Simplified Boiling Water Reactor Research Articles

A Predictive Machine Learning-Based Analysis for In-Tube Co-current Steam Condensation Heat Transfer in the Presence of Non-condensable Gases

AbstractThe primary objective of this study is to develop a predictive model that accurately estimates the condensation heat transfer coefficient (HTC) in the context of in-tube co-current flow condensation, with specific consideration given to the influence of non-condensable gases (NCGs). The need to find useful models and/or correlations that can accurately predict how well a passive condenser in the Economic Simplified Boiling Water Reactor will transfer heat during condensation is greatly warranted. This innovative cooling system utilizes gravity to condense water vapor, effectively dissipating heat from the containment vessel in the event of an accident and transferring the heat into the secondary cooling system. For the development of the forecasting model, we employed Multi-Gens Genetic Programming implemented in MATLAB. This approach possesses the capability of enabling visualization and articulating a transparent mathematical expression that directly establishes the connection between inputs and outputs. This model was specifically developed for forecasting the HTC during the condensation process, considering two distinct types of NCG: air, helium, and a mixture of air and helium, in addition to data for pure steam. The model was trained using a dataset comprising 2913 data points gathered from five experimental references. The model's input comprises a varied range of parameters, including local location ($$z$$ z ), temperature of the steam/NCG mixture ($${T}_{mix}$$ T mix ), condenser wall temperature ($${T}_{wall}$$ T wall ), coolant flow rate ($$\beta_{c}$$ β c ), total pressure ($${P}_{tot}$$ P tot ), condenser inner diameter ($${D}_{1}$$ D 1 ), condenser outer diameter ($${D}_{2}$$ D 2 ), molecular weight (MM), NCG mass fraction ($${w}_{NCG}$$ w NCG ), and mixture Reynolds number ($${Re}_{mix}$$ Re mix ). The output of our model corresponds to the condensation HTC ($$h$$ h ). Four specific correlations were examined with the third correlation attaining the highest anticipated values within a deviation range of ± 30, reaching 90.9%, exhibiting good performance in terms of both performance index and coefficient of determination. This correlation was validated, and its accuracy assessed by employing an unused training dataset that included nitrogen as a NCG. The outcomes showed that 92.94% of the predicted data fell within a deviation range of ± 30%. The findings of this study signify a notable advancement in the analysis of datasets obtained from experiments. Particularly, it delves into the impact of NCGs by considering their molecular weight and mass fraction.

Evaluated Material Attractiveness of Plutonium Composition from Economic Simplified Boiling Water Reactor (ESBWR)

The potential for misuse of nuclear fuel has prompted many to make efforts to prevent a country from acquiring nuclear explosive devices (weapons). Weapon utility equated with nuclear material attractiveness when applied to protection and security. Material attractiveness evaluated using an equation first developed by Masaki Saito, namely ATTR. ESBWR is one of the reactors of the BWR reactor type that is still operating. The purpose of this study is to evaluate Material Attractiveness based on the composition of plutonium in the ESBWR reactor, during reactor operation and after reactor operation. The ATTR concept utilizes the plutonium isotope composition to evaluate the material attractiveness aspect. Parameters such as BCM, Rossi-alpha, and neutron prompt life become additional aspects in evaluating material attractiveness. In the research results, the ATTR value decreased from the beginning of reactor operation until the reactor stopped operating. At the beginning of the reactor operation, it was categorizing as a weapon-grade with an ATTR value of 0.19 and when the reactor stopped operating it was categorizing as an unusable grade with an ATTR value of 0.012. At the time of cooling time up to 1x106 (one million) cooling time, the ATTR value increases by 0.019 which was categorizing as an unusable grade. After a cooling time of 1x106 (one million) years up to 1x107 (ten million) years, the ATTR value was 0.001 which categorized as an exempt level. This states that the increasing burnup value will further reduce the ATTR value. Likewise with the Rossi-Alpha and Bare Critical Mass values. Conversely, it will decrease the value of neutron lifetime. The ATTR value after the reactor operates up to one hundred years of cooling time increases and then decreases significantly after 1x106 (one million) years due to the half-life of plutonium isotopes. Likewise, the Rossi-Alpha and Bare critical mass values. However, it is different with the neutron fast lifetime.

Experimental investigation on local flow structures of upward cap-bubbly flows in a vertical large-size square channel

Gas–liquid two-phase flows are typical in engineering systems involving heat and mass transfers. The cross-sectional geometries and sizes of these flow channels vary, exerting a notable impact on the thermofluid behavior. To develop thermofluid models, it is imperative to obtain local measurements of two-phase flows and gain insights into their characteristics from these measurements. Numerous experimental studies have investigated the local flow characteristics in circular pipes and rectangular channels; however, few studies on square channels have been conducted, particularly for flow regimes beyond bubbly flows, such as cap-bubbly flows. Given the importance of two-phase flows in large square channels for advanced nuclear reactors, such as the economic simplified boiling water reactor (ESBWR), we experimented with upward cap-bubbly flows in a large square channel. Detailed cross-sectional distributions of the void fractions, axial gas velocities, and interfacial area concentrations for two bubble-size groups were obtained at three axial locations using local measurements of a four-sensor optical probe. Based on the database, the cap-bubbly flow characteristics were understood, including flow development in a large square channel. In addition, the existing drift-flux correlations for large circular pipes predicted the measured void fraction with an accuracy of approximately ± 10 %, whereas the existing interfacial area concentration correlations reasonably correlated with the measured interfacial area concentration with an accuracy of approximately ± 30 %. Furthermore, the database was used to calculate the covariances of the void fractions. The correlations for large circular pipes significantly underestimated the void fraction covariance of the larger bubble group, probably because of the peculiar void fraction distribution of the group in a large square channel. The other covariances were well predicted.

Thermal-Hydraulic comparative analysis of G-III + BWR and PWR passive safety features under Loss of coolant accident

As one of symbolic design features of Generation-III and III+ (G-III and G-III + ) nuclear reactors, the passive safety system has been implemented on majority of G-III and III + PWRs and BWRs. The passive safety systems in those reactors are designed differently yet adhere to identical fundamental principles. It would be interesting to examine the similarities and differences between the passive safety systems of G-III + PWR and BWR. System code simulations for Small Break and Large Break Loss of Coolant Accident for the Economic Simplified Boiling Water Reactor (ESBWR) and China’s advanced PWR had been conducted, respectively. The results showed that the passive safety systems of ESBWR and China’s Advanced PWR were comparable in design, and when dealing with the similar type of SBLOCA and LBLOCA, the passive safety components with the same functionality could all contribute to the core's cooling with stability and reliability, and the injection flow rate values were nearly equivalent. Separating the injection lines of ESBWR's safety systems guarantees that the action sequence could well remain stable. This design could prevent the injection flow rate and action sequence from being impacted by the interaction of safety injection systems. This work could serve as a reference for the design of subsequent new reactors, thereby contributing to the design of reactors with enhanced economics and safety.

Thermal-Hydraulic Safety Assessment of Full-Scale ESBWR Nuclear Reactor Design

Abstract The economic simplified boiling water reactor (ESBWR) is a boiling water nuclear reactor of generation III+. The U.S. Nuclear Regulatory Commission (NRC) approved the ESBWR design as the world's best light-water nuclear reactor in 2014. It has the lowest core damage frequency (industry standard indicator of safety) of any Generation III or III+ reactor. It can cool automatically for more than seven days without using electricity or human intervention. During the operation, the ESBWR is designed to produce electricity while emitting almost no greenhouse gases. The energy generated by an ESBWR will prevent the emission of approximately 7.5 million metric tons of CO2 per year compared to standard electricity production on the U.S. grid. The analysis present in this paper aimed to characterize the thermal-hydraulic simulations of full-scale ESBWR design. The analysis presented will help in recognizing the improvement needed in the reactor design and its passive safety systems. The analysis is performed for normal steady-state and postulated design basis accident scenarios (break in one of the reactor main-steam lines inside the contentment). The simulation results obtained by the code REALP/SCDAPSIM/MOD3.4 are compared with the TRACG04 and MELCOR2.1 code results to determine the code predictability and accuracy under accident conditions of the newly proposed design of the ESBWR nuclear reactor. A parametric study is also carried out with different in-containment break sizes to determine code results' sensitive nature due to natural circulation flow phenomena, which are highly unstable. The analysis shows that the code has produced reasonably accurate results under the tested system thermal-hydraulic conditions compared with the TRACG04 and MELCOR2.1 code simulation results. This agreement between the three codes simulation results demonstrated that the publicly available RELAP5 code model has adequate features to simulate the ESBWR thermal-hydraulics. It has been also demonstrated that for the postulated accident conditions, the design of passive safety systems is capable to capture the accident progression without any active power.

Analyzing Simplified BWR Inherent Safety System using IAEA Generic Boiling Water Reactor Simulator

The inherent safety of boiling water reactors (BWR) has been a vital research topic in the past decades. This study aimed to observe and analyze the simplified BWR inherent safety system incorporated in IAEA Generic BWR Simulator. This simulator represents important features of BWR and provides graphical information and real-time simulation data. The simulated BWR has 1300 MWe power with ABWR-type containment. To analyze its inherent safety system, three conditions are simulated, i.e., normal condition at 100% power, transient condition (feedwater pumps trip), and emergency condition (loss of coolant accident—LOCA). The simulations were performed for up to 30 minutes since the most critical events in all conditions occurred within that time frame. Sequences of transient and emergency conditions were described in detail with the help of an additional screen recorder and time counting software. Results of several parameters in all simulation conditions were compared and analyzed. It was concluded that the simulator could simulate the normal, transient, and emergency conditions and the simplified version of the BWR inherent safety system.

Time averaged tomographic measurements before and after dryout in a simplified BWR subchannel geometry

For the validation of advanced two-fluid CFD models at boiling water reactor (BWR) conditions, it is necessary to have good experimental data challenging for the code by reflecting relevant flow phenomena. The present experimental study aims to provide detailed film thickness distributions in a BWR-like subchannel geometry, including spacer grids and heat transfer. This is achieved using chloroform as a working fluid, indirectly heated by hot water channels simulating BWR fuel rods. X-ray equipment was used to produce tomographic 3D-data of time-averaged attenuation coefficients which essentially represent the liquid holdup. The conversion to film thickness was done by integrating the attenuation coefficient along lines perpendicular to the rod wall and using an effective chloroform attenuation coefficient determined by numerical simulation of the experimental setup, including X-ray sensor behavior. The simulation method was validated by using two different sensors types. Measurements were performed over the whole cross-section of the channel and an axial length of 11 cm. The experiments cover a range of liquid flow rates in the pre- and post-dryout regime.

Severe Accident Phenomena: A Comparison Among the NuScale SMR, Other Advanced LWR Designs, and Operating LWRs

During a severe accident in a nuclear reactor, there are a number of phenomenological events that can present a challenge to containment integrity. These include the generation and combustion of hydrogen, energetic fuel-coolant interactions, thermal attack of fission product barriers, core-concrete interactions, direct containment heating, and gradual overpressurization. The advanced design of the NuScale small modular reactor (SMR) has resulted in the reduced likelihood and severity of severe accident challenges to containment. This paper discusses the features of the NuScale design that reduce the likelihood of occurrence of these severe accident phenomena and also discusses the ability of containment to survive in the unlikely event that they do occur. The impact of severe accident phenomena for the NuScale design is compared and contrasted against other advanced light water reactors (ALWRs), such as the AP1000 reactor and the Economic Simplified Boiling Water Reactor (ESBWR), as well as the existing fleet, using information from publicly available documents.

Investigation of differences of phenomena of diffusiophoresis and thermophoresis from aerosol deposition in modified ART Mod 2 code

Fission product behavior assessment in containment vessel (CV) is one of the important areas in safety analyses because the CV is the final release protection. Modified ART Mod 2 code is used to study aerosol deposition phenomena in the CV. From Phébus FPT experiments, the phenomena of diffusiophoresis and thermophoresis on wet condensers were occurred in the CV. The two phenomena are recognized to be the same thing. However, this is not a universal view on these phenomena, which are evaluated separately in the modified ART Mod 2 code. In previous study on the modified ART Mod 2 calculation of Economic Simplified Boiling Water Reactor (ESBWR) and Phébus FPT experiments, there was more diffusiophoresis than thermophoresis in the case of simulating single volume of the CV while there was more thermophoresis for multiple volume case. This research aim is to conduct a ceteris paribus sensitivity analysis of representative parameters affecting diffusiophoresis and thermophoresis namely aerosol size, pressure, and gas temperature, under different nodalizations in the modified ART Mod 2 code using the Phébus FPT experiments to investigate the differences. As a result, differences of gas temperature between atmosphere and wall in single volume most affect diffusiophoresis while differences of temperature between atmosphere and wall of multiple volumes most affect thermophoresis.

Safety Features of Advanced and Economic Simplified Boiling Water Reactors

The Advanced Boiling Water Reactor (ABWR) and the Economic Simplified Boiling Water Reactor (ESBWR) are two kinds of contemporary, advanced, commercially available nuclear power reactors. Reactor internal pumps in an ABWR improve performance while eliminating the large recirculation pumps in earlier BWRs. The utilization of natural circulation and passive safety systems in the ESBWR design simplifies nuclear reactor system designs, reduces cost, and provides a reliable stability solution for inherently safe operation. The conceptually reliable stability solution for inherently safe ESBWR operation is developed by establishing a sufficiently high natural circulation flow line, which has a core flow margin at least 5% higher than the stability boundary flow at 100% rated power of a conventional BWR, and then by designing a high flow natural circulation system to achieve this high natural circulation flow line. The performance analyses for the ESBWR Emergency Core Cooling System (ECCS) show that: (1) the core remains covered with a large margin and there is no core heat up in the ESBWR for any break size, (2) the long-term containment pressure increases gradually with time, in the order of hours, and the peak pressure is below the design value with a large margin, and (3) the margins depend on the containment volumes and water inventories. These safety design features ensure inherently safe ESBWR operation. Enhanced safety features based on lessons learned from the Fukushima nuclear accident are added in ABWR’s and ESBWR’s safety designs. The major enhancements are the further prevention of station blackout and loss of ultimate heat sink.

Intracerebrovascular enzyme replacement therapy for CLN2 disease: A collaborative, multi-disciplinary approach

This chapter briefly reviews the different applications of natural circulation systems (NCSs) in various industries. Closed-loop NCSs are extensively used in solar water heaters, geothermal, fossil-fueled, and nuclear power plants. In addition, these systems are used in component-cooling applications such as transformers, electronic devices such as computer chips, and gas turbines. Although NCSs are mainly employed as heat transport devices, they can be engineered for noncooling applications such as passive controls, liquid fins, and study of low-velocity corrosion and deterministic chaos. Examples of open-loop natural circulation applications include solar chimneys, buoyancy pumps, air lift pumps, and building ventilation. The largest applications of NCSs are possibly in the chemical process industries. However, the highest power operating NCSs can be found in fossil-fueled power plants. The ESBWR (Economic Simplified Boiling Water Reactor) is the highest power (4500 MW) NCS designed so far. Mini loops with heat transport capability of the order of a few tens of Watts also can be found in the electronics industry.Some of the emerging applications of NCSs are in passive cooling of aircraft, vehicles, building ventilation, and solar thermal power plants. Due to the energy-saving potential of natural circulation, its application is increasing in various industry sectors. Natural circulation applications in electronics device cooling, solar thermal power plants, and residential buildings are expected to increase in the near future. In addition, its passive functioning without operator action or signal is important for enhanced safety and reliability of nuclear reactors, increasing their applications in the nuclear field.

Analysis of simplified BWR full core with serpent-2/simulate-3 hybrid stochastic/deterministic code

This paper presents an evaluation of a Monte Carlo (MC) neutron transport code as a tool to generate nuclear cross section data for nuclear reactor core simulators. The goal is not to replace deterministic lattice calculations with MC simulations but to provide an audit tool. A boiling water reactor (BWR) assembly is modeled with a deterministic lattice physics code CASMO-5 and with a MC code SERPENT-2 for a simplified set of histories and branch cases. The work reported in this paper is a continuation of authors’ previous analysis of a BWR in the reference 13 and SERPENT-2 is used instead of SERPENT-1 to overcome excessive memory usage and execution time of the latter. CASMO-5 and SERPENT-2 are compared with those of a hybrid CASMO-5+SERPENT-2 scheme which uses the depletion solver of CASMO-5 and the transport solver of SERPENT-2. Their results are compared for an assembly model, in terms of k-inf, macroscopic cross sections, assembly discontinuity factors and diffusion coefficients. The differences are less than 1% except for diffusion coefficients of 5% difference. Subsequently, a nuclear cross section data library is generated for SIMULATE-3 core simulator. A full core depletion calculation is performed and k-eff, axial and radial power distributions are compared. The discrepancies of k-eff between CASMO-5/SIMULATE-3 and SERPENT-2/SIMULATE-3 are smaller than 250pcm, and the differences of axial relative power fraction (RPF) root mean square errors are smaller than 8%. The differences of radial RPF root mean square errors are smaller than 1.5%.

Development and validation of a TRACE/PARCS core model of Leibstadt Kernkraftwerk cycle 19

The paper deals with the development of a TRACE/PARCS plenum to plenum model for the Swiss Boiling Water Reactor (BWR) Leibstadt (KKL), for cycle 19. It summarizes a verification of the model against an existing SIMULATE-3 model and a validation against Travelling Incore Probes (TIP) at various points of the cycle 19.First, the TRACE/PARCS agreement with SIMULATE-3, for a simplified BWR reactor is analysed. The discrepancies are less than 300pcm in terms of keff, 6.5% axially and 2% radially in terms of nodal power prediction across the reactor cycle. The discrepancies are due to the mapping of the cross sections when considering the complex default branch/history structure of CASMO-4; and to the modelling of the vessel in TRACE, the solution of the heat conduction in the fuel and the evaluation of the bypass flow.When the KKL cycle 19 model is considered, the TRACE/PARCS agreement with SIMULATE-3 is satisfactory, in terms of keff with discrepancies less than 700pcm across the reactor cycle; and in terms of Relative Power Fraction (RPF) as well, with discrepancies less than 9% axially and 2% radially, across the reactor cycle.Finally, when comparing to TIP measurements, the TRACE/PARCS methodology and models showed some similar discrepancies than SIMULATE-3, as long as the detector model is not used. When using its detector model to predict the TIP response, TRACE/PARCS shows larger discrepancies with TIP measurements.

Confidence interval estimation by bootstrap method for uncertainty quantification using random sampling method

Confidence interval estimation by the bootstrap method is investigated for the uncertainty quantification of neutronics calculation using the random sampling method. The random sampling method is a simple and practical technique to quantify an uncertainty (standard deviation) of the target parameter calculated by a core analysis code. It is noted that a statistical error is inevitably included in the estimated uncertainty because of the probabilistic method using random numbers. In order to estimate the statistical error of uncertainty, we focus on the bootstrap method. The bootstrap method is one of the resampling techniques to evaluate variance and confidence interval of a sample estimate (e.g. variance) without the assumption of normality. Through a lattice burnup calculation for a simplified boiling water reactor (BWR) fuel assembly, it is verified that the bootstrap method can reasonably estimate the confidence interval of uncertainty of infinite neutron multiplication factor (kinf) due to covariance data of JENDL-4.0. In the case of this problem, the distribution of kinf is well approximated by a normal distribution; thus, the confidence interval of uncertainty can be also estimated by the aid of chi-squared distribution. The merit using the bootstrap method is to simply estimate the confidence interval of uncertainty without the assumption of normality.

Validation of RELAP5/MOD3.2 Code for Flashing-Induced Instabilities in a Single Channel

This paper reports on the modeling and simulation of flashing-induced instabilities in naturalcirculation systems, with special emphasis on simplified boiling water reactors (SBWRs). In this work, flashing-induced oscillations have been studied by using an experimental test facility (SIRIUS-N) and RELAP5/MOD3.2 thermal hydraulic code. The behavior of the test facility is investigated for different values of core inlet temperature value. The results of the simulations have been compared qualitatively and quantitatively with experiments. In general, deviations are found between the numerical and experimental results, in spite of the close similarity between the SIRIUS-N facility and the definition of the system in the RELAP code. This result indicates that predictions regarding experimental facility, based on modeled system, should be carefully considered.

Assessment of GOTHIC and TRACE codes against selected PANDA experiments on a Passive Containment Condenser

Typical passive safety systems for ALWRs (Advanced Light Water Reactors) rely on the condensation of steam to remove the decay heat from the core or the containment. In the present paper the three-dimensional containment code GOTHIC and the one-dimensional system code TRACE are compared on the calculation of a variety of phenomena characterizing the response of a passive condenser submerged in a boiling pool. The investigation addresses the conditions of interest for the Passive Containment Cooling System (PCCS) proposed for the ESBWR (Economic Simplified Boiling Water Reactor).The analysis of selected separate effect tests carried out on a PCC (Passive Containment Condenser) unit in the PANDA large-scale thermal-hydraulic facility is presented to assess the code predictions. Both pure steam conditions (operating pressure of 3bar, 6bar and 9bar) and the effect on the condensation heat transfer of non-condensable gases heavier than steam (air) and lighter than steam (helium) are considered. The role of the secondary side (pool side) heat transfer on the condenser performance is examined too.In general, this study shows that both the GOTHIC and TRACE codes are able to reasonably predict the heat transfer capability of the PCC as well as the influence of non-condensable gas on the system. A slight underestimation of the condenser performance is obtained with both codes. For those tests where the experimental and simulated efficiencies agree better the possibility of compensating errors among different parts of the heat transfer models is outlined. Besides, the pool side heat transfer coefficient is indicated to differ between GOTHIC and TRACE, revealing that the model implemented in TRACE might be more accurate. Finally, both codes deviate more from the experiments for the tests with helium, which is explained by the emerging of a complex circulatory flow pattern in the experiments that the models fail to predict.

A minimum hot excess core design strategy for ESBWR

The Economic Simplified Boiling Water Reactor (ESBWR) is GEH’s next evolution of advanced BWR technology. There are 1132 fuel bundles in the core and the thermal power is 4500 MWt. As part of design simplification it uses natural circulation flow with no recirculation pumps or their associated piping. The control blades are the primary control mechanism to address the need for performing reactivity adjustments (using fine-motion drives) at or near rated steady state power. This introduces the potential for duty-related fuel failure, which has to be rigorously addressed as part of reliable design and operation. As means to mitigate this potential for duty-related fuel failure and also to support a simplified ESBWR operation, this study investigates the feasibility of a fuel cycle core design strategy. The objective is to design fuel bundles, and to use them for developing a core design, that minimizes (but does not eliminate) the use of control blades during operation. The reduction in use is envisioned in their number as well as movement in the core. In such a strategy, the effect of the burnable poison in the fuel (that largely drives the core reactivity) is enhanced, and operationally the control blades react modestly to maintain the core critical. While the logic is simple, challenges exist in developing such a design because it needs to balance the requirement for having enough blade inventory in the core to address design/operational constraints and uncertainties. The strategy is conceptualized as “minimum hot excess (reactivity)” design. It reduces the number of blades in the core during normal operation by 50% in comparison to a similar fuel cycle core design with regular inventory of control blades. Because of the increased burnable poison, the minimum hot excess core design strategy comes at a cost of fuel cycle efficiency. This cost is determined in terms of an increased enrichment for the fresh fuel batch fraction.

A PANDA integral test on the effect of light gas on a Passive Containment Cooling System (PCCS)

As part of the Euratom project TEMPEST (Testing and Enhanced Modelling of Passive Evolutionary Systems Technology for Containment Cooling), a series of five tests was performed in the PANDA facility to experimentally investigate the distribution of hydrogen inside the containment and its impact on the performance of the Passive Containment Cooling System (PCCS) designed for the Economic Simplified Boiling Water Reactor (ESBWR). In a postulated severe accident a large amount of hydrogen could be released in the Reactor Pressure Vessel (RPV) as a consequence of the cladding Metal–Water (M–W) reaction and discharged together with steam to the Drywell (DW) compartment. The retention of hydrogen in the DW, instead to be vented in the Wetwell (WW), has a positive effect toward the mitigation of the system pressure build-up. Hydrogen retention in the DW is a consequence of the stratification phenomena driven by the steam–hydrogen density difference. The paper presents the experimental results of the integral Test T1.2 performed in the PANDA facility. Helium was used to simulate hydrogen and the specific PANDA facility configuration included a dead-end volume, allowing for retaining a portion of the released helium in the DW compartment. The results from Test T1.2 showed that the containment end pressure is mainly determined by the redistribution of non-condensable gas inside the containment system and the temporary deterioration of the PCCS performance during the helium release phase plays a minor role.

Condensation Correlation for a Vertical Passive Condenser System

A condensation correlation was developed for vapor and air mixture condensation in a vertical tube based on experimental data and a mechanistic model based on heat and mass analogy model. Parametric computations were performed using a heat and mass analogy model for various operating parameters of the passive condenser system. The parameters investigated were noncondensable gas mass fraction Wbulk, mixture gas Reynolds number ReG, and Jacob number JaG. An alternating conditional expectation (ACE) regression algorithm was used to develop the condensation heat transfer correlation for the passive condenser. A total of 102600 data points was used as input to the ACE. Local condensation heat transfer correlations in terms of Nusselt number (Nucond) obtained were: Nucond = 0.08Wbulk–0.9ReG1.1·exp(-42.5JaG) for turbulent flow and Nucond = 160Wbulk–0.9·exp(-42.5JaG) for laminar flow. The correlations are valid for 0 ≤ Wbulk ≤ 0.5, 0 ≤ ReG ≤ 4 × 104, 0.002 ≤ JaG ≤ 0.05. The prediction of the developed correlation agreed well with the available experimental data. The correlations are useful in predicting the heat transfer characteristics of a passive containment cooling system (PCCS) in an economic simplified boiling water reactor. These correlations apply to the three modes of PCCS operation, namely through-flow mode, complete condensation mode, and cyclic condensation and venting mode.

Mass flow rate sensitivity and uncertainty analysis in natural circulation boiling water reactor core from Monte Carlo simulations

Our aim was to evaluate the sensitivity and uncertainty of mass flow rate in the core on the performance of natural circulation boiling water reactor (NCBWR). This analysis was carried out through Monte Carlo simulations of sizes up to 40,000, and the size, i.e., repetition of 25,000 was considered as valid for routine applications. A simplified boiling water reactor (SBWR) was used as an application example of Monte Carlo method. The numerical code to simulate the SBWR performance considers a one-dimensional thermo-hydraulics model along with non-equilibrium thermodynamics and non-homogeneous flow approximation, one-dimensional fuel rod heat transfer. The neutron processes were simulated with a point reactor kinetics model with six groups of delayed neutrons. The sensitivity was evaluated in terms of 99% confidence intervals of the mean to understand the range of mean values that may represent the entire statistical population of performance variables. The regression analysis with mass flow rate as the predictor variable showed statistically valid linear correlations for both neutron flux and fuel temperature and quadratic relationship for the void fraction. No statistically valid correlation was observed for the total heat flux as a function of the mass flow rate although heat flux at individual nodes was positively correlated with this variable. These correlations are useful for the study, analysis and design of any NCBWR. The uncertainties were propagated as follows: for 10% change in the mass flow rate in the core, the responses for neutron power, total heat flux, average fuel temperature and average void fraction changed by 8.74%, 7.77%, 2.74% and 0.58%, respectively.