Heat transport and void fraction in granulated debris

The paper discusses the boiling heat transfer from a porous bed with internal heat sources and refers to the configuration in a nuclear reactor after a partial core melt. The flow of coolant, the temperature and the local liquid/vapor distribution were investigated in a two-dimensional configuration. Experiments were conducted using monodisperse beds as well as a mixture of two different particle sizes with a total porosity below 20%. In some tests the bed was supported by a shell of porous material to create a gap along the bottom of the test container. Water was used for tests up to 9% of the critical pressure, while other tests were made with R134a up to 44% of the critical pressure. The maximum heating rate realized inductively was 730 kW/m². The experiments have been compared to analytical results with a one-dimensional approach.It is shown that in contrary to the situation in small cylindrical configurations the heat transfer was increased by large buoyancy driven convective flows. If there was a gap along the container bottom an additional flow of liquid improved the coolability of the bottom region even if the upper part of the particle bed was already overheated. In case of high density ratios (water at low pressure), the measurements indicated a strong enhancement of the coolant flow above a certain minimum heating rate resulting in decreasing vapor fraction values which were nearly independent of the system pressure. This was assumed to be caused by the appearance of vertical channels through which the vapor could flow through the particle bed.     

Dryout heat flux experiments with deep heterogeneous particle bed

A test facility has been constructed at Technical Research Centre of Finland (VTT) to simulate as accurately as possible the ex-vessel core particle bed in the conditions of Olkiluoto nuclear power plant. The STYX particle bed reproduces the anticipated depth of the bed and the size range of particles having irregular shape. The bed is immersed in water, creating top flooding conditions, and internally heated by an array of electrical resistance heating elements. Dryout tests have been successfully conducted at 0.1–0.7 MPa pressure for both uniformly mixed and stratified bed geometries. In all tests, including the stratified ones, the dry zone first formed near the bottom of the bed. The measured dryout heat fluxes increased with increasing pressure, from 232 kW/m² at near atmospheric pressure to 451 kW/m² at 0.7 MPa pressure. The data show some scatter even for the uniform bed. The tests with the stratified bed indicate a clear reduction of critical power due to the presence of a layer of small particles on top of the uniform bed. Comparison of data with various critical power (dryout heat flux) correlations for porous media shows that the most important parameter in the models is the effective particle diameter. Adiabatic debris bed flow resistance measurements were conducted to determine the most representative particle diameter. This diameter is close, but not equal, to the particle number-weighted average diameter of the bed material. With it, uniform bed data can be calculated to within an accuracy of 3–28% using Lipinski's 0-D model. In the stratified bed experiments, it appears that the top layer was partially fluidized, hence the measured critical power was significantly higher than calculated. Future experiments are being planned with denser top layer material to eliminate non-prototypic fluidization.     

Experiments on flows, boiling and heat transfer in porous media: Emphasis on bottom injection

This paper deals with basic experiments conducted to analyse the effect of the particles’ shape and size distribution on intrinsic properties of porous beds as well as two-phase flow and heat transfer in these porous media.Structural, transport properties, flow laws and heat transfer with phase-change phenomena in several kinds of porous media are presented and discussed. The porosity of stacks constituted by spheres of various sizes is analysed. A variation law of the porosity as a function of the standard deviation of the particle size distribution is proposed. The porosity, tortuosity, permeability and inertial coefficient of the flow law in randomly stacked fibres are established experimentally and theoretically. The porosity of such media is found to vary from 0.35 to 0.92 according to the fibre aspect ratio. Tortuosity and Kozeny–Carman parameters are determined by both electric and hydrodynamic methods. These parameters are found to vary with the porosity of the fibrous bed. New relations of permeability and inertial coefficient are derived from experimental results. Finally, a pressure drop relation is proposed for fibrous beds.Convective boiling phenomena, with emphasis to application on bottom injection, are experimentally determined for fibrous porous media. Temperature field determination evidences the formation of three distinct zones in the porous medium: a liquid zone, a two-phase zone and a superheated zone. For higher heat flux density, a fourth zone is found in which vapour and liquid are in thermal non-equilibrium. A one-dimensional analytical model of pressure drop in two-phase configuration has been performed. Comparisons with experimental data are found in good agreement with the results of this model for moderate heat fluxes. For higher heat flux values, discrepancies are found. These cases correspond to the appearance and the evolution of the thermal non-equilibrium two-phase zone. Heat transfer characteristics at the heated walls are analysed. Formation of vapour in the neighbourhood of the heated walls has a strong influence on the heat transfer coefficient. This behaviour may be related to the critical heat flux phenomenon encountered in usual ducts.     

Experimental results on the coolability of a debris bed with multidimensional cooling effects

Within the reactor safety research, the removal of decay heat from a debris bed (formed from corium and residual water) is of great importance. In order to investigate experimentally the long term coolability of debris beds, the scaled test facility “DEBRIS” (Fig. 1) has been built at IKE. A large number of experiments had been carried out to investigate the coolability limits for different bed configurations ( [Rashid et al., 2008], [Groll et al., 2008] and [0055]). Analyses based on one-dimensional configurations underestimate the coolability in realistic multidimensional configurations, where lateral water access and water inflow via bottom regions are favoured. Following the experiments with top- and bottom-flooding flow conditions this paper presents experimental results of boiling and dryout tests at different system pressures based on top- and bottom-flooding via a down comer configuration.A down comer with an internal diameter of 10 mm has been installed at the centre of the debris bed. The debris bed is built up in a cylindrical crucible with an inner diameter of 125 mm. The bed of height 640 mm is composed of polydispersed particles with particle diameters 2, 3 and 6 mm. Since the long term coolability of such particle bed is limited by the availability of coolant inside the bed and not by heat transfer limitations from the particles to the coolant, the bottom inflow of water improves the coolability of the debris bed and an increase of the dryout heat flux can be observed. With increasing system pressure, the coolability limits are enhanced (increased dryout heat flux).     

An experimental study on pressure drop and dryout heat flux of two-phase flow in packed beds of multi-sized and irregular particles

This paper is concerned with debris bed coolability in a postulated severe accident of light water reactors, where the debris particles are irregular and multi-sized. To obtain and verify the friction laws predicting the hydrodynamics of the debris beds, the drag characteristics of air/water single- and two-phase flow in a particulate bed packed with multi-sized spheres or irregular sand particles were investigated on the POMECO-FL test facility. The same types of particles were then loaded in the test section of the POMECO-HT facility to obtain the dryout heat fluxes of the particulate beds heated volumetrically. The effective (mean) particle diameter is 2.25 mm for the multi-sized spheres and 1.75 mm for the sand particles, determined from the Ergun equation and the measured pressure drop of single-phase flow through the packed bed. Given the effective particle diameter, both the pressure drop and the dryout heat flux of two-phase flow through the bed can be predicted by the Reed model. The experiment also shows that the bottom injection of coolant improves the dryout heat flux significantly and the first dryout position is moving upward with increasing bottom injection flowrate. Compared with top-flooding case, the dryout heat flux of the bed can be doubled if the superficial velocity of coolant injection is 0.21–0.27 mm/s. The experimental data provides insights for interpretation of debris bed coolability (how to deal with the multi-sized irregular particles), as well as high-quality data for validation of the coolability analysis models and codes.     

SILFIDE experiment: Coolability in a volumetrically heated debris bed

The SILFIDE facility was designed at EDF R&D to study the coolability of a debris bed in multidimensional configurations. The choice of induction heating mode was motivated by the necessity for the heat to be generated primarily within the solid particles instead of using external heaters. Particles were simulated by steel beads with diameters ranging from 2 to 7 mm. Coolability is significantly better in terms of CHF values in comparison with the Lipinski 1D formulation applied to the conditions (especially when considering vertically integrated power) where the dryout occurs first. The experiments also show that bottom coolant injection is at least two times more efficient than top coolant injection. With increasing thermal power, steady temperature overheats up to 200 °C above saturation were observed, and the bed was still coolable. Combined phenomena considered as responsible are discussed: steam flow cooling with or without entrained liquid droplets in post-dryout regime, and preferential paths of fluid in porous media. As a consequence, the critical heat flux definition under such conditions must be considered with care. Especially, a failure of coolability cannot necessarily be concluded only from the occurrence of dry zones.     

Post-dryout heat transfer in a multi-dimensional porous bed

Post-dryout behavior of a particulate debris bed was investigated numerically. A separate flow model using the concepts of relative permeabilities and the Leverett function was used to describe two-phase flow and heat transfer in the bed. The saturation distribution, liquid and vapor pressures and flows were calculated when heat generation rate (decay rate) was less than a critical value called the 'dryout heat flux'. When the heat generation rate was greater than the dryout heat flux, a dry zone was defined by extrapolating two-phase flow calculations. This is accomplished by solving the nonlinear partial differential equations governing pressures and temperature using an alternating direction implicit (ADI) method with an upwind scheme. Conduction, convection and radiation are taken into account in the dry zone. The maximum temperature in the bed, the melting heat fluxes, and the fractional contribution to heat transfer by conduction, convection and radiation for various bed configurations were investigated.     

The effect of lateral flooding on the coolability of irregular core debris beds

The coolability of ex-vessel core debris is an important issue in the severe accident management strategy of, e.g. the Nordic boiling water reactors. In a core melt accident, the molten core material is expected to discharge into the containment and form a porous debris bed on the pedestal floor of a flooded lower drywell. The debris bed generates decay heat which must be removed by boiling in order to stabilize the debris bed and to prevent local dryout and possible re-melting of the material. The STYX test facility which consists of a cylindrical bed of irregular alumina particles has been used to investigate the effect of lateral coolant inflow on the dryout heat flux of the particle bed. The lateral flow was achieved by downcomers attached on the sides of the test rig. The downcomers provide coolant into the lower region of the bed by natural circulation. Both homogenous and stratified bed configurations have been examined. It was observed that the dryout heat flux is increased by 22-25% for the homogenous test bed compared to the case with no lateral flooding. For the stratified configuration with a fine particle layer on top of the bed, no significant increase in the dryout heat flux was observed. The experiments have been analyzed by using the MEWA-2D code. Models which include explicit consideration of gas-liquid friction were used in the calculations in order to realistically capture the lateral flow configuration.     

Integral boundary layer heat transfer modeling for Tehran Research Reactor

In the present work the validity of applying the Boussinesq approximation in the analysis of natural convection heat transfer along nuclear fuel plates with large coolant channel aspect ratios is evaluated. The Boussinesq approximation is introduced into the integral boundary layer equations governing the system to describe the velocity and temperature distributions of the coolant in the cooling channels. The fuel plate temperature is related to the adjacent coolant fluid temperature by a fundamental law in conduction heat transfer. Air and water are considered as fluids. The coolant flow is assumed to be fully developed which is a convenient assumption for coolant channels having large aspect ratios. Obtained results indicate that the Boussinesq approximation is merely applicable over a limited range of coolant channel outlet fluid temperatures. The use of this approximation produces conservative estimation of the critical plate power for air flow and non-conservative estimation of the critical plate power for water flow.     

Performance evaluation of ultra-long lithium heat pipe using an improved lumped parameter model

Lithium heat pipes have broad applications in heat pipe cooling reactors and hypersonic vehicles owing to their ultra-high working temperature.In particular,when the length of the lithium heat pipe is ultra-long,the flow and heat transfer characteristics are more complex.In this study,an improved lumped parameter model that considers the Marangoni effect,bending effect,and different vapor flow patterns and Mach numbers was developed.There-after,the proposed model was verified using the University of New Mexico's Heat Pipe and HTPIPE models.Finally,the verified model was applied to simulate the steady-state operation of an ultra-long lithium heat pipe in a Heat Pipe-Segmented Thermoelectric Module Converters space reactor.Based on the results:(1)Vapor thermal resistance was dominant at low heating power and decreased with increasing heating power.The vapor flow inside the heat pipe developed from the laminar to the turbulent phase,whereas the liquid phase in the heat pipe was always laminar.(2)The vapor pressure drop caused by bending was approximately 22-23％of the total,and the bending effect on the liquid pressure drop could be ignored.(3)The Marangoni effect reduced the capillary limit by hindering the liquid reflux,especially at low vapor temperatures.Without considering the Marangoni effect,the capillary limit of the lithium heat pipe was overestimated by 9％when the vapor temperature was 1400 K.(4)The total thermal resistance of the heat pipe significantly increased with increasing adiabatic length when the vapor tempera-ture was low.Further,the wick dryness increased with increasing adiabatic length at any vapor temperature.Such findings improve on current knowledge for the optimal design and safety analysis of a heat pipe reactor,which adopts ultra-long lithium heat pipes.     

Experiments on microgravity boiling heat transfer by using transparent heaters

To clarify the relation between the liquid–vapor behavior and the heat transfer characteristics in the boiling phenomena, the structures of transparent heaters were developed for both flow boiling and pool boiling experiments and were applied to the microgravity environment realized by the parabolic flight of aircraft. In the flow boiling experiment, a transparent heated tube makes the heating, the observation of liquid–vapor behavior and the measurement of heat transfer data simultaneously possible. The heat transfer coefficient in the annular flow regime at moderate quality has distinct dependence on gravity provided that the mass velocity is not so high, while no noticeable gravity effect is seen at high quality and in the bubbly flow regime. The measured gravity effect was directly related to the behavior of annular liquid film observed through the transparent tube wall. In the pool boiling experiment, a structure of transparent heating surface realizes both the observation of the macrolayer or microlayer behavior from underneath and the measurements of local surface temperatures and the layer thickness. It was clarified in the microgravity experiments that no vapor stem exists but tiny bubbles are observed in the macrolayer underneath a large coalesced bubble at high heat flux. The heat flux evaluated by the heat conduction across the layer assumes less than 30% of the total to be transferred. The evaporation of the microlayers underneath primary bubbles just after the generation dominates the heat transfer in the microgravity, not only in the isolated bubble region but also in the coalesced bubble region.     

Boiling experiments for the validation of dryout models used in reactor safety

The coolability of fragmented corium is a major issue in reactor safety. Since the long-term coolability of such particle beds is limited by the availability of coolant inside the bed and not by heat transfer limitations from the particles to the coolant, the pressure field inside the debris has a strong effect on the cooling potential in multi-dimensional cases as expected in severe accidents in light water reactors (LWR). Therefore, the determination of the pressure field for two-phase flows in porous media is one central point of interest.In this context simulation models and in particular dryout models were developed for reactor safety analyses which have to be validated by reliable experimental data. Therefore, basic experimental investigations have been carried out with inductively heated steel balls of 6 or 3 mm diameter to provide a database for the validation and modification of the friction laws included in these dryout models.The performed boiling and dryout experiments show clearly that models without the explicit consideration of the interfacial drag cannot predict the pressure distribution inside a boiling particle bed, not even qualitatively. Against it, models with an explicit consideration of the interfacial drag can describe the distribution of pressure inside a boiling particle bed.     

Experimental investigations on single-phase heat transfer enhancement with longitudinal vortices in narrow rectangular channel

Four pairs of rectangular block as longitudinal vortex generators (LVG) were mounted periodically in a narrow rectangular channel to investigate fluid flow and convective heat transfer respectively in the narrow rectangular channel with LVG and without LVG. Both the channels have the same narrow gap (d) = 3 mm, the same hydraulic diameter (D_h) = 5.58 mm and the same length to diameter ratio (L/D_h) = 80.65. The experiments were performed with the channels oriented uprightly and uniform heat fluxes applied at the one side of the heating plate and single-phase water was used as test fluid. The parameters that were varied during the experiments included the mass flow rate, inlet liquid temperature, system pressure, and heat flux.In each of the experiments conducted, the temperature of both the liquid and the wall was measured at various locations along the flow direction. Based on the measured temperatures and the overall energy balance across the test section, the heat transfer coefficients for single-phase forced convection have been calculated. At the same time, in these experiments, the single-phase pressure drop across the channels was also measured. The correlations have been developed for mean Nusselt numbers and friction factors. Additionally, the visual experiments of infrared thermo-image recording the temperature on the outer wall of the heating plate have been conducted for validating the effects of LV.In these experimental investigations, both laminar regime and turbulent regime were under the thermo-hydraulic developing conditions, laminar-to-turbulent transition occurred in advance with the help of LV when Reynolds numbers vary between 310 and 4220. In laminar regime, LV causes heat transfer enhancement of about 100.9% and flow resistance increase of only 11.4%. And in turbulent regime, LV causes heat transfer enhancement of above 87.1% and flow resistance increase of 100.3%. As a result, LV can obviously enhance heat transfer of single-phase water, and increase flow resistance mildly.     

Thermo-hydraulic design verification of the neutral beam liner for the ITER vacuum vessel

The ITER vacuum vessel has upper, equatorial and lower port structures used for equipment installation, utility feedthroughs, vacuum pumping and access inside the vessel for maintenance. A neutral beam (NB) port of equatorial ports provides a path of neutral beam for plasma heating and current drive. An internal duct liner is built in the NB ports, and copper alloy panels are placed in the top and bottom of the liner to protect duct surface from high-power heat loads. Global NB liner models for the upper panel and the lower panel have been developed, and flow field and conjugate heat transfer analyses have been performed to find out pressure drop and heat transfer characteristics of the liner. Heat loads such as NB power, volumetric heating and surface heat flux are applied in the analyses for beam steering and misalignment conditions. For the upper panel, it is found that unbalanced flow distribution occurs in each flow path, and this causes poor heat transfer performance as well. In order to improve flow distribution and to reduce pressure losses, hydraulic analyses for modified cooling path schemes have been carried out, and design recommendations are made based on the analysis results. For the lower panel, local flow distributions and pressure drop values at each header and branch of the tube are obtained by applying design coolant flow rate. Together with the coolant flow field, temperature and heat transfer coefficient distributions are also acquired from the analyses. Based on the analysis results, it is concluded that the lower panel for the NB liner is relatively well designed even though the given heat loads are very severe.     

窄矩形通道两相流动实验回路设计研究

为了更好地研究某燃料堆内窄矩形冷却剂通道的流动传热特性,调研了窄矩形通道传热的研究现状和发展趋势,结合NP工程反应堆相关参数和实验需求,搭建了一套热工水力两相流实验回路用来研究分析某燃料冷却剂通道传热特性。该实验回路根据实际的反应堆运行操作要求,设计了与实际冷却剂通道一致的实验段,流动方向设定为竖直向下流动,采用双面加热,流道间隙尺寸设定为2.3 mm,通道宽度为67 mm（加热宽度为62 mm）,流道长度为1000 mm（加热长度为750 mm）,并通过实验对其进行了验证。结果表明,本文装置正确可行。      

200MW低温供热堆盒间流道流动传热数值分析

采用三维CFD软件Phoenics-3.2,计算了200MW低温供热堆燃料组件盒间的流场及温场。研究了旁通流量、控制棒提升等因素的影响。在考虑这些因素之后,得出了最佳旁通入流方案。     

倾斜下朝向加热表面汽泡行为可视化实验研究

以AP1000反应堆堆芯熔融物堆内滞留(IVR)策略为研究背景,采用去离子水为工质,在大气压下针对倾斜矩形结构开展下朝向加热表面汽泡行为的可视化实验研究。加热表面倾角从0°变化到30°,矩形窄缝尺寸从3 mm变化到8 mm。可视化观察到下朝向加热表面的汽泡滑移和汽泡变形现象,认为实验本体结构和下朝向加热表面布置是导致汽泡滑移和变形的诱因。通过对临界热流密度触发前后汽-液两相波动现象的可视化分析,认为汽-液波动界面的脱离是触发临界热流密度的主要原因。     

竖直及倾斜环隙流道内自然对流沸腾临界热负荷

以水为工质 ,在常压下对垂直和倾斜环隙流道内的自然对流沸腾临界热负荷进行了实验研究和理论分析 ,得到了计及进出口局部阻力的计算公式 ,讨论了流道几何尺寸、几何形状、倾角、压力和进出口局部阻力等因素对临界热负荷的影响 ,最后提出了一个新的 ,可用于计算竖直环隙、圆管及长方形流道内自然对流沸腾临界热负荷的半经验公式 ,其计算精度和适用范围较现有的计算公式有显著提高 ,原则上不受H/De 值大小的限制。     

Development of a critical heat flux mapping method for fin-structured surfaces

In this study, we performed critical heat flux (CHF) experiments using structured surfaces to validate the parameter effects and understand their physical meanings. Experimental results showed that the CHF has a peak value as the fin geometry changes. Fins with height of 0.5 mm produced the largest CHF, 1.7 MW/m², and fins longer than 2 mm reduced the CHF values. To explain the results, a CHF mapping method was developed describing the liquid supply-side and demand-side limits. The liquid demand-side limit is governed by the heat removal capability, mainly the nucleate boiling, calculated using the hot spot model. We consider three liquid supply-side limits restricting the liquid supply to the heating surface: capillary limit and counter-current flow limitations (CCFLs). The capillary limit is determined by balancing the capillary pressure and viscous dissipation in the liquid film on the fin side. The CCFL in the structure is calculated using the Wallis correlation and the CCFL in the free volume limits the liquid downward flow by the vapor jetting from the heating surface. The CHF map for our experimental results successfully describes the CHF trend of the structured surfaces. As a result, we concluded that CHF mapping method is an effective means of explaining CHF in pool boiling.     

Effects of annular crevices on pool boiling heat transfer

Effects of gap sizes (3.9–44.3 mm) of vertical annuli on nucleate pool boiling heat transfer of water at atmospheric pressure have been obtained experimentally. Through the tests, the conditions of tube bottom confinement (open or closed) have also been investigated and the whole results are compared with those of a single unconfined tube. According to the results, the annular condition gives much increase in heat transfer at moderate heat fluxes. The increase is much enhanced as the gap size decreases. At the same tube wall superheat (about 3.2 K) the heat flux of the least gap size is more than four times greater than that of the unconfined tube. Its effect is observed much greater for the bottom-closed tube condition. However, a deterioration of heat transfer occurs at high heat flux for confined boiling.