Around the world, countries are increasingly considering carbon-free energy generation options as the threat of climate change grows. Small modular reactor designs, promising such carbon-free energy generation, are thriving worldwide with novel and innovative technologies that improve safety as well as economic performance. Canada is also considering small modular reactors (SMRs) as a means of achieving net zero carbon emissions by 2050. Some of these reactor designs utilize pressurized water for cooling and moderator. Reactors with pressurized water have been subjected to steam generator tube ruptures in the past, and a detailed investigation into the possible consequences of such incidents in SMRs should be conducted. In this research, a model for one of the newer designs, the NuScale Integrated Small Modular Reactor, was developed with the RELAP5-3D code for assessing safety related transients. The NuScale Small Modular Reactor incorporates helical coil steam generators within its reactor pressure vessel, which are more efficient in terms of heat transfer than the U-tube steam generators that are widely used in nuclear reactors. In the first part of the research, a detailed model is created and used to obtain steady state conditions with parameters collected from NuScale’s Final Safety Analysis Report (FSAR). The Steam Generator Tube Rupture event is analyzed in the second part of the work. Slight differences in the broken and intact steam generator pressures as well as decay heat removal system flow rates are seen in the comparison of reference values and calculated results. Among the reasons for those differences could be that the correlations used by the RELAP5-3D code for heat transfer coefficient and pressure drop in the helical coil steam generators are different than those of the NuScale proprietary code NRELAP5, with which the analyses have been performed in the FSAR. Also, post-dryout heat transfer at the exit of helical coil steam generators and evaporator sections could cause differences in the outlet conditions of the steam, resulting in different mass flow rates as well. The final section of the research simulates a comparable but more severe tube rupture incident without the availability of decay heat removal systems in order to assess the reactor’s emergency core cooling system reaction. Passive decay heat removal systems are crucial components for removing heat after reactor shutdown through heat exchangers that are submerged in the reactor pool and connected to steam generators by a closed loop. The containment pressures, the containment wall temperatures, and the peak fuel clad temperatures are considered to be the key design constraints that must be observed. Future work on this subject could include modifying the source code, adding specific correlations for helical coil steam generators, and comparing the results, as well as quantifying uncertainties in the SGTR event. Main parameters in the quantification of uncertainties would be reactor power, single phase and two-phase discharge coefficients from the break, trip signals and delays as well as break size and location. / Thesis / Master of Applied Science (MASc)

Advanced computational tools are applied to simulate a nuclear power plant (NPP) control rod assembly ejection (CRE) accident. The impact of these reactivity-initiated accidents (RIAs) on core reactivity behavior, 3D power distribution and stochastic reactivity estimation are evaluated. The three tools used are: the thermal-hydraulic (TH) RELAP5 (R5) code, the neutronic (NK) PARCS (P3D) code, and the coupled version P3D/R5, with specially developed linkage using the environment code MATLAB. This study considers three different-size cores: NPP1 (2772 MWt); NPP2 (530 MWt); and NPP3 (1061 MWt). The three cores have the same general design and control rod assembly (CRA) positions, and the ejected CRA has similar worth and at the same rod ejection pace. The CRE is assessed under both hot zero power (HZP) and hot full power (HFP) conditions. The analyses indicate that RIA modeling and simulation should be carried out through a systematic coding and configuration approaches, otherwise the results will not capture the true transient behavior of the core under analysis. The simulation of one code depends on the appropriate configuration of parameters generated by the other code and on the correct determination of the TH/NK mapping weight factors for the various mesh regions in each of the models. From the design point of view, the standalone codes predict milder magnitude of power and reactivity increase compared to the coupled P3D/R5 simulation. The magnitudes of reduced peak power and reactivity become larger as the core size shrinks. The HFP simulation shows that the three NPPs have the same transient peak value, but the post-transient steady power is lower for a smaller core. The HZP analysis indicates that the transient peak is lower for the smaller core, but the post-transient power occurs at the same level. The three-dimensional (3D) power distributions are different among the HFP and HZP cases, but do not depend on the size of the core. The results indicate: i) HFP: core power increases in the area surrounding the ejected rod/bank assembly, and this increase becomes lower as the NPPs shrinks however, the power is well-distributed after the transient; and ii) HZP: the area surrounding the CRA stays hotter, but the 3D peak assembly factor becomes lower, during and after the transients, as the NPPs shrinks. These features confirm that the smaller cores yield a safer response to a given inserted reactivity compared to larger cores. A stochastic extended Kalman filter (EKF) algorithm is implemented to estimate the reactivity based on the reactor power profile, after the addition of random noise. The inverse point kinetics (IPK) deterministic method is also implemented and the results of the application of EKF and IPK are compared to the P3D/R5 simulation. The following sophisticated strategies made the EKF algorithm robust and accurate: the system is modeled by a set of continuous time nonlinear stochastic differential equations; the code uses a time step directly based on the power measured and applies that to the model for online discretization and linearization; filter tuning goes automatically up from the first time step; and the state noise covariance matrix is updated online at each time step. It was found that the IPK reactivity has higher noise content compared to the EKF reactivity for all cases. Thus, the EKF presents superior and more accurate results. Furthermore, under a small reactivity insertion, the IPK reactivity varies widely from positive to negative values: this variation is not observed within the EKF. A sensitivity analysis for three distinct standard deviation (SD) noise measurements suggests that EKF is superior to IPK method, independent of the noise load magnitude. As the noise content increases, the error between the IPK and P3D/R5 reactivity also increases. A sensitivity analysis for five distinct carry-over effects of different random noise loads indicates that the random addition of different noise loads to the reactor power does not change the overall performance of both algorithms. / Este trabalho aplica métodos computacionais avançados para simular a ejeção de barras de controle (CRE) em uma planta térmica nuclear (NPP). São avaliados o impacto da ocorrência de acidentes iniciados por reatividade (RIAs) na reatividade total, na distribuição da potência em três dimensões (3D) e na determinação da reatividade. As ferramentas utilizadas são: o código termo-hidráulico (TH) RELAP5 (R5), o código neutrônico (NK) PARCS (P3D), a versão acoplada P3D/R5, e o ambiente computacional MATLAB. Este estudo considera três reatores nucleares de diferentes tamanhos: NPP1 (2772 MWT); NPP2 (530 MWt); e NPP3 (1061 MWt). Os três núcleos possuem projeto similar e idêntica posição dos grupos das barras de controle (CRA), além do mesmo valor de reatividade diferencial das CRA ejetadas e idêntica velocidade de ejeção. A ocorrência da CRE é avaliada sob condições de hot zero power (HZP) e de hot full power (HFP). As análises indicam que a modelagem e a simulação de RIAs devem ser realizadas sistematicamente, caso contrário os resultados não irão refletir o comportamento em regime transitório do núcleo. A simulação de um modelo em um código depende da apropriada configuração de parâmetros gerados pelo outro código e da determinação adequada do mapeamento TH/NK para as várias malhas dos modelos. Do ponto de vista de projeto, a utilização de códigos independentes resulta em cálculos de potência e reatividade conservadores em comparação com os resultados utilizando-se P3D/R5. Os picos de potência e de reatividade são menores à medida que o núcleo encolhe. A simulação em condições de HFP resulta em valores de pico de potência similares durante transitório para as três NPPs, mas a potência de pós-transitórios é menor para o menor núcleo. A análise em condições de HZP também indica que o valor máximo durante o transitório é menor para o menor núcleo, mas o pós-transitórios ocorre aos mesmos níveis de potência das demais NPPS. A distribuição de potência em 3D também apresenta resultados distintos para condições de HFP e HZP, mas tais resultados são independentes do tamanho do núcleo: i) HFP: há um aumento da potência do núcleo em torno da CRE, mas tal comportamento diminui para núcleos menores - no entanto, a potência é bem distribuída após o transitório; e ii) HZP: há aumento de potência na área do CRE, mas o pico de potência em 3D é menor durante e depois dos transitórios para núcleos menores. Tais características indicam que os núcleos menores respondem de forma mais segura quando da inserção de reatividade em comparação a reatores de maiores dimensões. O método estocástico de filtragem de Kalman estendido (EKF) foi codificado para estimar a reatividade com base no perfil de potência da NPP, após a adição de ruído aleatório. O método determinístico da cinética pontual inversa (IPK) também foi implementado e os resultados da aplicação dos algoritmos do EKF e IPK foram comparados com os resultados da simulação do P3D/R5. As seguintes estratégias, implementadas neste trabalho, possibilitaram a aplicação robusta e precisa do EKF: o sistema foi modelado por um conjunto de equações diferenciais não-lineares estocásticas de tempo contínuo; o algoritmo obtém o passo de tempo diretamente da potência medida e aplica-o ao modelo para a discretização e linearização online; o ajuste do filtro ocorre automaticamente a partir do primeiro passo de tempo; e a matriz de covariância do ruído no estado é atualizada online. Verificou-se que a reatividade calculada pelo método IPK possui maior nível de ruído quando comparada ao EKF para todos os casos estudados. Portanto, o EKF apresenta resultados superiores e mais precisos. Além disso, sob uma pequena inserção de reatividade, a reatividade calculada pelo método IPK varia consideravelmente de valores positivos para negativos: esta variação não é observada com o EKF. Uma análise de sensibilidade para três desvios padrão (SD) sugere que o algoritmo EKF é superior ao método IPK, independente da magnitude do ruído. Com o aumento da magnitude do ruído, o erro entre as reatividades calculadas pelo IPK e pelo P3D/R5 aumenta. A análise de sensibilidade para cinco ruídos aleatórios indica que a adição de ruído na potência do reator não altera o desempenho global de ambos os algoritmos.

Advanced computational tools are applied to simulate a nuclear power plant (NPP) control rod assembly ejection (CRE) accident. The impact of these reactivity-initiated accidents (RIAs) on core reactivity behavior, 3D power distribution and stochastic reactivity estimation are evaluated. The three tools used are: the thermal-hydraulic (TH) RELAP5 (R5) code, the neutronic (NK) PARCS (P3D) code, and the coupled version P3D/R5, with specially developed linkage using the environment code MATLAB. This study considers three different-size cores: NPP1 (2772 MWt); NPP2 (530 MWt); and NPP3 (1061 MWt). The three cores have the same general design and control rod assembly (CRA) positions, and the ejected CRA has similar worth and at the same rod ejection pace. The CRE is assessed under both hot zero power (HZP) and hot full power (HFP) conditions. The analyses indicate that RIA modeling and simulation should be carried out through a systematic coding and configuration approaches, otherwise the results will not capture the true transient behavior of the core under analysis. The simulation of one code depends on the appropriate configuration of parameters generated by the other code and on the correct determination of the TH/NK mapping weight factors for the various mesh regions in each of the models. From the design point of view, the standalone codes predict milder magnitude of power and reactivity increase compared to the coupled P3D/R5 simulation. The magnitudes of reduced peak power and reactivity become larger as the core size shrinks. The HFP simulation shows that the three NPPs have the same transient peak value, but the post-transient steady power is lower for a smaller core. The HZP analysis indicates that the transient peak is lower for the smaller core, but the post-transient power occurs at the same level. The three-dimensional (3D) power distributions are different among the HFP and HZP cases, but do not depend on the size of the core. The results indicate: i) HFP: core power increases in the area surrounding the ejected rod/bank assembly, and this increase becomes lower as the NPPs shrinks however, the power is well-distributed after the transient; and ii) HZP: the area surrounding the CRA stays hotter, but the 3D peak assembly factor becomes lower, during and after the transients, as the NPPs shrinks. These features confirm that the smaller cores yield a safer response to a given inserted reactivity compared to larger cores. A stochastic extended Kalman filter (EKF) algorithm is implemented to estimate the reactivity based on the reactor power profile, after the addition of random noise. The inverse point kinetics (IPK) deterministic method is also implemented and the results of the application of EKF and IPK are compared to the P3D/R5 simulation. The following sophisticated strategies made the EKF algorithm robust and accurate: the system is modeled by a set of continuous time nonlinear stochastic differential equations; the code uses a time step directly based on the power measured and applies that to the model for online discretization and linearization; filter tuning goes automatically up from the first time step; and the state noise covariance matrix is updated online at each time step. It was found that the IPK reactivity has higher noise content compared to the EKF reactivity for all cases. Thus, the EKF presents superior and more accurate results. Furthermore, under a small reactivity insertion, the IPK reactivity varies widely from positive to negative values: this variation is not observed within the EKF. A sensitivity analysis for three distinct standard deviation (SD) noise measurements suggests that EKF is superior to IPK method, independent of the noise load magnitude. As the noise content increases, the error between the IPK and P3D/R5 reactivity also increases. A sensitivity analysis for five distinct carry-over effects of different random noise loads indicates that the random addition of different noise loads to the reactor power does not change the overall performance of both algorithms. / Este trabalho aplica métodos computacionais avançados para simular a ejeção de barras de controle (CRE) em uma planta térmica nuclear (NPP). São avaliados o impacto da ocorrência de acidentes iniciados por reatividade (RIAs) na reatividade total, na distribuição da potência em três dimensões (3D) e na determinação da reatividade. As ferramentas utilizadas são: o código termo-hidráulico (TH) RELAP5 (R5), o código neutrônico (NK) PARCS (P3D), a versão acoplada P3D/R5, e o ambiente computacional MATLAB. Este estudo considera três reatores nucleares de diferentes tamanhos: NPP1 (2772 MWT); NPP2 (530 MWt); e NPP3 (1061 MWt). Os três núcleos possuem projeto similar e idêntica posição dos grupos das barras de controle (CRA), além do mesmo valor de reatividade diferencial das CRA ejetadas e idêntica velocidade de ejeção. A ocorrência da CRE é avaliada sob condições de hot zero power (HZP) e de hot full power (HFP). As análises indicam que a modelagem e a simulação de RIAs devem ser realizadas sistematicamente, caso contrário os resultados não irão refletir o comportamento em regime transitório do núcleo. A simulação de um modelo em um código depende da apropriada configuração de parâmetros gerados pelo outro código e da determinação adequada do mapeamento TH/NK para as várias malhas dos modelos. Do ponto de vista de projeto, a utilização de códigos independentes resulta em cálculos de potência e reatividade conservadores em comparação com os resultados utilizando-se P3D/R5. Os picos de potência e de reatividade são menores à medida que o núcleo encolhe. A simulação em condições de HFP resulta em valores de pico de potência similares durante transitório para as três NPPs, mas a potência de pós-transitórios é menor para o menor núcleo. A análise em condições de HZP também indica que o valor máximo durante o transitório é menor para o menor núcleo, mas o pós-transitórios ocorre aos mesmos níveis de potência das demais NPPS. A distribuição de potência em 3D também apresenta resultados distintos para condições de HFP e HZP, mas tais resultados são independentes do tamanho do núcleo: i) HFP: há um aumento da potência do núcleo em torno da CRE, mas tal comportamento diminui para núcleos menores - no entanto, a potência é bem distribuída após o transitório; e ii) HZP: há aumento de potência na área do CRE, mas o pico de potência em 3D é menor durante e depois dos transitórios para núcleos menores. Tais características indicam que os núcleos menores respondem de forma mais segura quando da inserção de reatividade em comparação a reatores de maiores dimensões. O método estocástico de filtragem de Kalman estendido (EKF) foi codificado para estimar a reatividade com base no perfil de potência da NPP, após a adição de ruído aleatório. O método determinístico da cinética pontual inversa (IPK) também foi implementado e os resultados da aplicação dos algoritmos do EKF e IPK foram comparados com os resultados da simulação do P3D/R5. As seguintes estratégias, implementadas neste trabalho, possibilitaram a aplicação robusta e precisa do EKF: o sistema foi modelado por um conjunto de equações diferenciais não-lineares estocásticas de tempo contínuo; o algoritmo obtém o passo de tempo diretamente da potência medida e aplica-o ao modelo para a discretização e linearização online; o ajuste do filtro ocorre automaticamente a partir do primeiro passo de tempo; e a matriz de covariância do ruído no estado é atualizada online. Verificou-se que a reatividade calculada pelo método IPK possui maior nível de ruído quando comparada ao EKF para todos os casos estudados. Portanto, o EKF apresenta resultados superiores e mais precisos. Além disso, sob uma pequena inserção de reatividade, a reatividade calculada pelo método IPK varia consideravelmente de valores positivos para negativos: esta variação não é observada com o EKF. Uma análise de sensibilidade para três desvios padrão (SD) sugere que o algoritmo EKF é superior ao método IPK, independente da magnitude do ruído. Com o aumento da magnitude do ruído, o erro entre as reatividades calculadas pelo IPK e pelo P3D/R5 aumenta. A análise de sensibilidade para cinco ruídos aleatórios indica que a adição de ruído na potência do reator não altera o desempenho global de ambos os algoritmos.

The use of check valves in the nuclear industry is of great importance from a safety precaution point ofview (McElhaney, 1995). Choosing check valves for these high-pressurized systems comes with agreat challenge. The valves causes what is called check valve slams when closing, leading to a hugepressure wave traveling through the system. To prevent this from happening calculations have to bedone to see what kind of forces are generated during a check valve slam. When the forces are known itis easier designing systems that will endure these slams. A commonly used software in the nuclearindustry is RELAP5 (Reactor Excursion and Leak Analysis Program), its main purpose is to calculatetransients in piping systems. This program can also be used when calculating a check valve slam. Buthow precise is the code compared to the real event? By doing an experiment measuring pressures created by swing check valves during slams, the codewas compared to real data and analyzed to decide what was of importance when modeling for thesetypes of simulations. The RELAP5 code was not initially designed to calculate transients during a check valve slam. This isclearly shown when the code overestimates the pressure waves in the system when using themanufacturer data for the check valve model. Matching the data from the simulations in RELAP5 withthe data recorded from the experiment is not easy. The parameters used for this have no connection tothe specifications for the check valve, which means that transients are hard to estimate withoutexperimental data.

<p>Analyses of nuclear reactor safety have increasingly required coupling of full three dimensional neutron kinetics (NK) core models with system transient thermal-hydraulics (TH) codes. To produce results within a reasonable computing time, the coupled codes use different spatial description of the reactor core. The TH code uses few, typically 5 to 20 TH channels, which represent the core. The NK code uses explicit node for each fuel assembly. Therefore, a spatial mapping of coarse grid TH and fine grid NK domain is necessary. However, improper mappings may result in loss of valuable information, thus causing inaccurate prediction of safety parameters.</p><p>The purpose of this thesis is to study the sensitivity of spatial coupling (channel refinement and spatial mapping) and develop recommendations for NK-TH mapping in simulation of safety transients – Control Rod Drop, Turbine Trip, Feedwater Transient combined with stability performance (minimum pump speed of recirculation pumps).</p><p>The research methodology consists of spatial coupling convergence study, as increasing number of TH channels and different mapping approach the reference case. The reference case consists of one TH channel per one fuel assembly. The comparison of results has been done under steady-state and transient conditions. Obtained results and conclusions are presented in this licentiate thesis.</p>

Analyses of nuclear reactor safety have increasingly required coupling of full three dimensional neutron kinetics (NK) core models with system transient thermal-hydraulics (TH) codes. To produce results within a reasonable computing time, the coupled codes use different spatial description of the reactor core. The TH code uses few, typically 5 to 20 TH channels, which represent the core. The NK code uses explicit node for each fuel assembly. Therefore, a spatial mapping of coarse grid TH and fine grid NK domain is necessary. However, improper mappings may result in loss of valuable information, thus causing inaccurate prediction of safety parameters. The purpose of this thesis is to study the sensitivity of spatial coupling (channel refinement and spatial mapping) and develop recommendations for NK-TH mapping in simulation of safety transients – Control Rod Drop, Turbine Trip, Feedwater Transient combined with stability performance (minimum pump speed of recirculation pumps). The research methodology consists of spatial coupling convergence study, as increasing number of TH channels and different mapping approach the reference case. The reference case consists of one TH channel per one fuel assembly. The comparison of results has been done under steady-state and transient conditions. Obtained results and conclusions are presented in this licentiate thesis.

Analyses of nuclear reactor safety have increasingly required coupling of full three dimensional neutron kinetics (NK) core models with system transient thermal–hydraulics (TH) codes.  In order to produce results within a reasonable computing time, the coupled codes use two different spatial description of the reactor core.  The TH code uses few, typically 5 to 20 TH channels, which represent the core.  The NK code uses explicit one node for each fuel assembly.  Therefore, a spatial mapping of a coarse grid TH and a fine grid NK domain is necessary.  However, improper mappings may result in loss of valuable information, thus causing inaccurate prediction of safety parameters. The purpose of this thesis is to study the effectiveness of spatial coupling (channel refinement and spatial mapping) and develop recommendations for NK/TH mapping in simulation of safety transients.  Additionally, sensitivity of stability (measured by Decay Ratio and Frequency) to the different types of mapping schemes, is analyzed against OECD/NEA Ringhals–1 Stability Benchmark data. The research methodology consists of spatial coupling convergence study, by increasing the number of TH channels and varying mapping approaches, up to and including the reference case.  The reference case consists of one-to-one mapping: one TH channel per one fuel assembly.  The comparisons of the results are done for steady–state and transient results.  In this thesis mapping (spatial coupling) definition is formed and all the existing mapping approaches were gathered, analyzed and presented.  Additionally, to increase the efficiency and applicability of spatial mapping convergence, a new mapping methodology has been proposed.  The new mapping approach is based on hierarchical clustering method; the method of unsupervised learning that is adopted by many researchers in many different scientific fields, thanks to its flexibility and robustness.  The proposed new mapping method turns out to be very successful for spatial coupling problem and can be fully automatized allowing for significant time reduction in mapping convergence study. The steady–state results obtained from three different plant models for all the investigated cases are presented.  All models achieved well converged steady–state and local parameters were compared and it was concluded that solid basis for further transient analysis was found.  Analyzing the mapping performance, the best predictions for steady–state conditions are the mappings that include the power peaking factor feature alone or with any combination of other features.  Additionally it is of value to keep the core symmetry (symmetry feature).  The big part of this research is devoted to transient analysis.  The selection of transients was done such that it covers a wide range of transients and gathered knowledge may be used for other types of transients.  As a representative of a local perturbation, Control Rod Drop Accident was chosen.  A specially prepared Feedwater Transient was investigated as a regional perturbation and a Turbine Trip is an example of a global one.  In the case of local perturbation, it has been found that a number of TH channels is less important than the type of mapping, so a high number of TH channels does not guarantee improved results.  To avoid unnecessary averaging and to obtain the best prediction, hot channel and core zone where accident happens should be always separated from the rest.  The best performance is achieved with mapping according power peaking factors, and therefore this one is recommended for such type of perturbation. The regional perturbation has been found to be more challenging than the others.  This kind of perturbation is strongly dependent on mapping type that affects the power increase rate, SCRAM time, onset of instability, development of limit cycle, etc.  It has been also concluded that a special effort is needed for input model preparation.   In contrast to the regional perturbation, the global perturbation is found to be the least demanding transient.  Here, the number of TH channels and type of mapping do not have significant impact on average plant behaviour – general plant response is always well recreated.  A special effort has also been paid to investigate the core stability performance, in both global and regional mode.  It has been found that in case of unstable cores, a low number of TH channels significantly suppresses the instability.  For these cases number of TH channels is very important and therefore at least half of the core has to be modeled to have a confidence in predicted DR and FR.  In case of regional instability in order to get correct performance of out-of-phase oscillations, it is recommended to use full-scale model.  If this is not possible, the mapping which is a mixture of 1st power mode and power peaking factors, should be used. The general conclusions and recommendations are summarized at the end of this thesis.  Development of these recommendations was one of the purposes of this investigation and they should be taken into consideration while designing new coupled TH/NK models and choosing mapping strategy for a new transient analysis. / <p>QC 20130516</p>