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.     

燃料组件精细化定位格架模型开发及评价

为提高燃料组件子通道内两相局部参数预测的准确性,本文基于分布式阻力方法建立精细化定位格架模型,选用合适的摩擦阻力表达式,对格架上的交混翼进行精细化建模,采用Carlucci湍流交混模型计算湍流交混速率,引入阻塞因子计算由定位格架引起的湍流交混效应,并将建立的精细化定位格架模型植入子通道分析程序（ATHAS）,对压水堆子通道和棒束实验（PSBT）基准题进行计算分析。结果表明,本文开发的精细化定位格架模型能够提高燃料组件子通道内空泡份额和温度分布的预测准确性,为棒束通道流场、焓场计算和临界热流密度（CHF）预测奠定了基础。      

Measurements of shear stress in a square array rod bundle

A flush-mounted hot film sensor was used to determine the shear stress distribution on the centrally located rod in a 1.4 pitch to diameter ratio square array, nine rod bundle with axial flow. The film sensor was calibrated in a concentric annulus flow geometry. Shear stress measurements were made at a position 65 hydraulic diameters from the flow entrance for Reynolds numbers from 12 000 to 32 000. The circumferential variation of the shear stress was nearly sinusoidal around the central rod and the maximum and minimum values occurred at the maximum and minimum subchannel spacing. The peak to peak variation of the sinusoidal shear stress distribution is about 4 to 6% of the mean value.     

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.     

5×5棒束通道内流动转捩特性研究

棒束通道的特殊结构导致其内部流动转捩情况较为复杂,探究其内部流动转捩规律具有重要意义。本文针对棒束通道内的流动转捩特性开展实验与CFD模拟研究,通过实验获得了棒束通道内沿程阻力系数的变化规律;采用不同湍流模型进行了数值模拟。结果表明,SST k-ω模型能较好地反映实验结果。进一步对比了不同雷诺数工况下通道内不同位置的沿程阻力系数与湍流强度,发现对于不同子通道,中心子通道湍流强度与沿程阻力系数高于边角子通道;对于同一子通道,子通道中心处湍流强度与壁面切应力高于子通道边缘处。这一结果说明,受壁面影响,棒束内湍流强度、壁面切应力、阻力特性具有不均匀性,这些空间上的不均匀性相互作用会引起总体上棒束转捩点不明显。     

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.     

Calculated heat transfer development in bundles

In many cases heat transfer in rod bundles can be considered as a superposition of several simple heat transports. A number of practical problems can thus be solved if solutions for these elementary transport are available. Two elementary heat transports in rod bundle geometry are investigated, namely the transport from a fuel rod surface into the adjacent subchannel and the transport from one subchannel into the next one. The first transport is characterized in terms of the Nusselt or Stanton numbers, while the latter in terms of the Stanton gap number or mixing factor. Hydraulically developed flow is assumed, with no feedback of heat transport on the flow condition. A three-dimensional numerical calculation by means of the finite difference method is applied to determine the eigenvalue solution of the response on a step change in heating for both cases. The method is tested on an internally heated concentrical annulus. The result is compared with available experimental and theoretical predictions. It is found that the heat transfer between subchannels is developed considerably slower in comparison with the development of the heat transport from fuel rod to subchannel.     

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part I: Experiments

Lack of local void fraction data in a rod bundle makes it difficult to validate a numerical method for predicting gas–liquid two-phase flow in the bundle. Distributions of local void fraction and bubble velocity in each subchannel in a 4×4 rod bundle were, therefore, measured using a double-sensor conductivity probe. Liquid velocity in the subchannel was also measured using laser Doppler velocimetry (LDV) to obtain relative velocity between bubbles and the liquid phase. The size and pitch of rods were 10 and 12.5 mm, respectively. Air and water at atmospheric pressure and room temperature were used for the gas and liquid phases, respectively. The volume fluxes of gas and liquid phases ranged from 0.06 to 0.15 m/s and from 0.9 to 1.5 m/s, respectively. Experimental results showed that the distributions of void fraction in inner and side subchannels depend not only on lift force acting on bubbles but also on geometrical constraints on bubble dynamics, i.e. the effects of rod walls on bubble shape and rise velocity. The relative velocity between bubbles and the liquid phase in the subchannel forms a non-uniform distribution over the cross-section, and the relative velocity becomes smaller as bubbles approach the wall due to the wall effects.     

Axial static pressure variations in inner and side subchannels of a 61-tube wire-wrap bundle

Measurements of axial distribution of the static pressure in an inner and side subchannel of a 61 wire-wrap tube bundle obtained with water at atmospheric conditions are presented. The wire wrap configuration is different from those used by previous workers and more representative of a bundle for the blanket of a Gas Cooled Fast Reactor. The data display axial static pressure variations which are attributed to the interchannel cross flow induced by the wire-wrap configuration. The static pressure drop over one wire pitch agrees well with the bundle pressure drop based on a bundle average Reynolds number and a friction factor f = 0.436 Re^−0.263 (Re > 2000). The experimental data obtained with water provide a useful benchmark to model and check the accuracy of thermal-hydraulic codes used for the analysis of subchannel flow distribution and pressure drop in wire wrap tube bundle cooled with one-phase fluid.The nodal subchannel code COBRA-IV was modeled by adjusting the forced cross-flow function to match the measured axial static pressure distribution in an inner and side subchannel. Some discrepancy remained in the static pressure profile in the side channel attributed to the flow distortion at the bundle exit.     

Void fraction estimation within rod bundles based on three-fluid model and comparison with x-ray CT void data

An interfacial shear stress equation in the dispersed-annular two-phase flow regime has been developed, which is based on a three-fluid model consisting of a liquid film on a rod, vapor and entrained liquid associated with a vapor flow. It is an extension of J.G.M. Andersen's procedure that provides a two-fluid interfacial shear stress equation using the drift flux parameters C₀ and V_gj. This interfacial shear stress equation can take into account a phase and velocity distribution through an equivalence between the drift flux parameters and the interfacial shear stress.

Using the three-fluid subchannel analysis code TEMPO with the three-fluid interfacial shear stress model, the capability of a three-fluid calculation using the drift flux parameters C₀ and V_gj that reproduce a measured void fraction is demonstrated. A comparison was made with advanced X-ray computed tomography (CT) void fraction data within a 4×4 rod bundle in diabatic 1 MPa pressure conditions. The three-fluid velocity field was estimated to be in good agreement with the experimental result of a void fraction.     

Multi-dimensional analysis of two-phase flow inside subchannels of nuclear fuel assembly

In subchannel analysis, the conservation equations are solved for each channel in a complex fuel bundle, where the effects of fluid exchange between each subchannel are considered. The fluid exchange is commonly referred to as that caused by cross flow. Void drift is considered to be phenomenon resulting from attaining a hydrodynamic equilibrium state. Its mechanism has not been clarified, and the transport due to void drift is therefore estimated through empirical models in conventional subchannel analyses. Therefore, mechanistic model for the void drift phenomenon is required to apply the subchannel analysis to a variety of fuel bundle geometry. In this study, multi-dimensional analysis using two-fluid model was applied to two-phase flow inside a geometry simulating fuel bundle subchannels, for the purpose of clarifying the void drift mechanism. The comparison between the results of the numerical analysis and the experiment confirmed that the reliability of the numerical method used in this study. In this paper, a mechanistic model based on the Stanton number, which expresses the void diffusion coefficient based on the Lahey's proposal, was proposed.     

基于丝网传感器的5×5棒束通道空泡分布测量研究

为研究压水反应堆燃料组件棒束通道内的两相分布规律,设计并制造了适用于棒束通道的丝网传感器模块,开展了5×5棒束通道内空气-水泡状流的空泡分布测量实验,分析了棒束通道内空泡份额的分布规律及气泡尺寸对空泡分布的影响。实验结果表明,发生横升力方向反转的小气泡在壁面附近聚集、大尺寸气泡则聚集在子通道中心;常温常压下发生横升力方向反转的临界气泡直径在4~6 mm之间,证明了横升力模型在棒束通道中的适用性。      

Experimental techniques for liquid metal cooled fast breeder reactor fuel assembly thermal/hydraulic tests

Sensors and methods of experimental measurement being employed in fast breeder reactor fuel assembly tests are reviewed. Such tests are being carried out in sodium, water and air environments. In sodium tests direct measurement of bundle performance parameters such as temperature, flow, pressure, boiling inception, and void fraction are being performed. Development of improved instrumentation is needed for reliable fast-response, high-temperature pressure detection and small, more readily interpretable, void detectors. Water and air environment tests are being undertaken to measure parameters used in models which predict design behavior in sodium. Parameters being measured are subchannel average velocity, local axial and transverse velocities, wall shear stress, salt and other tracer concentrations, and turbulence parameters. Adequate techniques exist for measurement of each of these parameters.     

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.     

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.     

Numerical simulation of the hydrodynamic behavior of fuel rod with longitudinal cooling fins

Four processes which considerably affect the distribution of the local shear stress in turbulent cooling flow along a fuel rod with longitudinal fins are discussed. The effect of boundary layers' development, geometry driven secondary currents, roughness induced lateral motion and geometry imperfections were studied and compared. Turbulence was modeled by an energy-dissipation model with an algebraic stress model. The three-dimensional flow was numerically simulated using a parabolic pressure correction algorithm.     

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.     

A subchannel analysis of DUPIC fuel bundle for the CANDU reactor

Thermal characteristics of the reference DUPIC fuel has been studied for its feasibility of loading in the CANDU reactor. Half of the DUPIC fuel bundle has been modeled for a subchannel analysis of the ASSERT-IV Code which was developed by AECL. From the calculated mixture enthalpy, equilibrium quality and void fraction distributions in subchannels of the fuel bundle, it is found that the gravity effect may be pronounced in the DUPIC fuel bundle when compared with the standard CANDU fuel bundle. The asymmetric distribution of the coolant in the fuel bundle is known to be undesirable since the minimum critical heat flux ratio can be reduced for a given value of the channel flow rate. On the other hand, the central region of the DUPIC fuel bundle has been found to be cooled more efficiently than that of the standard fuel bundle in the subcooled and the local boiling regimes due to the fuel geometry and the fuel element power changes. Based upon the subchannel modeling used in this study, the location of minimum critical heat flux ratio in the DUPIC fuel bundle turned out to be very similar to that of the standard fuel when the equivalent values of channel power and channel flow rate are used. From the calculated mixture enthalpy distribution at the exit of the fuel channel, it is found that the subchannel-wise mixture enthalpy and void fraction peaks are located in the peripheral region of the DUPIC fuel bundle while those are located in the central region of the standard CANDU fuel bundle. Reduced values of the channel flow rates were used to study the effect of channel flow rate variation. The effect of the channel flow reduction on different thermal-hydraulic parameters have been discussed. This study shows that the subchannel analysis for the horizontal flow is very informative in developing new fuel for the CANDU reactor.     

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.     

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.