Experimental and numerical study on lead-bismuth heat transfer in a fuel rod simulator

As a task of the EU project IP EUROTRANS towards development of an Accelerator Driven System (ADS) dedicated to the transmutation of long-lived fission products, experiments and simulations were performed on the TALL test facility at KTH to investigate thermal hydraulics along a single fuel rod simulator cooled by lead-bismuth eutectic (LBE). The fuel rod simulator is concentrically inserted in a tube, so that an annular channel is formed for LBE flow. This paper presents the measured temperature profiles in the annular channel, and the comparisons with the simulation results of the CFX code. The primary objective is to help understanding the LBE heat transfer characteristics and qualifying the turbulence and heat transfer modeling for LBE application. The quantitative comparison between the calculated and measured temperatures of the LBE indicates that the simulation underestimates the experiment at most radial and axial positions. Finally the uncertainties in measurement and the deficiency in turbulence models resulting in such a disagreement were discussed, which will be directive and beneficial to future work in the field.     

A numerical and experimental study of water ingression phenomena in melt pool coolability

During a postulated severe accident, the core can melt and the melt can fail the reactor vessel. Subsequently, the molten corium can be relocated in the containment cavity forming a melt pool. The melt pool can be flooded with water at the top for quenching it. However, the question that arises is to what extent the water can ingress in the corium melt pool to cool and quench it. To reveal that, a numerical study has been carried out using the computer code MELCOOL. The code considers the heat transfer behaviour in axial and radial directions from the molten pool to the overlaying water, crust generation and growth, thermal stresses built-in the crust, disintegration of crust into debris, natural convection heat transfer in debris and water ingression into the debris bed. To validate the computer code, experiments were conducted in a facility named as core melt coolability (COMECO). The facility consists of a test section (200 mm × 200 mm square cross-section) and with a height of 300 mm. About 14 L of melt comprising of 30% CaO + 70% B₂O₃ (by wt.) was poured into the test section. The melt was heated by four heaters from outside the test section to simulate the decay heat of corium. The melt was water flooded from the top, and the depth of water pool was kept constant at around 700 mm throughout the experiment. The transient temperature behaviour in the melt pool at different axial and radial locations was measured with 24 K-type thermocouples and the steam flow rate was measured using a vortex flow meter. The melt temperature measurements indicated that water could ingress only up to a certain depth into the melt pool. The MELCOOL predictions were compared with the test data for the temperature distribution inside the molten pool. The code was found to simulate the quenching behaviour and depth of water ingression quite well.     

On heat transfer characteristics of real and simulant melt pool experiments

This paper presents results of analytical studies on natural convection heat transfer in scaled and/or simulant melt pool experiments related to the pressurized water reactor in-vessel melt retention issue. Specific reactor-scale effects of a large decay-heated core melt pool in the reactor pressure vessel lower plenum are first reviewed, and then the current analytical capability of describing the relevant physical processes in prototypical situations is examined. Experiments and experimental approaches are analyzed by focusing on their ability to represent prototypical situations. Calculations are performed to assess the significance of some selected effects, including variations in melt properties, pool geometry and heating conditions. In the present analysis, Rayleigh numbers are limited to 10¹², where uncertainties in turbulence modelling do not override other uncertainties. Calculations are performed to explore limitations of using side wall heating and direct electrical heating. The need for further experimental and analytical efforts is also discussed.     

A numerical investigation of natural convection heat transfer in horizontal spent-fuel storage cask

Natural convection heat transfer in a horizontally placed dry spent-fuel storage cask is numerical investigated. The commercial computational fluid dynamics (CFD) code, -3.2 is used and the laminar and turbulent model are employed. The numerical predictions obtained are compared with the experimental data reported by Nishimura et al. [J. Nucl. Sci. Technol. 33 (1996) 821]. The computational results corresponding to laminar model agree well with the experimental data, but the calculated results of turbulent model are higher. The velocity pattern and the isotherms are drawn. With the increasing of Rayleigh number, the heat transfer in the cask changes from conduction dominant mode to convection dominant mode. In the condition of Ra_m=1.3×10⁹, turbulent model prevails. The convective heat transfer is so strong that almost all temperature changes take place in the region near the wall of the cask. The Rayleigh number Ra_m and the Nusselt number Nu_m characterized by maximum temperature difference are defined to depict the heat transfer characteristics. It is found laminar and turbulent models predict the same trend but different value. The flow patterns in the cask can be divided to three regimes. In these three regimes, modified Nusselt numbers are proportional to the 0.7, 0.25 and 0 power of the modified Rayleigh number, respectively.     

Characterization of heat transfer processes in a melt pool convection and vessel-creep experiment

The results of an integral experiment on melt pool convection and vessel-creep deformation are presented and analyzed. The experiment is performed on a test facility, named Failure Of REactor VEssel Retention (FOREVER). The facility employs a 1/10-scaled 15Mo3-(German)-steel vessel of 400-mm diameter, 15-mm wall thickness and 750-mm height. A high-temperature (1300 °C) oxide melt is prepared in a SiC-crucible placed in a 50 kW induction furnace and is, then, poured into the 1/10th scale vessel. A MoSi₂ 50 kW electric heater is employed in the melt pool to heat and maintain its temperature at 1200 °C. The vessel is pressurized with argon at the desired pressure. In the FOREVER/C1 experiment, the vessel wall, maintained at about 900 °C and pressurized to 26 bars, was subjected to creep deformation in a 24-h non-stop test. The FOREVER/C1 test is the first integral experiment, in which a decay-heated oxidic naturally-convecting melt pool was maintained in long-term contact with the hemispherical lower head of a pressurized, creeping, steel vessel. A sizeable database was obtained on melt pool temperatures, melt pool energy split, heat transfer rates, heat flux distribution on the melt (crust)–vessel contact surface, vessel temperatures and, in particular the vessel wall creep rate as a function of time. The paper provides information on the FOREVER/C1 measured thermal characteristics and analysis of the observed thermal behavior. The coupled nature of thermal and mechanical processes, as well as the effect of other system conditions (such as depressurization) on the melt pool and vessel temperature responses are analyzed.     

A comparative study of correlations of critical heat flux of pool boiling

Nucleate pool boiling is desirable for many engineering systems. One challenge task for designing a system with nucleate pool boiling is to estimate the critical heat flux (CHF), which needs an accurate pool boiling CHF correlation. A few evaluations of pool boiling CHF correlations were reported, which used limited experimental data or covered limited correlations, resulting in inconsistent results. Therefore, it is difficult to determine which one is more appropriate for a given application. In this paper, a database containing 600 data points of pool boiling CHF of 12 pure liquids on plain surfaces having orientation angles of 0°?180° is compiled from 40 published papers. The reduced pressure is from 0.0001 to 0.98, and the 13 fluids are water, helium, nitrogen, hydrogen, R113, FC-72, FC-87, HFE-7100, ethanol, benzene, hexane, pentane, and methanol. With the database, 21 pool boiling CHF correlations are assessed. The most accurate one has a mean absolute deviation of 27.1%, indicating a need for developing more accurate correlations for engineering applications. Besides, the factors affecting the accuracy of correlations are analyzed and some valuable conclusions are obtained. The work lays a valuable foundation for the further study of pool boiling CHF correlations and provides a guide for choosing proper correlations for given applications. Several topics worthy of attention for future studies are suggested.     

Critical heat flux of oxidized zircaloy surface in saturated water pool boiling

In the present experimental study, the critical heat flux (CHF) of an oxidized zircaloy surface and its enhancement were investigated during saturated water pool boiling at atmospheric pressure. Three kinds of zircaloy specimens, oxidized at three different temperature conditions (i.e., 300, 450, and 600 °C), were prepared with a non-treated (i.e., fresh) zircaloy surface. The surfaces of the test specimens were characterized by an energy dispersive spectroscopy analysis, scanning electron microscopy image, and water contact angle measurement. The oxidized surface (OS) specimens increased the CHF, which could be because the oxidized surface improves the surface wettability (i.e., decreases the water contact angle). The OS specimens showed the similar water contact angles, and their CHF values became almost the same. In the present experimental conditions, the water contact angle could be considered as a reasonable parameter to explain the CHF data of test specimens. The CHF enhancement of the OS specimens was about 40%, as compared with the non-treated specimen, and interestingly, it was a comparable value to that of the specially treated zircaloy surfaces of the previous report, for a similar water contact angle condition. This implies that the oxidation process used in this work can be a simple, convenient, and cost-effective way to improve the CHF of the zircaloy surface. Using the present experimental data, the previous CHF correlations were assessed and discussed. Among the correlations tested, Kandlikar model best fitted the present CHF measurement data and enhancement factors.     

Numerical study on the heat transfer characteristics of LIVE-L4 melt pool with a partial solidification process

Using the source-based SIMPLE algorithm based on a fixed grid method, a two-dimensional numerical model for a convection-diffusion controlled mushy region phase-change problem was developed to investigate the heat transfer characteristics of LIVE L4 melt pool subjected to a partial solidification process in a Pressurized Water Reactor (PWR) lower plenum during a hypothetical severe accident. For the binary non-eutectic mixtures of L4 melt, a linear liquid fraction temperature relationship was implemented on the calculations of the velocity and enthalpy in the mushy zone. The effect of fluid flow in the melt pool was analyzed, and numerical results for the cases with and without phase change model were calculated to investigate the effects of solidification on the heat transfer characteristics of L4 melt pool. Numerical results indicated that the phase-change model could well predict the main parameters of melt pool, e.g. the melt pool temperatures, heat flux through the melt pool, and the crust thickness. Results also indicated that the predicted Nu number without solidification was overestimated by about 12%, compared with that with solidification.     

A heat transfer correlation based on a surface renewal model for molten core concrete interaction study

The prediction of heat transfer between corium pool and concrete basemat is of particular significance in the framework of the study of PWR's severe accident. Heat transfer directly governs the ablation velocity of concrete in case of molten core concrete interaction (MCCI) and, consequently, the time delay when the reactor cavity may fail. From a restricted hydrodynamic point of view, this issue is related to heat transfer between a heated bubbling pool and a porous wall with gas injection. Several experimental studies have been performed with simulant materials and many correlations have been provided to address this issue. The comparisons of the results of these correlations with the measurements and their extrapolation to reactor materials show that strong discrepancies between the results of these models are obtained which probably means that some phenomena are not well taken into account. The main purpose of this paper is to present an alternative heat transfer model which was originally developed for chemical engineering applications (bubble columns) by Deckwer. A part of this work is devoted to the presentation of this model, which is based on a surface renewal assumption. Comparison of the results of this model with available experimental data in different systems are presented and discussed. These comparisons clearly show that this model can be used to deal with the particular problem of MCCI. The analyses also lead to enrich the original model by taking into account the thermal resistance of the wall: a new formulation of the Deckwer's correlation is finally proposed.     

Application of flexibility model in modeling of flow boiling heat transfer

The mathematical modeling and computer simulation have been widely used in the analysis of system's dynamic characteristics, and often useful for system control. One of the popular methods for this purpose is the lumped parameter method. For flow boiling heat transfer system, the traditional lumped parameter modeling method has a problem that the heat transfer coefficients change suddenly at the boundary of coolant phase change. It can cause error. In this paper, an idea of flexibility model is developed to deal with the boundary problem and to improve the model of flow boiling heat transfer. The segments of coolant phase change's boundary are identified, and the membership functions which are derived from Fuzzy Mathematics are used to derive approximate expressions of heat transfer coefficient in those regions. The continuity of heat transfer coefficient can be described by those expressions. The membership functions are derived from mathematical analysis and transformation. The result shows that this idea is feasible and the conclusion is practicable.     

Heat transfer in heat exchangers of sodium cooled fast reactor systems

The present paper describes the heat transfer in heat exchangers of sodium cooled fast reactors. Practical empirical correlations regarding heat transfer coefficients for intermediate heat exchangers (IHXs) and air coolers (ACs) were derived using test data obtained at the fast reactor ‘Monju’ and ‘Joyo’ and also at the 50 MW steam generator facility (50 MW SG). The correlation proposed by Seban and Shimazaki was applicable to estimate the heat transfer coefficients in both flows of IHX, i.e., primary and secondary flows, when the Péclet number was larger than 30. When the Péclet number for shell-side was small, the Nusselt number decreased as a function of the Péclet number. It was clarified that this characteristic was not caused by the heat conduction in flow direction. The heat conduction effect can be neglected even in the natural circulation conditions of the Monju plant. As for the heat transfer coefficient of AC provided in the secondary heat transport system of the fast breeder reactor, data in the above mentioned three facilities were evaluated. As a result, empirical correlations were derived for the average heat transfer coefficients of a large capacity finned air cooler made of stainless steel. These correlations could contribute to analyze the plant dynamics with better accuracy than before.     

Analysis of heat source distribution in internal circulating surface heat transfer molten salt reactor

The Molten Salt Reactor (MSR) is one of the Generation IV nuclear reactor concepts that were selected by the Generation IV International Forum in 2000. The concept is based on liquid fuel instead of solid fuel assemblies. Besides the advantages, there are several aspects of operation that can hinder the realization of this reactor concept. In this paper, the authors investigate the neutronics behaviour of a new sub-concept that offers solutions for many of the technical problems. The analysis was performed using the particle transport code MCNPX 2.7. The paper focuses on the short-term and steady state heat source distribution in the fuel salt and in the graphite moderator. Accordingly, neither burn-up effects nor reactivity transients are considered. The sensitivity of the effective multiplication factor on different geometrical and material parameters was studied. The results obtained indicate that the main region of heat deposition is in the internal and external channels of the graphite moderator. Only a few percent of the total heat power is released in the graphite moderator, where the gamma and neutron related heat deposition is on the same scale. The results also prove that the heat source distribution does not change drastically upon the actuation of the control rods.     

Computational study of conjugate heat transfer in T-junctions

In this work we focus on the numerical prediction of temperature fluctuations induced in solid materials through turbulent mixing processes. As test case we use the mixing of two streams of different temperature in a T-junction. Due to the turbulent mixing of the two streams temperature fluctuations occur which are also transferred to the solid walls in contact with the fluid. Such fluctuations in the solid material may lead to thermal fatigue and are therefore relevant for the lifetime management of components used in nuclear power plants (NPP).We investigate the mixing in T-junctions made of different materials and having different pipe wall thicknesses. The temperature difference between the streams in the main and side branch is set to 75 °C and the mass flow rate in the main pipe is three times larger than in the side branch. In a first step we perform a set of simulations by using different formulations of the large-eddy simulation (LES) subgrid scale model, i.e. classical Smagorinsky model and dynamic procedure, to identify the influence of the modeled subgrid scales on the simulation results. The comparison between available experimental data and the numerical results reveals a good agreement when using the dynamic procedure. In a second step we address the temperature fluctuations in the solid wall subject to the wall thickness. The influence of the wall thickness is represented as a damping effect on the temperature fluctuations in radial direction in the pipe material. This study shows the capability of LES to predict thermal fluctuations in turbulent mixing.     

Effect of turbulent natural convection on sodium pool combustion in the steam generator building of a fast breeder reactor

A computational model is proposed to simulate sodium pool combustion considering the effect of turbulent natural convection in a vented enclosure of the steam generator building (SGB) of a fast breeder reactor. The model is validated by comparing the simulated results with the experimental results available in literature for sodium pool combustion in a CSTF vessel. After validation, the effects of vents and the location of the pool on the burning rate of sodium and the associated heat transfer to the walls are studied in an enclosure comparable in size to one floor of the steam generator building. In the presence of ventilation, the burning rate of sodium increases, but the total heat transferred to the walls of the enclosure is reduced. It is also found that the burning rate of sodium pool and the heat transfer to the walls of the enclosures vary significantly with the location of sodium pool.     

Thermocapillary on film boiling heat transfer from a non isothermal horizontal surface: A theoretical study from CANDU reactors

Film boiling heat transfer from a horizontal non-isothermal surface is formulated with due consideration to thermocapillary and thermal expansion where thermocapillary convection has been largely ignored in film boiling. The study is particularity important in nuclear reactor technology where non-isothermal heater is practically the general situation due to unavoidable non-axisymmetric neutronic flux in the fuel geometries (cylindrical geometries). Utilizing a simplified geometrical model, an analytical expression was derived. The above equation applied in a sigmoidal temperature profile results in a central stratification for film boiling along the heater's length.     

Experimental study on combustion characteristics of sodium fire in a columnar flow

In the operation of the sodium-cooled fast reactor, the accident caused by the leakage and combustion of liquid sodium is common and frequent in sodium-related facilities. This paper is based on an experimental study of sodium fire in a columnar flow, which was carried out to focus on the burning characteristics by analyzing the temperature fields in the burner. The injection of 200 °C liquid sodium with the flux of 0.5 m³/h was poured into a 7.9 m³ volume stainless steel cylindrical burner to shape a sodium fire, and the data of temperature fields in the burner have been collected by dozens of thermocouples which are laid in the combustion space and sodium collection plate. These results show that the sodium fire in a columnar flow is composed of the foregoing centered columnar fire, the subsequent spray fire caused by atomization and the pool fire on the collection plate. The temperature close to the burning sodium flow maximally reaches up to 950 °C. The radial temperatures apart from the sodium flow are relatively low and generally about 200 °C, and maximally just 300 °C even when close to the sodium collection plate. The maximum temperature of the burning sodium dropping on the collection plate rises in the center of plate, about 528 °C. This study is helpful to evaluate the combustion characteristics, formation process and composing forms of the sodium fire in the sodium-related facilities.     

矩形通道干涸点传热特性试验研究

在中国核动力研究设计院流动传热基础试验平台上进行了矩形通道干涸点传热试验。通过对各种热工水力参数的试验研究,得出结论:(1)随着进口含汽率的增加,干涸点热流密度减小,含汽率增加,壁面温度降低,传热系数减小;(2)随着质量流速的增大,干涸点热流密度增大,含汽率减小,壁面温度升高,传热系数增大;(3)随着系统压力的升高,干涸点热流密度增大,含汽率增加,壁面温度升高,传热系数增大。由试验数据与现有经验关系式的比较,发现这些关系式适合中高压、中低质量流速工况,而对低压、高质量流速工况存在较大的偏差。在古塔杰拉奇关系式的基础上,引入矩形通道尺寸和进口焓等影响传热的因素,得出了适用于矩形通道的干涸关系式。关系式与试验数据吻合良好。     

Experimental and numerical study on transient heat transfer for a twisted plate with different length in helium gas at various velocities

This study is aimed to investigate the transient heat transfer process between the solid surface and the coolant (helium gas) in very high temperature reactor or intermediate heat exchanger. Transient heat transfer from a twisted plate with different length in helium gas was experimentally and theoretically studied. The heat generation rate was increased with an exponential function, Q = Q₀exp(t/τ), where t is time and τ is period. Experiment was carried out at various periods ranged from 35 ms to 14 s. Platinum plates were twisted with the same helical pitch of 20 mm, and the effective lengths are 26.8, 67.8 and 106.4 mm (pitch numbers of 1, 3 and 5), respectively. It was clarified that the average heat transfer coefficient approaches quasi-steady-state value when the period τ is larger than about 1 s, and it becomes higher when τ is shorter than about 1 s. The heat transfer coefficient decreases with the increase of plate length. An empirical correlation for forced convection heat transfer for a twisted plate with various lengths was obtained based on the experimental data. Moreover, numerical simulation results were obtained for average surface temperature difference, heat flux and heat transfer coefficient of the twisted plates with different length and showed reasonable agreement with experimental data. Through the numerical simulation, distribution of heat transfer coefficient on heater surface, temperature distribution and velocity distribution were clarified.