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.     

CFD analysis of thermal-hydraulic behavior of supercritical water in sub-channels

Investigations on the thermal-hydraulic behavior in the supercritical water-cooled reactor (SCWR) fuel assembly have obtained a significant attention in the international SCWR community. However, there is still a lack of understanding and ability to predict the heat transfer behavior of supercritical fluids. In this paper, computational fluid dynamics (CFD) analysis is carried out to study the thermal-hydraulic behavior of supercritical water flows in sub-channels of a typical SCWR fuel assembly using commercial CFD code CFX-5.6. Three types of sub-channels, e.g. regular sub-channel, wall sub-channel and corner sub-channel, are analyzed. Effects of various parameters, such as boundary conditions and pitch-to-diameter ratios, on the mixing phenomenon in sub-channels and heat transfer are investigated. The turbulent mixing in tight lattice (P/D = 1.1) is lower than that in wide lattice (P/D > 1.1), whereas, the effect of pitch-to-diameter ratio on the turbulent mixing is slight at P/D > 1.1. The amplitude of turbulent mixing in wall sub-channel is slightly higher than that in regular sub-channel and is close to that in corner sub-channel. The mixing coefficient in the sub-channel at P/D ≥ 1.2 is in the range from 0.022 to 0.028. The results also show unusual behavior of turbulent mixing in the vicinity of the pseudo-critical point, and further investigation is needed. The mass mixing due to cross flow in wall sub-channel is much stronger than that in regular sub-channel at a same pitch-to-diameter ratio. The mass mixing in wall and regular sub-channels, especially at small pitch-to-diameter ratio, brings an unfavorable feedback to the heat transfer and strengthens the non-uniformity of the circumferential distribution of heat transfer. The strong mass mixing in corner sub-channel should be paid attention.     

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.     

Loss of flow accident and its mitigation measures for nuclear systems with SCWR-M

Based on a revised version of RELAP5, which can be used for super-critical pressure calculation, a model of mixed spectrum SCWR (SCWR-M) system is established. To analyze the transient behavior of SCWR-M and develop mitigation measures during loss of flow accident (LOFA), some important parameters, e.g. reactor coolant pump (RCP) coast-down time, Reactor Pressure Vessel (RPV) upper water volume and safety injection flow, etc., are chosen for the parametric analysis. The results achieved so far indicate that the SCWR-M system design is feasible and promising. Three important mitigation measures for LOFA of SCWR-M are derived from the results: RCP coast-down time of more than 15 s, RPV upper water volume of more than 27 m³, and safety injection of more than 5% of the system design flow.     

超临界流体的泄压过程研究

超临界水堆(SCWR)的LOCA研究是安全分析的重点和难点,其中压力容器的喷放泄压过程的研究至关重要。本文通过对反应堆压力容器进行简化,建立了简单容器喷放的数学物理模型,开发了超临界流体的喷放瞬态计算程序。将该程序的计算结果与超临界二氧化碳的泄压喷放过程的实验数据进行了比较,计算值与实验结果吻合良好,验证了模型的正确性。运用该验证后的程序对超临界水的容器喷放过程进行了深入研究和分析,分析了不同初始条件、破口面积及加热功率等对泄压过程瞬态特性的影响。结果表明,本文建立的简单容器模型能模拟从超临界到亚临界压力的喷放泄压过程。计算结果可为超临界水堆的LOCA分析提供理论基础。     

Heat transfer to a supercritical pressure fluid flowing in sub-bundle channels

Supercritical pressure water cooled reactor (SCWR) has been regarded as an innovative nuclear reactor. For the design and development of the SCWR, heat transfer performance under supercritical pressure is one of the most important indicators. In this paper, experimental data are presented on the heat transfer to a supercritical pressure fluid flowing vertically upward and downward in a small diameter heated tube and two sub-bundle channels with three heater rods and seven heater rods, using HCFC22 as the test fluid. Downstream of grid spacer for the sub-bundles, heat transfer enhancement was observed in the upward flow, but not in the downward flow. The enhancement was remarkable especially when the heat transfer deterioration occurs in the fully developed region unaffected by the spacer. The heat transfer correlation for the downstream region of the spacer was developed in the normal heat transfer of sub-bundles. In the fully developed region for the sub-bundle, occurrence of the heat transfer deterioration was suppressed or degree of the deterioration was moderated. At high mass velocity for downward flow in the seven rod sub-bundle, oscillation of heat transfer was observed in the region of the enthalpy over the pseudocritical point.     

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.     

ATHLET-SC程序的开发及适用性分析

由于超临界水堆（SCWR）在系统简化、降低成本和提高热效率上的优势,SCWR的研究在全球范围内得到广泛关注。在众多有关超临界水堆的研发工作中,开发适用于SCWR的系统分析程序是进行SCWR系统设计和安全评估的关键技术难题之一。本工作基于最佳估算系统分析程序ATHLET2.1A,增加了超临界热物性参数,开发出适用于SCWR的系统分析程序ATHLET-SC,将现有的ATHLET程序扩展到超临界压力状态。为评估修改后的程序的适用性,建立了混合能谱超临界水堆堆芯模型,并对该模型进行了功率瞬态计算。此外,对1个简化的超临界水冷却回路进行了稳定性分析。计算结果表明：修改过的ATHLET程序（ATHLET-SC）对SCWR系统的模拟具有良好的适用性。     

Measurement of L X-ray fluorescence cross-sections for elements with 45 ? Z ? 50 using synchrotron radiation at 8 keV

The L shell fluorescence cross-sections of the elements in range 45 ? Z ? 50 have been determined at 8 keV using Synchrotron radiation. The individual L X-ray photons, Ll, Lα, Lβ_I, Lβ_II, Lγ_I and Lγ_II produced in the target were measured with high resolution Si(Li) detector. The experimental set-up provided a low background by using linearly polarized monoenergetic photon beam, improving the signal-to-noise ratio. The experimental cross-sections obtained in this work were compared with available experimental data from Scofield [1] and [2] Krause [3] and [4] and Scofield and Puri et al. [5] and [6].These experimental values closely agree with the theoretical values calculated using Scofield and Krause data, except for the case of Lγ, where values measured of this work are slighter higher.     

Numerical Simulation of Fluid Flow and Heat Transfer of Supercritical Fluids in Fuel Bundles

A supercritical water-cooled reactor (SCWR) was proposed as a kind of generation IV reactor in order to improve the efficiency of nuclear reactors. Although investigations on the thermal-hydraulic behavior in SCWR have attracted much attention, there is still a lack of CFD study on the heat transfer of supercritical water in fuel channels. In order to understand the thermal-hydraulic behavior of supercritical fluids in nuclear reactors, the local fluid flow and heat transfer of supercritical water in a 37-element fuel bundle has been studied numerically in this work. Results show that secondary flow appears and the cladding surface temperature (CST) is very nonuniform in the fuel bundle. The maximum cladding surface temperature (MaxCST), which is an important design parameter for SCWR, can be predicted and analyzed using the CFD method. Due to a very large circumferential temperature gradient in cladding surfaces of the fuel bundle, the precise cladding temperature distributions using the CFD method is highly recommended.     

Measurement of photo-neutron cross-sections in Pb and Bi with 50-70 MeV bremsstrahlung

The photo-neutron cross-sections of ²⁰⁸Pb and ²⁰⁹Bi induced by 50-70 MeV bremsstrahlung have been measured by using the off-line γ-ray spectrometric technique in the electron linac at the Pohang Accelerator Laboratory. The experimental ²⁰⁸Pb(γ,xn) and the ²⁰⁹Bi(γ,xn) reactions cross-sections at the bremsstrahlung energy region of 50-70 MeV, which are determined for the first time, are in general good agreement with the theoretical values based on the TALYS 1.0 code. We observed that the photo-neutron cross-sections for the (γ,xn) reactions of ²⁰⁹Bi and ²⁰⁸Pb increase with increasing of bremsstrahlung energy from 50 to 70 MeV, which indicates the role of excitation energy. It was also observed that the (γ,xn) reaction cross-sections of the doubly magic shell nuclei ₈₂Pb¹²⁶ are always higher than those of the singly magic shell nuclei ₈₃Bi¹²⁶ in the bremsstrahlung energy of 50-70 MeV. This may be due to the fact that either the shell effect are washed out at the higher excitation energy or due to the lower fission cross-section of ²⁰⁸Pb compared to that of ²⁰⁹Bi. This observation indicates that there is a competition reaction between fission and neutron emission.     

Surface desorption and bulk diffusion models of tritium release from Li2TiO3 and Li2ZrO3 pebbles

The release of tritium from Li₂TiO₃ and Li₂ZrO₃ pebbles, in batch experiments, is studied by means of temperature programmed desorption. Data reduction focuses on the analysis of the non-oxidized and oxidized tritium components in terms of release limited by diffusion from the bulk of ceramic grains, or by first or second order surface desorption. By analytical and numerical methods the in-furnace tritium release is deconvoluted from the ionization chamber transfer functions, for which a semi-empirical form is established. The release from Li₂TiO₃ follows second order desorption kinetics, requiring a temperature for a residence time of 1 day (T_1dRes) of 620 K, and 603 K, of the non-oxidized, and the oxidized components, respectively. The release from Li₂ZrO₃ appears as limited by either diffusion from the bulk of the ceramic grains, or by first order surface desorption, the first possibility being the more probable. The respective values of T_1dRes for the non-oxidized component are 661 K, according to the first order surface desorption model, and 735 K within the bulk diffusion limited model.     

超临界水冷堆双排燃料组件子通道分析

研究基于Cobra-IV程序,开发了适用于超临界水冷堆燃料组件分析的子通道程序.针对超临界水冷堆慢谱双排组件,进行了稳态计算,获取了相关组件热工水力参数.在此基础上,针对单一通道进行了瞬态计算,分析了燃料棒线功率变化和冷却剂流量变化条件下,超临界水冷堆燃料组件的流动和传热的动态响应,为超临界水冷堆组件的优化设计提供了参考.     

竖直圆管通道内超临界水传热实验及数值模拟研究

为了对超临界水冷堆概念设计参数范围内超临界水的传热特性有进一步的了解,通过实验和数值模拟的方法对竖直上升圆管通道内超临界水的传热特性开展了研究,用实验数据对现有传热关系式和CFD计算模型进行了评估。通过实验数据与现有经验关系式的对比,发现现有大多数超临界传热关系式能够对本实验的壁温进行预测。使用实验数据对CFD模型进行了评估,结果表明在本实验参数条件下SST模型和RNG k-ε 模型的计算壁温与实验数据趋势基本一致。     

CFD analysis of thermal-hydraulic behavior in SCWR typical flow channels

Investigations on thermal-hydraulic behavior in SCWR fuel assembly have obtained a significant attention in the international SCWR community. However, there is still a lack of understanding and ability to predict the heat transfer behavior of supercritical water. In this paper, CFD analysis is carried out to study the flow and heat transfer behavior of supercritical water in sub-channels of both square and triangular rod bundles. Effect of various parameters, e.g. thermal boundary conditions and pitch-to-diameter ratio on the thermal-hydraulic behavior is investigated. Two boundary conditions, i.e., constant heat flux at the outer surface of cladding and constant heat density in the fuel pin are applied. The results show that the structure of the secondary flow mainly depends on the rod bundle configuration as well as the pitch-to-diameter ratio, whereas, the amplitude of the secondary flow is affected by the thermal boundary conditions, as well. The secondary flow is much stronger in a square lattice than that in a triangular lattice. The turbulence behavior is similar in both square and triangular lattices. The dependence of the amplitude of the turbulent velocity fluctuation across the gap on Reynolds number becomes prominent in both lattices as the pitch-to-diameter ratio increases. The effect of thermal boundary conditions on turbulent velocity fluctuation is negligibly small. For both lattices with small pitch-to-diameter ratios (P/D < 1.3), the mixing coefficient is about 0.022. Both secondary flow and turbulent mixing show unusual behavior in the vicinity of the pseudo-critical point. Further investigation is needed. A strong circumferential non-uniformity of wall temperature and heat transfer is observed in tight lattices at constant heat flux boundary conditions, especially in square lattices. In the case with constant heat density of fuel pin, the circumferential conductive heat transfer significantly reduces the non-uniformity of circumferential distribution of wall temperature and heat transfer, which is favorable for the design of SCWR fuel assemblies.     

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.     

Effect of corrosion potential on the corrosion fatigue crack growth behaviour of low-alloy steels in high-temperature water

The low-frequency corrosion fatigue (CF) crack growth behaviour of different low-alloy reactor pressure vessel steels was characterized under simulated boiling water reactor conditions by cyclic fatigue tests with pre-cracked fracture mechanics specimens. The experiments were performed in the temperature range of 240-288 °C with different loading parameters at different electrochemical corrosion potentials (ECPs). Modern high-temperature water loops, on-line crack growth monitoring (DCPD) and fractographical analysis by SEM were used to quantify the cracking response. In this paper the effect of ECP on the CF crack growth behaviour is discussed and compared with the crack growth model of General Electric (GE). The ECP mainly affected the transition from fast (‘high-sulphur’) to slow (‘low-sulphur’) CF crack growth, which appeared as critical frequencies ν_crit = f(ΔK, R, ECP) and ΔK-thresholds ΔK_EAC = f(ν, R, ECP) in the cycle-based form and as a critical air fatigue crack growth rate da/dt_Air,crit in the time-domain form. The critical crack growth rates, frequencies, and ΔK_EAC-thresholds were shifted to lower values with increasing ECP. The CF crack growth rates of all materials were conservatively covered by the ‘high-sulphur’ CF line of the GE-model for all investigated temperatures and frequencies. Under most system conditions, the model seems to reasonably well predict the experimentally observed parameter trends. Only under highly oxidizing conditions (ECP ? 0 mV_SHE) and slow strain rates/low loading frequencies the GE-model does not conservatively cover the experimentally gathered crack growth rate data. Based on the GE-model and the observed cracking behaviour a simple time-domain superposition-model could be used to develop improved reference CF crack growth curves for codes.     

Measurement of thermal neutron cross-section and resonance integral for the Ho(n,γ)Ho reaction using electron linac-based neutron source

The thermal neutron cross-section and the resonance integral of the ¹⁶⁵Ho(n,γ)^166gHo reaction have been measured by the activation method using a ¹⁹⁷Au(n,γ)¹⁹⁸Au monitor reaction as a single comparator. The high-purity natural Ho and Au foils with and without a cadmium shield case of 0.5 mm thickness were irradiated in a neutron field of the Pohang neutron facility. The induced activities in the activated foils were measured with a calibrated p-type high-purity Ge detector. The correction factors for the γ-ray attenuation (F_g), the thermal neutron self-shielding (G_th), the resonance neutron self-shielding (G_epi) effects, and the epithermal neutron spectrum shape factor (α) were taken into account. The thermal neutron cross-section for the ¹⁶⁵Ho(n,γ)^166gHo reaction has been determined to be 59.7 ± 2.5 barn, relative to the reference value of 98.65 ± 0.09 barn for the ¹⁹⁷Au(n,γ)¹⁹⁸Au reaction. By assuming the cadmium cut-off energy of 0.55 eV, the resonance integral for the ¹⁶⁵Ho(n,γ)^166gHo reaction is 671 ± 47 barn, which is determined relative to the reference value of 1550 ± 28 barn for the ¹⁹⁷Au(n,γ)¹⁹⁸Au reaction. The present results are, in general, good agreement with most of the previously reported data within uncertainty limits.     

Sensitivity analysis of numerically determined linear stability boundaries of a supercritical heated channel

The large change in density which occurs when supercritical water is heated above or near to the pseudocritical temperature in a vertical channel can result in the onset of flow instabilities (density wave oscillations). Near to the critical point, substance properties such as enthalpy, density, viscosity, etc. all have larger relative uncertainties compared to subcritical conditions. The goal of this study is to quantify the effect of these property uncertainties and system uncertainties on numerically determined stability boundaries. These boundaries were determined through an eigenvalue analysis of the linearised set of equations. The sensitivity analysis is performed in a forward way. The results show that the impact of the density and viscosity tolerance individually as well as that of the uncertainty of the imposed pressure drop are negligible. The tolerance on the derivative of the density with regard to the enthalpy propagates only noticeably at low N_SUB numbers (T_in > 370 °C). The friction factor and the heat flux distribution uncertainties have a comparable effect, being more pronounced near the bend in the stability curve. The most significant uncertainty was found to be that of the geometry, even a ±25 μm uncertainty on length scales results in a large uncertainty. The results also showed that the stability boundary is linked to the friction distribution rather than its average value, and that different correlations result in strong changes of the predicted boundary. This emphasizes the need for an accurate friction correlation for supercritical fluids. These findings are important to assess the design of experimental facilities which use scaling fluids.