On the transport mechanisms in simulated heterogeneous rod bundle subchannels

Experimental results are presented on fully developed turbulent flow through simulated heterogeneous rod bundle subchannels. The emphasis of this study is on the universality of the cross-gap turbulence convection transport with respect to symmetric versus asymmetric subchannels. The flow passage was formed by a rod asymmetrically mounted in a trapezoidal duct. The Reynolds number based on the equivalent hydraulic diameter and bulk average axial velocity is 26 300. The measurements include mean axial velocities, r.m.s. values of the fluctuating velocity components and the energy density spectra. The results demonstrate the existence of an unusual region near the asymmetric rod-to-wall gap characterized by high levels of axial turbulence intensity with a remarkably different type of distribution compared with a normal boundary layer. It is also shown that the strength of the cross-gap transport is subchannel geometry dependent. The distributions of wall shear stress and turbulence kinetic energy indicate that mean convection by secondary flow is also an important transport mechanism that should be taken into account in the analysis of momentum/heat transfer in rod bundle subchannels.     

稠密栅元不同子通道内湍流流动的RANS和URANS模拟

本工作采用RANS和非稳态雷诺平均纳维斯托克斯模拟（URANS）方法对稠密栅元内典型子通道——中心通道和壁面通道内的湍流流动进行CFD模拟。研究分析了稠密栅元子通道内的不同周向角度的主流速度、壁面剪应力、湍动能等参数。将模拟计算结果和实验测量结果进行对比,结果表明：RANS模拟在采用各向异性的湍流模型的情况下能较好地模拟P/D较大的稠密栅元通道,但对于P/D较小（P/D<1.1）的稠密栅元通道,CFD结果和实验数据存在较大差距。相比之下,URANS方法可模拟紧密栅元子通道间隙区的大尺度、准周期的流动振动,从而和实验数据拟合良好。推荐采用雷诺应力湍流模型(SSG,ORS)进行RANS模拟,而采用SAS湍流模型进行URANS模拟。     

Three-dimensional local coolant flow velocity field under the influence of wire-spacers in an FBR fuel subassembly

In order to evaluate the coolant cross-flow rate among subchannels of a wire-spaced FBR fuel subassembly, the three-dimensional Navier-Stokes equation was solved numerically for a detailed flow velocity distribution within several connected subchannels inside a subassembly, where consideration was focussed on setting up iteratively an approriate velocity field on boundary interfaces enclosing the subchannels under consideration as the boundary condition. Such subchannels may include a peripheral fuel pin.Some of the numerical results obtained are as follows: (1) In an annular channel coaxed with a wire-spaced fuel pin, the maximum azimuthal velocity component does not appear just at the upstream side of a wire spacer but it appears at the leading angle of 180° to the upstream side with respect to the wire-wrapping phase in a fully developed flow region apart from the entrance. (2) In a wire-spaced fuel pin bundle, the transverse velocity increases steeply in the vicinity of the upstream side of a wire-spacer, while it increases gradually with the development of wakes in the downstream side of a wire-spacer. (3) At the peripheral gaps the swirl flow is induced in the wire-wrapping direction along the inner surface of a wrapper tube and its circumferential evolution predicted in the present analysis is in good agreement with experimental data obtained by a MIT group.     

钠冷快堆燃料组件热工水力特性数值模拟与分析

利用CFD程序CFX,分别对7、19、37、61根棒组成的三角形排列螺旋绕丝定位的钠冷快堆燃料组件棒束通道进行了热工水力特性的分析研究,并将结果与子通道程序SuperEnergy进行了对比验证。重点考察了棒束通道轴向流动分布、横向流交混效应及子通道轴向温升,分析了定位绕丝的影响。结果表明,绕丝对棒束通道的横向流交混效应、轴向流动分布及子通道温升有着重要影响,且随棒束的增多,通道内的流动趋向复杂化,轴向流动不均匀性有升高趋势。     

单相4×4棒束流动试验的CFD方法验证

为研究计算流体力学（CFD）方法预测棒束通道内流场分布的准确性,基于网格敏感性分析所确定的网格方案,采用标准k-ε模型（SKE）、可实现k-ε模型（RKE）、标准k-ω模型（SKW）和剪切应力传输模型（SST模型）对单相棒束流动进行模拟,并将横向速度与轴向速度与试验结果进行量化比较。结果表明:4种湍流模型均能较好地预测棒束通道内的流场分布,其中SKE与RKE的在横向速度预测上相对偏差较小,为19.6%;对于近格架区域的横向流场分析,SKE模拟较优,反之RKE模拟较优;对于轴向速度的预测,SKE的相对偏差最小为4.9%;4种湍流模型均低估均方根（RMS）速度,但能够预测棒束通道内RMS速度的分布规律,近格架区域采用RKE,反之SST较优。本文的计算结果可为单相棒束流动CFD分析的最佳实践导则建立提供参考。      

Incipient Sodium Boiling Superheats in Bundle Geometry under Loss-of-Flow Conditions

Transient sodium boiling experiments were conducted using electrically heated pins arranged in 7-, 19- and 37-pin bundles to reproduce loss-of-flow conditions. The average degrees of superheat attained before inception of sodium boiling amounted to 47, 45 and 16°C respectively with the 7-, 19- and 37-pin bundles.

The experimental results indicated that the degree of superheat decreased with increasing number of heating pins in the bundle. This tendency can be explained from the fact that a larger bundle has a radially wider region of sodium saturation temperature at boiling inception comparatively—with the smaller cooling effect exerted by the peripheral subchannels—and consequently a larger number of active nuclei to trigger boiling and terminate the superheating phenomenon. No meaningful correlation was discerned between the degree of superheat and other factors like sodium velocity, rate of sodium temperature rise and intensity of applied heatflux.     

A turbulence model study for simulating flow inside tight lattice rod bundles

Performances of various turbulence models are evaluated for calculation of detailed coolant velocity distribution in a tight lattice fuel bundle. The individual models are briefly outlined and compared with respect to the prediction of wall shear stress and velocity field, for a fully developed flow inside a triangular lattice bundle. Comparisons clearly show the importance of proper modeling of the turbulence-driven secondary flows in subchannels. A quadratic k– model, which showed promising capability in this respect, is adjusted in its coefficients, and the adjusted model is applied to fully developed flow in an infinite triangular array, with various Reynolds numbers. The results show that the inclusion of adequate anisotropy modeling enables to accurately reproduce the wall shear stress distribution and velocity field in tight lattice fuel bundles.     

Multi-dimensional modeling of two-phase flow in rod bundles and interpretation of velocities measured in BWRs by the cross-correlation technique

Two-phase flow in rod bundles is of the atmost importance in nuclear technology since it is a naturally occurring phenomenon in BWRs under normal operational conditions, or in PWRs undergoing a severe transient.It has recently been shown that by neutron noise analysis (cross-correlation) techniques, in the upper half of a normally operating BWR, one measures two or even three two-phase flow velocities (two or three peaks in the cross-correlation function); this was also found to be the case in measurements performed in simple air-water loops with different stationary and adiabatic two-phase flows, the direct consequence of these findings being that no cross-sectionally averaged two-phase flow models can be successfully employed for interpreting this kind of non-intrusive velocity measurements.It is the aim of this work to present an as precise as possible interpretation of velocity measurements in BWRs by the cross-correlation technique, which is based on the radially non-uniform quality and velocity distribution in BWR type bundles, as well as on our knowledge about the spatial ‘field of view’ of the in-core neutron detectors. After formulating the three-dimensional two-fluid model volume/time averaged equations and pointing out some problems associated with averaging, we expound a little on the turbulence mixing and void drift effects, as well as on the way they are modilled in advanced subchannel analysis codes like THERMIT or COBRA-TF. Subsequently, some comparisons are made between axial velocities measured in a commercial BWR by neutron noise analysis, and the steam velocities of the four subchannels nearest to the instrument tube of one of the four bundles as predicted by COBRA-III and by THERMIT. Although as expected, for well-known reasons, COBRA-III predicts subchannel steam velocities which are close to each other, THERMIT correctly predicts in the upper half of the core three largely different steam velocities in the three different types of BWR subchannels (corner, edge and interior).In the upper part of the core where a pronounced radial steam velocity and quality profile exists in the bundles, we associate the main peak of the cross-correlation function with the steam velocities in the edge subchannels, the second peak with the steam velocities in the corner subchannel, and the third small peak with the steam velocities in the interior subchannels. This interpretation is verified by a computer simulation with synthetic signals as well as by a simple phenomenological analytical model, and it opens the way for utilizing this kind of measurements (to a certain degree and within certain error bounds) for verification of advanced subchannel analysis codes like THERMIT-2 or COBRA-TF and in particular, for improving the two-phase mixing correlations employed in these codes.     

Local heat transfer and hot-spot factors in wire-wrap tube bundle

Heat transfer coefficients and hot-spot factors have been determined from measured local temperatures and calculated local mass flux in seven adjacent tubes and associated subchannels of a 61 wire-wrap tube bundle characteristic of the blanket of a GCFR (Gas Cooled Fast Reactor). The bundle consisted of 2.11 cm OD stainless steel tubes on a triangular array with a pitch/diameter ratio of P/D = 1.05. The helical wire of 0.1067 cm in diameter was coiled on the tube with a respective initial orientation of 0–120–240°C and 30.48 cm helical pitch. The experiment used water at atmospheric pressure and temperature as coolant. The resulting dimensionless correlation for heat transfer is applicable to gases and all non-metal fluids in one phase flow when the fluid properties at subchannel bulk temperature are used. This correlation is based on local subchannel mass flux and is applicable to all wire-wrap configurations. Local subchannel mass fluxes were determined with a computer program COBRA IV and used to correlate the average Nusselt number for each subchannel in terms of local Reynolds number and fluid Prandtl number. The differences of up to 19% between that correlation and the one presented in earlier work are discussed in the text. The hot-spot factors on the convective heat transfer coefficient for tubes and subchannels are given as a function of Reynolds number based on a bundle average mass flux and a local subchannel hydraulic diameter. These factors are specific to the bundle configuration and are also dependent on the wire-wrap configuration.     

Turbulent flow in a model nuclear fuel rod bundle containing partial flow blockages

Local velocity and turbulence intensity measurements were obtained with a laser Doppler anemometer near flow blockages in an unheated 7 × 7 rod bundle. Sleeve blockages were positioned on the center nine rods to create area reductions of 70 and 90% in the center four subchannels of the bundle. Experimental results indicated that extensive flow disturbances existed downstream from the blockage clusters and showed that only minor disturbances can be expected upstream from the blockages. Recirculation zones for both 70 and 90% blockages were detected downstream from the blockage clusters and persisted for approximately three to five subchannel hydraulic diameters, depending on the degree of the blockage. The experimental velocity results obtained with blockage clusters located midway between grid spacers were successfully predicted using the COBRA subchannel computer program.     

Coolant mixing and subchannel velocities in an LMFBR fuel assembly

Experimental mixing studies were conducted using water with a 91-pin wire-wrapped fuel assembly to establish a data base for calibrating thermal-hydraulic codes and to supplement and clarify existing mixing data. An electrolytic tracer was employed in conjunction with an isokinetic sampling technique which permitted mixed mean subchannel concentrations and flowrates to be measured without incurring errors resulting from local subchannel gradients. Emphasis was placed upon the behavior of peripheral subchannels.

A complete set of mixing data was obtained which can be used to calibrate thermal-hydraulic codes. Isokinetic velocity measurements revealed that the pitch-average corner, edge, and central subchannel velocities were nearly equal to the bundle average velocity. It was shown that the average peripheral swirl velocity was approximately 1.2 times greater than predicted assuming the fluid follows the wire-wraps. Also the magnitude of the average swirl flow decreases with increasing bundle size. Parametric studies revealed that neither the velocity nor concentration profiles were sensitive to Reynolds number in the range Re = 9000–24000.     

快堆燃料组件棒束通道内流动和传热现象分析与研究

利用三维计算流体力学软件CFX 12.0对由7根带螺旋状定位绕丝的燃料棒组成的快堆燃料组件典型棒束通道内的流动和传热现象进行了数值模拟。模拟得到不同Re下的压降系数曲线与Nu曲线,并将计算结果与经验公式的计算结果进行了比较,两者符合较好。研究了组件内3类典型子通道的横向流交混效应,分析了3类典型子通道的横向流分布特点,发现角子通道横向流交混强度沿轴向波动较大,而3类子通道的横向流交混强度均存在周期性。研究了中心燃料棒壁面上3个截面的局部换热效应,发现在燃料棒与绕丝接触处传热效果最差,在事故分析时应重点关注。     

Analysis of dynamical flow structure in a square arrayed rod bundle

Large eddy simulation (LES) of turbulent flow in a bare rod bundle was performed, and a new concept about the flow structure that enhances heat transport between subchannels was proposed. To investigate the geometrical effect, the LES was performed for three different values of rod diameter over pitch ratio (D/P = 0.7, 0.8, 0.9). The computational domain containing 4 subchannels was large enough to capture large-scale structures wide across subchannels. Lateral flow obtained was unconfined in a subchannel, and some flows indicated a pulsation through the rod gap between subchannels. The gap flow became strong as D/P increased, as existing experimental studies had reported. Turbulence intensity profile in the rod gap suggested that the pulsation was caused by the turbulence energy transferred from the main flow to the wall-tangential direction. This implied that the flow pulsation was an unsteady mode of the secondary flow and arose from the same geometrical effect of turbulence. This implication was supported by the analysis results: two-points correlation functions of fluctuating velocities indicated two length-scales, P-D and D, respectively of cross-sectional and longitudinal motions; turbulence stress in the cross-sectional mean flow contained a non-potential component, which represented energy injection through the unsteady longitudinal fluid motion.     

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.     

Experimental investigation of turbulent transport of momentum and energy in a heated rod bundle

Turbulent air flow in a central channel of heated 37-rod bundles with triangular array at two different pitch-to-diameter ratios (P/D=1.12 and P/D=1.06) was investigated. Measurements were performed with a hot-wire probe with x-wires and an additional temperature wire. Time mean velocities, time mean fluid temperatures, wall shear stresses and wall temperatures, turbulent quantities such as the turbulent kinetic energy, all Reynolds stresses and all turbulent heat fluxes were measured at two different pitch-to-diameter ratios in a central channel of the bundle. It is shown that with decreasing gap width the turbulence field in rod bundles deviates significantly from that in a circular tube. Also, data on the power spectral density functions of the velocity and temperature fluctuations are presented. These data show the existence of large-scale periodic fluctuations of velocity and temperature in the gap region of two adjacent rods. These fluctuations are responsible for the high intersubchannel heat and momentum exchange. Spectral measurements with two hot wire probes imply a distinct similarity of motion of vortices in adjacent subchannels of the bundle.     

Evaluation of a numeric procedure for flow simulation of a 5 × 5 PWR rod bundle with a mixing vane spacer

The fuel assemblies of the Pressurized Water Reactors (PWR) are constituted of rod bundles arranged in a regular square configuration by spacer grids placed along its length. The presence of the spacer grids promote two antagonist effects on the core: a desirable increase of the local heat transfer downstream the grids and an adverse increase of the pressure drop due to the constriction on the coolant flow area. Most spacer grids are designed with mixing vanes which cause a cross and swirl flow between and within the subchannels, enhancing even more the heat transfer performance in the grid vicinity. The improvement of the heat transfer increases the departure from the nucleate boiling ratio, allowing higher operating power in the reactor. Due to these important thermal and fluid dynamic features, experimental and theoretical investigations have been carried out in the past years for the development of spacer grid design. More recently, the Computational Fluid Dynamics (CFD) using three dimensional Reynolds Averaged Navier Stokes (RANS) analysis has been used efficiently for this purpose. Many computational works have been performed, but the appropriate numerical procedure for the flow in rod bundle simulations is not yet a consensus. This work presents results of flow simulations performed with the commercial code CFX 11.0 in a PWR 5 × 5 rod bundle segment with a split vane spacer grid. The geometrical configuration and flow conditions used in the experimental studies performed by Karoutas et al. were assumed in the simulations. To make the simulation possible with a limited computational capacity and acceptable mesh refinement, the computational domain was divided in 7 sub-domains. The sub-domains were simulated sequentially applying the outlet results of a previous sub-domain as inlet condition for the next. In this study the k–ε turbulence model was used. The simulations were also compared with those performed by Karoutas et al. in half a subchannel and In et al. in one subchannel computational domains. Comparison between numerical and experimental results of lateral and axial velocities along of the rod bundle show good agreement for all evaluated heights downstream the spacer grid. The present numerical procedure shows better predictions than Karoutas et al. model especially further from the spacer grid where the peripheral subchannels have more influence in the average flow.     

Impact of gas in sodium flow on the temperature variation in an LMFBR rod bundle

The impact of gas in sodium flow on the temperature variation in an LMFBR rod bundle was studied in two types of experiments: (1) The gas fraction of the subchannels as well as the gas bubble spectra across the outlet of an unheated 61-rod bundle with wire spacers were measured in water/air flow. The distributions of the gas fractions at the inlet of the bundle were performed under uniform and non-uniform conditions. The results show that the distribution of the averaged gas fractions between the individual subchannels at the outlet of the bundle was almost the same as the distribution at the inlet. The measured bubble spectra show a dependency existing between the bubble frequencies, the bubble lengths, and the gas fraction in a subchannel. (2) A model for computing the transient temperature distributions within a heated rod was supported by experiments performed in a sodium/argon flow. For slug flow conditions a comparison indicates that the measured variations of wall temperatures can be well interpreted as being functions of the bubble contact time, rod power, and gas fraction in the flow.     

Flow measurements in rod bundle subchannels with varying rod-wall proximity

Detailed measurements of fully developed, turbulent, air flow through a five-rod sector of a 37-rod bundle have been conducted for the design geometry of the bundle, as well as for several cases with the central rod displaced towards the external tube wall and/or towards a neighboring rod, including cases with rod-wall and rod-rod contact. The wall shear stress on an outer rod reached minima at rod-wall and rod-rod gaps and maxima at open flow regions. The average and the minimum wall shear stresses decreased dramatically only for very small values of the rod-wall gap. Measurements of the mean velocity, Reynolds stresses and turbulent scales in the wall and inner subchannels are presented mostly as iso-contours. Isotachs bulged towards narrow gaps and corners, with the bulging becoming more pronounced as the rod-wall gap decreased. The local friction factor not only varied appreciably around the rod as the gap decreased, but also had values much larger than the average friction factor based on the subchannel bulk velocity, due to the variability of the local flow width.     

Analysis of flow distribution a PWR fuel rod bundle model containng A 90% blockage

An experimental investigation, covering a Reynolds number range from 2 × 10³ to 3.5 × 10⁴, was conducted to study the velocity and turbulence intensity distributions due to the presence of a blockage in an unheated 7 × 7 rod bundle. The blockage configuration, consisting of a 4 × 4 rod array, created a maximum flow area reduction of 90% in the central nine subchannels. The blockage sleeve length was 38.3 × rod diameter and the 90% blockage zone length extended for 16.4 × rod diameter. The results showed that upstream of the blockage, the flow was not influenced by the blockage until it reached the location where the inlet taper section of the swelling started. At the downstream end, the flow disturbance was extensive and persisted over a distance of about 83 rod diameters. Compared to the downstream velocity profiles, the turbulence intensity measurements however showed a faster recovery from the blockage influence. At the higher Reynolds number, velocity profiles calculated using the COBRA subchannel computer code compared consistently with the experimental data. The general flow behaviour of the various subchannels was reasonably well predicted. However, at low Reynolds number, due mainly to the frictional form loss calculation scheme in COBRA and uncertainty in the flow transition, the flow diversion due to the blockage to the surrounding unblocked subchannels was overestimated. The influence of the degree of recovery from the rod swelling on the flow was also studied using COBRA.     

Flow Transition Characteristics in 5×5 Rod Bundle Channel

The special geometric structure of the rod bundle channel can induce complicated flow transition of the coolant, and investigation on the flow transition rules is sufficiently important. In the current study, experimental and numerical study on the flow transition characteristics in the 5×5 rod bundle channel was carried out. Experiments were performed to obtain the variation characteristics of the resistance coefficient and CFD simulation was performed using different turbulence models in ANSYS Fluent. The results show that the simulation with SST k-ω turbulence model agrees well with the experimental data. The simulated turbulence intensity and resistance coefficient at different measurement locations and in different flow conditions were compared. For different subchannels, the turbulence intensity and the resistance coefficient are higher in the center subchannel than those in the edge subchannel. For the same subchannel, the turbulence intensity and the shear stress in the subchannel center are higher than those in the subchannel edge. This result indicates that the turbulence intensity, shear stress and resistance coefficient in the rod bundle are not uniform due to the influence of the wall surface. This non-uniform spatial interaction makes the transition point obscure.