Critical heat flux prediction in rod bundles under upward low mass flux densities

The analysis of experimental data and results of calculations for heat transfer crisis in heated channels under low upward coolant mass flux densities is presented. This analysis allows the determination of the basic features of the boiling crisis phenomenon. It is shown that the methods currently used for critical heat flux (CHF) prediction have insufficient accuracy in the given range of parameters. A new relationship for the CHF calculation is presented. It should be used for the water–water energy reactor (WWER) and uran–graphite channel reactor—Chernobyl-type (RBMK) rod bundles, and is verified by the test data. The comparison of results obtained by a new CHF correlation and the relationship used in RELAP5/MOD3.1 Code is presented. It is shown that the latter overpredicts the CHF values at atmospheric pressure and for x_cr>0.4 and does not provide conservative estimations for the RBMK fuel bundles.     

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。     

棒束通道内过冷沸腾起始点的实验研究

本文以去离子水为实验介质,在进口温度80～100 ℃、质量流速0～100 kg/(m²•s)、热流密度0～80 kW/m²的条件下对棒束通道内的过冷沸腾起始点（ONB）进行了实验研究。分析了部分热工参数和棒束特殊的几何结构对ONB的影响,通过引入雷诺数,对棒束通道内ONB的数据进行非线性回归分析,得到适用于棒束通道ONB的经验关系式。结果表明：新拟合得到的关系式能较准确地预测棒束通道内ONB的热流密度,其预测值的相对误差为14.75%。     

Prediction of Transient Boiling Transition in BWR Fuel Rod Bundles by Subchannel Analysis Program MENUETT

Transient CHF (critical heat flux) tests of a 4 X 4 rod bundle were analyzed by the subchannel analysis program MENUETT. MENUETT is based on a non-equilibrium, five equation, two-phase flow model and is available both for steady state and transient analyses. Turbulent mixing and void drift effects are taken into account to calculate cross flows in fuel rod bundles. The tendency of calculated subchannel mass fluxes and qualities agreed with experimental data. By using a critical quality correlation obtained from steady state CHF data, the position of the earliest boiling transition could be predicted regardless of non-uniform axial heat flux distributions. This transition occurrence time was predicted within a difference of 0.1～0.3 s from the experimental time. MENUETT applicability was confirmed for transient calculations predicting thermalhydraulic behavior in bundles.     

2×2稠密棒束内超临界水的传热特性试验研究

在压力p=23～28 MPa、质量流速G=350～1 000 kg/(m²•s)、热流密度q=200～1000 kW/m²的试验参数范围内,对2×2棒束内超临界水的传热特性进行了试验研究。试验得到了加热管周向壁温分布规律,并就出现周向温度差异的原因进行了分析。此外,给出了压力、质量流速及热流密度等系统参数对平均传热特性的影响,分析了低质量流速下出现的传热恶化现象。试验结果表明：加热管周向壁温并不均匀,边角子通道壁温最高,中心子通道壁温最低,周向壁温的高低与横截面流通面积的不均匀性紧密相关。随着热流密度的提高或质量流速的降低,超临界水的传热受到抑制,当q/G增大到一定程度时,棒束内发生传热恶化。     

Development of a bundle correction method and its application to predicting CHF in rod bundles

A bundle correction method, based on the conservation laws of mass, energy, and momentum in an open subchannel, is proposed for the prediction of the critical heat flux (CHF) in rod bundles from round tube CHF correlations without detailed subchannel analysis. It takes into account the effects of the enthalpy and mass velocity distributions at subchannel level using the first derivatives of CHF with respect to the independent parameters. Three different CHF correlations for tubes (Groeneveld's CHF table, Katto correlation, and Biasi correlation) have been examined with uniformly heated bundle CHF data collected from various sources. A limited number of CHF data from a non-uniformly heated rod bundle are also evaluated with the aid of Tong's F-factor. The proposed method shows satisfactory CHF predictions for rod bundles both uniform and non-uniform power distributions.     

含弯曲棒的全长燃料棒束沸腾传热CFD计算分析

采用计算流体动力学（CFD）分析方法模拟了含一根弯曲燃料棒（简称“弯曲棒”）的5×5全长燃料棒束内的沸腾传热现象。基于欧拉两流体模型和改进的壁面沸腾模型进行计算,并基于压水堆子通道和棒束实验( PSBT )基准题中的试验数据对计算方法进行了验证,计算所得截面平均空泡份额与试验数据吻合良好,说明了现有计算方法的可靠性。基于计算结果考察了弯曲棒对棒束通道内流场、温度场、空泡份额等关键参数的影响。研究结果表明,弯曲棒的存在对截面横向流动、流体温度、空泡份额等均未产生显著影响,但弯曲棒表面温度增加,气泡也易发生聚集,增加了发生临界热流密度（CHF）的风险。      

Stage Efficiency for Mixer-Settlers Process with Chemical Reactions

The importance of heat transfer in a narrow gap has been pointed out in relation to the in-vessel retention of molten core under a severe accident condition of a light water reactor. In this study, heat transfer experiment has been carried out using internally heated annuli with a narrow gap and closed bottom. Effects of gap clearances (1.0, 2.0, 4.0 mm) on the cooling process were examined. The inner wall initially heated up to 800°C was cooled down by water supplied to the upper plenum, the transient rod temperature being measured. From the temperature history, transient boiling curves were obtained, which were compared with predictions by existing heat transfer correlations for nucleate boiling critical heat flux (CHF) and film boiling. In narrow gap channels water penetration to the gap was restricted by counter flowing vapor, which lead to a decrease of heat transfer coefficients.     

Laminar free convection in open-ended vertical 7-rod bundles: experiments and porous model

The flow of ambient air induced solely by buoyancy, through a vertical rod bundle has been modelled as a phenomenon in a porous medium. The rods are at uniform heat flux condition and the circular shell adiabatic. The induced flow rate was found to be controlled by a parameter ψ dependent on the heat flux, rod diameter, length, fluid properties and the bundle permeability. Measurements performed on two 7-rod bundles corroborate the theoretical predictions. Longitudinally averaged heat transfer rates from the central and peripheral rods have also been measured and average information generated for the bundle.     

CFD modelling of subcooled boiling—Concept, validation and application to fuel assembly design

The paper describes actual Computational Fluid Dynamics (CFD) approaches to subcooled boiling and investigates their capability to contribute to fuel assembly design. In a prototype version of the CFD code CFX a wall-boiling model is implemented based on a wall heat flux partition algorithm. It can be shown, that the wall boiling model is able to calculate the cross sectional averaged vapour volume fraction of vertical heated tubes tests with good agreement to published experimental data. The most sensitive parameters of the model are identified. Needs for more detailed experiments are established which are necessary to support further model development. The model is applied for investigation of the phenomena inside a hot channel of a fuel assembly. Here the essential phenomenon is the critical heat flux. Although subcooled boiling represents only a preliminary state towards the critical heat flux occurrence, essential parameters like swirl, cross flow between adjacent channels and concentration regions of bubbles can be determined. By calculating the temperature of the rod surface the critical regions can be identified which may later on lead to departure from nucleate boiling and possible damage of the fuel pin. The application of up-to-date CFD with a subcooled boiling model for the simulation of a hot channel enables the comparison and the evaluation of different geometrical designs of the spacer grids of a fuel rod bundle.     

Single-phase CFD applicability for estimating fluid hot-spot locations in a 5 × 5 fuel rod bundle

High-thermal performance PWR spacer grids require both of low pressure loss and high critical heat flux (CHF) properties. Therefore, a numerical study using computational fluid dynamics (CFD) was carried out to estimate pressure loss in strap and mixing vane structures. Moreover, a CFD simulation under single-phase flow condition was conducted for one specific condition in a water departure from nucleate boiling (DNB) test to examine the applicability of the CFD model for predicting the CHF rod position. Energy flux around the rod surface in a water DNB test is the sum of the intrinsic energy flux from a rod and the extrinsic energy flux from other rods, and increments of the enthalpy and decrements of flow velocity near the rod surface are assumed to affect CHF performance. CFD makes it possible to model the complicated flow field consisting of a spacer grid and a rod bundle and evaluate the local velocity and enthalpy distribution around the rod surface, which are assumed to determine the initial conditions for the two-phase structure. The results of this study indicate that single-phase CFD can play a significant role in designing PWR spacer grids for improved CHF performance.     

压水堆棒束定位格架两相搅混特性数值研究

本文提出一种CFD方法用于评价压水堆燃料棒束定位格架两相搅混特性。针对两种典型的定位格架,采用CFX12.0进行了空气-水两相流动的数值模拟,并与采用氟里昂工质开展的临界热流密度（CHF）实验进行对比。结果表明,CFD方法可初步应用于评价格架下游汽泡的分布特性。     

Analysis of radiant heat transfer in a BWR fuel assembly

A computer code ‘CIDER’ was developed which analyzes radiant heat transfer in a BWR fuel rod bundle under loss of coolant conditions. In the code, (1) a channel box and fuel rods are considered to be gray bodies, (2) reflection and absorption of radiation beams in the atmosphere is neglected, (3) a fuel rod is approximated by a regular polygonal rod, and (4) radiant heat flux is calculated considering circumferential temperature distribution on each fuel rod surface, which is determined from radial and circumferential heat conduction calculations in a fuel rod. It was found that the conventional model with uniform cladding temperature overestimated heat flux about 30% in a typical situation, or correspondingly underestimated the temperature rises.     

3×3棒束通道内蒸汽对流换热特性数值分析

采用计算流体力学(CFD)方法,建立3×3棒束模拟体的数值模型,进行蒸汽冷却条件下的对流传热特性分析。结果表明:棒束通道内周向的壁面热流密度不均匀性明显,体现出流固耦合方法相比于均匀热流方法对传热细节模拟的优越性。蒸汽速度场、温度场、热流密度、换热系数等热工参数分布规律受入口效应、壁面效应、热源分布、物性参数等因素影响。压力的升高及氢气的加入均能提升通道内的换热性能。加热段换热系数沿程变化趋势与文献[13]中Deissier的趋势一致,CFD的换热系数结果与WCOBRA/TRAC程序中的关系式吻合较好。本文模拟方法可行,其结果可为后续的实验模拟体设计提供技术支持。     

An experimental study on the critical heat flux for low flow of water in a non-uniformly heated vertical rod bundle over a wide range of pressure conditions

An experimental study of the critical heat flux (CHF) has been performed for a water flow in a non-uniformly heated vertical 3 × 3 rod bundle under low flow and a wide range of pressure conditions. The experiment was especially focused on the parametric trends of the CHF and the applicability of the conventional CHF correlations to a return-to-power conditions of a main steam line break accident whose conditions might be a low mass flux, intermediate pressure, and a high inlet subcooling. The effects of the mass flux and pressure on the CHF are relatively large and complicated in the low pressure conditions. At a high mass flux or a low critical quality, the local heat flux at the CHF location sharply decreases with an increasing local critical quality. However, at a low mass flux or a high critical quality, the local heat flux at the CHF location shows a nearly constant value regardless of the increase of the critical quality. The CHF data at the very low mass flux conditions are correlated well by the churn-to-annular flow transition criterion or the flow reversal phenomena. Several conventional CHF correlations predict the present return-to-power CHF data with reasonable accuracies. However, the prediction capabilities become worse in a very low mass flux of below about 100 kg/(m² s).     

5×5棒束通道中简单支撑格架对流动过冷沸腾传热的影响分析

采用壁面热分配模型(即RPI模型)对PSBT基准题中的5×5均匀加热全长棒束过冷沸腾传热进行了数值模拟研究。重点分析了加热段末端搅混格架（MVG）下游简单支撑格架（SSG）对棒束通道内流动过冷沸腾传热特性的影响。在水力特性方面,研究发现SSG的形阻压降约为MVG的53%,且对棒束通道内的横向流动具有显著抑制作用。为反映SSG对搅混过程的影响,采用子通道平均横流速度比沿轴向的发展过程对其进行了分析。分析发现,在SSG附近横流速度比迅速衰减,衰减后的横流速度比与光棒束时的大小相当。由于SSG对横流过程的破坏,改变了发热表面的传热特性,在其下游气相迅速包覆加热表面,蒸发热流密度较无SSG情况偏高5%,加热段末端空泡份额偏高0.006,壁面过热度偏高0.3 ℃。     

带绕丝2×2棒束超临界水传热实验研究

针对两流程带绕丝定位的2×2棒束实验本体,开展了超临界水的流动传热实验研究。实验结果表明,在带绕丝的2×2棒束中,同一横截面上存在显著的周向温度不均匀现象。在较小的G/q工况下出现传热恶化现象,且存在二次恶化现象。由于绕丝的搅混作用,流道下游的传热恶化得到抑制。实验表明,棒束传热规律与单管类似,对比结果指出Bishop等（1964）的计算公式能较好地预测实验结果。同时与不带格架的2×2棒束相比,绕丝具有强化传热的作用。     

Assessment of a DNB-type theoretical critical heat flux model for rod bundles with non-uniform axial power shapes

A general critical heat flux (CHF) prediction method with a wide applicable range and reasonable accuracy is essential to the thermal-hydraulic design and safety analysis at the conceptual design stage for a new pressurized water reactor (PWR). In this study, the Korea Advanced Institute of Science and Technology (KAIST) liquid sub-layer dryout CHF prediction model for Departure from Nucleate Boiling (DNB) region has been implemented in a sub-channel analysis code, and investigated for the method's possible use in a rod bundle environment with various non-uniform axial power shapes. The KAIST model showed comparable prediction capability to Lin's method for bottom-, center-, and top-peaked heat flux shapes. The KAIST model, without any correction factors or empirical constants, turned out to be suitable to fulfill the needs for a basis of a general CHF prediction method as compared to Lin's method and Westinghouse-3 (W-3) correlation.     

Effective thermal conductivity of a heat generating rod bundle dissipating heat by natural convection and radiation

A numerical study of conjugate natural convection and surface radiation in a horizontal hexagonal sheath housing 19 solid heat generating rods with cladding and argon as the fill gas, is performed. The natural convection in the sheath is driven by the volumetric heat generation in the solid rods. The problem is solved using the FLUENT CFD code. A correlation is obtained to predict the maximum temperature in the rod bundle for different pitch-to-diameter ratios and heat generating rates. The effective thermal conductivity is related to the heat generation rate, maximum temperature and the sheath temperature. Results are presented for the dimensionless maximum temperature, Rayleigh number and the contribution of radiation with changing emissivity, total wattage and the pitch-to-diameter ratio. In the simulation of a larger system that contains a rod bundle, the effective thermal conductivity facilitates simplified modelling of the rod bundle by treating it as a solid of effective thermal conductivity. The parametric studies revealed that the contribution of radiation can be 38–65% of the total heat generation, for the parameter ranges chosen. Data for critical Rayleigh number above which natural convection comes into effect is also presented.     

自然循环系统摇摆条件下棒束通道内传热特性研究

棒束燃料元件子通道间流体存在搅混与横向二次流,流动及阻力特性相较矩形通道、圆管等简单通道更为复杂。核动力舰船、船舶、小型浮动核电站等会受到海浪影响,经常处于倾斜、摇摆、垂荡等瞬变运动下。目前的相关研究多集中在低压工况的研究领域,高温高压自然循环运动条件下的研究较少。本文采用实验研究方法,对自然循环系统摇摆条件下棒束通道内流动传热特性进行了研究,获得了过冷沸腾和饱和沸腾两种条件下摇摆角度和摇摆周期对棒束壁面温度变化和传热系数的影响,并获得了摇摆周期内棒束通道内的传热系数计算关系式。结果表明,饱和沸腾传热系数变化比过冷沸腾的剧烈;在本文实验工况范围内,棒表面传热系数波动幅值随着摇摆幅度的增大而增大;摇摆条件下棒束通道过冷沸腾和饱和沸腾工况时均传热系数基本不变。