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.     

Single-phase convective heat transfer in rod bundles

The convective heat transfer for turbulent flow through rod bundles representative of nuclear fuel rods used in pressurized water reactors is examined. The rod bundles consist of a square array of parallel rods that are held on a constant pitch by support grids spaced axially along the rod bundle. Split-vane pair support grids, which create swirling flow in the rod bundle, as well as disc and standard support grids are investigated. Single-phase convective heat transfer coefficients are measured for flow downstream of support grids in a rod bundle. The rods are heated using direct resistance heating, and a bulk axial flow of air is used to cool the rods in the rod bundle. Air is used as the working fluid instead of water to reduce the power required to heat the rod bundle. Results indicate heat transfer enhancement for up to 10 hydraulic diameters downstream of the support grids. A general correlation is developed to predict the heat transfer development downstream of support grids. In addition, circumferential variations in heat transfer coefficients result in hot streaks that develop on the rods downstream of split-vane pair support grids.     

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.     

压力管式超临界水堆极限事故下“无堆芯熔化”概念评估

在自主研发的事故分析程序SCTRAN的基础上,开发并验证了二维导热模型和辐射换热模型,并将改进后的SCTRAN应用于加拿大压力管式超临界水堆在失水事故（LOCA）叠加丧失紧急堆芯冷却系统（LOECC）事故中的堆芯安全评估,并对燃料棒到慢化剂之间的传热效率以及关键的影响因素进行了评估。计算结果表明,在LOCA叠加LOECC工况下,燃料棒到燃料通道的辐射换热和燃料棒到蒸汽的自然对流换热能够有效导出反应堆的衰变余热,最高功率的燃料组件内、外圈燃料棒的最高包壳温度分别为1278℃和1192℃,均低于不锈钢包壳的熔化温度,因此整个事故过程中不会发生堆芯熔化。      

Transient Thermal Characteristics of UO2 Fuel Rods

Transient characteristics of average temperature and heat flux of UO² fuel rods have been obtained with account taken of the effect of temperature dependence of thermal properties. The first order deviation of the temperature distribution inside the fuel rod is solved by modal expansion, and the coefficients and time constants obtained for the transfer functions. The results have been compared with those by the conventional method: the differences found as a result in the transfer functions for typical fuel rods are within 1 dB in gain and 5 degrees in phase when the volume-averaged fuel temperature is used in the conventional method.     

Heat transfer from a partially uncovered reactor core

This paper documents a model which has been developed for predicting the temperature distribution along a “flow channel” of a pressurized water reactor during simulated, uncovered core conditions. In the model, heat conduction along the fuel element, convection from the surface to the coolant, radiation exchange between the clad surface and steam, and surface exchange between adjacent fuel rods are considered. Variations of the thermophysical properties of the fuel road and of the coolant with temperature are accounted for, but oxidation of Zircaloy is not modeled. Extensive sensitivity studies on the effects of heat generation in the core, steam velocity, pressure level, uncovered core height, presence of hydrogen gas in the coolant, power skew, clad emissivity, and convective heat transfer correlations have been examined. The results show that the importance of radiation in comparison with convection increases with an increase in the fuel rod temperature, pressure, and clad emissivity.     

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.     

Effects gap heat transfer on LWR fuel behavior during an RIA transient: In-pile experimental results with helium and xenon fillet rods

Gap heat transfer characteristics and their effects on LWR fuel behavior during an RIA have been studied through the in-pile experiment with UO₂ pellet fuel rods. The report describes the experimental results obtained in the NSRR tests in which PWR type test fuel rods of helium and xenon filled as the gap gas have been irradiated in the pulse reactor, NSRR, to simulate the prompt heat up of RIAs. The relation between the cladding temperature history and the gap heat transfer conditions, and the effects of gap gas composition on fuel behavior and on the fuel failure threshold are discussed based on the in-pile experimental data.     

Characterization of heat transfer and temperature distributions in an electrically heated model of an LMFBR blanket assembly

This paper describes results of an experimental program to reduce uncertainties associated with the thermal-hydraulic design and analysis of LMFBR blanket assemblies. These assemblies differ significantly from fuel assemblies in design detail and operating conditions. In blanket assemblies, heat transfer occurs over a wide range of complex operating conditions. The range and complexity of conditions are the result of flux and power gradients which are an inherent feature of the blanket region and the power generation level in an assembly which can vary from 20 kW to 2 MW. To provide effective cooling of all assemblies and economical operation, coolant is metered to groups of assemblies in proportion to their ultimate power level. As a result, the assembly flow can be in the laminar, transition or turbulent range. Because of the wide range of heat generation rates and the range of coolant flow velocities, heat transfer from rods to coolant may take place in the forced, natural or mixed convection mode. Under low flow conditions, buoyancy affects the flow pattern in the bundle, and thus, alters the temperature distribution. The complexities are further compounded since, in addition to temperature gradients within an assembly, there are also significant temperature differences between adjacent assemblies. This results in heat transfer by conduction between adjacent assemblies, which tends to further distort flow and temperature patterns.Since these effects cannot be accurately predicted analytically, full-size radial blanket assembly heat transfer tests are being conducted using electrically heated fuel rod simulators in flowing sodium. A 61-rod electrically heated radial blanket assembly mockup of prototypic dimensions was designed, constructed and installed in a 200 gpm (45 m³/hr) sodium test loop.Heat transfer tests are being conducted over a wide range of power and sodium flow rates with this full-scale, vertical, electrical-resistance-heated rod bundle. The rod bundle is extensively instrumented by thermocouples located at six distinct elevations in the wire wrap and inside the heater cladding. Tests were conducted covering the flow range from fully turbulent to fully laminar with approximately constant power-to-flow ratio. The power input patterns included across bundle gradients of 2.8 to 1 and 2.0 to 1 maximum to minimum, uniform power input to all rods and a dished distribution with low power in the central row and high power in the two rows of rods adjacent to the duct walls.The test program provided experimentally measured axial and transverse temperature profiles for the test model over a range of anticipated plant operating conditions. The data were used to (a) determine the effect of Reynolds Number, power gradients and power-to-flow ratio on transverse and axial temperature profiles and particularly on peak and peripheral channel temperatures; (b) determine the effect of inter-assembly heat transfer on peak temperatures and temperature distributions; and (c) determine the effect of buoyancy on temperature profiles.     

Investigation on heavy liquid metal cooling of ADS fuel pin assemblies

In the framework of accelerator driven sub-critical reactor systems heavy liquid metals are considered as coolant for the reactor core and the spallation target. In particular lead or lead bismuth eutectic (LBE) exhibit efficient heat removal properties and high production rate of neutrons.However, the excellent heat conductivity of LBE-flows expressed by a low molecular Prandtl number of the order 10⁻² requires improved modeling of the turbulent heat transfer. Although various models for thermal hydraulics of LBE flows are existing, validated heat transfer correlations for ADS-relevant conditions are still missing. In order to validate the sub-channel codes and computational fluid dynamics codes used to design fuel assemblies, the comparison with experimental data is inevitable.Therefore, an experimental program composed of three major experiments, a single electrically heated rod, a 19-pin hexagonal water rod bundle and a LBE rod bundle, has been initiated at the Karlsruhe Liquid metal Laboratory (KALLA) of the Karlsruhe Institute of Technology, in order to quantify and separate the individual phenomena occurring in the momentum and energy transfer of a fuel assembly.     

Numerical investigation of supercritical water-cooled nuclear reactor in horizontal rod bundles

The commercial CFD code STAR-CD v4.02 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 rods and rod bundles. Reactors with vertical or horizontal flow in the core can be found. In vertically oriented core, symmetric characters of flow and heat transfer can be found and two-dimensional analyses are often performed. However, in horizontally oriented core the flow and heat transfer are fully three-dimensional due to the buoyancy effect. In this paper, horizontal rods and rod 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. In the rod bundle simulations, it is found that the geometry and orientation of the rod bundle have strong effects on the wall temperature distributions and heat transfers. In one orientation the square bundle has a higher wall temperature difference than other bundles. However, when the bundles are rotated by 90° the highest wall temperature difference is found in the hexagon bundle. Similar analysis could be useful in design and safety studies to obtain optimum fuel rod arrangement in a SCWR.     

Core performance of new concept passive-safety reactor “kamado” - safety, burn-up and uranium resource problem -

New concept of a passive-safety reactor “KAMADO” has a negligible possibility of core melting and flexibility of total reactor power. The reactor core of KAMADO consists of fuel elements of graphite blocks, which have UO₂ fuel rods and cooling water holes. These fuel elements are located in a reactor water pool of atmospheric pressure (1 atm) and low temperature (< 60°C). In case of LOCA, decay heat from fuel rods is removed by conduction heat transfer to the reactor water pool. Since the cooling water does not contact a fuel rod directly, core design has much flexibility without considering dry-out limitation and Minimum Critical Power Ratio (MCPR). Additionally an effective use of spent fuel is expected.     

Turbulent flow simulation in a wire-wrap rod bundle of an LMFBR

The pressure drop and heat transfer characteristics of wire-wrapped 19-pin rod bundles in a nuclear reactor subassembly of liquid metal cooled fast breeder reactor (LMFBR) have been investigated through three-dimensional turbulent flow simulations. The predicted results of eddy viscosity based turbulence models (k-?, k-ω) and the Reynolds stress model are compared with those of experimental correlations for friction factor and Nusselt number. The Re is varied between 50,000 and 150,000 and the ratio of helical pitch of wire wrap to the rod diameter is varied from 15 to 45. All the three turbulence models considered yield similar results. The friction factor increases with reduction in the wire-wrap pitch while the heat transfer coefficient remains almost unaltered. However, reduction in the wire-wrap pitch also enhances the transverse flow velocity in the cross-sectional plane as well as the local turbulence intensity, thereby improving the thermal mixing of coolant. Consequently, the presence of wire wrap reduces temperature variation within each section of the subassembly. The associated reduction in differential thermal expansion of rods is expected to improve the structural integrity of the fuel subassembly.     

Turbulent heat transfer to longitudinal flow through a triangular array of circular rods

Temperature distribution and heat transfer to longitudinal turbulent, fully developed flow through triangular arrays of smooth circular rods are analysed for liquids with Prandtl number 1 and 1. Nusselt number is plotted versus pitch and turbulence for constant heat flow and for constant temperature on the rod surface, and the optimum pitch is determined. The influence of Prandtl number on Nusselt number is analysed.     

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.     

Measurements of the flow characteristics of the lateral flow in the 6 × 6 rod bundles with Tandem Arrangement Vanes

It is very important to increase the heat transfer efficiency in rod bundles in order to prevent the hot spot on the surface of fuel rods in view of the thermal hydraulic safety of nuclear power plants. It is representative to mount vanes in the support grid, which generate swirling flow. It is necessary to measure the flow pattern for investigating the thermal hydraulic flow characteristics in subchannels. In this study, it is performed to measure experimentally the flow field in cross-sections of the 6 × 6 rod bundles with new type vanes - Tandem Arrangement Vanes (TAV) by using Laser Doppler Anemometry. Through measurements, data are acquired at a nominal Reynolds number of 50,000 and for three streamwise locations at 3, 10, and 20 hydraulic diameters. Many previous experimental studies by the existing split mixing vanes show small turbulent length scales and short retention time till 10D_h after spacer grid. On the other hand, the TAVs proposed in the present study generate the big enforced swirl flow more than 20D_h after spacer grid and heat transfer effect are maintained through this distance.     

Comparison of single and multicell heat transfer analyses near nuclear reactor assembly walls

A “multicell” approach to the problem of heat transfer near the wall of a nuclear reactor fuel assembly is compared to the “single cell” approach. Steady state, fully developed heat transfer is considered in assemblies without grid or wire spacers. Results of the multicell approach indicate significant discrepancies in temperature predictions occur when calculations are based on eight fuel elements as compared to the results based on a single fuel element (cell). The multicell analysis includes the effect of mass flux distribution across the subassembly, and the resulting heat transfer trends are not consistent with the single cell approach. These trends are discussed and the utility of the multicell approach is demonstrated.     

Thermohydraulic analysis of high-Prandtl-number fluid in complex duct simulating first wall in fusion reactor

For fusion reactors, molten salt is one of the candidates for coolant materials. Molten salt is a high-Prandtl-number fluid; thus, it is necessary to enhance the heat transfer coefficient. It is proposed that rods are inserted into a duct to enhance the heat transfer coefficient. The flow field behind the rod in the duct is visualized to compare experimental data with simulation results. The trends and distributions in the numerical simulation are the same as those in the experiment, and furthermore, the magnitudes of the time and space scales in the numerical simulation are of the same order as those in the experiment. Thermohydraulic numerical analysis confirmed that the heat transfer coefficient is improved by inserting the rod when the fluid is a high-Prandtl-number fluid and the flow field is in the turbulent region. However, it is necessary for the rods to be arranged in the streamwise direction.     

The temperature distribution in liquid metal cooled fuel elements

This article presents the results of experimental and analytical studies of temperature distributions and heat transfer in reactor cores with hexagonal fuel element assemblies. The temperatured is tributions in fuel elements in the central region and at the plane walls are analyzed. Some information i s given on the overheating of fuel element cladding under the spacing fins. Effects related to the redistribution of coolant flow rates over the crosssection of the assembly in the transition from turbulent to laminar flow are discussed.Translated from Atomnaya Énergiya, Vol. 22, No. 5, pp. 372–378, May, 1967.     

液态铅铋合金湍流普朗特数及RANS模型优选

工程上常采用RANS湍流模型进行热工水力相关的数值模拟,然而液态铅铋合金（LBE）具有独特的热物性,常规湍流普朗特数模型和RANS湍流模型对其流动与传热模拟的适用性有待研究。为更准确地描述绕丝燃料组件内LBE的流动与换热过程,本文基于大涡模拟对湍流普朗特数模型和RANS湍流模型进行优选。首先,采用四种湍流普朗特数模型对绕丝燃料组件内LBE的流动与传热过程进行大涡模拟,对比分析实验数据和模拟结果并进行模型优选。基于优选的湍流普朗特数模型,评价RANS湍流模型对LBE数值模拟的适用性和准确性。结果表明,Cheng湍流普朗特数模型和SST k-ω模型对LBE流动与传热模拟的准确性和适用性最高。