Thermal Stratification Model Research Articles

Analysis of the effect of thermal stratification on the natural circulation decay heat removal of sodium-cooled fast reactor

Thermal stratification is an important phenomenon in the process of natural circulation decay heat removal in sodium-cooled fast reactors (SFR). It affects the establishment of the natural circulation and the flow rate of the natural circulation in a station black out (SBO) accident, and therefore affects the safety of the reactor. In safety evaluation, programs are often required to perform analysis for various conditions and long-term transients. However, it is difficult to meet this requirement by adopting a multi-dimensional method or one-dimensional and multi-dimensional coupling method. Therefore, this paper proposes applying a thermal stratification model to the system analysis program THACS to analyze the thermal stratification phenomenon. First, the thermal stratification model is validated with experimental data. The validated model is applied to analyze a station black out accident in the SFR. The lumped parameter model and thermal stratification model are used respectively for the hot pool. By comparing the calculation results of the two models, the effect of thermal stratification of the hot pool on key parameters such as the natural circulation flow rate of the primary circuit, natural circulation flow rate in the inter-wrapper region, average core outlet temperature, maximum core fluid temperature, and the maximum temperature of cladding was analyzed, and the effect of thermal stratification on natural circulation decay heat removal of the SFR was evaluated. This work can provide a reference for the safety analysis of the reactor and contribute to developing a more conservative safety analysis and evaluation strategy.

Development of reduced-order thermal stratification model for upper plenum of a lead–bismuth fast reactor based on CFD

After an emergency shutdown of a lead-bismuth fast reactor, thermal stratification occurs in the upper Plenum, which negatively impacts the integrity of the reactor structure and the residual heat removal capacity of natural circulation flow. The research on thermal stratification of reactors has mainly been conducted using an experimental method, a system program, and computational fluid dynamics (CFD). However, the equipment required for the experimental method is expensive, accuracy of the system program is unpredictable, and resources and time required for the CFD approach are extensive. To overcome the defects of thermal stratification analysis, a high-precision full-order thermal stratification model based on CFD technology is prepared in this study. Furthermore, a reduced-order model has been developed by combining proper orthogonal decomposition (POD) with Galerkin projection. A comparative analysis of thermal stratification with the proposed full-order model reveals that the reduced-order thermal stratification model can well simulate the temperature distribution in the upper plenum and rapidly elucidate the thermal stratification interface characteristics during the lead-bismuth fast reactor accident. Overall, this study provides an analytical tool for determining the thermal stratification mechanism and reducing thermal stratification.

Experimental Investigation on Formation Mechanism of Jet Fires in Transformer Oil Filled Equipment with External Thermal Load

ABSTRACT Liquid jet fire was one of the typical fires that endangered industrial safety. Especially, the oil-filled equipment of the substation was subjected to an external thermal load, which caused liquid jet fire. However, less literature was available for the formation mechanism of liquid jet flame. Thus, this paper conducted a systematic experiment to reveal the formation mechanism of transformer oil jet fire with various heat release rates (33 kW, 73 kW, 132 kW, and 212 kW). In this paper, the formation mechanism of transformer oil jet fire was clarified. Experimental observation showed that the formation process of transformer oil jet fire can be divided into three stages. The gas–liquid two-phase flow occurred during the formation of transformer oil jet fire. The correlation between the overpressure peak and the heat release rate was established. The medium thermal response behavior can be divided into three stages. When the medium temperature reached the boiling point, the jet fire appeared. The thermal stratification model of a transformer oil jet was established. The correlation between the degree of liquid stratification and dimensionless heat release rate was established. The thermal convection and radiation determined the heat transfer mechanism of oil during the formation of jet fire.

Uncertainty Quantification of the 1-D SFR Thermal Stratification Model via the Latin Hypercube Sampling Monte Carlo Method

A one-dimensional (1-D) thermal stratification (TS) model was recently developed in our research group to predict the TS phenomenon in pool-type sodium-cooled fast reactors. This paper performs uncertainty quantification (UQ) of the 1-D TS model to evaluate its performance by considering the aleatoric uncertainties that existed in the model parameters and to identify the plausible sources of the epistemic uncertainties. The Latin hypercube sampling–Monte Carlo method (LHS-MC), which is elaborated with an example in this paper to facilitate its understanding and implementation, is used for the UQ process. The advantages of LHS-MC, including both better stability and better accuracy than the conventional random sampling–Monte Carlo method with fewer realizations, are demonstrated in this paper. In total, 648 temperature measurements acquired from nine experimental transients performed in a university-scale Thermal Stratification Experimental Facility are used to evaluate the performance of the computational 1-D TS model. The UQ result shows that 77.5% of the experimental data can be predicted by the 1-D TS model within uncertainty ranges, which indicates the good performance of the computational model when the aleatoric uncertainties are correctly captured. The rest 22.5% of the experimental data are found located outside of the uncertainty ranges, which reveals the existence of the epistemic uncertainties caused by the lack of understanding of the TS phenomenon and defects in the 1-D model. The simple jet model currently employed by the 1-D TS model is thought to be one of the attributors to these defects.

AP1000 IRWST numerical analysis with GOTHIC

The AP1000 Passive Residual Heat Removal (PRHR) system plays a significant role as it helps to remove the core decay heat, using the In-containment Refueling Water Storage Tank (IRWST) as a heat sink. The IRWST is located above the core, promoting natural circulation and allowing to be the mid-term heat-sink for the reactor core. The thermo-hydraulic pool behavior during an accident has an influence in the containment pressure and temperature, as happens in the pressure suppression pool in BWR reactors.Due to the importance of the IRWST performance on the AP1000 containment, a numerical analysis of a scaled experiment has been done using the GOTHIC code. Firstly, an IRWST scaled-down model is created, a mesh sensitivity analysis is performed, and the results obtained are compared against experimental results available in the literature. It is found the importance of the mesh discretization for the proper thermal-stratification modeling. Then, the reference model setup and mesh are applied in a full-scale prototypic model. The mesh influence on the thermal stratification is analyzed, as well as its impact on the AP1000 containment pressure. The mesh and setup for the full-scale model are selected to be implemented in a full containment 3D model in future works.

Sensitivity analysis of the 1-D SFR thermal stratification model via discrete adjoint sensitivity method

This paper presents a parameter sensitivity analysis on a thermal stratification (TS) model by using the discrete sensitivity method. The TS model was recently developed in our research group to efficiently predict the TS phenomenon in pool-type Sodium-cooled Fast Reactors. The fluid temperature gradient was considered as the figure of merit in the sensitivity analysis because it best characterizes the thermal stratification phenomenon. The sensitivities of the fluid temperature gradient with respect to four different parameters were investigated, including jet volumetric flow rate Qjet, jet temperature Tjet, heat capacity of the ambient fluid Cp,amb, and static thermal conductivity of the ambient fluid kc,amb. The sensitivity analysis was conducted through both the conventional forward sensitivity method and the advanced adjoint sensitivity method, which is more effective in cases where the number of outputs is small and the number of input parameters is large.The sensitivities obtained in this study suggested that perturbations in Qjet, Cp,amb, and kc,amb could introduce either positive or negative changes to the temperature gradient, depending on the axial location and the elapsed time of the experiment. However, an increase in Tjet always decreased the temperature gradient. Moreover, the impact of Tjet on the maximum temperature gradient was several times higher than that of the other three parameters, which indicated that additional attention may need to be paid to the occurrence of thermal stratification in the sodium pool when the impinging jet has a large temperature change. This study also provides a step-by-step example for the application of the discrete adjoint sensitivity method to the time-dependent nonlinear systems.

Enhancing the One-Dimensional SFR Thermal Stratification Model via Advanced Inverse Uncertainty Quantification Methods

Thermal stratification (TS) is a thermal-fluid phenomenon that can introduce large uncertainties to nuclear reactor safety. The stratified layers caused by TS can lead to temperature oscillations in the reactor core. They can also result in damages to both the reactor vessel and in-vessel components due to the growth of thermal fatigue cracks. More importantly, TS can impede the establishment of natural circulation, which is widely used for passive cooling and ensures the inherent safety of numerous reactor designs. A fast-running one-dimensional (1-D) model was recently developed in our research group to predict the TS phenomenon in pool-type sodium-cooled fast reactors. The efficient 1-D model provided reasonable temperature predictions for the test conditions investigated, but nonnegligible discrepancies between the 1-D predictions and the experimental temperature measurements were observed. These discrepancies are attributed to the model uncertainties (also known as model bias or errors) in the 1-D model and the parameter uncertainties in the input parameters. In this study, we first recognized through a forward uncertainty analysis that the observed discrepancies between the computational predictions and the experimental temperature measurements could not be explained solely by input uncertainty propagation. We then performed an inverse uncertainty quantification (UQ) study to reduce the model uncertainties of the 1-D model using a modular Bayesian approach based on experimental data. Inverse UQ serves as a data assimilation process to simultaneously minimize the mismatches between the predictions and experimental measurements, while quantifying the associated parameter uncertainties. The solutions of the modular Bayesian approach were in the form of posterior probability density functions, which were explored by rigorous Markov Chain Monte Carlo sampling. Results showed that the quantified parameters obtained from the inverse UQ effectively improved the predictive capability of the 1-D TS model.

Experimental analysis of thermal behavior in cryogenic propellant tank with different pressurants

The thermal behavior of cryogenic propellant tanks is crucial issue in the operation of cryogenic propulsion systems. Herein, ground experiments were conducted in a 600-mm-diameter cryogenic tank filled with liquid nitrogen. As pre-pressurants, gaseous helium and gaseous nitrogen (of the same species as the liquid), were used to investigate its effect in accordance with actual propulsion systems. The tank was sealed after pre-pressurization to observe the self-pressurization. The evaporation rate and heat flow in the tank were estimated based on pressure and temperature measurements. In addition, the axial liquid temperature distribution was obtained through the liquid draining from the tank bottom, and a thermal stratification model was developed. These results demonstrated that the type of pre-pressurant significantly affected the thermal behavior in the tank. A higher evaporation rate and higher liquid internal energy rise rate with a thicker thermal layer were observed in the helium pre-pressurization case. The lower nitrogen partial pressure in the helium case enhanced the vaporization and growth of the thermal layer. Estimation of the power balance in the tank demonstrated that not only the ullage but also the heat mass of the tank provided heat for the evaporation and thermal layer. The evaporation occurs mainly at the contact point between the tank skin and liquid surface. The nitrogen vapor rises in a thin layer along the tank skin because of buoyancy under nitrogen pre-pressurization; however, buoyancy is lower under helium pre-pressurization, and a radial vapor flow is probably produced from the contact point instead, leading to a higher heat flux to the liquid.

Three-dimensional flow model development for thermal mixing and stratification modeling in reactor system transients analyses

Mixing, thermal-stratification, and mass transport phenomena in large pools or enclosures play major roles for the safety of reactor systems. Depending on the fidelity requirement and computational resources, various modeling methods, from the 0-D perfect mixing model to 3-D Computational Fluid Dynamics (CFD) models, are available. Each is associated with its own advantages and shortcomings. It is very desirable to develop an advanced and efficient thermal mixing and stratification modeling capability embedded in a modern system analysis code to improve the accuracy of reactor safety analyses and to reduce modeling uncertainties.An advanced system analysis tool, SAM, is being developed at Argonne National Laboratory for advanced non-LWR reactor safety analysis. While SAM is being developed as a system-level modeling and simulation tool, a reduced-order three-dimensional module is under development to model the multi-dimensional flow and thermal mixing and stratification in large enclosures of reactor systems. This paper provides an overview of the three-dimensional finite element flow model in SAM, including the governing equations, stabilization scheme, and solution methods. Additionally, several verification and validation tests are presented, including lid-driven cavity flow, natural convection inside a cavity, laminar flow in a channel of parallel plates. Based on the comparisons with the analytical solutions and experimental results, it is demonstrated that the developed 3-D fluid model can perform very well for a wide range of flow problems.

Thermal Stratification Modeling in the Inner Coastal Bays

ABSTRACT Lee, G.S.; Cho, H.Y., and An, S.M., 2018. Thermal Stratification Modeling in the Inner Coastal Bays. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 1451–1455. Coconut Creek (Florida), ISSN 0749-0208. Hypoxia occurs repeatedly when water quality deterioration and damage to the aquaculture industry are reported in coastal inner bays. In general, hypoxia occurs when stratification develops, and the oxygen consumption rate of the water layers and sediment increases. Therefore, prediction of hypoxic water masses affecting the survival of marine benthos should be preceded by a stratification prediction. In this study, stratification at Dang-dong bay, the inner bay of Jinhae Bay located on the southern coast of Korea, was investigated using a vertical eddy diffusion model focused on the heat budget at the water surface. Air temperature, wind speed, vapor pr...

Development of thermal stratification in a rotating cryogenic liquid hydrogen tank

Accurate prediction of thermal stratification in cryogenic propellant container is of significance to space missions. In the present paper, a thermal stratification model, considering phase change transmission at the liquid vapor interface, is developed and adopted to investigate the pressurization performance and stratification development in a rotating liquid hydrogen tank. Heat exchange associated with viscous flow is particularly considered to ensure that the flow and heat exchange are continuous when Ra is in the range of 0.1 to 1015. The calculated results show that the stratified layer in a rotating tank develops more slowly than in a non-rotating tank. With the rotation rate increasing from 1.0 deg/s to 4.0 deg/s, the required time of stratification developing fully has increased approximately 1.82 times. The speed of the stratification development with aspect ratio of 0.5 is approximately 2.27 times faster than that with aspect ratio of 1.0. The fluid stratification under different gravity levels express different developing speed, slower developing speed is observed at the micro-gravities. More than 10 times consumed time needs to reach fully field stratification at 10−4g0 comparing at 1g0. Meanwhile the ullage pressure increases faster with the greater gravity level. It is also found that the liquid–vapor phase change has great influence on the tank pressure. The deviation of ullage pressure increased reaches by 18.27% with the consideration of phase change. It is suggested that phase change effect should be accounted for in the prediction of thermal stratification and ullage pressure of liquid hydrogen tank.

저수지 수온성층 해석능력 제고를 위한 적정 EFDC 매개변수 선정

본 연구에서는 대표적 3차원 수리 수질해석모형인 EFDC의 수온성층해석 능력 제고를 위해 적정 매개변수를 도출하고자 하였다. 이를 위해 태양복사 분포, 하상 초기온도, 활성 하상 수온층 깊이, 열전달계수 등 태양에너지와 관련된 5가지 매개변수에 대하여 용담호 수온성층해석 결과를 비교 분석하였다. 모의기간은 2005년 6월부터 12월까지였으며 수온 성층 재현성 수행 결과는 통계 지표인 AME, RMSE, <TEX>$R^2$</TEX>을 적용하여 비교하였다. 그 결과 IASWRAD는 하상으로 분포하는 경우, 활성 하상 수온층 깊이는 10m를 사용하는 것이 타당할 것으로 판단되었다. 본 연구에서 도출된 결과는 EFDC 모형의 수온성층모의시 적용 가이드라인으로 활용될 수 있을 것이다. In this study, a methodology was devised to overcome that difficulty for thermal stratification modeling using EFDC. For the increase of reproductability for thermal stratification analysis, the effect of parameter such as distribution of solar radiation, depth of active bed temperature layer, heat transfer coefficients were analyzed. The simulation period was from June to December in 2005 and statistical index is used to analyze the model results. The results showed that distribution of solar radiation is zero and depth of active bed temperature layer is 10 m are suitable for simulation of thermal stratification in Yongdam Dam reservoir. This study results can be used for guideline to analyze the thermal stratification of large dam reservoir in Korea.

Analysis of self-pressurization phenomenon of cryogenic fluid storage tank with thermal diffusion model

Self-pressurization phenomenon is one of the most important problems in the storage of cryogenic liquid. Until now, it has been difficult to predict exact pressurization process due to its complex non-equilibrium thermal behavior. This paper analyzes the self-pressurization with the trend of pressurization curves from experiment using liquid nitrogen with various heat leaks and liquid fractions. The trend of pressurization curves are classified on the basis of shape of pressurization curve. The qualitative relation between transient period, heat leak and liquid fractions is suggested. Thermal diffusion model (TDM) considering thermal stratification and thermal equilibrium model (TEM) can properly predict the respective pressurization curves with suitable condition for each model.

Limnological Structure of Titan's Hydrocarbon Lakes and Its Astrobiological Implication

Cassini radar recently detected several putative liquid hydrocarbon lakes in the polar region of Saturn's moon Titan. Such lakes may contain organic sediments deposited from the atmosphere that would promote prebiotic-type chemistry driven by cosmic rays, the result of which could be the production of more complex molecules such as nitrogen-bearing organic polymer or azides. The physical properties of the lake and their temporal evolution under Titan's present climatic setting were investigated by means of a one-dimensional lake thermal stratification model. Lakes can undergo various evolutions, depending on the initial composition and depth of the lake and hydrocarbon abundance in the near-surface atmosphere. Pure methane ponds, which may occasionally form when heavy methane hailstones reach the surface, would be transitory in that they would evaporate, freeze up, and eventually dry up. On the other hand, lakes filled with a mixture of methane, ethane, and nitrogen would be more stable; and freezing or drying would not necessarily occur in most cases. Such lakes undergo a seasonal cycle of thermal stratification in spring and early summer and convective overturning in other seasons. The summer thermal stratification near the lake surface could be destabilized by bottom heating as a result of an enhanced geothermal heat flux, e.g., in the vicinity of cryovolcanoes. Most likely the composition of the lake and atmosphere would come to equilibrium by way of a small amount of evaporation, but the lake-atmosphere system could be repeatedly brought out of equilibrium by irregular precipitation. The viability of prebiotic-like chemistry in the lake may depend on many lake parameters, such as temperature, liquid or frozen state, and convective mixing. Moreover, convective mixing may drive suspension of solid acetylene and other sediments on the lake bottom and redistribution of dissolved gases, which might be relevant for putative life-forms that consume hydrogen and solid acetylene.

Thermal structure of putative hydrocarbon lakes on Titan

Abstract Possible hydrocarbon lakes on Titan’s surface, as seem to be present according to recent radar observations, may play an important role in Titan’s chemical evolution in that they would protect organic material from photochemical destruction and may enable the production of new organic species therein. The lake temperature and its spatial and seasonal variation are important in that they control the solubility of chemical species and the liquid density which in turn affects the lake temperature via lake overturning. The lake temperature is calculated by a thermal stratification model of a lake coupled to a 3-dimensional atmospheric general circulation model. The lake temperature varies by up to 7 K with season, particularly at high latitudes. Slow lake overturning occurs in autumn and winter, which intensifies the seasonality at deeper layers. The solubility of minor species is controlled by the annual minimum lake temperature which decreases with latitude, as with the solubility. Virtually all solid minor species would sink in the lake, but due to seasonal lake overturning light species can be readily suspended rather than being permanently deposited on the lake bottom. Near-surface methane mixing ratio in the atmosphere undergoes similar seasonal variation, depending on the lake composition, because the thermodynamic equilibrium between gas and liquid is sensitive to the temperature.

Sensitivity of the thermal stratification model eddy diffusion dimension 1 using a factorial experimental design

Engineering use of ecological models requires, as a precondition, appropriate validation and sensitivity testing. Using one such well‐validated thermal stratification model, the application of an industrial statistical technique for multifactor sensitivity testing is described. This method, of fractional factorial numerical experimentation, permits identification of important model parameters (here wind speed and internal mixing mechanisms), as well as potential interactions between two or more factors.

Analysis and Optimization of Thermal Stratification and Self-Pressurization Effects in Liquid Hydrogen Storage Systems—Part 1: Model Development

Abstract This paper reports on analyses and optimization studies of problems associated with liquid hydrogen thermal stratification and self-pressurization in cryogenic vessels. Three different pressure rise models were employed to calculate the self-pressurization and boil-off rates. These are a homogeneous model, a surface-evaporation model, and a thermal stratification model. The first two models are based on the assumption that no temperature gradients exist in the tank, while the thermal stratification model takes the temperature distribution into account. Employing the thermal stratification model, temperature gradients and their effect on the pressure rise rates in liquid hydrogen tanks are analyzed.

Thermal Stratification Modeling of Lakes with Sediment Heat Flux

A sediment heat flux submodel was developed, based on the findings of related limnological studies, and incorporated into a mixed‐layer (integral‐energy) lake‐stratification model. The basic and modified versions of the mixed‐layer model were applied to three years of field data for four different lakes. The inclusion of the submodel was necessary to adequately calibrate the model to the stratification conditions observed in the two shallow transparent lakes. The stratification regimes of the two other deeper lakes were accurately simulated without accommodating sediment heat flux. These results suggest that the accurate simulation of thermal stratification in shallow transparent lakes requires consideration of sediment heat flux. Sediment and water budgets calculated with the modified model support the developed sediment heat flux submodel.

Mixed layer modelling with respect to ocean-atmosphere interactions in the eastern Indian Ocean

As a precursor to the embedding of a thermal stratification model of the ocean into an Ocean General Circulation Model (OGCM) we have compared the performance of an integral (or bulk) (Kraus-Turner) and a differential (Eddy Diffusion Dimension 1) thermal stratification model for the eastern Indian Ocean. Forced with the Comprehensive Ocean-Atmosphere Data Set (COADS) and Subjectively Estimated Cloudiness in the Australian Region (SECAR) data sets, both models successfully stimulated the annual cycle in sea surface temperature. On the other hand, their predictions of the mixed layer depth differed substantially. Whereas the differential model slightly underestimated the winter mixed layer depth, the winter mixed layer depths calculated by the bulk model were substantially larger than the observed values. An additional analysis of the simulated heat storage cycle of the eastern Indian Ocean with respect to the activity of tropical-extratropical cloudbands in the Australian region has reveaved a strong relationship between these two parameters. The results have shown that a stronger activity of the tropical-extratropical cloudbands coincides with periods of heat transfer oriented from the ocean to the atmosphere.

Decision support systems for stored water quality: 2. An example application

The components of an environmental decision support system (EDSS) were outlined in Part 1 of this paper. Here, an example application is given using a range of data from the database in order to assess the utility of one specific model chosen from the modelbase: the one-dimensional thermal stratification model, EDD1. The model is applied to a range of lake types worldwide.