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.     

Experimental heat transfer in supercritical water flowing inside channels (survey)

This literature survey is for heat transfer to supercritical water flowing in channels. The objectives are to assess the work that was done 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 a few in other flow geometries including bundles. In general, the experiments showed that there are three heat transfer modes in fluids at supercritical pressures: (1) normal heat transfer, (2) deteriorated heat transfer with lower values of the heat transfer coefficient (HTC) and hence higher values of wall temperature within some part of a test section compared to those of normal heat transfer and (3) improved heat transfer with higher values of the HTC and hence lower values of wall temperature within some part of a test section compared to those of normal heat transfer. The deteriorated heat transfer usually appears at high heat fluxes and lower mass fluxes. Also, a peak in HTC near the critical and pseudo-critical points was recorded. Due to the limited number of publications that are devoted to heat transfer in bundles cooled with water at supercritical pressures, more work is definitely needed to provide the additional information for design purposes.     

高压及超临界压力下螺旋管内单相水摩擦压降特性实验研究

在较宽的参数范围内对高压及超临界压力下单相水流经立式螺旋管的摩擦压降特性进行实验研究。研究表明,对于高压工况,在高雷诺数Re条件下的水力粗糙区,管壁粗糙度对摩擦压降的影响要远大于二次流的影响,故单相水在螺旋管内的摩擦压降基本可直接采用直管的相关公式来预测;对于超临界压力工况,在物性变化剧烈的拟临界区内,采用高压工况计算公式所得的摩擦压降预测值要明显偏低于实验值。     

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 in Pipes and Rod Bundles During Flow of Supercritical-Pressure Water

The current ideas on heat-transfer processes at supercritical pressure and on the hydraulic resistance in pipes and rod bundles are briefly presented in order to determine the computational relations for reactors cooled by water with supercritical parameters. The most widely used relations for calculating heat transfer in normal heat transfer regimes are analyzed and a comparison is made with the latest experimental data. Recommendations are made for calculating the hydraulic resistance coefficients and heat-transfer coefficients in pipes and rod bundles in a normal heat-transfer regime without degradation, which can be used to make new experimental and computational recommendations.     

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.     

超临界水在垂直管内换热及流动不稳定性研究

清华大学核能与新能源技术研究院在建的250 MWt高温气冷堆核电站示范工程(HTR-PM)中蒸汽发生器二回路为亚临界水,由于反应堆能提供750℃的高温氦气,二回路水可提高到超临界压力和温度,采用多堆带一机方案可与超临界蒸汽透平机组匹配,因此研究超临界水在管内的流动、传热以及流动不稳定现象非常重要。本文通过使用RNGk-ε模型耦合强化壁面函数,发现模拟结果与Yamagata等的实验数据符合较好。基于此模型,分析了超临界流体流动时换热系数的变化规律,并采用瞬态计算方法,线性增大加热功率,分析了流动不稳定现象,发现流体一旦进入不稳定区,进出口流量的波动非常严重,甚至出现倒流,应尽可能避免此类现象。     

高温气冷堆螺旋管式直流蒸汽发生器热工水力学

高温气冷堆蒸汽发生器具有一次侧氦气工质、二次侧直流、螺旋管结构、工作温度高等特点,其热工水力特性与传统压水堆自然循环蒸汽发生器存在很大区别。针对高温气冷堆蒸汽发生器的特点,对其基础热工水力及特有热工水力学问题进行了阐述,主要包括螺旋管内单相及两相流阻及换热计算、横掠螺旋管束流阻及换热计算、温度均匀性及两相流不稳定性等。同时介绍了清华大学核能与新能源技术研究院针对高温气冷堆蒸汽发生器热工设计、温度均匀性及两相流不稳定性等热工水力学问题所开发的一维稳态程序、一维瞬态程序、二维分析程序和方法,并对分析结果和结论进行了讨论。相关研究方法、程序和结论对其他相似参数螺旋管和直管式直流蒸汽发生器具有参考和借鉴意义。     

环形通道内定位格架对超临界水传热的影响

定位格架对棒束内流动传热具有极重要的影响,目前定位格架对超临界水传热的影响仍无相应的试验数据。本文基于上海交通大学完成的超临界水在环形通道内的对流传热试验,评价了传统定位格架对下游传热系数衰减关联式的适用性。试验结果表明,定位格架的面积阻塞比对格架下游传热系数衰减规律有很大影响;在超临界压力与次临界压力条件下,定位格架下游传热系数衰减规律也有较大的差异。     

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。     

Experimental Study on Heat Transfer Characteristics of Vertical 5×5 Heated Rod Bundles around Critical Pressure with R-134a

With the aim of researching the heat transfer characteristics around the critical pressure in rod bundle geometry, the behaviors of the heating surface temperatures at the vertical 5×5 heated rod bundles with R-134a were experimentally investigated under both pressurizing and depressurizing processes, where the pressure constantly decreases from supercritical to subcritical and constantly increases from subcritical to supercritical under constant inlet thermal conditions. As the pressure approaches the critical pressure, a DNB type or a dryout type of CHF was induced, and then the post-CHF was kept until the vicinity of the critical pressure. Under the supercritical pressure, the post-CHF disappeared due to the extinction of boiling phenomena, but the heat transfer deterioration was induced in a certain pressure range. In the depressurizing process, the heating surface temperatures followed the trajectory of temperature behaviors as in the pressurizing process except for the quenching point. The quenching point from the post-CHF moved to the lower pressure side than the pressure as for the CHF in the pressurizing process. This phenomenon was considered as the hysteresis phenomenon frequently observed in pool boiling curve characteristics.     

Thermal and Stability Considerations of Super LWR during Sliding Pressure Startup

The feasibility of the sliding pressure startup of a high-temperature supercritical-pressure light water reactor (super LWR, SCLWR-H) is assessed from both thermal and stability considerations. In the sliding pressure startup, nuclear heating starts at subcritical pressure and the reactor is pressurized to supercritical pressure at a low power and high enough flow rate. The reactor power and flow rate are then raised gradually to the rated normal values at constant supercritical operating pressure. During startup, the maximum cladding surface temperature must not exceed 620°C. For two-phase flow at subcritical pressures, the homogeneous equilibrium model is used. The thermal-hydraulic and coupled neutronic thermal-hydraulic stabilities during pressurization and power-raising are investigated by a frequency-domain linear analysis for both supercritical-pressure and subcritical-pressure operating conditions. The same stability criteria as those of BWRs are used. From the analysis results, a sliding pressure startup procedure is proposed for super LWR. The thermal criteria are satisfied by keeping the core power between the maximum allowable limit and minimum limit required for turbine startup and operation. The thermal-hydraulic stability and coupled neutronic thermal-hydraulic stability can be maintained by applying an orifice pressure drop coefficient at the inlet of fuel assembly and by controlling the power and flow rate during startup.     

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。     

箭鱼形翅片微通道流动换热特性研究

超临界二氧化碳布雷顿循环是第4代核能采用的新一代热能循环系统。紧凑式微通道换热器作为超临界二氧化碳布雷顿循环的高低温回热器,其流动换热特性直接影响整体热电转化的效率。降低回热器的流动阻力,同时维持较高的换热效率是微通道换热器优化设计的重要研究内容。箭鱼形翅片微通道设计借鉴仿生学原理,理论上可显著降低流动阻力。本文以超临界二氧化碳为流动工质,建立箭鱼形翅片换热器的模型并进行三维数值模拟,分析不同排列下的箭鱼形翅片设计对换热器流动换热特性的影响。同时对箭鱼形翅片设计与传统商用折线形微通道换热器流动换热特性进行对比分析。研究分析表明,在相同雷诺数下,箭鱼形翅片微通道的努塞尔数为折线形流道的2倍,而压降仅为其1/2,所以箭鱼形翅片微通道换热器的流动换热特性明显优于折线形换热器。通过优化分析,发现箭鱼形翅片设计最优的排列间距为沿流动方向的翅片间距L_a＝8 mm,垂直于流动方向的翅片间距L_b＝6 mm。     

Flow and Heat Transfer Characteristics of Swordfish Fin Microchannel

The supercritical carbon dioxide Brayton cycle is a new generation of thermal cycle used in the fourth generation of nuclear energy. As a high or low temperature recuperator of supercritical carbon dioxide Brayton cycle, the thermal hydraulic characteristics of the compact microchannel heat exchanger directly affect the power cycle efficiency. Reducing flow resistance of the temperature recuperator while maintaining high heat transfer efficiency is an important research for microchannel heat exchanger optimization design. The swordfish fin microchannel design considering bionics theory can significantly reduce the flow resistance. In this work, the swordfish fin heat exchanger model was established with supercritical carbon dioxide fluid as the flow medium. The effect of swordfish fin design with different arrangements on heat transfer characteristics was analyzed by three-dimensional numerical simulation. At the same time, the thermal hydraulic characteristics of swordfish fin design were compared with those of traditional commercial Z-shaped microchannel heat exchanger. The results show that under the same Reynolds number, the Nusselt number of the swordfish fin microchannel is twice as much as that of the Z-shaped microchannel, but the pressure drop is only half of that. Therefore, the thermal hydraulic performance of swordfish fin microchannel heat exchanger is obviously better than that of Z-shaped heat exchanger. It is obtained from optimization analysis that the optimal pitches for swordfish fin design is that the L_a＝8 mm along the flow direction, and the L_b＝6 mm perpendicular to the flow direction.     

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.     

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.     

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。     

针翅管传热与压降特性研究

以润滑油为换热介质,对整体针翅管传热与阻力特性进行了理论分析与试验研究,研究结果可为针翅管的优化设计提供参考。在换热介质纵向冲刷换热管的条件下,对不同针翅长度的3种整体针翅管与光管进行了传热与阻力试验。结果表明：整体针翅管对润滑油换热具有很好的强化能力,在本试验范围内,整体针翅管对油流体扰动强烈,换热强度是同条件下光管的2~6倍;针翅长度是影响针翅管压降的主要因素,在雷诺数达300时,压降曲线出现转折。     

Friction Pressure Drop and Heat Transfer Coefficient of Two-Phase Flow in Helically Coiled Tube Once-Through Steam Generator for Integrated Type Marine Water Reactor

Two-phase friction pressure drop and heat transfer coefficients in a once-through steam generator with helically coiled tubes were investigated with the model test rig of an integrated type marine water reactor. As the dimensions of the heat transfer tubes and the thermal-fluid conditions are almost the same as those of real reactors, the data applicable directly to the real reactor design were obtained. As to the friction pressure drop, modified Kozeki's prediction which is based on the experimental data by Kozeki for coiled tubes, agreed the best with the experimental data. Modified Martinelli-Nelson's prediction which is based on Martinelli-Nelson's multiplier using Ito's equation for single-phase flow in coiled tube, agreed within 30%. The effect of coiled tube on the average heat transfer coefficients at boiling region were small, and the predictions for straight tube could also be applied to coiled tube. Schrock-Grossman's correlation agreed well with the experimental data at the pressures of lower than 3.5 MPa. It was suggested that dryout should be occurred at the quality of greater than 90% within the conditions of this report.