An analytical method of evaluating the effect of rod displacement on circumferential temperature and heat flux distributions in turbulent flow through unbaffled rod bundles

An analytical method of evaluating the circumferential variations of temperature and heat flux fields inside and around a displaced fuel rod in triangular rod bundles in turbulent flow is presented with illustrative examples. The analysis consists mainly of the derivation of the simultaneous solutions of a set of heat conduction equations for fuel, cladding and coolant under the assumption of fully developed flow and heat transfer conditions. The local coolant velocity distribution, which is necessary for deriving the temperature field in coolant, is determined by solving the Navier-Stokes equation and the turbulent mixing of coolant is taken into consideration. The results show how the circumferential variations in the temperature and heat flux fields on the outer surface of the cladding increase the lower the ratio and the larger the fuel rod displacement due to thermal conduction and peripheral coolant flow velocity distribution.     

Matrix calculation of radiant heat transfer in LWR fuel bundles under accident conditions

A computer code was developed for calculating the radiant heat transfer in a LWR fuel bundle under accident conditions. The calculation method is a modular one: a fuel bundle or its part is divided into unit cells, each of which is composed of a coolant subchannel surrounded by several segments of solid or imaginary faces. The view factor matrix in each cell is expanded over the whole bundle using the concept of ‘boundary face’ between cells, and the resultant heat transfer equations are simultaneously solved for solid wall temperatures. The geometrical flexibility of this method is suitable for treating various simulation experiments for accidents. The method is also effective for repeated calculations of the radiant heat transfer reflecting state or material property changes when analyzing fuel rod behaviour under accident conditions.     

Measurement of Number Albedo of Backscattered Photons for Tin and Lead

A computer code, which calculates the transients of heat flux from simulated nuclear fuel rods by using the transients of rod surface temperature and the heat conduction equation in the rod, was developed in order to investigate the heat transfer modes throughout the reflood phase in PWR-LOCA experiments. The code was applied to the Slab Core Reflood Tests which are part of the Large Scale Reflood Test Program at the Japan Atomic Energy Research Institute. For defining the heat transfer modes during reflood, it is important to obtain accurate heat flux from rod under a wide rod temperature change ranging higher than 1,300 to 300 K and a rapid rod temperature change due to quench, which are principal features in heat transfer during reflood phase. Therefore, the effects of both temperature dependency on physical properties of rod and the axial heat conduction along rod on the heat flux calculation were first investigated. As the results, it was made clear that the temperature dependency on the physical properties should be taken into account and that the effect of axial heat conduction along the rod was negligible except in a very short length of rod at the quench front. The results calculated by the code for the Slab Core Tests when compared with the existing correlations could define the heat transfer modes clearly all through the reflood phase but the recommendations for further investigations were suggested.     

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。     

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。     

CFD analyses in tight-lattice subchannels and seven-rod bundle geometries of a Super Fast Reactor

This paper presents CFD analyses in heat unsymmetric subchannels and heat symmetric seven-rod bundle geometries of a Super Fast Reactor (Super FR) fuel assembly using STAR-CD. The purpose of CFD analyses in heat unsymmetric subchannels is to evaluate the effect of the power differences on the heat transfer in subchannels of the Super Fast Reactor. For heat symmetric seven-rod bundles, the effects of the gap clearance between the fuel rod and the assembly wall and the displacement of the fuel rod on the circumferential temperature distributions and Maximum Cladding Surface Temperature (MCST) are analyzed. The results show that larger power difference between fuel rods gives larger circumferential temperature difference of the hottest fuel rods. Considering cross flow between edge and ordinary subchannels, 1 mm gap between the fuel rod and the assembly wall is better for small MCST although the circumferential temperature difference in edge subchannel is large. MCST increases exponentially with the displacement. The relative error of displacement should be less than 1% if the allowable increment of MCST due to displacement is less than 6 °C.     

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。     

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.     

FARST — A computer code for the evaluation of FBR fuel rod behavior under steady-state/transient conditions

FARST, a computer code for the evaluation of fuel rod thermal and mechanical behavior under steady-state/transient conditions has been developed. The code characteristics are summarized as follows:

1. (i) FARST evaluates the fuel rod behavior under the transient conditions. The code analyzes thermal and mechanical phenomena within a fuel rod, taking into account the temperature change in coolant surrounding the fuel rod.

2. (ii) Permanent strains such as plastic, creep and swelling strains as well as thermoelastic deformations can be analyzed by using the strain increment method.

3. (iii) Axial force and contact pressure which act on the fuel stack and cladding are analyzed based on the stick/slip conditions.

4. (iv) FARST used a pellet swelling model which depends on the contact pressure between pellet and cladding, and an empirical pellet relocation model, designated as “jump relocation model”.

The code was successfully applied to analyses of the fuel rod irradiation data from pulse reactor for nuclear safety research in Cadarache (CABRI) and pulse reactor for nuclear safety research in Japan Atomic Energy Research Institute (NSRR).The code was further applied to stress analysis of a 1000 MW class large FBR plant fuel rod during transient conditions. The steady-state model which was used so far gave the conservative results for cladding stress during overpower transient, but underestimated the results for cladding stress during a rapid temperature decrease of coolant.     

Analysis on split failure of cladding of high burnup BWR rods in reactivity-initiated accident conditions by RANNS code

A computer code RANNS was developed to analyze fuel rod behaviors in the reactivity-initiated accident (RIA) conditions. RANNS performs thermal and finite-element mechanical calculation for a single rod in axis-symmetric geometry, where fuel pellet consists of 36 equal-volume ring elements and cladding metallic wall consists of eight equal-thickness ring elements and one outer oxide element. The code can calculate temperature profile inside the rod, contact pressure generated by pellet–clad mechanical interaction (PCMI), stress–strain distribution and their interactions elaborately. An experimental analysis by RANNS begins with pre-test conditions of irradiated rod which are given by the fuel performance code FEMAXI-6.In the present study, analysis was performed on the simulated RIA experiments in the “nuclear safety research reactor” (NSRR), FK-10 and FK-12, with high burnup BWR rods in a cold-start up condition, and stress–strain evolution in the PCMI process was calculated extensively. In the analysis, the pellet–clad bonding was assumed both in the heat conduction and in mechanical restraint. The calculated hoop strain increase was compared with the measured strain gauge data, and satisfactory agreement was obtained. Simulation calculations with broader power pulses anticipated in RIA of commercial BWR were carried out and the resulted cladding hoop stress was compared with the failure stress estimated by comparison of analysis with experimental data.     

Analysis of mechanical load on cladding induced by fuel swelling during power ramp in high burn-up rod by fuel performance code FEMAXI-6

Mechanical load on cladding induced by fuel swelling in a high burn-up BWR type rod was analyzed by a fuel performance code FEMAXI-6. The code was developed for the analysis of LWR fuel rod behaviors in normal operation and transient conditions using finite element method (FEM).During a power ramp for the high burn-up rod, instantaneous pellet swelling can significantly exceed the level that is predicted by a “steady-rate” swelling model, causing a large circumferential strain in cladding. This phenomenon was simulated by a new swelling model to take into account the fission gas bubble growth. As a result it was found that the new model can give reasonable predictions on cladding diameter expansion in comparison with PIE data. The bubble growth model assumes that the equilibrium state equation holds for a bubble under external pressure, and simultaneous solution is obtained with both bubble size determination equation and diffusion equation of fission gas atoms. In addition, a pellet-clad bonding model which has been incorporated in the code to assume solid mechanical coupling between pellet outer surface and cladding inner surface predicted the generation of bi-axial stress state in the cladding during ramp.     

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.     

Power up-grading study for the first Egyptian research reactor

In the present work, power up-grading study is performed, for the first Egyptian Research Reactor (ET-RR-1), using the present fuel basket with 4×4 fuel rods, (17.5 mm pitch), and a proposed fuel basket with 5×5 fuel rods, (14.0 mm pitch), without violating the thermal hydraulic safety criteria. These safety criteria are; fuel centerline temperature (fuel melting), clad surface temperature (surface boiling), outlet coolant temperature, and maximum heat flux (critical heat flux ratio). Different thermal reactor powers (2–10 MW) and different core coolant flow rates (450, 900, 1350 m³ h⁻¹) are considered. The thermal hydraulic analysis was performed using the subchannel code COBRA-IIIC for the estimation of temperatures, coolant velocities and critical heat flux. The neutronic calculations were performed using WIMS-D4 code with 5 — group neutron cross section library. These cross sections were adapted to use in the two-dimensional (2-D) diffusion code DIXY for core calculations. The study concluded that ET-RR-1 power can be upgraded safely up to 4 MW with the present 4×4-fuel basket and with the proposed 5×5-fuel basket up to 5 MW with the present coolant flow rate (900 m³ h⁻¹). With the two fuel arrays, the reactor power can be upgraded to 6 MW with coolant flow rate of 1350 m³ h⁻¹ without violating the safety criterion. It is also concluded that, loading the ET-RR-1 core with the proposed fuel basket (5×5) increases the excess reactivity of the reactor core than the present 4×4 fuel matrix with equal U-235 mass load and gave better fuel economy of fuel utilization.     

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。      

燃料棒周向导热对超临界水堆堆芯子通道分析的影响

本文在子通道程序的燃料棒模型中引入三维导热方程,使该模型能用来模拟燃料棒的周向导热情况。采用改造后的子通道程序对混合谱超临界水堆设计中的两种燃料组件结构进行计算分析,研究燃料棒周向导热对超临界水堆燃料组件子通道分析的影响。结果表明：热谱组件的子通道计算中,燃料棒周向导热的影响不能忽略;快谱组件的子通道计算中,燃料棒周向导热的影响基本可忽略。     

An experimental study on rewetting phenomena in transient conditions of bwrs

It is known that rod temperature rise after boiling transition (BT) is not excursive and that the peak cladding temperature (PCT) is suppressed by rewetting to return to nucleate boiling, even if BT occurs under severe conditions exceeding abnormal operational transients for a BWR. The purpose of this study is to develop and verify the rewetting correlation. The rewetting correlation was developed based on single rod data, as a function of quality, mass flux, pressure and heat flux. The transient thermal-hydraulic code used in the BWR design analysis (SCAT) with this rewetting correlation was compared with transient rod temperature result after the occurence of BT obtianed by the 8×8 and 4×4 rod bundle. It is concluded that the transient code with the developed rewetting correlation predicts the PCT conservatively, and the rewetting time well.     

Validation of the nuclear design code system for the HTTR using the criticality assembly VHTRC

The high temperature engineering test reactor is the first block-type HTGR designed for a 950 °C outlet gas temperature which uses low-enriched uranium fuel with burnable poison rod. For validation of the nuclear design code system for the HTTR, a critical assembly of VHTRC had been constructed. The calculation uncertainties of effective multiplication factor, neutron flux distribution, burnable poison reactivity worth, and control rod worth, temperature coefficients were evaluated. Calculation accuracy of a Monte Carlo code is also evaluated.     

Heat transfer to liquid metals flowing turbulently and longitudinally through closely spaced rod bundles : Part I

This paper presents results of a theoretical study of heat transfer to liquid metals in fully developed turbulent, in-line flow through unbaffled, spacer-free rod bundles. The bundles have equilateral triangular arrangement; and the rod spacings, rod design, and ranges of independent variables covered were chosen with reference to liquid-metal-cooled nuclear reactor applications. Three different sets of thermal boundary conditions are considered: (A) uniform heat flux in the axial direction with uniform temperature in the circumferential direction, on the outer surface of the cladding; (B) uniform heat flux in both directions, on the outer surface of the cladding; and (C) uniform heat flux in both directions on the inner surface of the cladding. The results of the third set are presented in Part II.     

Heat transfer in turbulent longitudinal flow through unbaffled assemblies of fuel rods

A numerical analysis of heat transfer in turbulent longitudinal flow through assemblies of unbaffled fuel rods is presented. The solution applies to triangular or rectangular arrays of fuel rods with fully developed velocity and temperature profiles, for fluids with Prandtl number 1 and « 1. In the case of liquid metals, the thermal resistance of the cladding and bond are considered, but the turbulent heat transport component is neglected. For common liquids the circumferential turbulent heat transfer is considered. Results are compared in the range of dimensionless rod spacing of 1.0–1.6. Theoretical predictions and experimental results of other authors dealing with the problem show relatively good agreement.     

Modification of thermal hydraulic code,THEATRe, with fuel rod behavior models and its application to reactivity-initiated accident (RIA)

During reactor operation, many complex changes occur in fuel rod which affects its thermal, mechanical and material properties. These changes also affect the reactor response to the transient and accident situations. Realistic simulation of fuel rod behavior under transients such as reactivity-initiated accident (RIA) is of great significance. In this study, thermal hydraulic analysis code THEATRe (Thermal Hydraulic Engineering Analysis Tool in Real-time) has been modified by addition of fuel rod behavior models for dynamic simulation of nuclear reactor. Transient changes in gas-gap parameters were taken into account by modeling the gas-gap behavior. Thermo-mechanical behavior of fuel rod is modeled to take into account the thermal, elastic and plastic deformation. To simulate RIA, point reactor kinetics model is also incorporated in the THEATRe code. To demonstrate the transient fuel rod behavior, AP1000 reactor is modeled and three hypothetical RIA cases are simulated. The RIA is considered at three different reactor power levels, i.e. 100, 50 and 1% of nominal power. The investigated parameters are fuel temperature, cladding stress and strain, fuel and cladding thermal conductivity and heat transfer coefficient in gas-gap. Modified code calculates the fuel rod temperatures according to updated fuel, clad and gas-gap parameters at the onset of steady-state operation and during the transient. The modified code provides lower steady-state fuel temperature as compared to the original code. Stress and strain analyses indicate that the hoop and radial strain is higher at high power locations of the fuel rod; therefore, gap closure process will initially occur in the central portion of the fuel rod and it should be given more emphasis in the safety analysis of the fuel rod and nuclear reactor during accidents and transients.