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.     

An experimental study of turbulent flow through a square-array rod bundle

Using laser-Doppler anemometry and calibrated Preston tubes, experiments were performed in water (80°C, 0.6 MPa) to obtain information on the distributions of wall shear stresses, mean axial velocities and turbulence intensities for fully developed adiabatic flow through a six-rod bundle at a Reynolds number of 5 × 10⁵. The rods were arranged in a square array with a pitch to a diameter ratio of 1.15 and a wall-distance to diameter ratio of 0.62. The core flow in the central subchannel appears to be similar to pipe flow, but in the gap regions much higher turbulence intensities are encountered. The skewed wall shear stress profiles together with the deformed constant-velocity lines suggest the presence of secondary flows in the corner subchannels.     

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.     

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.     

棒束子通道湍流交混特性的数值模拟研究

为了提高核反应堆系统的经济性和安全性,本文采用CFD方法对棒束子通道间湍流交混效应进行研究。对子通道建模,选取SST k-ω模型进行计算,完成了网格敏感性分析。采用类比浓度计算法与间隙湍流热流法对湍流交混系数进行计算。计算结果表明：雷诺数较小时,单相湍流交混系数随雷诺数的增大而增大;当雷诺数达到一定值时,单相湍流交混系数近似为定值;采用类比浓度计算法与间隙湍流热流法计算所得的湍流交混系数无太大差别。本文拟合得到了适用于单相工况的湍流交混系数计算公式。     

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.     

Prediction of the single-phase turbulent mixing rate between two parallel subchannels using a subchannel geometry factor

This paper presents a simple method for predicting the single-phase turbulent mixing rate between adjacent subchannels in nuclear fuel bundles. In this method, the mixing rate is computed as the sum of the two components of turbulent diffusion and convective transfer. Of these, the turbulent diffusion component is calculated using a newly defined subchannel geometry factor F^* and the mean turbulent diffusivity for each subchannel which is computed from Elder's equation. The convective transfer component is evaluated from a mixing Stanton number correlation obtained empirically in this study. In order to confirm the validity of the proposed method, experimental data on turbulent mixing rate were obtained using a tracer technique under adiabatic conditions with three test channels, each consisting of two subchannels. The range of Reynolds number covered was 5000–66 000. From comparisons of the predicted turbulent mixing rates with the experimental data of other investigators as well as the authors, it has been confirmed that the proposed method can predict the data in a range of gap clearance to rod diameter ratio of 0.02–0.4 within about ±25% for square array bundles and about ±35% for triangular array bundles.     

The structure of turbulent flow through a wall subchannel of a rod bundle

An experimental investigation was performed to establish reliable information on the transport properties of turbulent flow through subchannels of rod bundles. Detailed data were measured of the distributions of the time-mean velocity, the turbulence intensities in all directions and hence, the kinetic energy of turbulence, of the shear stresses in the directions normal and parallel to the walls and of the wall shear stresses for a wall subchannel of a rod bundle of four parallel rods. The pitch to diameter ratio of the rods equal to the wall to diameter ratio was 1.07, the Reynolds number of this investigation was Re = 8.7 × 10⁴.On the basis of the data measured the eddy viscosities in the directions normal and parallel to the walls were calculated. Thus, detailed data of the eddy viscosities in direction parallel to the walls in rod bundles were obtained for the first time. The experimental results were compared with predictions by the VELASCO code. There are considerable differences between calculated and measured data of the time-mean velocity and the wall shear stresses. Attempts to adjust the VELASCO code against the measurements were not successful. The reasons of the discrepancies are discussed.     

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.     

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。     

Evaluation of the conduction shape factor with a CFD code for a liquid–metal heat transfer in heated triangular rod bundles

A heat transfer due to conduction through a coolant itself is not negligible in a liquid–metal cooled reactor (LMR). This portion of a heat transfer is frequently described with a conduction shape factor during the thermal-hydraulic design of an LMR. The conduction shape factor, which is highly dependent on a pitch-to-diameter (P/D) ratio, is defined as the ratio of the local conduction heat flux at a gap between two subchannels to the reference heat flux calculated by the averaged subchannel temperatures. The shape factors in heated triangular rod arrays for three different pitch-to-diameter ratios are generated through CFX calculations in the present study. The flow paths of 1.0–2.0 m in length are meshed into 180,000–360,000 volumes depending on the flow velocities. The SSG Reynolds stress model is used as a turbulent model in the calculations. The evaluated data fell between the heated-rod data and the plane-source data obtained by theoretical investigations. The conduction shape factors were found to be independent of the heating pattern of the rod arrays. Based on the evaluated data, a correlation for a liquid sodium coolant is suggested, which will improve the accuracy of the subchannel analysis codes for the thermal-hydraulic design of an LMR. When it is compared with the existing correlations, the suggested correlation is expected to enhance the reliability of the conduction shape factor because the data is evaluated by a more realistic numerical experiment.     

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.     

CFD investigations of helical wire-wrap fuel pin bundle and its comparison with straight wire bundle

Computational Fluid Dynamics (CFD) investigations of a fast reactor fuel pin bundle wrapped with helical and straight spacer wires have been carried out and the advantages of using helical spacer wire have been assessed. The flow and temperature distributions in the fuel pin bundle are obtained by solving the statistically averaged 3-Dimensional conservation equations of mass, momentum and energy along with high Reynolds number k-ε turbulence model using a customized CFD code CFDEXPERT. It is seen that due to the helical wire-wrap spacer, the coolant sodium not only flows in axial direction in the fuel pin bundle but also in a transverse direction. This transverse flow enhances mixing of coolant among the sub channels and due to this, the friction factor and heat transfer coefficient of the coolant increase. Estimation of friction factor, Nusselt number, sodium temperature uniformity at the outlet of the bundle and clad hot spot factor which are measures of the extent of coolant mixing and non-homogeneity in heat transfer coefficient around fuel pin are paid critical attention. It is seen that the friction factor and Nusselt number are higher (by 25% and 15% respectively) for the helical wire wrap pin bundle compared to straight wire bundle. It is seen that for 217 fuel pin bundle the maximum clad temperature is 750 K for straight wire case and the same for helical wire is 720 K due to the presence of transverse flow. The maximum temperature occurs at the location of the gap between pin and wire. The ΔT between the bulk sodium in the central sub-channel and peripheral sub-channel is 30 K for straight wire and the same for helical wire is 18 K due to the presence of secondary transverse flow which makes the outlet temperature more uniform. The hotspot factor and the hot channel factors predicted by CFD simulation are 10% lower than that used in conventional safety analysis indicating the conservatism in the safety analysis.     

PIV and CFD Study of Turbulent Flow Behavior in Rod Bundle

At the downstream of the spacer grid in a PWR fuel assembly, local disturbance damps out along the flow direction and the flow returns to stable eventually. The turbulent flow and mixing behavior of the coolant are key factors affecting the economy and safety of a nuclear reactor, and need in-depth investigations. In the present paper, the turbulent flow of water in a 3×3 rod bundle was studied using PIV (particle image velocimetry) and CFD. First-order mean velocity and second-order turbulent statistics were obtained. It is found that the velocity in the central subchannel is higher than that in the gap region, but the streamwise root-mean-square velocity behaves inversely. Large-scale flow pulsation induced by the strong streamwise velocity gradient between adjacent subchannels, is observed in the rod bundle, and the wave length increases with Reynolds numbers. In addition, the measured turbulent mixing coefficient is 10% higher than that predicted by the Castellana correlation for PWRs, but this deviation reduces with the increase of Reynolds numbers.     

棒束内湍流流动特性的PIV与CFD研究

在压水堆燃料组件的定位格架下游,局部扰动沿流动方向逐渐衰减,流场最终趋于稳定。光滑棒束区冷却剂的湍流流动和交混特性是影响反应堆经济性和安全性的重要因素,有必要进行深入研究。本文采用粒子图像测速（PIV）与数值模拟(CFD)相结合的方法,对3×3小规模棒束内水的流动特性进行研究,得到了一阶平均流速以及二阶湍流统计信息。结果表明,中心子通道的速度明显高于棒间隙区,但轴向均方根速度呈现出相反的变化趋势。在相邻子通道横向速度梯度的作用下,棒束内出现了大尺度的流量脉动现象,且脉动波长随雷诺数的增加而增大。此外,实验得到的湍流交混系数较压水堆采用的Castellana公式预测值偏高10%左右,这一偏差随雷诺数的增加有减小的趋势。     

Heat transfer, momentum losses and flow mixing in a 61-tube bundle with wire-wrap

Friction factors and heat transfer coefficients were obtained in the laminar and turbulent regions for a 61-tube wire-wrapped hexagonal bundle in a water flow loop. Circumferential static pressure and temperature profiles of tubes, and the flow patterns produced by injection of dye at the periphery of the bundle revealed a strong local effect of the wire-wrap. The increase in heat and momentum transfer resulting from the wire-wrap was more pronounced in the laminar region than in the turbulent region. Correlations for the friction factors and Nusselt numbers were developed from the data and compared with the literature.     

Experimental study on the Reynolds number dependence of turbulent mixing in a rod bundle

An experimental study for Reynolds number dependence of the turbulent mixing between fuel-bundle subchannels, was performed. The measurements were done on a triangular array bundle with a 1.20 pitch to diameter relation and 10 mm rod diameter, in a low-pressure water loop, at Reynolds numbers between 1.4 × 10³ and 1.3 × 10⁵.The high accuracy of the results was obtained by improving a thermal tracing technique recently developed. The Reynolds exponent on the mixing rate correlation was obtained with two-digit accuracy for Reynolds numbers greater than 3 × 10³. It was also found a marked increase in the mixing rate for lower Reynolds numbers.The weak theoretical base of the accepted Reynolds dependence was pointed out in light of the later findings, as well as its ambiguous supporting experimental data.The present results also provide indirect information about dominant large scale flow pulsations at different flow regimes.     

An investigation of the constitutive relations for intersubchannel transfer mechanisms in horizontal flows as applied in the ASSERT-4 subchannel code

In this paper, the influence that the constitutive relations used to represent some of the intersubchannel transfer mechanisms has on the predictions of the ASSERT-4 subchannel code for horizontal flows is examined. In particular the choices made in the representation of the gravity driven phase separation phenomena are analyzed. This is done by comparing the predictions of the ASSERT subchannel code with experimental data on void fraction and mass flow rate, obtained for two horizontal interconnected subchannels. ASSERT uses a drift flux model which allows the two phases to have different velocities. In particular ASSERT contains models for the buoyancy effects which cause phase separation between adjacent subchannels in horizontal flows. This feature, which is of great importance in the subchannel analysis of CANDU reactors, is implemented in the constitutive relationship for the relative velocity. In order to isolate different intersubchannel transfer mechanisms, three different subchannel orientations are analyzed. These are the two subchannels at the same elevation, the high void subchannel below the low void subchannel, and the high void subchannel above the low void subchannel. It is observed that for all three subchannel orientations ASSERT does a reasonably good job of predicting the experimental trends. However, certain modifications to the representation of the gravitational phase separation effects which seem to improve the overall predictions are suggested.     

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.     

Simulation of turbulent flow inside different subchannels in tight lattice bundle

In this paper, both steady and unsteady Reynolds Averaged Navier Stokes (RANS and URANS) methodology are applied to the prediction of turbulent flow inside different subchannels in tight lattice bundles.Two typical configurations of subchannels (i.e., wall subchannel and center subchannel) are chosen to be investigated. In this work the application of different turbulence models implemented in the commercial code CFX v12 is shown. The validity of the methodology is assessed by comparing computational results of axial velocity, wall shear stress and turbulent intensity distributions with the experimental data (Krauss, 1996; Krauss and Meyer, 1998). This study shows that RANS simulation with anisotropic turbulent model produces excellent agreement with experiment, whereas it failed to predict the flow behavior accurately in the case of tightly packed geometries (P/D < 1.1). On the other hand, the URANS simulation is in good agreement with the results in tightly packed geometries with flow oscillation in the gap region. The effects of the Reynolds number and the bundle geometry on the flow oscillation are investigated in details.