Thermal conductivity of Fe-Si alloys and thermal stratification in Earth?s core
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Zhang, Youjun↗
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Studying the effect of the upper internal structure design on thermal stratification in sodium fast reactors
Thermal stratification and mixing in large reactor pools can pose significant issues with regard to operation and safety of nuclear plants. While significant work has been done in this area on light water reactors it is more critical for sodium reactors and there is far less data with regard to low Prandtl number fluids. Here this paper focuses on the effect of the upper internal structure on the formation of thermal stratification in a scaled sodium fast reactor upper plenum. Six different upper internal structure configurations were tested to observe the effect on thermal stratification. The degree of stratification was quantified using the stratification number. Each configuration was tested from low to high flow rates at a temperature difference of 50 and 100 °C. Over this broad array of testing, it was observed that higher flow rates, more porosity in the upper internal structure design, and a smaller temperature difference yielded a lower degree of stratification. This information can be used to aid in the design of the upper internal structure in a sodium fast reactor. Furthermore, this high resolved temperature data can be used to verify models under prototypic low Prandtl numbers.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
A status review on the thermal stratification modeling methods for Sodium-cooled Fast Reactors
The thermal stratification phenomenon plays a crucial role in the safety of various nuclear systems, including the Gen-III + Light Water Reactors (LWR) and the Gen-IV reactors. The phenomenon is of particular importance for the pool-type Sodium-cooled Fast Reactors (SFRs) because it may cause neutronic and thermal-hydraulic in- stabilities in the reactor core, or lead to damages of both the reactor vessel and in-vessel components due to the growth of thermal fatigue cracking. More significantly, thermal stratification could impede the establishment of the natural circulation during accidental scenarios and introduce uncertainties to the core safety of SFRs. Efforts for modeling of the thermal stratification in SFRs have been made for decades to prevent or mitigate the damage caused by the phenomenon. This paper gives a review of the advances that have been made in recent 10 years on the computational modeling methods for thermal stratification phenomenon in SFRs. These methods can be generally drawn into two categories. The first one is the system-level methods which provide fast-running but approximate calculations, and the second one is the CFD methods which provide high-resolution calculations at high computational expense. Finally, after introducing the efforts that have been made to improve the one- dimensional (1-D) models, the paper envisioned the possible research directions that could be pursued to enhance the modeling of thermal stratification in the near future.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
An Efficient 1-D Thermal Stratification Model for Pool-Type Sodium-Cooled Fast Reactors
Investigating thermal stratification in the upper plenum of a sodium fast reactor (SFR) is presently a technology gap in SFR safety analysis. Understanding thermal stratification will promote safe operation of the SFR before its commercial deployment. Stratified layers of liquid sodium with a large vertical temperature gradient could be established in the upper plenum of an SFR during a down-power or a loss-of-flow transient. These stratified layers are unstable and could result in uncertainties for the core safety of an SFR. In order to predict the occurrence of the thermal stratification efficiently, we developed a one-dimensional (1-D) transport model to estimate the temperature profile of the ambient fluid in the upper plenum. This model demands much less computational effort than computational fluid dynamics (CFD) codes and provides calculations with higher fidelity than historical system-level codes. Two flow conditions were considered separately in the current study depending on if in-vessel components are presented in the upper plenum. For the condition where in-vessel components, specifically the upper internal structure, are presented, we assumed that the impinging sodium was evenly dispersed in the ambient fluid within the distance between the bottom of the in-vessel component and the jet inlet surface. For the condition where no in-vessel components are presented, we assumed that the impinging sodium was evenly dispersed in the ambient fluid within the jet length, which was determined through data-driven trainings. The newly developed 1-D model showed similar performance with the CFD model in both cases. However, due to the assumption of flat profiles of the impinging jet axial dispersion rate, nonnegligible discrepancies between the 1-D prediction and the measured data were observed.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Benchmark Specification for Select Experiments Conducted at the University of Wisconsin-Madison Thermal Stratification Test Facility
The Department of Energy (DOE)-Nuclear Energy University Programs (NEUP) supported the creation and operation of the Thermal Stratification Test Facility (TSTF) at the University of Wisconsin Madison (UWM) as part of a larger effort to understand thermal stratification behavior in liquid-metal-cooled reactors. The TSTF was designed to simulate transients in a reactor plenum that are known to cause thermal stratification. High-reliability and high-resolution measurements of the flow and temperature were collected for use as experimental benchmarks to support validation efforts for computational models. The results of these tests contribute to the greater understanding of thermal stratification behavior of liquid sodium under various configurations and operating conditions. The six TSTF tests selected for benchmarking are a set of forced circulation tests at a fixed flow rate with different Upper Internal Structure (UIS) configurations in the test section (no UIS, solid UIS, and a UIS with flow area of 4, 8, 12, and 100%). This report provides a complete description of the benchmark problems, including all key test facility details, descriptions of each test condition, and measured data for comparison with modeled results.
42 ENGINEERING↗
A Computational-experimental Study to Simulate Mixing and Thermal Stratification in SFRs
This NEUP project 16-10579 entitled “A Computational-Experimental Study to Simulate Mixing and Thermal Stratification in SFRs”, has investigated important phenomena of thermal stratification and mixing in Sodium-cooled Faster reactors (SFRs). A liquid metal experimental set-up was built at Kansas State University to generate high fidelity experimental data and validate computational models. The scope of the work involved - scaled down design of experimental facility, construction and commissioning of the new facility, conducting thermal-hydraulics experiments relevant to the physics of thermal stratification and mixing in the plena, developing 3D CFD models of the experiments, developing SAS4A/SASSYS-1 system model of the liquid metal experimental facility , survey of previous data in literature on stratification experiments and recommendations for improved models.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
THERMAL STRATIFICATION IN A POOL-TYPE GEOMETRY
Sodium fast reactors are poised to be a leading candidate for the next generation of commercial reactor deployment. Before licensing can be completed it is important that information be gathered which examines reactor transients during loss of flow accidents. During loss of flow accidents thermally stratified layers can form in the reactor pool. The formation of thermal stratification in the primary pool of a sodium fast reactor during a loss of flow accident can cause cyclic thermal fatigue on the reactor vessel potentially leading to crack formation and weld failure. Computational models have been built to analyze the formation and persistence of thermal stratification during accident transients, but are not currently validated by experimental data. A thermal stratification research facility has been developed and tested to research thermal stratification with loss of flow type conditions. Data from the experiments will be used to validate computational models. The facility can simulate both protected and unprotected loss of flow accident transients in the temperature range of 200-325 [C] with flow rates from 2 gpm to 20 gpm.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
The role of thermal stratification on the co‐spectral properties of momentum transport above an Amazonian forest
The influence of thermal stratification on the turbulent kinetic energy balance has been widely studied; however, its influence on the turbulent stress remains less explored in the presence of tall vegetated canopies and less ideal micrometeorological conditions. Here, the impact of thermal stratification on turbulent momentum flux is considered in the roughness sublayer (RSL) and the atmospheric surface layer (ASL) using the Amazon Tall Tower Observatory (ATTO) in Brazil. A scalewise co‐spectral budget (CSB) model is developed using standard closure schemes for the pressure–velocity decorrelation. The CSB revealed that the co‐spectrum ${F}_{wu}\left({k}_x\right)$ between longitudinal (u') and vertical (w') velocity fluctuations is impacted by the energy spectrum of the vertical velocity ${E}_{ww}\left({k}_x\right)$ and the much less studied longitudinal heat‐flux co‐spectrum ${F}_{u{\theta}_{\mathrm{v}}}\left({k}_x\right)$, where ${\theta}_{\mathrm{v}}^{\prime }$ are temperature fluctuations and ${k}_x$ is the longitudinal wavenumber. Under stable, very stable, and dynamic–convective conditions, the scaling exponent ${F}_{wu}\left({k}_x\right)$ in for the inertial subrange (ISR) scales is dominated by ${F}_{u{\theta}_{\mathrm{v}}}\left({k}_x\right)$ instead of ${E}_{ww}\left({k}_x\right)$. A near ${k}_x^{-7/3}$scaling in ${F}_{u{\theta}_{\mathrm{v}}}\left({k}_x\right)$ robust to large variations in thermal stratification is found, whereas the Kolmogorov ISR scaling for ${E}_{ww}\left({k}_x\right)\sim {k}_x^{-5/3}$ is not found. The scale‐dependent decorrelation time between u' and w' is dominated by ${\epsilon}^{-1/3}{k}_x^{-2/3}$ in the ISR, but is nearly constant for eddies larger than the vertical velocity integral scale, regardless of stability. Implications of these findings for generalized stability correction functions that are based on the turbulent stress budget instead of the turbulent kinetic energy budget are discussed.
canopy turbulence↗
A Multilayer Reservoir Thermal Stratification Module for Earth System Models
Thermal stratification in reservoirs is a critical process that regulates downstream riverine energy and biogeochemical cycling. Current stratification models either simplify reservoir geometry or neglecting the effects of reservoir operation. Here we present a new multi-layer reservoir stratification model that can be coupled to earth system models at regional or global scale. With a multi-layer vertical discretization, we introduce a newly developed storage-area-depth dataset to improve parameterization of advection processes in and out of the reservoir. The new model better represents vertical temperature gradient and subsequently temperature of water released to downstream. The stratification model is applied to 1400 reservoirs over the contiguous US and validated against observed surface, profile, and outflow temperature data over 130 reservoirs subjected to various levels of regulation. The Nash-Sutcliffe values are higher than 0.5 for about 77% of the validated reservoirs using surface temperature while the average values of root mean square error and bias are 3.6oC and -1.1oC, respectively. Using the new reservoir storage-area-depth dataset improves the simulation of surface temperature at over 69% of the validated reservoirs compared to using simplified reservoir geometry. The reservoir stratification model contributes to improving predictive understanding of anthropogenic impact on terrestrial hydrological, ecological and biogeochemical cycles.
Yigzaw, Wondmagegn↗
Implications of Shear and Thermal Stratification on Wind Turbine Tip-Vortex Stability
The interaction between wind turbines in a wind farm through their wakes is a phenomenon that has been studied for decades and is still relevant today. Turbines clustered together in arrays will often operate in the wake of other upstream turbines which may lead to significant power losses and fatigue loads. For modern large-scale wind turbines, the mean shear velocity profile and thermal stratification are major components of the atmospheric boundary layer so it is important to understand their impact on near-wake development. Additionally, veer is present due to the rotation of the Earth. The impact of shear, thermal stratification and veer on the stable wake length of turbines with a dynamic control strategy is studied numerically in this work using a suite of highly resolved large-eddy simulations. Instantaneous flow fields are extracted from the simulations and used to conduct proper orthogonal decomposition (POD) and compute the mean kinetic energy fluxes by different POD modes to better understand the tip-vortex instability mechanisms. Our findings show that the dynamic pitch control scheme is able to shorten the stable wake length to about 1.5R in uniform flow. Shear can significantly affect the break up of wind turbine tip-vortices as well as the shape and stable length of the wake, whereas thermal stratification seems to only have limited contribution to the spatial development of the near-wake field. Veer causes the wake boundary to skew but has a limited impact on the wake length.
length thermal stratification↗
Numerical investigation of the influence of shear and thermal stratification on the wind turbine tip‐vortex stability
Summary The interaction between wind turbine wakes and atmospheric turbulence is characterised by complex dynamics. In this study, two major components of the atmospheric boundary layer dynamics have been isolated, namely, the mean velocity profile shear and the thermal stratification, to examine their impact on the near‐wake development by undertaking a series of highly resolved large‐eddy simulations. Subsequently, instantaneous flow fields are extracted from the simulations and used to conduct Fourier analysis and proper orthogonal decomposition (POD) and compute the mean kinetic energy fluxes by different POD modes to better understand the tip‐vortex instability mechanisms. Our findings indicate that shear can significantly affect the breakup of the wind turbine tip‐vortices and the shape and stable length of the wake, whereas thermal stratification seems to only have limited contribution to the spatial development of the near‐wake field. Finally, our analysis shows that the applied perturbation frequency determines the tip‐vortex breakup location as it controls the onset of the mutual inductance instability.
17 WIND ENERGY↗
Do ambient shear and thermal stratification impact wind turbine tip-vortex breakdown?
Modern wind turbines experience uneven inflow conditions across the rotor, due to the ambient flow’s shear and thermal stratification. Such conditions alter the shape and length of turbine wakes and thus impact the loads and power generation of downstream turbines. To this end, understanding the spatial evolution of the individual wakes under different atmospheric conditions is key to controlling and optimising turbine arrays. With this numerical study we aim to obtain a better understanding of the fundamental physics governing the near-wake dynamics of wind turbines under shear and thermal stability, by examining their tip-vortex breakup mechanisms. Our approach considers scale-resolving simulations of a single turbine wake under a linear shear profile as well as the application of harmonic tip perturbations to trigger flow instabilities. For the subsequent analysis we use the proper orthogonal decomposition (POD) method to extract coherent structures from the flow, and we also calculate mean kinetic energy fluxes to quantify each coherent structure’s contribution to wake recovery. The wake’s helical spiral is found to hinder wake recovery for all studied ambient flow conditions, whereas the mutual inductance instability has positive MKE flux leading to an enhanced wake recovery. Finally, the ambient shear has the largest impact on the local MKE flux with respect to downstream location by changing the shape of the curve and location of extrema, whereas thermal stratification has only a minimal impact on the magnitude of the near-wake local MKE flux distribution.
17 WIND ENERGY↗
Assessment of Thermal Stratification in Versatile Test Reactor Transients
The Versatile Test Reactor (VTR) is a fast-spectrum test reactor currently being developed in the United States under the direction of the US Department of Energy. The conceptual design of the 300 MWth pool-type sodium-cooled fast reactor (SFR) has been led by the US National Laboratories in collaboration with General Electric-Hitachi and Bechtel National Inc. Safety performance analysis for the VTR conceptual design is being performed with the systems thermal-hydraulics (SYSTH) module of the SAS4A/SASSYS-1 liquid-metal reactor safety analysis code system. Since the current model of the VTR employs a simple perfect mixing model for large plena like the hot pool, it is not able to predict temperature variations that may develop during the transient. Prior work simulating the response of SFRs to postulated events like the Protected Station Blackout (PSBO) has shown that the phenomenon of thermal stratification, where stable thermal layers accumulate in the hot pool, may delay the transition to natural circulation and thus impact the predicted transient progression. Thus, an effort has begun to model this transient by integrating a Computational Fluid Dynamics (CFD) model of the hot pool into the SAS4A/SASSYS-1 model of the Primary Heat Transport System during the simulation of the PSBO event. A three-dimensional Volume-Of-Fluid CFD model of the VTR hot pool has been developed for the co-simulation of SAS4A/SASSYS-1 with CFD. In this work, the standalone SAS4A/SASSYS-1 calculation and the standalone CFD calculation based on the SAS4A/SASSYS-1 calculation result were produced on the Idaho National Laboratory High Performance Computing cluster, SAWTOOTH. At this time, only the standalone CFD and SAS4A/SASYS-1 simulation results are provided.
99 GENERAL AND MISCELLANEOUS↗
Thermal Stratification Study in a Liquid Sodium Experimental Facility
Update on the use of fiber optic temperature sensing technologies for examining thermal stratification in a liquid sodium facility. Research discusses techniques for measuring temperature with optical fibers as well as presenting data from research.
Optical Fibers↗
Assessment of Sodium Thermal Stratification Models Utilizing the TSTF Benchmark
As a result of certain transient scenarios, a thermally stratified layer of liquid sodium can develop in the bulk coolant volumes of a sodium-cooled fast reactor (SFR). In addition to the effects a stratification layer has on the temperature of the heat transport system, a stratification layer can also influence the transition to and establishment of natural circulation flow, which plays an important role in passive cooling and the inherent safety of a pool-type SFR. Therefore, the ability to accurately capture thermal stratification phenomena is important when demonstrating the safety basis of a pool-type SFR during transient sequences. The present work assesses various computational models with different fidelities in their ability to predict thermal stratification in the upper plenum of an SFR. Each computational model will be assessed using the data generated at the Thermal Stratification Test Facility (TSTF) located at the University of Wisconsin-Madison. Using measured flow rate and inlet temperature data, the measured temperature distributions of the tests are compared to the predictions of the lumped volume-based models in SAS4A/SASSYS-1, a 1D-based model in SAM, and a 3-D computational fluid dynamics (CFD) model using STAR-CCM+. The relative performance of the various computational methods is assessed with respect to key metrics such as bulk coolant temperature distribution and plenum exit temperature. A total of eight tests are analyzed, covering different combinations of flow rates (3 and 10 GPM) and upper internal structure (UIS) configurations (none, solid, porous, and open) The perfect mixing model of SAS4A/SASSYS-1 provides the highest accuracy when the flow rate is high and there is no UIS in the test vessel, as high flow rate injection promotes thermal mixing of the sodium in the test vessel. For most of the analyzed tests, the stratified volume model of SAS4A/SASSYS-1 is able to predict the delay in the outlet temperature drop and temperature distribution in the test vessel by a small number of layers to represent thermal stratification. However, the stratified volume model can only simulate a maximum of three temperature layers within a volume and when a layer approaches the elevation of the outlet, the predicted outlet temperature can demonstrate rapid, non-physical changes. The 1-D axial mixing model of SAM provides results that agree reasonably well with the measured data in the prediction of the temporal evolution of the outlet temperature with the exception of the case with a high flow rate and no UIS. The SAM 1-D model has a similar level of accuracy to CFD results when it comes to predicting the outlet temperature. CFD shows overall good agreement in predicting the temperature distribution in the test vessel and outlet temperature. As CFD can model the test vessel geometry in detail, it performs well in the cases of complex geometries such as tests that included a UIS and internal flow through the UIS resulting in active mixing of the coolant in the test vessel. Each of the models discussed in the present work has the potential to be useful during the various stages of reactor design, analysis, and licensing. The lumped-volume approach can be applied for fast turnaround safety calculations to obtain overall reactor behavior during transients. The 1-D models provide improved accuracy when stratification is expected for a relatively low increase in the computational cost. The CFD model can be utilized for confirmatory analysis of the 1-D model, when experimental measurements are not available.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Fluid Flow, Thermal Stratification, and Inclusion Motion During Holding Period in Steel Ladles
In the current study, the fluid flow and thermal stratification during the holding period are numerically simulated. The standard k–ε two-equation turbulence model is adopted to describe the turbulence. The trajectories of inclusions are calculated by the discrete phase model (DPM) considering the stochastic effect of turbulence. Two different initial conditions for the flow field are compared: the quiescent state of flow and the fluid flow induced by gas stirring. Significant differences are observed between these cases. In practice, the holding period starts from the shut-off of the gas blowing. Thus, it is proposed that the flow field at the terminal of gas stirring should be considered for the simulation of the fluid flow, heat transfer, and inclusion motion during the holding period.
36 MATERIALS SCIENCE↗
Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling
Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.
Bayesian optimization↗
Assessing the use of portable air cleaners for reducing exposure to airborne diseases in a conference room with thermal stratification
The COVID-19 pandemic has highlighted the need for strategies that mitigate the risk of aerosol disease transmission in indoor environments with different ventilation strategies. It is necessary for building operators to be able to estimate and compare the relative impacts of different mitigation strategies to determine suitable strategies for a particular situation. Using a validated CFD model, this study simulates the dispersion of exhaled contaminants in a thermally stratified conference room with overhead heating. The impacts of portable air-cleaners (PACs) on the room airflow and contaminant distribution were evaluated for different PAC locations and flow rates, as well as for different room setups (socially distanced or fully occupied). To obtain a holistic view of a strategy's impacts under different release scenarios, we simultaneously model the steady-state distribution of aerosolized virus contaminants from eight distinct sources in 18 cases for a total of 144 release scenarios. The simulations show that the location of the source, the PAC settings, and the room set-up can impact the average exposure and PAC effectiveness. For this studied case, the PACs reduced the room average exposure by 31%-66% relative to the baseline case. Some occupant locations were shown to have a higher-than-average exposure, particularly those seated near the airflow outlet, and occupants closest to sources tended to see the highest exposure from said source. We found that these PACs were effective at reducing the stratification caused by overhead heating, and also identified at least one sub-optimal location for placing a PAC in this space.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗