Passive safety systems in a nuclear reactor allow to simplify the overall plant design, beside improving economics and reliability, which are considered to be among the salient goals of advanced Generation IV reactors. This work focuses on investigating the application of a self-actuated, gravity-driven shutdown system in a small lead-cooled fast reactor and its dynamic response to an initiating event. The reactor thermal-hydraulics and neutronics assessment were performed in advance. According to a first-order approximation approach, the passive insertion of shutdown assembly was assumed to be influenced primarily by three forces: gravitational, buoyancy and fluid drag. A system of kinematic equations were formulated a priori and a MATLAB program was developed to determine the dynamics of the assembly. Identifying the delicate nature of the balance of forces, sensitivity analysis for coolant channel velocities and assembly foot densities yielded an optimal system model that resulted in successful passive shutdown. Transient safety studies, using the multi-point dynamics code BELLA, showed that the gravity-driven system acts remarkably well, even when accounting for a brief delay in self-actuation. Ultimately the reactor is brought to a sub-critical state while respecting technological constraints.
This paper describes the design, implementation and characterisation of an Autonomous Reactivity Control (ARC) system in a small modular lead-cooled fast reactor. The aim of this work was to demonstrate the applicability of the ARC system and to study its dynamic behaviour during an anticipated transient without scram. A simplified one-dimensional model was developed to calculate the heat transfer within the ARC system, and the reactivity worth as a function of the neutron poison’s insertion into the active core was obtained via static neutronic calculations. By coupling the aforementioned models, the ARC’s time-dependent reactivity was derived as a function of the coolant outlet temperature variation. This model was implemented into the BELLA multi-point dynamics code and transient simulations were run. A control rod ejection accident was studied leading to an unprotected transient overpower scenario, in which 350 pcm reactivity was inserted during one second. It was shown that the ARC system provides a forceful negative reactivity feedback and that steady-state temperatures after the transient were reduced by almost 300 K compared to an identical transient without its action. In this scenario, the ARC system managed to stabilise the coolant outlet temperature at a value 100 K above nominal conditions. The implementation of an ARC system provided the reactor with a passively actuated self-regulating reactivity control system able to insert large amounts of negative reactivity in a short amount of time.
Monte Carlo burnup simulations continue to be seen as computationally very expensive numerical routines despite recent developments of associated methods. Here, we suggest a way of improving the computing efficiency via optimisation of the length of the time steps and the number of neutron histories that are simulated at each Monte Carlo criticality run. So far, users of Monte Carlo burnup codes have been required to set these parameters at will; however, an inadequate choice of these free parameters can severely worsen the computing efficiency. We have tested a large number of combinations of the free parameters on a simplified and fast solver, and we have observed that the computing efficiency was maximized when the computing cost of all Monte Carlo neutron transport calculations (summed over all time steps) was approximately comparable to costs of other procedures (all depletion simulations, the loading and processing of neutron cross sections, etc.). In this technical note, we demonstrate these results, and we also derive a simple theoretical model of the convergence of Monte Carlo burnup simulations that conforms to these numerical results. Here, we also suggest a straightforward way to automatise the selection of the optimal values of the free parameters for Monte Carlo burnup simulations.
We show here that computing efficiency of Monte Carlo burnup simulations depends on chosen values of certain free parameters, such as the length of the time steps and the number of neutron histories simulated at each Monte Carlo criticality run. The efficiency can thus be improved by optimising these parameters. We have set up a simple numerical model that made it possible for us to test a large number of combinations of the free parameters, and suggest a way to optimise their selection.
In this chapter, an overview of the verification, validation, and uncertainty quantification process is offered. First, the context of the dialog with the safety authorities is explained, and the need for a thorough code validation procedure able to meet the regulatory safety requirements is highlighted. Then, the concept of code verification is introduced, and the main steps are described. The validation process is depicted next. Emphasis is made upon the identification of the physical phenomena of interest and upon the choice of adequate computational tools to capture them. The targeted validity domain of these computational tools and its dependence on available and accurate experimental data are detailed with respect to the issue of scaling. Finally, an overview of selected techniques for uncertainty and sensitivity analysis is provided.
This thesis investigates Monte Carlo methods applied to criticality and time-dependent problems in reactor physics. Due to their accuracy and flexibility, Monte Carlo methods are considered as a “gold standard” in reactor physics calculations. However, the benefits come at a significant computing cost. Despite the continuous rise in easily accessible computing power, a brute-force Monte Carlo calculation of some problems is still beyond the reach of routine reactor physics analyses. The two papers on which this thesis is based try to address the computing cost issue, by proposing methods for performing Monte Carlo reactor physics calculations more efficiently. The first method addresses the efficiency of the widely-used k-eigenvalue Monte Carlo criticality calculations. It suggests, that the calculation efficiency can be increased through a gradual increase of the neutron population size simulated during each criticality cycle, and proposes a way to determine the optimal neutron population size. The second method addresses the application of Monte Carlo calculations to reactor transient problems. While reactor transient calculations can, in principle, be performed using only Monte Carlo methods, such calculations take multiple thousands of CPU hours for calculating several seconds of a transient. The proposed method offers a middle-ground approach, using a hybrid stochastic-deterministic scheme based on the response matrix formalism. Previously, the response matrix formalism was mainly considered for steady-state problems, with limited application to time-dependent problems. This thesis proposes a novel way of using information from Monte Carlo criticality calculations for solving time-dependent problems via the response matrix.
This thesis presents a compilation of work focused on Monte Carlo crit-icality, kinetics and burnup calculations in reactor physics. Performing suchcalculations usually comes at a high computing cost. Therefore, the main mo-tivation behind the presented work is lowering the computing cost of MonteCarlo calculations. To this end, three new methods for improving the comput-ing efficiency are proposed: a method for neutron population control in MonteCarlo criticality calculations; a hybrid stochastic-deterministic response ma-trix method for reactor kinetics calculations; and an optimisation method forMonte Carlo burnup calculations.
The first method gradually increases the neutron population size over thesuccessive cycles in Monte Carlo criticality calculations. This enables fasterfission source iterations at the beginning of a calculation where the sourcemay contain errors from the initial cycle while at the same time preventingthe source bias from dominating the error later in the calculation. The methodis tested on a set of full-core PWR criticality calculations.
The second method is based on the response matrix formalism which de-scribes a system by a set of response functions. The response functions arecomputed during Monte Carlo criticality calculations. These functions arethen used in a deterministic set of equations for solving a space-time depen-dent problem. The method is demonstrated on a set of absorber movementtransients in a PWR-type mini-core.
The third method sets the time step length and the number of neutronhistories simulated during each time step of Monte Carlo burnup calculationsaccording to the fraction of the computing cost assigned to the depletion solu-tions (and other procedures that are repeatedly executed before starting theactive cycles) and the overall computing cost of a Monte Carlo burnup calcu-lation. Optimal values of this fraction are studied in a set of test calculations.
Additionally, numerical tests on tally error convergence in Monte Carlocriticality calculations and stability of Monte Carlo burnup calculations arepresented. The context and the outcomes of the work are summarized inthe main body of the thesis while the details are presented in the appendedpublications.
Monte Carlo criticality calculations of large, loosely-coupled problems are long known to suffer from slow convergence of the tally errors due to cycle-to-cycle fission source correlations. In several recent studies, it was suggested that these correlations could be possibly attributed to the neutron clustering phenomenon that is visible in calculations with a small number of neutrons per iteration cycle (batch size). Nevertheless, other studies have also shown the error convergence rate in such loosely-coupled problems to be batch size-independent during active criticality cycles. Here, we aim to address this inconsistency by studying the error convergence in a large number of test calculations, varying the neutron batch size from small to large. In our tests, we have observed that the presence of visible neutron clusters does not increase the cycle-to-cycle fission source correlations and does not worsen the convergence rate of the tally errors.
We present a source convergence acceleration method for Monte Carlo criticality calculations. The method gradually increases the neutron population size over the successive inactive as well as active criticality cycles. This helps to iterate the fission source faster at the beginning of the simulation where the source may contain large errors coming from the initial cycle; and, as the neutron population size grows over the cycles, the bias in the source gets reduced. Unlike previously suggested acceleration methods that aim at optimisation of the neutron population size, the new method does not have any significant computing overhead, and moreover it can be easily implemented into existing Monte Carlo criticality codes. The effectiveness of the method is demonstrated on a number of PWR full-core criticality calculations using a modified SERPENT 2 code.
We present a stability test of the explicit Euler and predictor-corrector based coupling schemes in Monte Carlo burnup calculations of the gas fast reactor fuel assembly. Previous studies have identified numerical instabilities of these coupling schemes in Monte Carlo burnup calculations of thermal-spectrum reactors due to spatial feedback induced neutron flux and nuclide density oscillations, where only sufficiently small time steps could guarantee acceptable precision. New results suggest that these instabilities are insignificant in fast-spectrum assembly burnup calculations, and the considered coupling schemes can therefore perform well in fast-spectrum reactor burnup calculations even with relatively large time steps. Note: Some figures in this technical note may be in color only in the electronic version.
APROS code is a multifunctional process simulator which combines System Thermal-Hydraulic (STH) capabilities with ID,'3D reactor core neutronics and full automation system modeling. It is applied for various tasks throughout the complete power plant life cycle including R&D, process and control engineering, and operator training. Currently APROS is being developed for evaluation of Generation IV conceptual designs using Lead-Bismuth Eutectic (LBt) alloy coolant. TALL-3D facility has been built at KTH in order to provide validation data for standalone and coupled STH and Computational Fluid Dynamics (CFD) codes. The facility consists of sections with measured inlet and outlet conditions for separate effect and integral effect tests (SETs and lETs). The design is aimed at reducing experimental uncertainties and allowing fall separation of code validation from model input calibration. In this paper we present the development of experimental TALL-3D lest matrix for comprehensive validation of APROS code. First, the representative separate effect and integral system response quantities (SRQs) arc defined. Second, sources of uncertainties are identified and code sensitivity analysis is carried out to quantify the effects of code input uncertainties on the code prediction. Based on these results the test matrixes for calibration and validation experiments arc determined in order to minimize the code input uncertainties. The applied methodology and the results arc discussed in detail.
Integrated Deterministic Probabilistic Safety Assessment (IDPSA) methodology is a powerful tool for identification of failure domains when both stochastic events and physical time dependent processes are important. Computational efficiency of deterministic models is one of the limiting factors for detailed exploration of the event space. Pool type designs of Generation IV heavy liquid metal cooled reactors introduce importance of capturing intricate 3D flow phenomena in safety analysis. Specifically mixing and stratification in 3D elements can affect efficiency of passive safety systems based on natural circulation. Conventional 1D System Thermal Hydraulics (STH) codes are incapable of predicting such complex 3D phenomena. Computational Fluid Dynamics (CFD) codes are too computationally expensive to be used for simulation of the whole reactor primary coolant system. One proposed solution is code coupling where all 1D components are simulated with STH and 3D components with CFD codes. However, modeling with coupled codes is still too time consuming to be used directly in IDPSA methodologies, which require thousands of simulations. The goal of this work is to develop a computationally efficient surrogate model (SM) which captures key physics of complex thermal hydraulic phenomena in the 3D elements and can be coupled with 1D STH codes instead of CFD. TALL-3D is a lead-bismuth eutectic thermal hydraulic loop which incorporates both 1D and 3D elements. Coupled STH-CFD simulations of TALL-3D typical transients (such as transition from forced to natural circulation) are used to calibrate the surrogate model parameters. Details of current implementation and limitations of the surrogate modeling are discussed in the paper in detail.
APROS is a multifunctional simulator, suitable for various tasks throughout the complete power plant life cycle from design to operator training. The code combines the System-Thermal Hydraulic (STH) capabilities with 1D/3D reactor core neutronics and full automation system modelling. APROS is widely used for dynamic studies in light water nuclear reactor technology. Currently the simulation capabilities of the code are being developed for evaluation of Generation IV nuclear reactor designs that use liquid metals (e.g. Lead-Bismuth Eutectic (LBE) alloy) as cooling media. However, validation of APROS code has been limited to light water cooled systems (test facilities and reactors). Therefore validation is required for the LBE thermal-hydraulic models. In this work, we use data from the Thermal-hydraulic Accelerator-Driven System (ADS) Lead bismuth Loop (TALL) facility constructed at KTH. In total, 10 transient data sets from TALL experiments were used for APROS LBE fluid model integral validation. TALL facility model consisting of the primary LBE loop, the secondary oil loop and the ultimate water heat sink was developed using APROS Graphical User Interface (GUI). Five System Response Quantities (SRQs) were considered in the validation process: LBE temperatures at four locations of the facility and the LBE mass flow. Uncertainty analysis was employed in the validation process. Results of quantitative code validation are presented in the paper. Suggestions for improvements of the validation methodology, experimental conditions and approaches to reduction of experimental uncertainty are discussed in detail.
Until recently, reactor transient problems were exclusively solved by approximate deterministic methods. The increase in available computing power made it feasible to approach the transient analyses with time-dependent Monte Carlo methods. These methods offer the first-principle solution to the space-time evolution of reactor power by explicitly tracking prompt neutrons, precursors of delayed neutrons and delayed neutrons in time and space. Nevertheless, a very significant computing cost is associated with such methods. The general benefits of the Monte Carlo approach may be retained at a reduced computing cost by applying a hybrid stochastic-deterministic computing scheme. Among such schemes are those based on the fission matrix and the response matrix formalisms. These schemes aim at estimating a variant of the Greens function during a Monte Carlo transport calculation, which is later used to formulate a deterministic approach to solving a space-time dependent problem. In this contribution, we provide an overview of the time-dependent response matrix method, which describes a system by a set of response functions. We have recently suggested an approach where the functions are determined during a Monte Carlo criticality calculation and are then used to deterministically solve the space-time behaviour of the system. Here, we compare the time-dependent response matrix solution with the transient fission matrix and the time-dependent Monte Carlo solutions for a control rod movement problem in a mini-core reactor geometry. The response matrix formalism results in a set of loosely connected equations which offers favourable scaling properties compared to the methods based on the fission matrix formalism.
Presented is a stochastic-deterministic, response matrix method for transient analyses of nuclear systems. The method is based on the response matrix formalism, which describes a system by a set of response functions. We propose an approach in which these response functions are computed during a set of Monte Carlo criticality calculations and are later used to formulate a deterministic set of equations for solving a space-time dependent problem. Application of the response matrix formalism results in a set of loosely connected equations, which leads to a favourable linear scaling of the problem. The method offers a simplified approach compared to previously proposed response matrix methods by avoiding phase-space expansions in sets of basis functions. We describe the method starting with the fundamental neutron transport considerations, provide a demonstration on two absorber movement transients in a 3 × 3 assembly PWR mini-core geometry, and compare the solutions against time-dependent Monte Carlo simulations.
SEALER is a small lead-cooled reactor, designed by LeadCold Reactors for commercial power production in off-grid applications, such as Arctic communities and mining operations. For the purpose of safety-informed design, and independent verification of transient performance, KTH and LeadCold are developing BELLA, a lumped-parameter dynamics code for simulation of protected and un-protected transients in liquid metal cooled reactors. In the present contribution, results from a preliminary benchmark on UTOP and ULOF transients between BELLA and SAS4A/SASSYS-1 are presented. Whereas the codes predict very similar fuel and clad temperatures during the UTOP simulation, discrepancies in natural convection mass flow following a loss-of-flow event are identified and discussed.
In this paper, the conceptual design of a small lead-cooled nuclear reactor intended to replace diesel-power in off-grid applications is presented. In a vessel of dimensions making it transportable by air, the targeted design performance is to produce 3 MW of electrical power for up to 30 years without reloading of fuel. Consequently, the inner vessel can be sealed, delaying malevolent access to the nuclear fuel and improving security. Alumina forming alloys are applied to ensure long term corrosion protection of fuel cladding tubes, steam generator tubes and primary vessel over the operational temperature regime. Moreover, decay heat can be removed in a completely passive manner by natural convection from the core to the primary coolant and by thermal radiation from the primary vessel to the environment. Finally, the source term is such that relocation of population residing beyond 1 km from the reactor will not be required even in the case of a complete core melt.
Flow-accelerated corrosion and erosion (FACE) phenomena can be crucial for performance of structural elements in heavy liquid metal (HLM) cooled reactor systems. Existing experimental observations indicate that turbulent flow characteristic can affect FACE, but there is no quantitative data that can be used for model development and validation. Main recirculation pump impellers, which operate at high relative velocities and rotational flow conditions can be especially vulnerable to FACE. For comparison, the core internals operate at lower velocities and in axial flow conditions, but at higher temperatures and neutron fluence. Hence, systematic experimental data is needed to improve our knowledge on FACE phenomena. The Separate Effect Test Facility for Flow-Accelerated Corrosion and Erosion (SEFACE) is designed to obtain such experimental data including high relative velocities (up 20 ms−1) and high temperatures (400 to 550 °C) of liquid lead. This article focuses on the hydrodynamic design of SEFACE. The aim of the design is to achieve well defined flow conditions for experiments and ensure safe operation of the facility. First, we examine three design concepts (i.e., forced convection loop, rotating cylinder, and rotating disk) and motivate the choice of the rotating disk approach for SEFACE. Second, we discuss different design options, i.e., a confined rotor–stator test chamber and the unconfined rotating disk configuration. We used Reynolds-Averaged Navier Stokes (RANS) calculations to identify and solve the issues stemming from the high rotational speed. These include, for instance, lead free surface deformation, radial pressure buildup, and axial bending forces due to asymmetric test chamber. The CFD-derived torque and power predictions in rotor–stator and rotating disk systems are verified with selected empirical turbulent friction factor correlations or/and DNS calculations. We demonstrate that the developed hydrodynamic design of SEFACE solves identified issues and enables obtaining experimental data under well-defined flow conditions. The findings are deemed to also be applicable to the design of rotating disk-type FACE installations for other liquid mediums.
Long-term material compatibility in heavy liquid metal (HLM) remains a challenge for the successful deployment of HLM-based technologies. Flow-accelerated corrosion and erosion (FACE) phenomena can lead to continual material deterioration, which needs to be considered throughout the reactor design stage. Nonetheless, known experimental data are inadequate to cover all the prototypical flow regimes during LFR's operation. Modelling of the FAC/FACE phenomena remains mostly in lumped parameter/subchannel scales, where the FAC model is coupled to the bulk flow of the pipe or subchannel. These methodologies might produce a sufficient prediction for the core internals; however, this might not be suitable for the pump impeller due to comparatively greater relative velocity and the occurrence of transient flow patterns near the rotating impeller. To establish an understanding of the connection between turbulence and FACE, the liquid lead-based Separate Effect Flow Accelerated Corrosion and Erosion (SEFACE) facility is currently under design at KTH in the framework of the Sustainable Nuclear Energy Research In Sweden (SUNRISE) project. SEFACE attempts to investigate FACE phenomena in the liquid lead and produce quantifiable validation data for model development. The paper divides itself into two parts. Part I refers to the study of operational conditions in SEFACE via Reynolds Averaged Navier Stokes (RANS) simulation, while Part II deals with the recent attempt on modelling time-dependent flow shear on rotating disks based on large eddy simulation (LES). The paper begins with a brief review of prior studies on flow-accelerated corrosion. Following that, the SEFACE facility's design concept is laid out considering several physical and operational constraints. A periodic wedge of the SEFACE test chamber is chosen to examine the facility's time-averaged behaviour. The k-ω shear stress transport (SST) model was employed for the simulations. The torque prediction on the rotating disk system is verified with the empirical frictional factor prediction. The latest hydrodynamic design enables SEFACE to be spun at 1200 revolutions per minute (corresponding to a maximum velocity of 21 m/s) without causing free surface deformation or excessive pressure. SEFACE permits the collecting of experimental data under the effect of various relative velocities in a single experiment round. The second part of the paper focuses on a recent attempt to determine the wall shear stress distribution on a rotating disk using wall-modelled large eddy simulation (WMLES S-Omega). The obtained amplitude and frequency of wall shear stress fluctuations will aid model development in future.