Steam Generator Tubes Research Articles

Role of constraint volume and heat flux on the design of evaporator tubes of steam generator by entropy generation minimization

This paper proposes a design methodology for evaporator tubes of a steam generator by applying the entropy generation minimization (EGM) approach. A two-phase flow-based entropy generation model for steam generator evaporator tubes is developed, with coolant volume as a constraint. For a target steam generation rate, the total entropy generation of the evaporator circuit is minimized using system volume and furnace heat flux as two constraints. It is observed that for a fixed steam generation rate, with increasing evaporator diameter, the furnace height decreases while the cross-sectional area increases. The analysis reveals that for a steam generation rate of 100 kg/s and a fixed circuit volume of 47 m3, increasing the heat flux from 36 to 50 kW/m2 shifts the EGM point from an evaporator diameter of 62 mm to 84 mm, respectively. On the other hand, the minimum point shifts to a diameter of 43 mm when the heat flux is decreased to 25 kW/m2. The present study concludes that the selection of the constraint volume for designing the evaporator downcomer circuit for a target steam generation rate should be done based on the available furnace heat flux to choose the most efficient design.

Measurement of Steam-Generator-Tube Vibration Damping Caused by Anti-Vibration-Bar Supports

Abstract In 2013, Atomic Energy of Canada Limited (now Canadian Nuclear Laboratories) experimentally measured the damping of a straight tube with a variety of tube supports to examine low-frequency damping. These tests were motivated by the discovery of severe tube damage caused by in-plane fluidelastic instability (FEI) in the U-bend regions of new replacement recirculating steam generators (SG). The measurements were intended to assess the applicability of existing design guidelines for estimating the support-related damping of a tube. In the tests, the damping ratios of a single steam generator tube were measured using both log-decrement and power-based methods. Noncontacting excitation and position-sensing techniques were employed to improve accuracy. Initial baseline tests explored configurations with no support and drilled-hole supports of different hole sizes, and these results were compared with previously published work. Subsequent tests were performed to measure damping of tube vibration parallel to flat-bar supports. Most of the tests were performed with the tube fully submerged in still water. The tests examined the effects of fluid (water or air), natural frequency, gap width, preload, and vibration normal to the bars. This paper describes the test apparatus, methods, and analysis techniques. A summary of the results is presented. The initial baseline results showed that the damping ratios measured without any supports and with a drilled-hole support were consistent with previously published data. However, the subsequent measurements showed that, contrary to a published design guideline, the anti-vibration bars resulted in no significant additional viscous or squeeze-film damping when the vibration was parallel to the bars. On the other hand, the results did show that anti-vibration bars could introduce significant in-plane Coulomb-type damping if there was sufficient tube-to-support preload or impacting.

Numerical simulation of boiling dynamics in liquid Lead-Bismuth injected with multi-rupture high-pressure water jets

Once a steam generator tube rupture (SGTR) accident occurs in a lead-based fast reactor, it can trigger a domino effect of heat transfer tube ruptures, leading to a loss-of-flow accident involving multiple ruptures. This paper employs numerical methods to investigate the jet boiling phenomenon associated with the injection of sub-cooled water into high-temperature lead‑bismuth eutectic (LBE) through multiple nozzles. It explores how nozzle spacing, number, and diameter impact jet characteristics. Additionally, it analyzes flow characteristics and heat transfer mechanisms from the perspective of jet interaction. The study identifies critical areas within the multi-nozzle jet, specifically the three-phase mixing region, LBE entrainment region, water core region, and steam plume region. In scenarios where nozzle spacing is narrow or nozzle diameters differ significantly, the jet's base may undergo fragmentation. The jet process is categorized into two stages: the transition stage and the stable stage. During the stable stage, the mass flow rate of sub-cooled water remains relatively constant, with nozzle spacing exerting minimal influence on it. When considering the cross-sectional area of a single nozzle, an increase in nozzle diameter elevates the normalized mass flow rate, whereas the number and diameter of nozzles have little effect on it. Jet penetration depth is inversely related to nozzle spacing. As the number and diameter of nozzles increase, penetration depth initially rises and then decreases. Nozzle spacing has a minor influence on the jet's steam volume, while the number and diameter of nozzles are positively correlated with steam volume. Conversely, the number and diameter of nozzles negatively correlate with normalized steam volume.

Motion planning for a quadruped robot in heat transfer tube inspection

Steam generators (SGs) are essential in nuclear power facilities and require regular inspection to maintain their safety and operational effectiveness. This paper presents a quadruped robot designed to inspect SG heat-transfer tubes. The point-to-point crawling-motion planning problem of the robot is addressed by integrating an improved A* algorithm with an offline motion-posture library established for the tube-sheet environment. The planner can provide the global path, the step size for each crawling cycle, and the strategic placement of footholds. The proposed method can facilitate the robot in navigating obstacles on a tube sheet, seamlessly adapt to various postures and step lengths, and eliminate the necessity for turning or superfluous posture adjustments, thereby ensuring crawling efficiency. The efficacy of the proposed planner is validated rigorously through simulations and experimental trials using an actual SG tube sheet.

Research on Assessment Method for Cognitive Influence Factors of Nuclear Power Plant Operators Based on Fuzzy Analytic Hierarchy Process and Deep Learning of Electroencephalogram Signals

This study explores the factors influencing the cognitive processes of operators in digital nuclear power plants, with a focus on the correlation between these factors and electroencephalogram (EEG) features. Initially, based on expert consultations, seven factors were considered: stress, time, fatigue, procedural complexity, user interface experience, procedural clarity, and efficiency. From these, four were identified as the most crucial for each stage of the cognitive process, highlighting their significant roles in influencing cognitive performance and potentially correlating with distinct EEG characteristics. These were assessed using the fuzzy analytic hierarchy process (FAHP) to determine the weightings of influences across the cognitive stages of monitoring, decision making, and execution. Employing a simulated scenario of a steam generator tube rupture, subjective questionnaires were utilized to gauge participant perceptions of influencer impacts at each stage, calculating human factors fuzzy synthetic values. Concurrently, EEG signals were segmented by operational steps, extracting around 114 features across the time, frequency, and time-frequency domains, which were then dimensionally reduced to 17 principal components via adaptive principal components analysis (APCA). A correlation analysis was performed between the human factors fuzzy synthetic values and the APCA-reduced EEG features of participants. Subsequently, the EEG feature columns of the eight selected participants were used as inputs to construct a transformer-based self-attention network model to evaluate the participants’ human factors fuzzy comprehensive values. The findings confirm the transformer model’s efficacy in assessing these values, evidencing a significant correlation between the EEG features and human factors fuzzy synthetic values. Integrating FAHP with machine learning methodologies, this model proficiently estimated operators’ cognitive states during various cognitive processes, significantly enhancing human-machine interface design and the operational safety and efficiency at nuclear power plants.

Numerical simulation of the dynamic interaction characteristics between Wood’s metal and water under coolant injection mode

The accident of the steam generator tube rupture in the lead-bismuth-cooled fast reactor or the core meltdown in the light water reactor may cause violent heat and mass transfer between the melt and the coolant, potentially further damaging the reactor. Therefore, it is essential to study the corresponding mechanisms. In this study, numerical simulations are utilized to investigate the dynamic interactions between Wood’s metal and subcooled water in the coolant injection (CI) mode, focusing on jet behavior and critical cavity parameter changes. By analyzing these factors, this research aims to clarify the interfacial evolution and interaction mechanisms between the melt, water, and air, thereby tackling the problem of inadequate observation in experiments. A user-defined function (UDF) was employed to simulate the flow characteristics of the melt during the solidification process. This approach effectively addressed the limitation of Fluent’s inherent solidification model, where the fluid no longer participates in turbulent velocity calculations after solidification. In addition, an equivalence method was proposed according to the characteristics of two-dimensional simulations in Fluent. Comparisons with Cheng’s experimental results show that the equivalent model can accurately predict jet penetration characteristics while significantly reducing the demand for computational resources. According to this equivalence method, this research developed a new correlation for predicting the maximum jet penetration depth in the CI mode. The above results provide new perspectives for understanding the dynamic interactions between metals and coolants, which is significant for the application and optimization of technologies in the nuclear field.

A semi-analytical time-domain model with explicit fluid force expressions for streamwise fluidelastic instability of a single and multiple flexible tube array

Fluidelastic instability (FEI) within steam generator tube arrays poses a significant safety concern for nuclear power plants. Traditionally assumed to manifest in the transverse direction, recent failures at the San Onofre Nuclear Generating Station have underscored the importance of understanding streamwise FEI (SFEI). These incidents have spurred analytical investigations into SFEI, but progress has been hindered by the lack of explicit fluid force formulations, particularly in semi-analytical SFEI models. This paper presents a novel semi-analytical time-domain SFEI model featuring an ideal geometry-based decay function and meticulously derived explicit fluid elastic force expressions. The proposed model supports both frequency-domain stability analysis and true time-domain response analysis, and it is applicable to configurations featuring either a single elastic tube in a rigid array or multiple flexible tubes in an array. Additionally, the tube motion phases are obtained by comparing time-domain responses and employing modified multi-tube frequency-domain SFEI analyses. The stability thresholds predicted for a parallel triangular array using our theoretical model closely align with reported experimental data, thereby validating its accuracy. Our work supplements and advances semi-analytical modeling, alleviating implementation challenges for analyzing SFEI phenomena.

Separate effect experimental test and theoretical investigate of pressure wave propagation and pressure rising process upon SGTR accident in advanced LFRs

Steam Generator Tube Rupture accident (SGTR) accident is one of the main safety events to the industrial application of Lead-cooled Fast Reactors (LFRs). This paper presents a separate effect test facility, called Lead-bismuth Eutectic Steam generator tube rupture Test facility (LEST), for testing high-pressure subcooled water jetting into a Lead Bismuth Eutectic (LBE) pool, and analyzes experimental data of maximum initial pressure peak, dynamic pressure attenuation together with the pressure rising process upon SGTR. The experimental analyses put forward a general equation form together with a dimensionless number of the initial pressure peak associated with a high-pressure Newtonian fluid injecting into another low-pressure Newtonian fluid, and the derivation of the general equation form is specifically applied to match a further semi-empirical equation for an initial maximum pressure peak with 5–10 MPa water injection in SGTR. The attenuation curve of dynamic pressure wave in each experiment is matched, and more weakening conditions can change the pressure peak from concentrated and non-period peak group to approximate period 1.4–3.7 s pulse group. The size relationship between pipe length L and nozzle diameter D, which L/D=12, is set to divide SGTR into small wall rupture and tube shear fracture, further three stages of pressure rising are distinguished in the tube shear fracture. This work provides experimental data to help determining the severity of SGTR and assessing the consequences of this event as part of the safety case for the industrial application of LFRs.

Numerical study on heat transfer characteristics of LBE cross flow tube bundle under rolling conditions

Combined with the neutron economy and good heat transfer performance, lead–bismuth fast reactor (LFR) has a larger prospect for marine applications. Helical coiled once-through tube steam generator (HCOTSG) is also a typical heat exchanger option for LFR. It is widely adopted in a variety of energy utilization fields, such as petrochemical industry. Study on Lead-bismuth eutectic (LBE) cross flow of tube bundle under moving conditions is necessary for obtaining the flow and heat transfer characteristics of LBE HCOTSG in marine conditions. A numerical method to simulate the heat transfer characteristic of LBE cross tube bundle flow under rolling conditions is proposed. The influence of the rolling conditions on the models with different tube arrangements are investigated. The temperature fluctuation curves with time and the time-averaged heat transfer characteristics are compared and analyzed. The results of the influence of rolling conditions under different working conditions and different tube bundle arrangements are obtained. The improvement ratio under inclined arrangement and staggered arrangement is more than 20 %, but the improvement under inline arrangement can only reach 10–15 %. Among the calculated models under different rolling conditions, the maximum heat transfer improvement reached 27.3 %. Besides, the circumferential temperature results under different conditions were also compared to analyze the influence of rolling conditions. This study may contribute to the application of LBE HCOTSG under marine conditions.

A cumulative damage model for tubes in nuclear power plants subject to continuous degradation and multi-effect shocks under dynamic environments

Continuous degradation and shocks are two vital damage mechanisms for tubes under dynamic environments in nuclear power plants (NPPs). In this work, we presented a cumulative damage model to evaluate the reliability of tubes in NPPs, which accounts for continuous degradation and random shocks. The dynamic environments were assumed to obey a homogenous Markov process. Continuous degradation was described as a general stochastic process with independent increments. A multinomial distribution was used to depict the multiple effects of Poisson-distributed shocks on tubes. The influence of dynamic environments on the cumulative damage process of tubes was also explicitly modeled. Closed-form reliability measures were derived, such as reliability functions and mean time to failure (MTTF) of tubes. Drawing upon a case study from the existing literature, the analytical solution was validated through a comparative analysis with the outcomes of Monte Carlo simulation (MCS) and other methodologies referenced in the literature. As a practical engineering application, the reliability of steam generator tubes made of Alloy 690 within pressurized water reactors (PWRs), which are susceptible to primary side stress corrosion cracking (PWSCC) and the effects of water hammer, was calculated. The findings indicate that the probabilities of steam generator tube rupture (SGTR) as estimated by the model and those inferred from operational experience have the same order of magnitude.

A case study to address the limitation of accident scenario identifications with respect to diverse manual responses

Probabilistic safety assessment (PSA) is a tool for securing the operational safety of nuclear power plants. One unique benefit of PSA is to identify accident scenarios leading to undesirable consequences. Since these accident scenarios result from highly complicated combinations of automatic and manual responses, a huge number of simulations are generally required with a precise thermal-hydraulic (TH) code. Therefore, current PSA typically reduces the number of TH code runs by focusing on limited numbers of safety-critical components with reasonable engineering assumptions. Nevertheless, it has been pointed out that the current catalog of accident scenarios in PSA may be insufficient to some extent. In order to corroborate this claim, in this work, 14,348,907 simulation conditions were randomly generated after combining 79 manual responses identified from the emergency operating procedure of a steam generator tube rupture (SGTR) event in a reference nuclear power plant. Results show that about 14.7 % of the simulations correspond to an undesirable consequence pertaining to the SGTR. Accordingly, in terms of enhancing the quality of PSA results, the results of this study support that it is inevitable to develop a promising way to reduce the amount of computational resources required by large numbers of TH code runs.

Effects of high-temperature and high-pressure immersion corrosion durations on the fretting tribo-corrosion behaviors of Inconel 690 alloy

An Inconel 690 alloy tube acting as a steam generator tube has been widely applied in the second and third generations of nuclear power plants using pressurized water reactors. However, its entire service process is always accompanied by high-temperature and high-pressure (HTHP) liquid medium corrosion and various fretting mechanical damage behaviors. This study first immerses the Inconel 690 alloy tube in HTHP corrosive medium for different lengths of time (0, 4, 8, and 12 h); then, a fretting tribo-corrosion test rig is used to investigate the effect of different fretting mechanical parameters on the surface damage mechanism and electrochemical dynamic response of each test sample. Results show that the corrosion rate of the Inconel 690 alloy tube has significantly increased after being treated by HTHP immersion corrosion, which is mainly due to the pre-existing corrosion products.

Experimental study on thermal-hydraulic performance of helically coiled tubes steam generator of lead-bismuth reactor

The advantages of the helically coiled tube steam generator lie not only in its high heat transfer efficiency but also in its compact structure, which is initially used in Pb–Bi–SCO2 reactors, and its main function is to transfer the heat from the lead-bismuth side to the SCO2 side. In this experiment, two sets of helical heat exchanger tubes are selected as the objects of investigation. Experiments are conducted on the heat transfer performance of a helical tube to study the influence of structural parameters, mass flux, pressure, and heat flux on the heat transfer characteristics during subcooled boiling and post-dryout. Considering the results of the study, new heat transfer characteristic correlations are derived for the subcooled boiling and post-dryout heat transfer regions, which provide data and theoretical support for the engineering application and thermal hydraulic analysis of steam generators.

Study on the effect of geometry and material property on collapse pressure of a helical steam generator tube under external pressure

In this paper, a numerical study was conducted to analyze the effect of the geometry (tube thickness, ovality, and helical diameter) and material properties of once through steam generator tubes subjected to external pressure on collapse pressure. The outer diameter of the steam generator tube was fixed at 17 mm, and the tube thickness was changed to 2.5 mm, 2.29 mm, and 1.27 mm. Ovality was considered for three cases of 0 %, 4 %, and 8 %, and three cases for helical diameter were considered: 577 mm, 937 mm, and 1297 mm. As material properties, elastic perfectly plastic property that ignores plastic hardening and real material property that reflect plastic hardening were considered. At the helical diameter (Dm/do ≥ 34) considered in this paper, the effect of collapse pressure due to helical bending did not appear on ovalities and both material properties. On the other hand, the wall thickness affected the collapse pressures according to the material properties when ovality occurred (>0 %). This is explained because the collapse mechanism varies depending on the thickness.

Thermal analysis of V-pad thermocouple used on once-through steam generator tubes

Once-Through Steam Generators (OTSGs) are used in the oil sands industry to produce steam, which is injected into oil sands reservoirs to produce bitumen. OTSGs consist of a combustion zone where natural gas is combusted to generate thermal energy, which boils water within tubes that pass through the OTSG. In a typical OTSG, the temperature at the external wall of the tubes can reach as high as 500 °C, or even higher. Temperature measurement of the tube wall is critical for safe operation and this can be determined by using thermocouples. However, the placement of the thermocouple and its shield to protect it on the tube outer wall interferes with heat transfer and, thus, the measured temperature from the thermocouple may not be equal to the bare tube (no thermocouple) temperature. Here, we examine how the placement of a thermocouple on a tube wall in an OTSG affects the tube wall temperature by using finite-element-based heat transfer modelling. Depending on the foulant thickness, and the placement of the thermocouple, the local tube wall temperature increases by 45 to 55 °C. The results show that using thermocouples with shields can yield a temperature measurement error of order of 15–30 °C above the actual bare tube temperature. The results provide a basis for correcting the thermocouple/shield derived value to the actual temperature of the tube wall.

Numerical simulation and model development of drag coefficient of bubbles in gas-liquid metal two-phase flow

The occurrence of a steam generator tube rupture (SGTR) accident in a lead-bismuth cooled fast reactor results in the formation of steam bubbles in the liquid lead-bismuth eutectic (LBE). This may degrade heat transfer and power transients in the reactor core due to the migration and accumulation of steam bubbles. To investigate the dynamics of steam bubbles flowing in liquid LBE, it is essential to develop an accurate model for the bubble drag coefficient. In this paper, a three-dimensional numerical model is first established to simulate the injection of high-pressure steam bubbles into a high-temperature LBE molten pool. The model is based on the CLSVOF method. By analyzing the trajectory, velocity, and diameter of bubbles, and combining them with the force equilibrium equation for bubbles, the values of the drag coefficient for bubbles are determined. On this basis, the suitability of current empirical drag models for bubble migration in LBE is evaluated. Finally, the optimal drag coefficient model is selected and further improved. Results reveal that the prediction error of the optimized model for the bubble drag coefficient in liquid LBE is within ±15 %.

Modelling the Influence of the Tube Support Plate on the Eddy Current Testing of the Steam Generator: Sensitivity Study & Validation

Eddy current testing (ECT) of Steam Generator (SG) tubes is part of the maintenance program of Nuclear Power Plants. Tube Support Plates (TSP) are usually only considered as extraneous signals for tube inspection. However, for long-term operation of SGs, there is a safety concern related to the build-up of deposits in the TSPs flow holes. The clogging-up of the TSPs flow holes affect the safe thermal-hydraulic operation of SGs. The deposits come from the feedwater train and are mostly iron oxides (magnetite) with a weak electrical conductivity and magnetite permeability.The ability of ECT probes to detect and characterize TSPs deposits is therefore of great interest. The most common and industrial ECT technique, the bobbin coil, averages the surrounding electromagnetic field over 360°, whereas the geometry of tri-foiled and quadri-foiled TSPs, and thus of clogging, is rather complex and non- axisymmetric, hence motivating the evaluation of the performance of conventional ECT rotating probes used for SGs tubes inspection. Although simulation is a powerful tool to support such a study, it requires dedicated models to be made available to NDT experts, and CEA develops ECT physical models in CIVA for this purpose. In addition to standard fast CIVA modules based on 3D semi-analytical or 2D numerical calculations restricted to canonical or axisymmetric parts, respectively, CEA develops a module dedicated to the simulation of SG tube inspection based on a 3D numerical simulation. This module allows tube deformation such as ovalization, bending or tube expansion. It also allows the addition of external objects such as anti-vibration bars, different geometries of tube support plates and now their clogging by deposits. This model is used to study various influent parameters and to perform benchmarks in the framework of a scientific collaboration between the CEA and the IRSN. Here, the specificity of the TSPs and their clogging justifies qualifying the simulation model before evaluating the influence of material and geometry properties of the deposit as well as the performance of the inspection techniques. We present the main features of the simulation module in CIVA, its experimental validation, and the main trends in the distortion of the simulated signal as a function of variation in the clogging description.

Assessment of Source Terms and Potential Doses Due to Steam Generator Tube Rupture of VVER-1200 at the El Dabaa Nuclear Power Plant in Egypt

Assessment of Source Terms and Potential Doses Due to Steam Generator Tube Rupture of VVER-1200 at the El Dabaa Nuclear Power Plant in Egypt

Non-uniform boiling heat transfer characteristics and calculation evaluation in U-tube steam generator tube bundle

U-tube steam generator, as one of the core equipment in nuclear power plants, has lateral non-uniform heating on the secondary side, which complicates the progress of heat transfer on the secondary side of the evaporator by causing fluid cross mixing. However, there is relatively little research on the properties of transverse non-uniform heat transfer in the secondary side tube bundle of the evaporator under natural circulation conditions with the free liquid surface. Therefore, to conduct comparative experiments and studies between uniform and non-uniform heating, an experimental setup with the natural circulation of the free liquid surface and the ability of transverse non-uniform heating was constructed, considering the characteristics mentioned above for the secondary side of the evaporator. The results indicate that higher proportions of gas-phase distribution are frequently found in the tube bundle on the high-power side, and corresponding positions usually have higher water temperature, heat transfer capacity, and heat transfer coefficient. Besides, four heat transfer correlations that are suitable for pool boiling are estimated, and the results show that the Rohsenow correlation has the best applicability to compute the heat transfer coefficient for uniform heating experiments while performing worse in non-uniform heating experiments. The main reason is the lack of consideration for the factors of fluid cross mixing in traditional correlations.

Wear work-rate measurement for different steam generator tube layouts in two-phase cross flow

Tube-to-support contact damage is directly related to the wear work-rate in steam generator tube bundles. Generally, the work-rate is related to two main factors: the contact force between the tube and the supports, and the sliding distance during this contact. This work presents an experimental study of the wear work-rate of the APR1400 steam generator tube bundle array layouts. The three array layouts, rotated square, rotated triangle and normal triangle, are tested in single phase and two-phase flow. The test apparatus was designed to accurately measure the work-rate of the three arrays. The approach followed in this work is to appropriately measure the contact force and sliding distance during the impact, which leads to an accurate calculation of the work-rate. Based on the results of this study, array layout effect on the work-rate was analyzed by statistical analysis. The measurements were performed for different flow velocities, covering a wide range to include post- and pre-critical flow velocity of each array. Results showed a substantial difference in the mean work-rate between the rotated square array and the triangular arrays. Furthermore, the larger gap size between the vibrating tube and the supports resulted into higher work-rates for all void fractions.