermoelectric properties of the refined HPTEG prototype. The steady-state calculation shows that when the input power of the HPTEG prototype is 5500 W, the maximum temperature is about 987 K, and the thermoelectric conversion efficiency is about 10.64%. The startup calculation show that the heat pipe startup is completed at about 14400 s. The shutdown calculation shows that at 6% shutdown power, the system tends to be stable after about 20000 s, and the maximum temperature is about 716 K. This study provides data support for the subsequent design modification of the future HPTEG principle prototype and provides ideas for the 3D transient calculations of the solid-state heat pipe reactors. [ABSTRACT FROM AUTHOR]

For the interest of readers who do not need to deal with detailed mathematics, a succinct summary of the newly developed GSP N theory ( Chao, 2017 ) is given in this technical note. A streamlined presentation of the idea, concept, logic, formulation and the physics of the theory is given here such that the readers can more easily comprehend the overall picture and the explicit resulting equations to be used in implementation. The mathematical details are referred to the previous papers (Chao, 2016, 2017). All the relevant equations for the P 3 equivalent GSP 3 ( 3 ) theory are explicitly given. Issues of numerical implementation of the theory are discussed, and potentially viable methods are suggested and conceptually described. [ABSTRACT FROM AUTHOR]

This paper presents a Very High Temperature Gas-Cooled Reactor (VHTR) core analysis of the McCARD and DeCART-2D with High Temperature Engineering Test Reactor (HTTR) benchmark problem. The numerical results of the HTTR benchmark problem are demonstrated, the capability for VHTR core analysis of McCARD is validated by using the experiment data, and that of DeCART-2D is verified by comparing the numerical results with those of McCARD. The detail HTTR benchmark problem and specification of core geometry and material are also described. Also, a method of approximation for the complex geometry of the VHTR core is described for modelling in computational code. In terms of the multiplication factor and temperature coefficient, the numerical results of McCARD are easily compared with the HTTR experiment data. Because the DeCART-2D can solve 2-dimensional (2D) geometry, the simulation of 2D HTTR fuel rod, block, and core problem is performed with DeCART-2D and McCARD. The numerical results between them are around 200–400 pcm, meaning that DeCART-2D can be used to analyze VHTR core. [ABSTRACT FROM AUTHOR]

The fission gas removal system plays a critical role in the development of the Thorium Molten Salt reactors. An axial gas-liquid separator is adopted in the gas removal system. To predict the bubble trajectories in swirling flow is essential for designing such gas-liquid separator, since the separation efficiency is closely related to the bubble trajectory. In this paper, we proposed a numerical method to predict the bubble motion. This method is a modified Lagrangian approach in that the velocity of the continuous phase is obtained by approximating the velocity profiles from CFD. Combing the known velocity distribution with explicit mathematical expression and the force model for a single bubble, a mathematical model to calculate the bubble motion is well posed. Calculations with various bubble sizes and Reynolds numbers were carried out. By comparing the simulation results with the experimental data, we concluded that the numerical results agree well with the experimental data. The maximum error of the separation length is less than 10%, which is accurate enough for the determination of the dimension of the separator. [ABSTRACT FROM AUTHOR]

The condensation on containment shell drives the nearby gas downwards creating a natural convection in containments which plays a key role for long-term passive containment cooling. In late phase of accident where hydrogen and steam accumulate in containment, recovery of containment cooling can cause the loss of steam-inert status for the containment atmosphere leading to hydrogen risk in containment. This process is analyzed in this paper focusing on the natural convection driven by wall condensation, and its influence on hydrogen distribution. Firstly, both convective heat transfer model and condensation model are validated with two separate effect experiments. The analogy argument among monument, heat and mass transfer is adopted in GASFLOW-MPI to analysis monument, mass and energy transfer between structure surface and fluid. The simulation result shows good agreement with experiment data. Then a simplified containment model including two steam generator compartments and pressurizer compartment is built and analyzed with GASFLOW-MPI with a postulated accident condition. To avoid long time calculation, the initial condition is calculated with a methodology that is designed to estimate containment status during severe accident provided by EPRI. Two cases are simulated, one without steam injection, where the natural convection drives only by condensation. Other one considers the decay heat that is postulated as a constant steam injection to simulate the natural circulation in containments. Result shows that, during the containment cooling, a transient stratification will occur, leading to high concentration of steam in the dome while low concentration at bottom. This is because the condensed gas is driven downwards near containment shell, pushing steam-rich gas at bottom upwards. The stratification of steam results in a reverse stratification of hydrogen, with high concentration at bottom while low concentration in the dome. Combustibility cloud shows that there is still a stratification of combustibility in containment, though the hydrogen distribution is quite uniform at the end of computation. Therefore, the hydrogen risk should be concerned when implementing containment cooling, especially the local hydrogen concentrate happening at the bottom of containment. [ABSTRACT FROM AUTHOR]

• Modeling of the SNF decay heat removal from the CASTOR RBMK-1500 cask is provided. • Different simplifications in the fuel basket geometry were analyzed. • 2D modelling gives the highest temperature of the fuel load. • Difference between max temperatures in 2D and most realistic 3D modelling is 10 °C. Nuclear fuel is the most important component in a nuclear reactor that has a limited-service life and needs to be reprocessed or carefully handled before the geological disposal which would be the final step in its management. In order it could be disposed of in a geological repository, spent nuclear fuel activity and decay heat should be reduced. For this purpose, it is stored in water pools and interim storage facilities. In interim storage facilities, spent nuclear fuel very often is placed in spent nuclear fuel casks. All storage casks must fulfil safety requirements. The main thermal parameter for cask safety is fuel load temperature which must not exceed the maximum defined value. In this paper, thermal processes in the CASTOR RBMK-1500 storage cask are numerically analyzed using 2D and 3D models. Several simplifications were applied to the cask numerical models and the effects on the internal temperature distribution were analyzed. [ABSTRACT FROM AUTHOR]

The aim of this paper is the mathematical derivation, and numerical analysis of the fractional-space neutron point kinetics (F-SNPK) equations for nuclear reactor dynamics. The classic neutron point kinetics (CNPK) equations are one of the most important models of reduced order in nuclear engineering, that been the subject of countless studies and applications to understand the reactor dynamics and its effects. The F-SNPK derived in this work is an extended model respect to CNPK. The F-SNPK model was derived considering a fractional-space law for the neutron density current where the differential operator is the fractional order (FO), also known as anomalous diffusion exponent. The physical meaning is related with non-Fickian effects (anomalous diffusion), which in F-SNPK gives rise to a new term called in this work anomalous diffusion source that considers neutron leakage, and it depends on the geometric buckling and anomalous diffusion exponent. The numerical analysis shows that the neutron leakage is greater with decreasing anomalous diffusion exponent. [ABSTRACT FROM AUTHOR]

The process of heat removal and depressurization is one of the most significant issues in nuclear safety design. The spray system and the passive containment cooling system (PCCS) are two essential safety arrangements to protect the integrity of the containment and the apparatus. In the present study, the performance of the combined cooling system is investigated by using three-dimensional CFD simulations. The interactions between spray system and external PCCS are analyzed. The numerical results reveal that neither the single passive containment cooling nor the spray system can remove heat and depressurize the containment efficiently under all circumstances. Whereas the combined passive and spray cooling system proposed in this paper can overcome the insufficiency and take the advantages of both the two systems. The mechanism for the superiority of the combined system is explained through the droplets phase change, vapor transportation, wall condensation and film cooling heat transfer processes. [ABSTRACT FROM AUTHOR]

Effects of rolling motion on flow characteristics in a natural circulation system were investigated experimentally and numerically. The numerical results from validated code were mainly used to provide detailed information for the discussion and analysis of experimental results. The results indicate that under rolling motion condition, the phasic difference between flow rate and frictional pressure drop of narrow rectangular channel is negligible. Angular acceleration is the eigenvalue for the effects of rolling motion on flow rate under single-phase natural circulation condition. When angular acceleration is approximately equal, even though either the angle or the period of rolling motion is different, peak, trough and time-averaged values of flow rate are approximately equal. Under rolling motion and single-phase natural circulation conditions, the phenomenon that dimensionless time-averaged mass flow rate is smaller than that under steady state condition is controlled by the nonlinear relationship between mass flow rate and the resistance of loop. The factor also causes the result that the absolute difference of dimensionless flow rate between peak and steady state is smaller than that between trough and steady state. The startup model which is proposed in present paper can be used to predict the flow characteristics of single-phase natural circulation system at startup stage of rolling motion favorably. The self-developed code can simulate instantaneous flow characteristics of single-phase natural circulation system under rolling motion and steady state conditions correctly. The resistance correlations for steady state flow can be directly applied to calculate instantaneous resistance of narrow rectangular channel under rolling motion condition with satisfying agreement with experimental results. [ABSTRACT FROM AUTHOR]

Heat pipe radiator, featured with remarkable advantages in heat transfer efficiency and inherent safety with small specific mass and little weight, are widely adopted to the heat-rejection system for space nuclear power reactors. In this paper, physical and numerical models are developed to obtain the startup and transient behaviors of radiator unit with a potassium (K) heat pipe covered by fin under space environment. The heat transfer limit theory is adopted as criteria for heat pipe operation success. Numerical results indicated that according to the internal vapor flow regimes, the K heat pipe startup could be divided into three distinct stages. The K heat pipe started up from frozen state successful and rapidly until the expected operation state is reached. Among the different heat transfer limits, only the sonic limit due to choked flow restricts the K heat pipe during the second stage. Overall, for the heat-rejection system of space nuclear power reactor, the heat pipe radiator unit can effectively radiated waste heat to the space environment in 5 min and responses fast under transient conditions. [ABSTRACT FROM AUTHOR]

Study of transient behavior and design of control for large reactors, such as the Advanced Heavy Water Reactor (AHWR) requires accurate mathematical models. An 80th order space–time kinetics model which describes the core neutronics behavior of AHWR is available but it is nonlinear and stiff. The modern control design and analysis studies with this model are accompanied by serious numerical ill-conditioning problems. Hence, there is a strong motivation for obtaining a reduced order model which preserves the input–output behavior accurately. In this paper, we have explored the application of balanced truncation technique to obtain a reduced order model from the original high order model of the AHWR. The reduced order model thus obtained was examined from the view point of transient performance by comparing its response with that of the original model and it is found to yield a very good approximation. We also carried out the comparative study between different reduced order models of AHWR, namely, Davison’s technique, Marshall’s technique, singular perturbation analysis and balanced truncation by comparing their performances with respect to each other and with the original model. All of these methods are found to be effective, however the overall accuracy in the approximation using the balanced truncation approach is found to be far more superior. [ABSTRACT FROM AUTHOR]

The paper presents a variant of the Woodcock free flight distance sampling algorithm. Instead of a majorant cross section of the whole system, an arbitrarily chosen cross section can be used for sampling the free flight distance. As the sampling cross section is permitted to be smaller than the maximum of the cross sections, the novel algorithm may cause particle weights to become negative. This technique circumvents the major drawback of conventional Woodcock sampling when a localized heavy absorber implies much more frequent path sampling than required thereby rendering the calculation ineffective. Theoretical derivation is shown for heterogeneous medium. A one dimensional analytical and numerical model is presented for basic optimization study of the free sampling parameters and an applied case illustration is shown using a GPU-based radiotherapy Monte Carlo code. [ABSTRACT FROM AUTHOR]

An alkali metal heat pipe radiator is proposed for the Russian TOPAZ-II space reactor power system to replace the original pumped loop radiator with three advantages. First, the single point failure problem of the original radiator can be avoided. Second, because only the NaK manifold needs to be armored, the specific mass would be reduced and the reliability and survivability can be improved. Third, the heat pipe has nearly isothermal characteristics and high heat transfer capabilities. In the present paper, the high temperature heat pipes using potassium as working fluid, wire screen mesh as wick layer, made of stainless steel are adopted to remove waste heat by radiation. An integral carbon-carbon fin covering and connecting heat pipes as whole heat transfer radiator is selected for its higher thermal conductivity and lower self-weight. A detailed steady state numerical calculation using the finite element method coupled with finite difference method is performed to predict the heat rejection characteristics of the heat pipe radiator. Heat transfer performances of the new concept heat pipe radiator and the pumped loop radiator are compared with key parameters. The results show that the designed heat pipe radiator satisfies the waste heat rejection requirements of the TOPAZ-II power system under the normal operating conditions and has an ideal redundancy. The isothermal and safety of heat pipe radiator is also better than that of pumped loop radiator. [ABSTRACT FROM AUTHOR]

Monte Carlo codes allow for the calculation of precise representation of complex HTR geometry including the double heterogeneity of a fuel. Various approaches to coated fuel particles (TRISO) placement can be applied and the impact on criticality calculations have been already assessed by several authors. Because static neutron transport simulations are affected by different fuel lattice modeling, it can be expected that the systematic discrepancies should appear during burnup calculation as well. In this paper we compare the impact of different TRISO placement and packing factor in the model on the results of the depletion simulation. For numerical tests we chose simplified model of the fuel block from High Temperature Reactor of prismatic type and the continuous energy Monte Carlo burnup code MCB5. Burnup dependent discrepancies of k inf and nuclide concentrations have been successfully observed. Five arrangement models of fuel kernels have been compared in our work: cuboidal lattice truncated by fuel rod, cubic and hexagonal lattices without rod truncation, cubic lattice with stochastic geometry option and rod filled with one layer of randomly located particles. We put emphasis on the constant mass of fuel kernels in the system and correlate obtained results with physical and statistical aspects of TRISO packing so as to explain observed discrepancies. [ABSTRACT FROM AUTHOR]

The neutron transport equation in the integral form is of difficult solution and therefore, schemes for obtaining an equivalent differential formulation are used. In this paper is used the discrete ordinates method (S N method) in order to obtain the equivalent differential formulation. Inspired in the GLS method (Galerkin least square method) a variant of the GLS (Brooks and Hughes, 1982; Ern and Guermond, 2004; Johnson, 1990) method denoted GpLS (Galerkin partial least-square) is proposed for solving this equivalent differential formulation. The convergence rates as well as the robustness of GLS method are preserved by the GpLS method that possesses computational lower cost. Simulations comparing the convergence rates of GpLS method with other methods are presented, confirming the best performance of GpLS method. The numerical experiments were made using fixed source in multiplying medium, with the objective to test the robustness of GpLS method. All the numerical experiments presented confirm the good properties of approximation of GpLS method. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. The Jacobian-free Newton–Krylov method shows no difficulty in solving the two-phase flow drift flux model with a discrete flow regime map. In addition to the Jacobian-free approach, the preconditioning matrix is obtained by using the default finite differencing method provided in the PETSc package, and consequently the labor-intensive implementation of complex analytical Jacobian matrix is avoided. Extensive and successful numerical verification and validation have been performed to prove the correct implementation of the models and methods. Code-to-code comparison with RELAP5-3D has further demonstrated the successful implementation of the drift flux model. [ABSTRACT FROM AUTHOR]

The phenomenon of numerical instabilities present in the Monte Carlo burnup calculations has been shown and explained by many authors using models of LWR, often simplified. Some theoretical considerations about origins of oscillations are very general, however it may be difficult to apply it easily to other models as a prediction of stability. Physics of HTR core differs significantly from the properties of light water system and the reliable extrapolation of the current numerical results is not possible. Moreover, most of the works concerning HTR burnup calculations put no emphasis on the spatial stability of the simulation and apply very long time steps. The awareness in this field of research seems to be not sufficient. In this paper, we focus on the demonstration of depletion instabilities in the simulations of HTR core dedicated for deep burnup of plutonium and minor actinides. We apply various methodology of time step implemented in advanced Continuous Energy Monte Carlo burnup code MCB version 5. Stability analysis is very rare for the full core calculations and the awareness of the oscillation’s problem is obligatory for the reliable modeling of a fuel cycle. In the summary of this work we systematize and discuss factors related to the stability of depletion and review available solutions. [ABSTRACT FROM AUTHOR]

Nodal diffusion codes have been successfully used for decades as a primary tool of commercial power reactor design, safety calculations and plant cycle simulations. The large-size, small-leakage property of these reactor cores and the appropriately generated and applied auxiliary parameters (such as albedos, discontinuity factors etc.) provide a calculation environment, where diffusion theory is fairly accurate, giving the industry the ultimate advantage of fast neutronic computation. Recently, several efforts have been made to extend this methodology to small-core, high-leakage research reactors, in which the validity of diffusion theory is not straightforward. In this paper, the appropriate generation of the diffusion coefficients and their effect on the overall performance of the simulations are investigated in light of recent developments. For the numerical analysis, the two-dimensional DIMPLE benchmarks and the BME TR core benchmark problems were chosen. Group constants were generated with the Serpent 2 Monte Carlo code, while nodal diffusion calculations were carried out with the PARCS code. The results were assessed in terms of multiplication factor, assembly level power and two-group flux distributions. [ABSTRACT FROM AUTHOR]

• Analysis of components account for the high positive lead void reactivity. • Reaction-wise and Nuclide-wise decomposition analysis of lead void reactivity. • Calculation of spatial distribution of lead void reactivity worth. • A low void reactivity lead-cooled fast reactor design M2LFR-1000. Liquid metal-cooled reactor (LMR), including lead-cooled fast reactor (LFR), may have strong positive void reactivity coefficient due to the hard neutron spectrum, which is unfavorable for reactor reactivity control. This paper presents a detailed research on the lead void effect for deeper understanding on the causes. Through analytical analysis and numerical simulation, the lead void effect was decomposed into several components, and the spatial distribution of lead void worth was also calculated. The calculation results have shown that spectral hardening effect, which will cause an increase in fertile fission (mainly 238U) and decrease in the capture rate of all heavy nuclides, accounts for the high positive lead void reactivity. Meanwhile, it has been further concluded that high positive lead void reactivity mainly exists in active region. Finally, comparison between two different lead coolant lost scenarios were carried out to further prove these conclusions. [ABSTRACT FROM AUTHOR]

The four-year Numerical Multi-Physics (NUMPS) project funded by the Academy of Finland was initiated at VTT Technical Research Centre of Finland in September 2012, for the purpose of studying and developing high-fidelity computational methods for nuclear reactor analysis. The project is built around calculation codes developed at VTT, and it aims at the coupled three-dimensional modeling of neutronics, thermal hydraulics and fuel behavior of nuclear reactors. The work involves the continuous-energy Monte Carlo code Serpent and CFD code PORFLO, together with two light-weight solvers, COSY and FINIX, coupled to Serpent at source code level. This paper is a review on the current status and development activities, reflecting the status of the NUMPS project at the beginning of its second complete year. [ABSTRACT FROM AUTHOR]

There are two distinct aspects to this paper. Firstly, it is shown that the A N form of the SPN equations can be derived from a suitably discretised form of the even parity transport equation. The procedure for doing this is explained and some limitations of SPN_A N theory are illustrated. Secondly, to show the magnitude of the errors in A N theory we have taken the problem of an infinitely repeating lattice in which the cell structure is symmetric but can contain any number of sub-regions. The regions can be elliptical and/or rectangular. Because of the repeating lattice, we can express the flux in the cell in the form of a Fourier series. The expansion coefficients of the series may then be obtained from a set of linear equations. It is found that the series converges very slowly and a large number of terms is required which can significantly increase the computational time required for accurate solutions. Use is made of a high order SN ( N = 200) method to compare and test convergence of the Fourier method for an exact case and for the SPN equivalent. [ABSTRACT FROM AUTHOR]

AP1000 passive containment cooling system water storage tank (PCCWST) is set at the top of a shield building. Its function is to hold the water which will flow by gravity to help cool the containment vessel in the highly unlikely event of an emergency – one of the AP1000 plant’s innovative passive safety systems. The huge amount of water may pose a threat to the integrity of the shield building during an earthquake. In this paper, both modal characteristics and transient response of a scaled elevated water tank model were studied by a shaking table experiment. The acceleration of the supporting structure and displacement of water sloshing were recorded under transient loading. Four numerical models were built, including two-mass equivalent model, single lumped-mass model, and finite element models using Fluid30 and Fluid80 elements. The advantages and disadvantages of different numerical methods were discussed. Moreover, finite element (FE) models of AP1000 shield building were established considering the fluid–structure interaction (FSI) effect. The sloshing phenomenon in PCCWST under resonant three-cycle sine (RTCS) wave and seismic loading was studied. The response of shield building under seismic loading was also studied. The results showed that the maximum von Mises stress occurred at the corner of the air inlet. The shaking table experiment can provide a benchmark for seismic response of an elevated water tank. The FE model of shield building may help improve the design of the AP1000 and CAP1400 in the future. [ABSTRACT FROM AUTHOR]

A multi-phase hydrodynamic code using volume of fluid method (VOF) is used to simulate the molten droplet deformation, and the surface waves at the stages of pressure propagation and expansion in steam explosion (SE). Both melt-liquid system and melt-gas system are simulated using the code. A benchmark case of Joseph et al.’s experimental data (1999) is performed to validate the code. In this paper, effects of vapor film and surface tension on the droplet behavior under high pressure pulse are investigated. In addition, effects of material density and pressure pulse magnitude on the droplet deformation, and the growth of surface waves are also analyzed. Results of simulation analysis suggested that vapor film can be neglected and the effect of surface tension is not significant for hydrodynamic process under high pressure pulse. Results of simulation also demonstrate that material density and pressure pulse play a significant role in the process of droplet deformation and surface wave growth. The research shows that the effect of hydrodynamic deformation is significant for droplet fragmentation, and droplet penetration can more likely be achieved by surface wave instability at the stages of propagation and expansion in steam explosion. [ABSTRACT FROM AUTHOR]

The paper presents a closed-form solution of the first-order Transport-Driven Diffusion (TDD) proposed by Picca and Furfaro (2014). The solution is rigorously derived for two source configurations (i.e. Dirac’s delta and rectangular source) to explicitly describe the contribution of the uncollided component and the collided diffuse term. The results are employed to compare the solution of first-order Transport-Driven Diffusion (TDD T with T = 1) with the analytical diffusion approximation as well as to validate numerical solution of the TDD 1 . The comparison with higher-order TDD (i.e., (TDD T with T > 1) is also reported. [ABSTRACT FROM AUTHOR]

In this paper, the overlapping local/global (OLG) iteration method based on deterministic S N transport/p-CMFD calculations was extended to hexagonal core geometry. For this framework, a deterministic S N transport code and p-CMFD equation solver was implemented on triangular cell base. These two calculations are iteratively performed with proper boundary condition update until it reaches converged solution, which is then compared with the direct whole-core transport solution. Two variations from the original overlapping local/global iterative scheme are also introduced and tested: (1) zeroth local calculation of fixed-k problem type with initially guessed incoming angular flux and multiplication factor, and (2) local calculation with non-overlapping region (nonoverlapping local/global iteration). Several numerical test results show OLG system has been successfully implemented on hexagonal core geometry and its variations improve the computational efficiency. [ABSTRACT FROM AUTHOR]

In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations. [ABSTRACT FROM AUTHOR]

External or internal hazards, combined with multiple failures of components and safety systems or human errors can lead to a reactor core melt. In that case the reactor pressure vessel is the last barrier to keep the molten materials inside the reactor and to prevent further challenges to the nuclear power plant structures and consequently to the environment. In-vessel melt retention by external vessel cooling is a possible mitigative severe accident measure. Up to the moment it is not considered as a severe accident management strategy for VVER-1000 reactors. In this paper we analyse the possibility of in-vessel melt retention for a generic pressurized water VVER-1000 reactor during the late in-vessel phase of a postulated station blackout scenario. We developed a numerical model describing the thermal behaviour of a segregated molten pool situated in the lower plenum of the reactor pressure vessel and the thermo-mechanic behaviour of the vessel wall. The finite element code ANSYS® was used for the simulations. The results show that the highest thermo-mechanical loads are observed in the vertical part of the vessel wall, which is in contact with the molten metal. Parameter studies on the thickness of the metal layer have also been performed. Without flooding, the vessel wall will fail, as the necessary temperature for a balanced heat release from the external surface via radiation is near to or above the melting point of the steel. However, the external flooding could help the retention of the corium within the reactor pressure vessel. [ABSTRACT FROM AUTHOR]

The Classical Neutron Point-Kinetic (CNPK) equations are a system of stiff nonlinear ordinary differential equations for the neutron density, which have been subject of countless studies and applications with different approaches in the last seventy years. In this paper we carry out the numerical analysis of the Fractional Neutron Point-Kinetics (FNPK) model for two simple cases of reactivity insertion processes: Case (1) Ramp insertion of reactivity, and Case (2) Sinusoidal form. The FNPK model considers a relaxation time associated with a rapid variation in the neutron flux density, which is considered in the differential operator of fractional order, it is known as anomalous diffusion exponent. Different values of the relaxation time with one-group of delayed neutron precursors were used for this numerical analysis. The results of the neutron flux density with the FNPK model were compared with the CNPK equations for ramp and sinusoidal reactivity insertion processes. In both cases, the neutron density behavior described by the first model, for different relaxation times and anomalous diffusion coefficient values, over-predicts the behavior obtained with the CNPK equations. [ABSTRACT FROM AUTHOR]

• A numerical simulation method for the coupling flow and heat transfer process of liquid metal HCOTSG is proposed. • The correctness of the method is validated by comparing with relevant experimental research, and the maximum error is less than 25%. • The flow and heat transfer characteristics of liquid metal HCOTSG under different working conditions are analyzed. Much attention has been focused on the Liquid Metal Fast Reactor (LMFR) as one of the most promising concepts for GEN-IV reactors. Helical coil once-through tube steam generator (HCOTSG) is a proposed form of steam generator. Due to its unique advantages, HCOTSG is widely used in various reactor power systems, including LMFR. In this paper, a numerical approach is proposed to simulate heat transfer from the primary side (liquid metal) and secondary side (water/steam). The liquid lead-bismuth eutectic (LBE) is flowing in the shell side and pressurized water is flowing in the tube side. FLUENT CFD commercial code is adopted for the simulations. The robustness of the method is validated by comparing it with relevant experimental research, and the maximum error is less than 25%. Based on this method, the distribution of thermal-hydraulic parameters inside HCOTSG is obtained and the flow and heat transfer characteristics are analyzed. The influence of boundary conditions and geometric parameters on the flow and heat transfer in HCOTSG is analyzed. The comprehensive performance of different models is compared with the comprehensive performance evaluation index. The optimal geometric arrangement scheme for the working conditions is recommended. Compared with the reference model, the comprehensive performance can be improved by up to 14%. This study provides a numerical simulation method reference for the study of flow and heat transfer characteristics and structural design optimization of liquid metal HCOTSG. [ABSTRACT FROM AUTHOR]

• A Fine Mesh Finite Difference method based on the Flat Source Region level is proposed. • Two-Level acceleration scheme is performed to accelerate the solution of FMFD system. • Fourier analysis and numerical results show that FMFD with TL is more efficiency than CMFD. Normally, the pin-cell-based C oarse M esh F inite D ifference (CMFD) method is directly used to accelerate the high-fidelity neutron transport calculations. However, the acceleration effect still has a bottleneck due to the fact that only the pin-cell homogenized flux can be used to update the fine-mesh flux, such as the flat-source-region flux for MOC calculation. In this paper, a F ine M esh F inite D ifference (FMFD) method based on the F lat S ource R egion (FSR) level is proposed and implemented in a two-dimensional transport code using M ethod O f C haracteristics (MOC). FMFD could avoid the mapping error from pin-cell-wise mesh to fine FSR mesh. However, the solution of the FMFD system is time-consuming since the scale of the FMFD system is much larger than that of the pin-cell-based CMFD system. Therefore, T wo- L evel (TL) acceleration scheme is performed where the pin-cell-based CMFD is used to accelerate the solution of FMFD system. Both of these two acceleration methods are based on the G eneralized E quivalence T heory (GET). Fourier analysis and numerical results show that FMFD with TL is more efficiency than conventional CMFD. [ABSTRACT FROM AUTHOR]

• Further understanding of the increasing trend of noise levels in KWU pre-KONVOI PWRs. • Modelling of most plausible noise sources in PWRs using commercial code, SIMULATE-3K. • Investigate and predict reactor noise response due to realistic in-core perturbation. • Induced neutron noise reflects imposed vibrational patterns. • Noise spectral analysis allows to characterize noise sources. This work is a contribution towards the development of computational methods that allow investigation and prediction of reactor noise response due to in-core perturbations such as vibrations of reactor internals and fluctuations in thermal-hydraulic parameters. Further improvements are made to the modelling approach to allow for vibrations of fuel assemblies at higher vibrational modes. Modelling of such realistic noise sources, and assessment of the induced noise response are presented in this paper. Results show that the simulation of individual noise sources and their combinations affect the neutron noise phenomenology. The neutron noise induced radially and, in particular, axially, reflects the imposed vibrational patterns associated to the higher modes of the fuel assemblies. The results provide confidence in the application of the developed methodology based on commercial time-domain codes for modelling of realistic noise scenarios and numerical noise analyses of the PWR cores. [ABSTRACT FROM AUTHOR]