Supercritical-water heat transfer in a vertical bare tube

This paper presents selected results on heat transfer to supercritical water flowing upward in a 4-m-long vertical bare tube. Supercritical-water heat-transfer data were obtained at pressures of about 24 MPa, mass fluxes of 200-1500 kg/m² s, heat fluxes up to 884 kW/m² and inlet temperatures from 320 to 350 °C for several combinations of wall and bulk-fluid temperatures that were below, at or above the pseudocritical temperature.In general, the experiments confirmed that there are three heat-transfer regimes for forced-convective heat transfer to water flowing inside tubes at supercritical pressures: (1) normal heat-transfer regime characterized in general with heat transfer coefficients (HTCs) similar to those of subcritical convective heat transfer far from critical or pseudocritical regions, which are calculated according to the Dittus-Boelter type correlations; (2) deteriorated heat-transfer regime with lower values of the HTC and hence higher values of wall temperature within some part of a test section compared to those of the normal heat-transfer regime; and (3) improved heat-transfer regime with higher values of HTC and hence lower values of wall temperature within some part of a test section compared to those of the normal heat-transfer regime.This new heat-transfer dataset is applicable as a reference dataset for future comparison with supercritical-water bundle data and for a verification of scaling parameters between water and modeling fluids.Also, these HTC data were compared to those calculated with the original Dittus-Boelter and Bishop et al. correlations. The comparison showed that the Bishop et al. correlation, which uses the cross-section average Prandtl number, represents HTC profiles more correctly along the heated length of the tube than the Dittus-Boelter correlation. In general, the Bishop et al. correlation shows a fair agreement with the experimental HTCs outside the pseudocritical region, however, overpredicts by about 25% the experimental HTCs within the pseudocritical region. The Dittus-Boelter correlation can also predict the experimental HTCs outside the pseudocritical region, but deviates significantly from the experimental data within the pseudocritical region. It should be noted that both these correlations cannot be used for a prediction of HTCs within the deteriorated heat-transfer regime.     

Experimental heat transfer of supercritical carbon dioxide flowing inside channels (survey)

A new reactor concept under development at AECL has the main design objective of achieving a 50% reduction in unit energy cost relative to existing reactor designs. The approach builds on using existing operating supercritical water (SCW) experience and turbines in coal-fired power plants.This SCW CANDU^®2 research includes investigating heat transfer and pressure drop at supercritical conditions using carbon dioxide as a modelling fluid as a cheaper and faster alternative to using SCW. Therefore, the objectives are to assess the work that was done with the supercritical carbon dioxide and to understand the specifics of heat transfer at these conditions.Our exhaustive literature search, which included over 450 papers, showed that the majority of experimental data were obtained in vertical tubes, some data in horizontal tubes and just few in other flow geometries.Three modes of heat transfer at supercritical pressures have been recorded: (1) so-called normal heat transfer, (2) improved heat transfer, characterized by higher-than-expected heat transfer coefficient (HTC) values than in the normal heat transfer regime and (3) deteriorated heat transfer, characterized by lower-than-expected HTC values than in the normal heat transfer regime.     

Heat transfer to supercritical fluids flowing in channels—empirical correlations (survey)

This literature survey is devoted to the problem of heat transfer of fluids at supercritical pressures including near critical region.

The objectives are to assess the work that was done in the area of heat transfer at supercritical pressures, to understand the specifics of heat transfer at these conditions, to compare different prediction methods for supercritical heat transfer in tubes and bundles, and to choose the most reliable ones.

The comparisons showed there is a significant difference in heat transfer coefficient values calculated according to various correlations. Only some correlations show similar results, which are quite close to the experimental data for normal supercritical heat transfer in water and carbon dioxide. Also, no one correlation can accurately predict the magnitude and onset of deteriorated heat transfer.

The exhaustive literature search, which included hundreds of papers, showed that the majority of correlations were obtained in tubes and just few of them in other flow geometries including bundles.

The variations in the prediction of supercritical heat transfer are related to the significant changes in thermophysical properties near the critical and pseudocritical points. Therefore, a discussion on the general trends of various thermophysical properties at near critical and pseudocritical points is also included.

Based on several chosen correlations, the heat transfer coefficients and temperature profiles in the CANDU-X reactor cooled with supercritical water were calculated.     

Development of supercritical water heat-transfer correlation for vertical bare tubes

This paper presents an analysis of heat-transfer to supercritical water in bare vertical tubes. A large set of experimental data, obtained in Russia, was analyzed and a new heat-transfer correlation for supercritical water was developed. This experimental dataset was obtained within conditions similar to those in supercritical water-cooled nuclear reactor (SCWR) concepts.The experimental dataset was obtained in supercritical water flowing upward in a 4-m long vertical bare tube with 10-mm ID. The data were collected at pressures of about 24 MPa, inlet temperatures from 320 to 350 °C, values of mass flux ranged from 200 to 1500 kg/m² s and heat fluxes up to 1250 kW/m² for several combinations of wall and bulk-fluid temperatures that were below, at, or above the pseudocritical temperature.A dimensional analysis was conducted using the Buckingham Π-theorem to derive the general form of an empirical supercritical water heat-transfer correlation for the Nusselt number, which was finalized based on the experimental data obtained at the normal and improved heat-transfer regimes. Also, experimental heat transfer coefficient (HTC) values at the normal and improved heat-transfer regimes were compared with those calculated according to several correlations from the open literature, with CFD code and with those of the proposed correlation.The comparison showed that the Dittus-Boelter correlation significantly overestimates experimental HTC values within the pseudocritical range. The Bishop et al. and Jackson correlations tended also to deviate substantially from the experimental data within the pseudocritical range. The Swenson et al. correlation provided a better fit for the experimental data than the previous three correlations at low mass flux (∼500 kg/m² s), but tends to overpredict the experimental data within the entrance region and does not follow up closely the experimental data at higher mass fluxes. Also, HTC and wall temperature values calculated with the FLUENT CFD code might deviate significantly from the experimental data, for example, the k-? model (wall function). However, the k-? model (low Reynolds numbers) shows better fit within some flow conditions.Nevertheless, the proposed correlation showed the best fit for the experimental data within a wide range of flow conditions. This correlation has an uncertainty of about ±25% for calculated HTC values and about ±15% for calculated wall temperature. A final verification of the proposed correlation was conducted through a comparison with other datasets. It was determined that the proposed correlation closely represents the experimental data and follows trends closely, even within the pseudocritical range. Finally, a recent study determined that in the supercritical region, the proposed correlation showed the best prediction of the data for all three sub-regions investigated.Therefore, the proposed correlation can be used for HTC calculations in SCW heat exchangers, for preliminary HTC calculations in SCWR fuel bundles as a conservative approach, for future comparison with other datasets and for the verification of computer codes and scaling parameters between water and modelling fluids.     

Investigation of forced convection heat transfer of supercritical pressure water in a vertically upward internally ribbed tube

In the present paper, the forced convection heat transfer characteristics of water in a vertically upward internally ribbed tube at supercritical pressures were investigated experimentally. The six-head internally ribbed tube is made of SA-213T12 steel with an outer diameter of 31.8 mm and a wall thickness of 6 mm and the mean inside diameter of the tube is measured to be 17.6 mm. The experimental parameters were as follows. The pressure at the inlet of the test section varied from 25.0 to 29.0 MPa, and the mass flux was from 800 to 1200 kg/(m² s), and the inside wall heat flux ranged from 260 to 660 kW/m². According to experimental data, the effects of heat flux and pressure on heat transfer of supercritical pressure water in the vertically upward internally ribbed tube were analyzed, and the characteristics and mechanisms of heat transfer enhancement, and also that of heat transfer deterioration, were also discussed in the so-called large specific heat region. The drastic changes in thermophysical properties near the pseudocritical points, especially the sudden rise in the specific heat of water at supercritical pressures, may result in the occurrence of the heat transfer enhancement, while the covering of the heat transfer surface by fluids lighter and hotter than the bulk fluid makes the heat transfer deteriorated eventually and explains how this lighter fluid layer forms. It was found that the heat transfer characteristics of water at supercritical pressures were greatly different from the single-phase convection heat transfer at subcritical pressures. There are three heat transfer modes of water at supercritical pressures: (1) normal heat transfer, (2) deteriorated heat transfer with low HTC but high wall temperatures in comparison to the normal heat transfer, and (3) enhanced heat transfer with high HTC and low wall temperatures in comparison to the normal heat transfer. It was also found that the heat transfer deterioration at supercritical pressures was similar to the DNB at subcritical pressures.     

Hydraulic resistance of fluids flowing in channels at supercritical pressures (survey)

This literature survey is devoted to hydraulic resistance of water and carbon dioxide flows at supercritical pressures. The objectives are to assess previous studies that were done in the area of hydraulic resistance of fluids at supercritical pressures flowing in channels of various geometries and to understand the specifics of pressure drop at these conditions. The literature search showed that the majority of experimental data were obtained in vertical tubes, some data were obtained in horizontal tubes and just a few of them in other flow geometries including bundles. In general, hydraulic resistance data are limited compared to the heat transfer data at supercritical pressures. Differences in pressure drop between supercritical and subcritical forced convection seem to be related to significant variations in thermophysical properties near the critical and pseudocritical points. Due to these variations, satisfactory analytical and numerical methods have not yet been developed especially in turbulent flows and at high heat fluxes. In general, the pressure drop in supercritical fluid flow consists of four components: pressure drop due to frictional resistance, due to local flow obstruction, due to acceleration of flow and due to gravity. The total pressure drop at supercritical pressures can be estimated using general correlations for pressure drop at subcritical pressures with correction factors for the effect of significant thermophysical properties variations and high heat fluxes. Only one paper was devoted to pressure drop in tight short bundles cooled with water at supercritical pressures. Therefore, more experimental work is needed to estimate the total pressure drop in various bundle designs with the objective of providing reliable information for designing supercritical water nuclear reactors.     

Experimental investigation of heat transfer for supercritical pressure water flowing in vertical annular channels

An experiment has recently been completed at Xi’an Jiaotong University (XJTU) to obtain wall-temperature measurements at supercritical pressures with upward flow of water inside vertical annuli. Two annular test sections were constructed with annular gaps of 4 and 6 mm, respectively, and an internal heater of 8 mm outer diameter. Experimental-parameter ranges covered pressures of 23-28 MPa, mass fluxes of 350-1000 kg/m²/s, heat fluxes of 200-1000 kW/m², and bulk inlet temperatures up to 400 °C. Depending on the flow conditions and heat fluxes, two distinctive heat transfer regimes, referring to as the normal heat transfer and deteriorated heat transfer, have been observed. At similar flow conditions, the heat transfer coefficients for the 6 mm gap annular channel are larger than those for the 4 mm gap annular channel. A strong effect of spiral spacer on heat transfer has been observed with a drastic reduction in wall temperature at locations downstream of the device in the annuli. Two tube-data-based correlations have been assessed against the experimental heat transfer results. The Jackson correlation agrees with the experimental trends and overpredicts slightly the heat transfer coefficients. The Dittus-Boelter correlation is applicable only for the normal heat transfer region but not for the deteriorated heat transfer region.     

Experimental investigation on heat transfer from a heated rod with a helically wrapped wire inside a square vertical channel to water at supercritical pressures

A supercritical water heat transfer test section has been built at Xi’an Jiaotong University to study the heat transfer from a 10 mm rod inside a square vertical channel with a wire-wrapped helically around it as a spacer. The test section is 1.5 m long and the wire pitch 200 mm. Experimental conditions included pressures of 23–25 MPa, mass fluxes of 500–1200 kg/m² s, heat fluxes of 200–800 kW/m², and inlet temperatures of 300–400 °C. Wall temperatures were measured with thermocouples at various positions near the rod surface. The experimental Nusselt numbers were compared with those calculated by empirical correlations for smooth tubes. The Jackson correlation showed better agreement with the test data compared with the Dittus-Boelter correlation but overpredicted the Nusselt numbers almost within the whole range of experimental conditions. Both correlations cannot predict the heat transfer accurately when deterioration occurred at low mass flux and relatively high heat flux in the pseudocritical region. Comparison of experimental data at two different supercritical pressures showed that the heat transfer was more enhanced at the lower supercritical pressure but the deterioration was more likely to occur at the higher pressure, meaning increased safety. Based on a comparison with an identical channel without the helical wrapped wire, it was found that the wire spacer does not enhance the heat transfer significantly under normal heat transfer conditions, but it contributes to the improvement of the heat transfer in the pseudocritical region and to a downstream shift of the onset of the deterioration. The Jackson buoyancy criterion is found to be valid and works well in predicting the onset of heat transfer deterioration occurring in the experiments without wire.     

低雷诺数条件下超临界压力CO_2换热实验研究

在低雷诺数条件下(Rein=1970和750),对超临界压力CO2在垂直圆管(d=2 mm)内向上流动和向下流动时的对流换热进行了实验研究。实验结果表明:当Rein=1970时,在热流密度较高的情况下,在管子的入口处向上流动会出现局部壁面温度峰值和谷值,而在向下流动时未观察到此类似现象;当Rein=750时,向上、向下流动壁面温度的变化趋势和换热规律类似。     

复合换热管过冷沸腾换热实验与关联式评价

以去离子水为实验介质,在单面受热流密度条件下,开展了聚变装置偏滤器的过冷流动沸腾强化换热特性实验研究,将内肋强化换热技术与内插扭带结构相结合,利用两者的协同强化传热效应,设计出一种复合换热管。实验参数为：质量流速,992～4 960 kg/(m2·s);压力,04～2 MPa;入口过冷度,8701～11921 ℃;热流密度,1～163 MW/m2。对4种强化换热管（光管、内插扭带管、内螺纹肋管和复合换热管）的管内过冷流动沸腾换热特性和综合性能评价指标（PEC）进行了对比实验。结果表明：与其他3种管道相比,复合换热管的对流换热系数和PEC最高,传热特性最好。研究了复合换热管的扭带扰动比、螺距、压力和质量流速对管内两相流动对流换热系数的影响规律,发现对流换热系数与螺距、质量流速呈正比,与扭带扰动比、压力呈反比。最后对比了4个现有的过冷流动沸腾换热经验公式,并在无量纲模型基础上,增加了扰动比和螺径比（t/Dh）进行修正,利用非线性拟合方法提出了适合复合换热管过冷流动沸腾的努塞尔数新公式。     

超临界压力下竖直圆管内不同流体的传热特性

为了深入认识超临界压力下不同流体传热中的共性反映出的传热机理及物性导致的特性差异,以水和氟利昂R134a为工质分别在SWAMUP回路和SMOTH回路上开展了竖直圆管内上升流传热试验。在正常传热、传热强化、小质量流速时浮升力导致传热恶化和大质量流速时加速效应导致传热恶化的工况中,氟利昂和水的换热系数（HTC）随无量纲温度表现出一致的变化规律。浮升力无量纲数_πB增大,换热系数与经典关系式计算值之比减小;加速效应无量纲数_πA较小时,换热系数比随_πA的增大而增大,达到峰值后换热系数比随_πA的增大而减小。_πB对超临界水试验数据的相关性更佳,而_πA对超临界氟利昂试验数据的相关性更好。无量纲数表征的超临界压力下传热规律的高度相似性初步验证了以模化流体氟利昂R134a研究超临界水传热特性是合理可行的。     

超临界氢气在弯管中的流动换热计算

为探究超临界氢气流经喷管喉部时的流动换热特性,通过ANSYS FLUENT软件模拟超临界氢气在180°弯管中的流动换热现象,得到了氢气在弯管中的流场分布以及不同位置处的壁面温度分布。研究发现:由于离心力作用,管内氢气流动在弯管段向外侧径向偏移,产生了垂直于主流方向的二次流现象,使得内侧氢气流速低于外侧;由于弯管段的流量分布不均,导致弯管外侧换热得到强化,内侧则出现传热恶化现象。在本文研究工况下,弯管段出口附近的内侧壁面区域,壁面温度达到最高,传热恶化最为显著。      

超临界水四棒束传热数值分析

超临界水冷堆(SCWR)开发的关键是棒束内超临界水(SCW)的热工水力特性。本文针对超临界水四棒束流动传热实验进行CFD数值模拟,SSG湍流模型的计算结果与实验结果吻合良好。分析结果表明,流动方向对棒束截面内流量分布有显著影响。与下降流相比,尽管上升流时棒束间流动搅混较弱,但上升流时棒束截面流量及壁面周向温度分布更加均匀,加热棒壁面温度更低。可见,棒束横截面上的流量分布是影响加热棒壁面流动传热的主要因素。     

不同管束布置方式下含有空气的蒸汽自然对流冷凝换热特性分析

为研究非能动安全壳冷却系统（PCCS）热交换器管束布置对自然对流条件下含有空气的蒸汽冷凝换热特性的影响,采用气体组分输运方程和冷凝模型耦合,对单管、单排到五排管束通道内冷凝换热过程进行数值研究。研究发现,管束区内存在由于管间高浓度空气层干扰使冷凝换热能力减弱的“抑制效应”,以及由于水蒸气壁面冷凝导致气体横向流动使壁面冷凝能力强化的“抽吸效应”。对不同管束结构下2种效应对冷凝换热的影响进行分析,结果表明,随着管束排数的增加,2种效应对冷凝换热的影响逐渐增强,导致冷凝管周向局部冷凝换热能力不均匀性增加,其中五排管束周向局部冷凝换热系数（HTC）最大值为单管的2.3倍,最小值仅为单管的44.7%。在双排、三排和四排管束中,正四边形布置管束的冷凝换热能力优于正三角形布置,而五排管束中,正三角形布置的冷凝换热能力更强。本研究可对PCCS热交换器管束布置优化提供参考。      

含绕丝2×2棒束内超临界水传热试验研究

以超临界水冷堆燃料性能验证试验为背景,对带有螺旋绕丝的2×2棒束内超临界水的传热特性进行了试验研究。试验参数范围为：压力23～28 MPa,质量流速400～1 000 kg/(m²•s),壁面热流密度200～1 000 kW/m²。通过试验,获得了加热管周向壁温的分布规律,并分析了热流密度、质量流速、压力、螺旋绕丝对壁温和换热系数的影响。研究结果表明,加热管周向壁温呈现非均匀、非对称分布的特性,最高壁温出现在边角子通道或螺旋绕丝覆盖的位置。在拟临界区,换热系数随热流密度的升高或质量流速的降低而迅速减小,而随压力的变化较微弱。相对于光滑2×2棒束,螺旋绕丝不仅改变了周向壁温分布规律,同时也提高了平均换热系数。     

超临界CO2在螺旋管中的流动换热特性研究

超临界蒸发器应用到核电中,可大幅提高机组的热效率。超临界压力流体的热物性在准临界温度附近变化非常剧烈,会对其流动和换热产生很大的影响。研究超临界压力流体在螺旋管内的流动和换热规律,有利于对超临界螺旋管蒸发器的设计。本文采用RNG k-ε和SST k-ω模型对超临界CO₂在螺旋管中的流动换热情况进行了数值模拟,发现SST k-ω模型模拟结果与实验结果符合得更好。基于此模型,分析了不同进口质量流速及不同热流密度对管壁温和换热系数的影响,发现随着质量流速的减小、热流密度的增加,峰值向远离h_pc的一侧偏移。最后讨论并分析了周向壁温和换热系数的分布情况,发现壁温在φ＝315°处最高,需在实验操作或实际运行中加以监控,以保障螺旋管蒸发器的安全运行。     

CFD in supercritical water-cooled nuclear reactor (SCWR) with horizontal tube bundles

The commercial CFD code STAR-CD 4.02 is used as a numerical simulation tool for flows in the supercritical water-cooled nuclear reactor (SCWR). The basic heat transfer element in the reactor core can be considered as round tubes and tube bundles. Reactors with vertical or horizontal flow in the core can be found. In a vertically oriented core, symmetric characters of flow and heat transfer can be found and two-dimensional analyses are often performed. However, in a horizontally oriented core the flow and heat transfer are fully three-dimensional due to the buoyancy effect. In this paper, horizontal tubes and tube bundles at SCWR conditions are studied. Special STAR-CD subroutines were developed by the authors to correctly represent the dramatic change in physical properties of the supercritical water with temperature. From the study of single round tubes, the Speziale quadratic non-linear high-Re k-? turbulence model with the two-layer model for near wall treatment is found to produce the best results in comparison with experimental data. In tube bundle simulations, it is found that the temperature is higher in the top half of the bundle and the highest tube wall temperature is located at the outside tubes where the flow rate is the lowest. The secondary flows across the bundle are highly complex. Their main effect is to even out the temperature over the area within each individual recirculation region. Similar analysis could be useful in design and safety studies to obtain optimum fuel rod arrangement in a SCWR.     

三角布置棒束内超临界水传热实验研究

在超临界水多功能实验装置上开展了三角布置棒束内超临界水流动传热实验研究,通过实验观测到了通道内棒束周向温度分布不均匀现象和定位格架导致的传热强化现象,获得不同热流密度、质量流量及压力范围内的传热实验数据,拟合得到预测偏差为±15%的三角布置棒束超临界水传热关系式。      

Heat transfer to supercritical pressure carbon dioxide flowing upward through tubes and a narrow annulus passage

A heat transfer test facility, SPHINX, which uses carbon dioxide as a medium at supercritical pressures, has been built at KAERI. A series of experiments are under way for various geometries including tubes of several diameters and narrow annulus passages of a concentric and eccentric layout. The experiments aim to collect heat transfer data and to provide an empirical heat transfer correlation required for a SCWR design. In this paper the test results for tubes of 4.4 mm and 9.0 mm IDs, and a concentric annular passage (8 mm × 10 mm × L1800 mm) are presented for certain combinations of the heat fluxes and mass fluxes. The heat transfer coefficients produced in the tests were compared with those from the existing heat transfer correlations with different media. A new correlation was introduced for the experiment data presented in this paper.     

水平光管内超临界水在大比热容区内的传热与交混特性数值模拟研究

对超临界压力水在管径为32 mm 3 mm、长度为8 m的水平光管内的流动和传热特性进行数值模拟研究。探讨不同压力、流量、热负荷下管内换热系数的变化特征;重点分析超临界水的交混特性,对比分析流动通道内二次流动的特性及演变规律,进而对二次流动的变化规律给出合理的解释;利用无量纲的Gr/Re2和Gr/Re2.7对交混特性中自然对流与强制对流的相对大小进行定量描述,以解释超临界水在水平管内的流动与换热特征。