Validation of a methodology for thermal stratification analysis in sodium‐cooled fast reactors

Thermal stratification phenomena usually occur in the upper plenum after a scram of sodium‐cooled fast reactors, which should be closed concerned in the fields of structural integrity assessment and residual heat removal capacity. A 2‐dimensional analysis program under cylindrical coordinate was developed for predicting the in‐vessel thermal hydraulics. Non‐orthogonal block‐structured grids were generated to resolve the problems with complex structures. A second‐order discrete scheme based on midpoint rule was applied to the spatial discretization of convection and diffusion terms. Two sets of experiments characterized by distinct shapes of their apparatuses were used for the validation, mainly from the viewpoints of vertical temperature distribution and rising behaviors of the stratification interface. Results show that RANS‐type turbulent models make the significant impacts on different flow regimes. In the calculation of a scaled model with plenty of stagnant sodium in the upper region, the realizable k ? ε model (RKE) considering the mean deformation rate gives better outcomes than the standard k ? ε model (SKE). For the plant‐type upper plenum with considerable flow rate along the entire height, buoyancy modeling is the crucial issue to follow the upward movement of the interface and the relaxation process of the temperature gradient. In this case, employment of the turbulent Prandtl number reflecting the damping effect by incorporating the local Richardson number well reproduced the experimental results.     

Buoyancy driven flow in a hot water tank due to standby heat loss

Results of experimental and numerical investigations of thermal behavior in a vertical cylindrical hot water tank due to standby heat loss of the tank are presented. The effect of standby heat loss on temperature distribution in the tank is investigated experimentally on a slim 150 l tank with a height to diameter ratio of 5. A tank with uniform temperatures and with thermal stratification is studied. A detailed computational fluid dynamics (CFD) model of the tank is developed to calculate the natural convection flow in the tank. The distribution of the heat loss coefficient for the different parts of the tank is measured by experiments and used as input to the CFD model. Water temperatures at different levels of the tank are measured and compared to CFD calculated temperatures. The investigations focus on validation of the CFD model and on understanding of the CFD calculations.The results show that the CFD model predicts satisfactorily water temperatures at different levels of the tank during cooling by standby heat loss. It is elucidated how the downward buoyancy driven flow along the tank wall is established by the heat loss from the tank sides and how the natural convection flow is influenced by water temperatures in the tank. When the temperature gradient in the tank is smaller than 2 K/m, there is a downward fluid velocity of 0.003–0.015 m/s. With the presence of thermal stratification the buoyancy driven flow is significantly reduced. The dependence of the velocity magnitude of the downward flow on temperature gradient is not influenced by the tank volume and is only slightly influenced by the tank height to tank diameter ratio. Based on results of the CFD calculations, an equation is determined to calculate the magnitude of the buoyancy driven flow along the tank wall for a given temperature gradient in the tank.     

Three-dimensional analysis and investigation of the thermal and hydrodynamic behaviors of cylindrical storage tanks

A numerical analysis of the three-dimensional temperature and velocity fields in horizontal cylindrical storage tanks was performed. The phenomena of laminar natural convection and vertical stratification of temperature were considered. The developed three-dimensional transient computing code solves the equations of energy and momentum through the finite volume method. The simulation of fluid cooling process inside the tank showed the formation of stratified temperature profiles that matched those obtained experimentally. Based on several simulations, a correlation was proposed for determining the degree of thermal stratification inside the tank regarding thermal and geometrical parameters. From this correlation, an expression was proposed to predict the fluid temperature profiles along the time. This information is very important in many applications, such as in thermosiphon solar water heating systems, where the global efficiency of the system increases with the thermal stratification degree of the working fluid. Another case studied considered that the tank was connected to solar collectors, aiming at investigating the influence of the inlet jet position with and without a baffle plate on the preservation of the thermal stratification. Results showed that the baffle plate modified the velocity and temperature fields close to the inlet jet, allowing a better thermal stratification. Also the suitable choice of the inlet jet position allowed the formation of a more effective thermal stratification. Some other aspects of the internal dynamics of this kind of storage tank are presented and discussed. For the cases studied, the inlet jet next to the top led to a greater thermal stratification. However, it was verified that when the inlet jet temperature remains constant for a long period of time, and thus its temperature approaches the temperature of the water inside the tank, for the same height, the temperature profiles obtained become similar to the case of the inlet located at usual height of 2/3 of the diameter.     

Thermal stratification in a hot water tank established by heat loss from the tank

This paper presents numerical investigations of thermal stratification in a vertical cylindrical hot water tank established by standby heat loss from the tank. The transient fluid flow and heat transfer in the tank during cooling caused by standby heat loss are calculated by means of validated computational fluid dynamics (CFD) models. The measured heat loss coefficient for the different parts of the tank is used as input to the CFD model. Parametric studies are carried out using the validated models to investigate the influence on thermal stratification of the tank by the downward flow and the corresponding upward flow in the central parts of the tank. Tank design parameters such as tank volume, height to diameter ratio and insulation and different initial conditions of the tank are investigated.It is elucidated how thermal stratification in the tank is influenced by the natural convection and how the heat loss from the tank sides will be distributed at different levels of the tank at different thermal conditions. The results show that 20–55% of the side heat loss drops to layers below in the part of the tank without the presence of thermal stratification. A heat loss removal factor is introduced to characterize the effect of the buoyancy driven flow on exchange of heat loss between tank layers by natural convection. Based on results of the parametric studies, a generalized equation for the heat loss removal factor is obtained by regression which takes into account the influences of tank volume, height to diameter ratio, tank insulation and initial conditions of the tank. The equation is validated for a 150–500 l tank insulated with 0–7 cm mineral wool and a tank height to diameter ratio of 1–5. The equation will be implemented in an existing tank optimization and design program for calculation of thermal performance of a hot water tank.     

Numerical Study of Convection Melting Inside Ice Storage Systems by the Lattice Boltzmann Model

Abstract

The internal melt ice-on-coil tank with horizontal pipes is widely used in ice storage systems. The tank’s discharge process is greatly affected by the natural convection process that is caused by melting of the phase change material outside the pipes. To achieve an optimal arrangement of the pipes, a double-population lattice Boltzmann model was developed to simulate the transient solid-liquid phase change behavior in a section of an internal-melt ice-on-coil thermal storage tank with nine aligned built-in horizontal pipes. The evolutions in the phase change interface and melting rate was illustrated with different pipe shapes and pipe connections. Based on the melting rate, the whole melting process was divided into three stages: sharp decrease stage, continuous decrease stage, and snail-melting stage. The numerical results showed that a high melting rate was obtained by preferentially assigning the high-temperature pipes to the upper part of the tank, while a stable melting rate could be obtained when high-temperature pipes were preferentially assigned to the bottom part of the tank.     

CFD simulation of thermal hydraulic characteristics in a typical upper plenum of RPV

A comparative computational fluid dynamics (CFD) study was conducted on the three different types of pressurized water reactor (PWR) upper plenum, named TYPE 1 (support columns (SCs) and control rod guide tubes (CRGTs) with two large windows), TYPE 2 (SCs and CRGTs without windows), and TYPE 3 (two parallel perforated barrel shells and CRGTs). First, three types of upper plenum geometry information were collected, simplified, and adopted into the BORA facility, which is a 1/5 scale system of the four-loop PWR reactor. Then, the geometry, including the upper half core, upper plenum region, and hot legs, was built using the Salome platform. After that, an unsteady calculation to simulate the reactor balance operation at hot full power scenario was performed. Finally, the differences of flowrate distribution at the core outlet and temperature distribution and transverse velocity inside the hot legs with different upper plenum internals were compared. The results suggest that TYPE 1 upper plenum internals cause the largest flowrate difference at the core outlet while TYPE 3 leads to the most even distributed flowrate. The distribution and evolution pattern of the tangential velocity inside hot legs is highly dependent on the upper plenum internals. Two counter-rotating swirls exist inside the TYPE 1 hot leg and only one swirl revolving around the hog leg axis exist inside the TYPE 2 hot leg. For TYPE 3, two swirls like that of TYPE 1 rotating around the hot leg axis significantly increase the temperature homogenization speed. This research provides meaningful guidelines for the future optimization and design of advanced PWR upper plenum internal structures.     

Thermal Modelling of a Natural Convection Solar Water Heating System with a Thermal Trap Collector

A mathematical model has been developed to study the performance of a solar water heating system with a thermal trap flat plate collector and in which the flow of water between the collector and the storage tank is maintained by natural convection. An expression has also been developed for the mass flow rate in terms of known parameters. The model yields exact expressions for the temperature of water in the storage tank as a function of time in terms of collector's parameters and the solar insolation. Numerical calculations have been performed to compare the performance of the hot water heating system with a thermal trap collector with the one with an ordinary flat plate collector.     

Fluid thermal stratification in a non-isothermal liquid hydrogen tank under sloshing excitation

To the safe space operation of cryogenic storage tank, it is significant to study fluid thermal stratification under external heat leaks. In the present paper, a numerical model is established to investigate the thermal performance in a cryogenic liquid hydrogen tank under sloshing excitation. The interface phase change and the external convection heat transfer are considered. To realize fluid sloshing, the dynamic mesh coupled the volume of fluid (VOF) method is used to predict the interface fluctuations. A sinusoidal excitation is implemented via customized user-defined function (UDF) and applied on tank wall. The grid sensitivity study and the experimental validation of the numerical mode are made. It turns out that the present numerical model can be used to simulate the unsteady process in a non-isothermal sloshing tank. Variations of tank pressure, liquid and vapor mass, fluid temperature and thermal stratification are numerically investigated respectively. The results show that the sinusoidal excitation has caused large influence on thermal performance in liquid hydrogen tank. Some valuable conclusions are arrived, which is important to the depth understanding of the non-isothermal performance in a sloshing liquid hydrogen tank and may supply some technique reference for the methods of sloshing suppression.     

Natural convection in a partially porous cavity: Roads to chaos

Abstract

A numerical study of a periodic and chaotic behavior of natural convection in a square cavity, with a porous layer is presented. The cavity under study consists of two opposite vertical walls of which the lower half walls are hot (hold high temperature) and the upper half walls are cold (hold low temperature), whereas the horizontal walls are adiabatic. The porous medium is located in the lower part of the cavity. The natural heat transfer and the Darcy Brinkman equations are solved by using the finite volume method and the TDMA. The results show that thermal natural convection evolves towards a deterministic chaos by following Curry York scenario.     

Thermal response of a series- and parallel-connected solar energy storage to multi-day charge sequences

The thermal response of a multi-tank thermal storage was studied under variable charge conditions. Tests were conducted on an experimental apparatus that simulated the thermal charging of the storage system by a solar collector over predetermined (prescribed) daylong periods. The storage was assembled from three standard 270 L hot-water storage tanks each charged through coupled, side-arm, natural convection heat exchangers which were connected in either a series- or parallel-flow configuration. Both energy storage rates and tank temperature profiles were experimentally measured during charge periods representative of two consecutive clear days or combinations of a clear and overcast day. During this time, no draw-offs were conducted. Of particular interest was the effect of rising and falling charge-loop temperatures and collector-loop flow rate on storage tank stratification levels. Results of this study show that the series-connected thermal storage reached high levels of temperature stratification in the storage tanks during periods of rising charge temperatures and also limited destratification during periods of falling charge temperature. This feature is a consequence of the series-connected configuration that allowed sequential stratification to occur in the component tanks and energy to be distributed according to temperature level. This effect was not observed in the parallel charge configuration. A further aspect of the study investigated the effect of increasing charge-loop flow rate on the temperature distribution within the series-connected storage and showed that, at high flow rates, the temperature distributions were found to be similar to those obtained during parallel charging. A disadvantage of both the high-flow series-connected and parallel-connected multi-tank storage is that falling charge-loop temperatures, which normally occur in the afternoon, tend to mix and destratify the storage tanks.     

Experimental study on the heat transfer characteristics of fluoride salt in the new conceptual passive heat removal system of molten salt reactor

A new conceptual design of a passive residual heat removal system (PRHRS) has been proposed for molten salt reactor. High‐temperature heat pipes are used in this new design to improve the system inherent safety and make the PRHRS more compact. An experimental system using fluoride salt FLiNaK has been constructed to validate and support the future design of PRHRS of molten salt reactors. In this research, tests on the natural convection heat transfer of FLiNaK in the drain tank with an inclined heat pipe inserted at different heights were performed. The temperature distribution of fluoride salt in the tank was analyzed. The height of heat pipe and the bulk temperature of FLiNaK have little influence on the normalized salt temperature distribution. However, with the height of heat pipe increasing, the temperature difference of molten salt decreases and heat transfer coefficient of natural convection increases. In addition, the empirical correlations of natural convection heat transfer between liquid FLiNaK and inclined heat pipe are obtained within the range of Rayleigh numbers from 3.97 × 10⁶ to 1.16 × 10⁷. The comparisons show that a good agreement with less than 5% deviation is obtained between the proposed correlations and the test data.     

Numerical analysis of convective flow and thermal stratification in a cryogenic storage tank

In this study, the liquid–vapor mixture model was used for a numerical study of natural convective flow in a cryogenic tank with a capacity of 4.9?m³ under various conditions of heat flux and filling level to understand the early stages of convective flow phenomena and the consequent thermal stratification of cryogenic liquid. Two cryogens—liquefied natural gas (LNG) and liquefied nitrogen (LN₂)—were compared to observe their effects. LN₂ exhibited faster vaporization owing to its lower heat of vaporization. It was observed that higher heat flux and lower filling level led to faster vaporization and relatively vigorous heat transfer, showing early thermal stratification.     

Numerical analysis of transient mixed convection flow in storage tank: influence of fluid properties and aspect ratios on stratification

Sensible heat storage in fluids generates thermal stratification. In order to improve thermodynamic system efficiency, stratification should be promoted much more. To this scope, this article presents a numerical study of transient mixed convection. The study investigates the use of different fluids as a heat storage medium in cylindrical cavities with different aspect ratios. The effect of the fluids is made through the variation of physical properties represented through the Prandtl number. The system consists of a cavity with fluid injection at the top and fluid discharge at the bottom. Transient, two-dimensional, mixed convection flows in a thermal storage tank have been studied using finite volume method. The governing equations are the conservation equations for laminar natural convection flow based on the Boussinesq approximation. Forced convection flow is superimposed through the use of appropriate boundary conditions (inflow and outflow conditions). The study considers three representative fluids i.e. Torada oil, ethylene glycol and water. It considers also cavities with aspect ratios varying from 3 to 1/3. Flow analysis is made through typical transient temperature distributions for the three fluids and for different configurations. The performances of thermal energy storage using these fluids are analyzed through the transient thermal storage efficiency.     

Natural Convection of a Binary Fluid in a Slightly Inclined Shallow Cavity

ABSTRACT

This article reports an analytical and numerical study of the natural convection in an inclined shallow cavity filled with a binary fluid. Newmann boundary conditions for temperature are applied to the long side walls of the enclosure, while the two short ones are assumed to be impermeable and insulated. The solutal buoyancy force are induced either by the imposition of constant fluxes of solute on the walls (double-diffusive convection, a = 0) or by temperature gradients (Soret effects, a = 1). The governing parameters for the problem are the thermal Rayleigh number,Ra_T, the Lewis number Le, the buoyancy ratio ?, the inclination of the cavity Θ, the Prandtl numberPr, the aspect ratio of the cavity A, and the constant a. For convection in an infinite layer (A > > 1), an analytical solution of the steady form of the governing equations is obtained on the basis of the parallel flow approximation. The critical Rayleigh numbers for the onset of supercritical and subcritical convection are predicted by the present model. Also, it is demonstrated that, for small enough inclinations around the horizontal plane, multiple steady states exist, some of which are unstable. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. Good agreement is observed between the analytical prediction and the numerical simulations.     

A computational fluid dynamic study of the filling of a gaseous hydrogen tank under two contrasted scenarios

The filling of a horizontal hydrogen tank designed for light duty vehicles is investigated by means of multi-physics numerical simulations. The simulation approach, implemented in OpenFOAM, includes compressible Reynolds-Averaged Navier-Stokes (RANS) modeling of the fluid flow and heat transfer in the solid parts. The simulations are carried out for 2D-axisymmetric and 3D configurations. Two filling scenarios of the tank, leading to two distinct thermal behaviors, i.e. homogeneous versus heterogeneous, are simulated and compared to the experimental data issued from the HyTransfer project. In the homogeneous case, where no thermal stratification occurs, the 2D and 3D simulation results are close to the experimental ones. A phenomenon of jet flapping is identified via the 3D simulation. In the heterogeneous case, where thermal stratification occurs, the 3D simulation captures an averaged temperature close to the experimental one, as well as the instant at which the thermal gradients appear. It also captures the deflection of the jet, which is a central element in the emergence of the thermal gradients.     

A Numerical Study for the Role of Natural Convection in the Melting of a GaSb/InSb/GaSb Sandwich System

The role of natural convection in the melting of a GaSb/InSb/GaSb sandwich system was numerically investigated. The melting process was assumed unsteady, and the governing equations of the model were solved by the finite difference method using a boundary fixing technique. The solutal natural convection (caused by concentration gradients) in the melt enhances melting in the lower part of the sample, and the thermal natural convection (caused by temperature gradients) is responsible for the development of a melt-solid interface that is slightly concave toward the crystals. These results are in qualitative agreement with the experimental observations made previously by the authors.     

Prediction and identification of the evolution of solar-heated hot water temperature in a stratified tank in static mode using artificial neural networks

The results of analyses of thermal stratification using different initial water temperature profiles are reported and discussed. Stratification proved to be the main factor in the cooling process, since although ambient temperature is also a determining factor, in this case it played a lesser role because the tank’s location inside the laboratory meant that it remained almost constant.     

Chaotic behavior of LNG after stratification in main stream region of storage tank

A study of the chaotic behavior of liquefied natural gas (LNG) after stratification in the main stream region of a storage tank was conducted. Based on non-linear dynamics, a 2-dimensional Rayleigh-Benard convection model was developed to simulate the convection, Lorenz equations of LNG convection were deduced from conservation equations, and the Runge-Kutta method was used to solve the equations. The results showed that when Pr = 1.33, 106 < r < 1470, chaos was obtained, which meant that the velocity field and the temperature field were highly unsteady. In addition, the influence of temperature and scale factor on the solutions and the corresponding range of parameters were studied. The results revealed that the chaos in LNG convection resulted from the interaction of buoyancy and viscid forces. A small quantity of heat impacting the storage tank would lead to a strong and unstable convection of LNG in the main stream region.     

The Influence of Baffles on the Natural Convection in Trapezoidal Cavities

This article presents an investigation into natural convection in trapezoidal cavities. It examines a cavity whose floor and upper inclined walls are both adiabatic, while the vertical walls are isothermal. For these isothermal walls, we consider two thermal boundary conditions. Under the first condition, the short wall on the left side is heated as the tall one on the right side is cooled. The second condition is the reverse of the first—the short wall is cooled as the tall one is heated. Considering laminar conditions and a two-dimensional system, steady-state computations are carried out to assess the effects of one and two baffles, the baffle's height (H _b ), Rayleigh number, 10³ ≤ Ra ≤ 10⁶, and three Prandtl number values. To demonstrate the various effects, the results from several designed case studies are shown in terms of isotherms, streamlines, and local and average Nusselt numbers in order. Predictions reveal that the second baffle decreases the cavity's fluid flow and heat transfer. As the height of the baffle rises, the heat transfer drops drastically. Also, two baffles produce more pronounced thermal stratification than only one.     

Influence of surface radiation on the transition to unsteadiness for a natural convection flow in a differentially heated cavity

Abstract

The influence of surface radiation on the transition to the unsteady state in natural convection is studied numerically. The configuration of the differentially heated square cavity with adiabatic horizontal walls is chosen to generate an internal natural convection flow. It is known that radiative transfers reduce the temperature difference between the adiabatic walls, which consequently reduces the thermal stratification of the central zone and increases the velocity flow. Many studies have focused on the stationary regime, but few of them have investigated the transition to unsteady flow. For this purpose, the effect of the wall emissivity on the critical Rayleigh number and the associated critical frequency was studied for a given cavity length. The cavity length and mean temperature of isothermal walls are set for the whole study. The results show that all these values are between the values obtained without radiation and those obtained for perfectly conducting horizontal walls. The critical Rayleigh number decreases with emissivity while the associated frequency increases. Moreover, the symmetry of fluctuating properties of the flow is changed when the radiation is taken into account.