Review and proposal for best fit of wire-wrapped fuel bundle friction factor and pressure drop predictions using various existing correlations

The aim of this paper is to provide an overview of the existing wire-wrapped fuel bundle friction factor/pressure drop correlations and to qualitatively evaluate which of the existing friction factor correlations are the best in retracing the results of a large set of the experimental data available on wire-wrapped fuel assemblies tested under different coolant conditions.     

Hydride fuel for LWRs—Project overview

This special issue of Nuclear Engineering and Design consists of a dozen papers that summarize the research accomplished in the DOE NERI Program sponsored project NERI 02-189 entitled “Use of Solid Hydride Fuel for Improved Long-Life LWR Core Designs”. The primary objective of this project was to assess the feasibility of improving the performance of pressurised water reactor (PWR) and boiling water reactor (BWR) cores by using solid hydride fuels instead of the commonly used oxide fuel. The primary measure of performance considered is the cost of electricity (COE). Additional performance measures considered are attainable power density, fuel bundle design simplicity, in particular for BWRs, safety, attainable discharge burnup, and plutonium (Pu) transmutation capability.Collaborating on this project were the University of California at Berkeley Nuclear Engineering Department (UCB), Massachusetts Institute of Technology Nuclear Science and Engineering Department (MIT), and Westinghouse Electric Company Science and Technology Department. Disciplines considered include neutronics, thermal hydraulics, fuel rod vibration and mechanical integrity, and economics.It was found that hydride fuel can safely operate in PWRs and BWRs having comparable or higher power density relative to typical oxide-fueled LWRs. A number of promising applications of hydride fuel in PWRs and BWRs were identified: (1) Recycling Pu in PWRs more effectively than is possible with oxide fuel by virtue of a number of unique features of hydride fuel-reduced inventory of ²³⁸U and increased inventory of hydrogen. As a result, the hydride-fueled core achieves nearly double the average discharge burnup and the fraction of the loaded Pu it fissions in one pass is double that of the MOX fuel. (2) Eliminating dedicated water moderator volumes in BWR cores, thus enabling significant increase of the cooled fuel rod surface area as well as the coolant flow cross-section area in a given fuel bundle volume while reducing the heterogeneity of BWR fuel bundles, thus achieving flatter pin-by-pin power distribution. The net result is an increase in the core power density and a reduction of the COE.A number of promising oxide-fueled PWR core designs were also found in this study: (1) The optimal oxide-fueled PWR core design features a smaller fuel rod diameter (D) of 6.5 mm and a larger pitch to rod diameter (P/D) ratio of 1.39 than that presently practiced by industry of 9.5 mm and 1.326. This optimal design can provide a 27% increase in the power density and a 19% reduction in the COE provided the PWR can be designed to have the coolant pressure drop across the core increased from the reference 0.20 MPa (29 psi) to 0.414 MPa (60 psi). Under the set of constraints assumed in this work, hydride fuel was found to offer comparable power density and economics as oxide fuel in PWR cores when using fuel assembly designs featuring square lattice and grid spacers. This is because pressure drop constraints prevented achieving sufficiently high power using hydride fuel with a relatively small P/D ratio of around 1.2 or less, where it offers the highest reactivity and a higher heavy metal (HM) loading. (2) Using wire-wrapped oxide fuel rods in hexagonal fuel assemblies, it is possible to design PWR cores to operate at ∼50% higher power density than the reference PWR design that uses grid spacers and a square lattice, provided 0.414 MPa coolant pressure drop across the core could be accommodated. Uprating existing PWRs to use such cores could result in up to 40% reduction in the COE. The optimal lattice geometry is D = 9.34 mm and P/D = 1.37. The most notable advantages of wire-wraps over grid spacers are their significantly lower pressure drop, higher critical heat flux, and improved vibration characteristics.The achievement of the highest power gains claimed in this study is possible as long as mechanical components like assembly hold-down devices (both in PWRs and in BWRs) and steam dryers (only in BWRs) are appropriately upgraded to accommodate the higher coolant pressure drop and flow velocities required for the high-performance LWR designs. The compatibility of hydride fuel with Zircaloy clad and with PWR and BWR coolants need yet be experimentally demonstrated. Additional recommendations are given for future studies that need to be undertaken before the commercial benefits from use of hydride fuel could be reliably quantified.     

Effects of wire-spacer shape in LMR on thermal–hydraulic performance

In this work, analyses of three-dimensional flow and convective heat transfer in wire-wrapped fuel assemblies with different shaped wire-spacers have been carried out using Reynolds-averaged Navier–Stokes equations with shear stress transport turbulence model. Three cross-sectional shapes of wire-spacer, circle, hexagon and rhombus have been tested. All the assemblies have been analyzed for single pitch of wire-spacer with periodic boundary conditions applied at inlet and outlet of the calculation domain. It is found that the assemblies exhibit the directional periodicity in radial gradients between the adjacent subchannels due to presence of wire-spacer. The overall pressure drop is highest in case of rhombus shaped wire-spacer assembly followed by hexagonal shaped. Although circular shaped wire-spacer gives lowest peak temperature as well as lowest overall temperature difference in the assembly, the rhombus shaped wire-spacer assembly gives highest Nusselt number on fuel rod surface.     

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.     

Shape optimization of wire-wrapped fuel assembly using Kriging metamodeling technique

In this work, shape optimization of a wire-wrapped fuel assembly in a liquid metal reactor has been carried out by combining a three-dimensional Reynolds-averaged Navier–Stokes analysis with the Kriging method, a well-known metamodeling technique for optimization. Sequential quadratic programming (SQP) is used to search the optimal point from the constructed metamodel. Two geometric design variables are selected for the optimization and design space is sampled using Latin Hypercube Sampling (LHS). The optimization problem has been defined as a maximization of the objective function, which is as a linear combination of heat transfer and friction loss related terms with a weighing factor. The objective function value is more sensitive to the ratio of the wire spacer diameter to the fuel rod diameter than to the ratio of the wire wrap pitch to the fuel rod diameter. The optimal values of the design variables are obtained by varying the weighting factor.     

快堆燃料组件热工流体力学计算研究

对于钠冷快堆,在燃料和包壳最高温度等设计限值下,为获得较高的堆芯出口温度,需深入分析燃料组件内的热工流体力学问题,准确预测组件内的冷却剂温度分布。本文在CRT模型和F.C.Engel等人工作的基础上,提出了ICRT压降关系式,用以计算冷却剂在湍流区、过渡流区和层流区的棒束压降;引入CRT模型和WEST对流传热模型,改进了SUPERENERGY子通道分析程序,并将改进程序与原程序计算结果进行了对比,结果表明：最热子通道出口温度略有降低,液膜温压略有增加;并用计算流体力学软件CFX对中国实验快堆单盒燃料组件活性段进行了三维数值模拟,将计算结果用CRT模型、ICRT压降关系式及改进后的SUPERENERGY子通道分析程序进行了验证,相互符合较好。     

Proposal for pressure drop prediction for a fuel bundle with grid spacers using Rehme pressure drop correlations

The aim of this paper is to correlate experimentally measured pressure drop data across grid spacers to the set of correlations proposed by Rehme, based on the experiments performed in a water loop at the Scalbatraio Laboratory of Pisa University (2003), as well as in a water loop of the KALLA test facility (2008). Based on the presented study one can state that using slightly modified Rehme/Dalle Donne pressure drop correlations for pressure drop prediction in a fuel bundle with grid spacers, it is possible to obtain very good agreement with the experimental measurements of the fuel assembly pressure drops in various segments of a fuel assembly, provided that the grid spacer blockage factor can be estimated to a reasonable degree of confidence.     

Pressure drop and friction factor correlations of supercritical flow

The determination of the in-tube friction pressure drop under supercritical conditions is important to the design, analysis and simulation of transcritical cycles of air conditioning and heat pump systems, nuclear reactor cooling systems and some other systems. A number of correlations for supercritical friction factors have been proposed. Their accuracy and applicability should be examined. This paper provides a comprehensive survey of experimental investigations into the pressure drop of supercritical flow in the past decade and a comparative study of supercritical friction factor correlations. Our analysis shows that none of the existing correlations is completely satisfactory, that there are contradictions between the existing experimental results and thus more elaborate experiments are needed, and that the tube roughness should be considered. A new friction factor correlation for supercritical tube flow is proposed based on 390 experimental data from the available literature, including 263 data of supercritical R410A cooling, 45 data of supercritical R404A cooling, 64 data of supercritical carbon dioxide (CO₂) cooling and 18 data of supercritical R22 heating. Compared with the best existing model, the new correlation increases the accuracy by more than 10%.     

Expression of Few-Group Effective Microscopic Cross Sections in BWR Burnup Calculations

A practical method is proposed to express few-group effective microscopic cross sections for BWR burnup analysis. A set of few-group cross sections is prepared for an infinite square lattice of fuel rods as a function of the ratios of number density of nuclides such as ²³⁵ U, ²³⁸U and ²³⁹Pu, and the water quantity around a fuel rod. Spatial variation of few-group cross sections in the fuel assembly is taken into account by adjusting the water quantity around a fuel rod.

Numerical studies show that the present method can evaluate effective few-group cross sections within the accuracy of 3% in comparison with a two-dimensional integral transport calculation.     

Fuel performance analysis for PWR cores

Attainable discharge burnups for oxide and hydride fuels in PWR cores were investigated using the TRANSURANUS fuel performance code. Allowable average linear heat rates and coolant mass fluxes for a set of fuel designs with different fuel rod diameters and pitch-to-diameter ratios were obtained by VIPRE and adopted in the fuel code as boundary conditions. TRANSURANUS yielded the maximum rod discharge burnups of the several design combinations, under the condition that specific thermal-mechanical fuel rod constraints were not violated. The study shows that independent of the fuel form (oxide or hydride) rods with (a) small diameters and moderate P/Ds or (b) large diameters and small P/Ds give the highest permissible burnups limited by the rod thermal-mechanical constraints. TRANSURANUS predicts that burnups of ∼74 MWd/kg U and ∼163 MWd/kg U (or ∼65.2 MWd/kg U oxide-equivalent) could be achieved for UO₂ and UZrH_x fuels, respectively. Furthermore, for each fuel type, changing the enrichment has only a negligible effect on the permissible burnup. The oxide rod performance is limited by internal pressure due to fission gas release, while the hydride fuel can be limited by excessive clad deformation in tension due to fuel swelling, unless the fuel rods will be designed to have a wider liquid metal filled gap. The analysis also indicates that designs featuring a relatively large number of fuel rods of relatively small diameters can achieve maximum burnup and provide maximum core power density because they allow the fuel rods to operate at moderate to low linear heat rates.     

快堆组件数值模拟研究

为详细研究快堆组件棒束中的流动换热特性,本工作采用Fluent程序对169棒束快堆燃料组件进行三维数值模拟。结果表明,在流量为10.92~18.67 kg/s时,计算得到的压降与已公开发表文献结果的相对偏差小于3.41%。内子通道的相对温度升高,呈现出周期为1/3螺距的波动,内子通道的局部温度比子通道程序SUPERENERGY计算的结果更高。根据模拟计算结果可更为准确地预测棒束通道内的流动换热情况,为今后组件棒束热工水力学设计提供参考。     

Hydraulic characteristics of wire-wrapped rod bundles

Existing hydraulic data such as pressure fields, velocity fields, friction factors, flow split and sweeping flows were reviewed and summarized. In addition equations were suggested to calculate subchannel friction factors, flow split and flow sweeping. It was concluded that sufficient data and analysis exist to generate a complete physical model to characterize turbulent flow in wire-wrapped rod bundles; there are inadequate data to construct a physical model to describe laminar and natural circulation flow. Potential hydraulic problems related to rod bundle dimensional tolerances, non-nominal and/or time-dependent pressure drop characteristics should be resolved.     

Preface: IAEA specialists' meetings on radiation damage units in graphite and ferritic and austenitic steel

A porous body model, new in its application for predicting temperature distributions in wire-wrapped fuel rod assemblies, has been developed. The model developed for thermal transport in wire-wrapped rod bundles is similar in principle to the one which has long been successfully used for heat transfer in fixed beds of packed solids. Although the model is applicable to bundles in forced and mixed (combined forced and free) convection, attention in this paper is confined to bundles operating in forced (negligible natural) convection only. The results obtained from this analysis were found to predict available data with as good a precision as does the more complex analysis.     

Development of an advanced PWR fuel for OPR1000s in Korea

The advanced PWR fuel for the OPR1000s in Korea, PLUS7, has been developed to enhance thermal performance, high burnup capability and fuel reliability against grid-to-rod fretting wear and debris. The outstanding design features of PLUS7 include mixing vane mid-grids for increasing thermal performance and minimizing vibration-induced fretting wear, optimized fuel dimensions and advanced zirconium alloys for high burnup capability of 72,000 MWD/MTU, and an optimized fuel rod diameter for reducing pressure drop and improving neutron economy. The fuel assembly and its components performances have been verified through a wide spectrum of mechanical, thermal hydraulic, vibration and fretting wear tests. Based on the verification test results and the evaluations with the help of the KNF design code system, it is found that the PLUS7 fuel will maintain its integrity up to the envisaged burnup of 72,000 MWD/MTU. In addition, the PLUS7 fuel performances were evaluated to be considerably improved in comparison with the current fuel used in the OPR1000s.     

Steady state thermal-hydraulic analysis of hydride-fueled grid-supported BWRs

A steady state thermal-hydraulic analysis was performed to estimate the power density attainable with hydride-fueled boiling water reactor (BWR) cores with respect to that of an existing oxide BWR core chosen as reference. The power-limiting constraints taken into account were the minimum critical power ratio (MCPR), core pressure drop, fuel average and centerline temperature, cladding outer temperature, flow-induced vibrations and power/flow ratio.The study consisted of two independent analyses: a whole core analysis and a single bundle analysis. The whole core analysis was performed, with a fixed core volume, for both hydride and oxide fuel over hundreds of combinations of rod diameter-rod pitch, referred to as “geometries”, in the ranges 0.6 ≤ D ≤ 1.6 cm and 1.1 ≤ P/D ≤ 1.6. For each geometry, the maximum achievable steady state core power was calculated. Preliminary neutronics results derived from a companion neutronic study were then overlaid on the whole-core thermal-hydraulic results to estimate the reduction in maximum achievable power caused by the application of neutronic constraints. The single bundle analysis was performed to compare in greater detail the thermal-hydraulic performance of a limited number of hydride and oxide fuel bundles having D and P values similar to those of the reference oxide bundle, and for which the compliance with neutronic constraints was demonstrated in a companion neutronic study.The study concluded that, if the core pressure drop is not allowed to increase above the reference core value, the power density increase attainable with hydride fuel is estimated to be in the range 0-15%. If the pressure drop is allowed to increase up to a value 50% higher than the reference core value, the power density increase is estimated to be in the range 25-45%. These power density increases, which are defined with respect to the reference oxide core, decrease about 10% if the comparison is made with respect to oxide designs resembling the most recent commercial high-performance oxide cores.The power gain capability of hydride fuel is primarily due to the possibility of: (1) replacing volumes occupied by water rods and water gaps in oxide fuel cores with fuel rods, thus increasing the heat transfer area per core volume, and (2) flattening the bundle pin-by-pin power distribution.The actual achievement of the above-mentioned power density increase is however conditioned to the compliance of hydride-fueled cores to safety requirements related to core behavior during transients, hydrodynamic stability and steam dryer performance, which are fields of study not addressed in this work. A potential 25-45% power density increase justifies however interest for further investigation on this alternative fuel.     

脉动流下棒束通道内相位差及瞬态流场研究

事故条件及海洋条件下反应堆处于非稳态工况,堆芯燃料组件内热工水力行为具有瞬变及多因素耦合特性,对反应堆的安全提出更高挑战,因此有必要对燃料组件内瞬态特性进行研究。本文通过测量棒状燃料组件内压降和流量之间延迟时间开展棒束通道脉动流条件下相位差研究,对比了相位差在不同振幅、不同流动状态下的变化特性,并分析了定位格架对脉动流相位差的作用特点。另外,基于粒子图像测速（PIV）技术开展了脉动流条件下棒束通道内流场分布特性研究,对比了相同流量条件下稳态工况与瞬态工况下流场分布差异,分析了主流具备不同加速度时棒束通道内流场分布特征。实验结果表明：定位格架可减小脉动流下棒束通道内相位差;棒束通道内流场演化滞后于主流量变化。实验结果有助于揭示燃料组件在非稳态条件下瞬态特性,并为燃料组件的设计和优化奠定基础。     

燃料组件5×5格架多跨模型CFD模拟方法研究

本文详细描述了某典型燃料组件5×5格架模型CFD分析的几何模型简化、网格划分、求解及后处理等过程。在5×5结构单跨模型上研究了弹簧刚突对搅混特性及压降的影响,并采用简化弹簧刚突的5×5格架模型实现了包含11层格架的多跨模型计算。单跨模型计算结果表明,弹簧刚突结构强化了横向流动,利于换热,Nu提高了8%,但弹簧刚突格架模型较简化弹簧刚突模型压降损失增加了40%。多跨模型计算得到了多层格架全程流动换热特性,为燃料组件自主研发中定位格架数量及布置的设计优化以及DNB预测计算提供了有效的CFD分析方法。     

Control rod drop analysis by finite element method using fluid–structure interaction for a pressurized water reactor power plant

The control rod drop analysis is very important for safety analysis. For seismic and loss of coolant accident event, the control rod assemblies shall be capable of traveling from a fully withdrawn position to 90% insertion without any blockage and within specified time and displacement limits. The analysis has been executed by analytical method using in-house code. In this method, several field data are needed. These data are obtained from nuclear, thermal–hydraulic and mechanical design groups, peculiar codes, those work groups need to cooperate together.Following the enhancement of a computer and development of the multi-physics analysis code, a new method for the control rod drop analysis is proposed by finite element method. This analysis model incorporates the structure and fluid parts, termed as a fluid and structure interaction (FSI). Because a control rod is submerged inside a guide tube of a fuel assembly, the FSI boundary condition is applied. In this model, it is assumed that the fluid is incompressible laminar flow. The structures are modeled with the solid elements because there is no deformation due to the fluid flow. The analysis two-dimensional plane model is created in the analysis with considering an axi-symmetric geometry. Therefore, the proposed analysis model will be very simple and the design data from other fields will be unnecessary.The analysis results are compared with those of the in-house code, which have been used for a commercial design. After validation, it is found that the present analysis gives a useful tool in the design of the control rod and fuel assembly.     

快堆带绕丝棒束组件低雷诺数下的水力特性分析

低雷诺数(Re)流动存在于正常运行或事故停堆工况的各类组件中,对于快堆的安全运行具有重要意义。利用CFX程序对低Re下的中国实验快堆不同类型的带绕丝棒束组件的水力特性进行了分析。结果表明,通过利用1个螺距的带绕丝棒束组件计算得到的低Re下的水力特性与实验结果以及Engel关系式符合较好。通过利用4个螺距的带绕丝棒束组件计算结果表明,绕丝产生的横向流动使组件6个壁面上压力分布有所不同,但在流动充分发展时,每个面轴线方向的压降按螺距均匀分布,从而进行带绕丝棒束组件水力特性测量时,需在组件同一面上按照整数倍螺距来布置测点,才能避免由于横向流动对测量带来的影响。