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.     

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.     

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 ℃。     

冷却剂与含格架燃料棒束多场耦合分析

燃料棒束作为压水堆燃料组件的组成部分,其热工和结构特性直接关系到反应堆的安全。本文利用ANSYS WORKBENCH软件分析了冷却剂在5×5含定位格架燃料棒束通道内流动的分布,采用冷却剂与燃料棒束多场耦合的方式研究了燃料棒束的流动传热特性和结构形变特性。结果表明：定位格架扰动冷却剂形成横向二次流并在下游棒束间形成绕流;多场耦合条件下二次流峰值速度和平均速度均小于单流场的;二次流与燃料棒的热应力使棒束发生形变,功率和流动分布的不均匀导致形变在轴向和径向的不均匀;相较于无格架情况,定位格架的存在使冷却剂的搅混流动更加明显,冷却剂对燃料棒冲击增大;在有、无定位格架两种情况下棒束形变均很小,可保持原本结构的稳定。     

Experiment and numerical simulation of bubbly two-phase flow across horizontal and inclined rod bundles

Experimental and numerical analyses were carried out on vertically upward air-water bubbly two-phase flow behavior in both horizontal and inclined rod bundles with either in-line or staggered array. The inclination angle of the rod bundle varied from 0 to 60° with respect to the horizontal. The measured phase distributions indicated non-uniform characteristics, particularly in the direction of the rod axis when the rods were inclined. The mechanisms for this non-uniform phase distribution is supposed to be due to: (1) Bubble segregation phenomenon which depends on the bubble size and shape; (2) bubble entrainment by the large scale secondary flow induced by the pressure gradient in the horizontal direction which crosses the rod bundle; (3) effects of bubble entrapment by vortices generated in the wake behind the rods which travel upward along the rod axis; and (4) effect of bubble entrainment by local flows sliding up along the front surface of the rods. The liquid velocity and turbulence distributions were also measured and discussed. In these speculations, the mechanisms for bubble bouncing at the curved rod surface and turbulence production induced by a bubble were discussed, based on visual observations. Finally, the bubble behaviors in vertically upward bubbly two-phase flow across horizontal rod bundle were analyzed based on a particle tracking method (one-way coupling). The predicted bubble trajectories clearly indicated the bubble entrapment by vortices in the wake region.     

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.     

Comparison of thermo-hydraulic performances of large scale vortex flow (LSVF) and small scale vortex flow (SSVF) mixing vanes in 17 × 17 nuclear rod bundle

Spacer grids in the nuclear fuel rod assembly maintain a constant distance between rods, secure flow passage and prevent the damage of the rod bundle from flow-induced vibration. The mixing vanes attached to the spacer grids generate vortex flows in the subchannels and enhance the heat transfer performance of the rod bundle. Various types of mixing vanes have been developed to produce cross flows between subchannels as well as vortex flows in the subchannels.The shapes of the mixing vane have been improved to generate larger turbulence and cross flow mixing. In the present study, two types of large scale vortex flow (LSVF) mixing vanes and two types of small scale vortex flow (SSVF) mixing vanes are examined. SSVF-single is conventional split type and SSVF-couple is split type with different arraying method. LSVF mixing vane has different geometry and arraying method to make large scale vortex. 17 × 17 rod bundle with eight spans of mixing vanes is simulated using the IBM 690 supercomputer. The FLUENT code and IBM supercomputer is employed to calculate the flow field and heat transfer in the subchannels.Turbulence intensities, maximum surface temperatures of the rod bundle, heat transfer coefficients and pressure drops of the four kinds of mixing vanes are compared. LSVF mixing vanes produced higher turbulence intensity and heat transfer coefficient than SSVF mixing vanes. Consequently, LSVF mixing vane increases the thermal efficiency and safety of the rod bundle.     

Investigation of pre- and post-dryout heat transfer of steam-water two-phase flow in a rod bundle

Pre- and post-dryout heat transfer experiments were performed for steam-water two-phase flow in a 5 × 5 rod bundle under conditions of total mass fluxes from 80 to 320 kg/m²s, inlet qualities from 0.1 to 0.8, heat fluxes from 3 to 26 W/cm² and a pressure of 3 MPa. Heater rod surface temperatures or heat transfer coefficients predicted by several correlations were compared with experimental data with emphasis on the applicability of the correlations to the present experimental conditions which were pertinent to thermal-hydraulic conditions during a LOCA in a nuclear reactor. The Chen and Biorge et al. correlations underestimated heat transfer coefficients in the pre-dryout region. The Varone-Rohsenow prediction which accounted for the thermal nonequilibrium effect, calculated heater rod surface temperatures relatively well in the post-dryout region over the whole region of the present experimental conditions. The Dittus-Boelter and Groeneveld correlations predicted heater rod surface temperatures relatively well in the post-dryout region under high total mass flux conditions, but underestimated considerably under low total mass flux conditions.     

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.     

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.     

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%。     

Method of Critical Power Prediction Based on Film Flow Model Coupled with Subchannel Analysis

A new method was developed to predict critical powers for a wide variety of BWR fuel bundle designs. This method couples subchannel analysis with a liquid film flow model, instead of taking the conventional way which couples subchannel analysis with critical heat flux correlations. Flow and quality distributions in a bundle are estimated by the subchannel analysis. Using these distributions, film flow rates along fuel rods are then calculated with the film flow model. Dryout is assumed to occur where one of the film flows disappears. This method is expected to give much better adaptability to variations in geometry, heat flux, flow rate and quality distributions than the conventional methods.

In order to verify the method, critical power data under BWR conditions were analyzed. Measured and calculated critical powers agreed to within ±7%. Furthermore critical power data for a tight-latticed bundle obtained by LeTourneau et al. were compared with critical powers calculated by the present method and two conventional methods, CISE correlation and subchannel analysis coupled with the CISE correlation. It was confirmed that the present method can predict critical powers more accurately than the conventional methods.     

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.     

Steady-state, local temperature fields with turbulent liquid sodium flow in nominal and disturbed bundle geometries with spacer grids

The operating reliability of nuclear reactors calls for a reliable strength analysis of the highly loaded core elements, one of its prerequisites being the reliable determination of the three-dimensional velocity and temperature fields. To verify thermohydraulics computer programs, extensive local temperature measurements in the rod claddings of the critical bundle zone were performed on a heated 19-rod bundle model with sodium flow and provided with spacer grids (P/D = 1.30; W/D = 1.19). The essential results are:- Outside the spacer grids, the azimuthal temperature variations of the side and corner rods are approximately 10-fold those of rods in the central bundle zone.- The spacer grids investigated give rise to great local temperature peaks and correspondingly great temperature gradients in the axial and azimuthal directions immediately around the support points.- Continuous reduction of a subchannel by rod bowing results in substantial rises of temperature which, however, are limited to adjacent cladding tubes.     

Laminar free convection in open-ended vertical 7-rod bundles: numerical

Solely buoyancy induced flow and heat transfer have been investigated numerically in two open-ended 7-rod bundles of differing arrangements. The circular geometry of the six peripheral rods was replaced by equivalent curved trapezium to get rid of non-orthogonal intersections of the grid lines on the rod boundary. Solutions were initiated assuming a value of dimensionless inlet velocity and then progressed longitudinally until the pressure equals that of the ambient. The flat axial velocity profile at inlet gradually changes with the axial distance. The radial velocity profiles show the diminishing entry effects as the flow develops axially. At high heat input, the bundle height is insufficient for the flow to be fully developed. Numerically evaluated volume flow rates are in excellent agreement with the measured values for both the bundles under investigation.     

Dynamic Model Representing Condensate Feedwater System of BWR Plants

In order to study the effect of burst temperature on the coolant flow channel restriction, burst tests of fuel bundles were performed. Each bundle consisted of 49 rods (7×7 rods), and bursts were conducted in flowing steam. Burst temperature was changed by changing the internal gas pressure in rods. After the burst, the ballooning behavior of each rod and the degree of coolant flow area restriction in the bundle were measured.

Maximum swelling of rod occurs when the burst temperature is around α and α+β phase boundary, and this phenomenon is almost the same as that in single rod burst tests. Maximum coolant flow area restriction is also observed in this condition.     

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。     

Critical Heat Flux in a Heater Rod Bundle Cooled by R-134a Fluid near the Critical Pressure

In the development of supercritical pressure water cooled reactors, it is important to understand the characteristics of a heat transfer near the thermodynamic critical point. An experimental study on the critical heat flux near the critical pressure has been performed with a 5 × 5 square array heater rod bundle cooled by R-134a fluid (P _c = 4:059MPa, T _c = 101°C). The critical power has been accurately measured up to the reduced pressure of 0.99 (4.03 MPa). The critical power decreases sharply at a pressure of about 3.8–3.9 MPa as the pressure approaches the critical pressure. For the low mass fluxes of 50 to 250kg/m², a sharp decrease in the critical power is not observed near the critical pressure. The CHF phenomenon near the critical pressure no longer leads to an inordinate increase in the heated wall temperature such as the case of DNB at normal pressure conditions. In the pressure region close to the critical pressure, there is a threshold pressure at which the CHF phenomenon disappears. When the pressure exceeds the threshold pressure, the wall temperature increases monotonously without a CHF occurrence according to the power level applied to the heater rods. The threshold pressure moves toward the lower pressure region gradually with an increasing mass flux.     

带定位格架棒束通道内两相流型研究

在空气-水两相流动工况下,将RBI光学探针测得的时序波形和目测相结合,对AFA-2G 33定位格架组成的棒束通道内存在的两相流型进行了识别。通道水力当量直径为8.98mm,元件的棒径为9.5mm,栅距为12.6mm,棒壁距为2.65mm。液相和气相表观速度范围分别为0.40-2.69m/s,0.02-2.99m/s。试验获得了流型图。结果表明,定位格架结构,特别是交混叶片对定位格架附近区域两相流型变化有重要影响,在棒束通道内的同一截面上存在不同种类流型。     

Flow Structure of Subcooled Boiling Water Flow in a Subchannel of 3 × 3 Rod Bundles

In this paper, the interfacial flow structure of subcooled water boiling flow in a subchannel of 3 × 3 rod bundles is presented. The 9 rods are positioned in a quadrangular assembly with a rod diameter of 8.2mm and a pitch distance of 16.6 mm. Local void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter, and liquid velocity have been measured using a conductivity probe and a Pitot tube in 20 locations inside one of the subchannels. A total of 53 flow conditions have been considered in the experimental dataset at atmospheric pressure conditions with a mass flow rate, heat flux, inlet temperature, and subcooled temperature ranges of 250–522 kg/m s, 25–185 kW/m², 96.6–104.9°C, and 2–11 K, respectively. The dataset has been used to analyze the effect of the heat flux and mass flow rate on the local flow parameters. In addition, the area-averaged data integrated over the whole subchannel have been used to validate some of the distribution parameter and drift velocity constitutive equations and interfacial area concentration correlations most used in the literature.