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.     

Turbulent diffusion of heat between connected flow passages Part 1: Outline of problem and experimental investigation

Mixing by turbulent diffusion and secondary flow between the parallel subchannels of ducts simulating smooth, bare rod bundles has been investigated both experimentally and analytically. This paper, part 1, outlines the problem and reports experimental results; part 2 deals with the computer prediction of turbulent flow in rod bundles.The experimental work was performed on a long wind tunnel which was designed to achieve an axially unchanging, fully developed temperature profile at the tunnel exit. This is believed to be the first substantial investigation of inter-subchannel mixing using this technique. Detailed measurements were made over a range of Reynolds numbers and in three configurations simulating pitch to diameter ratios of 1.833, 1.375 and 1.1.The results of the experimental work confirm the major findings of previous investigations, in particular that the inter-subchannel mixing rates are considerably higher than predicted by simple diffusion theory, and are relatively insensitive to variations in the gap width between the rods. Effective diffusivities through the gap appear to be strongly anisotropic and there is no evidence of secondary flows.     

Turbulent diffusion of heat between connected flow passages Part 2: Predictions using the “κ-” turbulence model

Mixing by turbulent diffusion and secondary flow between the parallel subchannels of ducts simulating smooth, bare rod bundles has been investigated both experimentally and analytically. This paper, part 1, outlines the problem and reports experimental results; part 2 deals with the computer prediction of turbulent flow in rod bundles.The experimental work was performed on a long wind tunnel which was designed to achieve an axially unchanging, fully developed temperature profile at the tunnel exit. This is believed to be the first substantial investigation of inter-subchannel mixing using this technique. Detailed measurements were made over a range of Reynolds numbers and in three configurations simulating pitch to diameter ratios of 1.833, 1.375 and 1.1.The results of the experimental work confirm the major findings of previous investigations, in particular that the inter-subchannel mixing rates are considerably higher than predicted by simple diffusion theory, and are relatively insensitive to variations in the gap width between the rods. Effective diffusivities through the gap appear to be strongly anisotropic and there is no evidence of secondary flows.     

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.     

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.     

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.     

方形组件紧密栅格内非稳态流动行为的研究

棒束子通道间冷却剂的交混作用能显著降低棒束周向壁面的温差,为进一步了解紧密栅棒束内特殊的流场结构,以水为工质,对P/D=1.1的双排六棒束方形通道内的流动进行了试验研究与数值模拟。采用流场示踪方法,在Re =2 000～40 000范围内拍摄了紧密栅内棒壁间瞬态流动可视化信息,捕捉到大尺度类周期性脉动结构,并获得了该脉动流的相关特征参数。结果表明：当Re≥5 000时,大尺度脉动流发生,并在实验工况内呈很强的周期性,脉动流的波长与Re无关,脉动主频率与Re成正比;采用SSG湍流模型对相同截面通道内的流动进行了非稳态计算,模拟出棒壁狭缝处的大尺度类周期性脉动行为,计算所得脉动流各项参数与试验值符合良好。     

基于双区域模型的钠冷快堆组件子通道分析程序的开发与验证

子通道分析程序是钠冷快堆堆芯热工水力设计和安全分析的重要工具。本文为计算和分析钠冷快堆组件在径向均匀与倾斜功率分布工况下的热工水力特性,利用双区域绕丝交混模型开发了一款适用于钠冷快堆组件分析的子通道程序SPLICA,并与FFM2A 19棒束实验数据与WARD 61棒束实验数据进行了对比验证。由于本文开发的子通道分析程序SPLICA使用了详细的绕丝交混模型,与经过二次开发后的COBRA程序的计算结果相比,对于FFM2A实验SPLICA程序计算得到的结果与实验结果符合得更好。这两个实验数据的验证结果证明了本文开发的子通道分析程序的准确性以及对高流量工况和低流量工况均具有良好的适用性。本程序能为钠冷快堆组件热工水力分析提供有效的设计和研究手段。     

Simulation of flow pulsations in a twin rectangular sub-channel geometry using unsteady Reynolds Averaged Navier-Stokes modelling

An unsteady Reynolds Averaged Navier-Stokes (URANS) based turbulence model, the Spalart-Allmaras (SA) model, was used to investigate the flow pulsation phenomena in compound rectangular channels for isothermal flows. The studied geometry was composed of two rectangular sub-channels connected by a gap, on which experiments were conducted by Meyer and Rehme (1994) and were used for the validation of numerical results. Two case studies were selected to study the effect of the advection scheme. The results from the first order upwind advection scheme had clear symmetry and periodicity. The frequency of flow pulsations was under predicted by almost a factor of two. Due to inevitable numerical diffusion of the first order upwind scheme, a second order accurate in space advection scheme was also considered. The span-wise velocity contours, velocity vector plots, and time traces of the velocity components showed the expected cross-flow mixing between the sub-channels through the gap. The predicted kinetic energy in the unsteady velocity fluctuations showed two clear peaks at the edges of the gap. The dynamics of the flow pulsations were quantitatively described through temporal auto-correlations and power spectral functions. The numerical predictions were in agreement with the experiments. Studies on the effect of the Reynolds number and the computational length of the domain were also performed. The numerical results reproduced the relationship between the Reynolds number and the frequency of the flow pulsations. The impact of the channel length was tested by simulating a longer channel with respect to the base case. It was found that the channel length did not significantly affect the numerical predictions. Simulations were also performed using the standard k-? model. While the flow pulsations were predicted with this model, the frequency of the pulsation was in poor agreement with the experimentally measured value.     

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.     

Measurements of frequencies and spatial correlations of coherent structures in rod bundle flows

Cross-wire anemometry was used to identify and characterize coherent flow pulsations in isothermal air flow near the gap regions of a five-rod bundle with a design pitch-to-diameter ratio of 1.149 and contained in a quasi-trapezoidal duct. It was confirmed that such pulsations are quasi-periodic and contribute significantly to the velocity fluctuations across the gap. The frequency of pulsations was found to decrease with diminishing rod–wall gap size in the range between 0.015D and 0.250D, where D is the rod diameter. The pulsations in a rod–wall gap and an adjacent rod–rod gap were strongly coupled and occurred at the same frequency as one rod was displaced towards the duct wall.     

Analysis of low Reynolds number turbulent flow phenomena in nuclear fuel pin subassemblies of tight lattice configuration

This paper focuses on the numerical simulation of low Reynolds (Re) number turbulence flow phenomena in tightly packed fuel pin subassemblies and in channels of irregular shape such as eccentric annuli. Highlighted phenomena include (i) turbulence-driven secondary flows inside a subchannel, (ii) local turbulent-laminar transition in the narrow gap region, and (iii) global flow pulsation across the gap along the channel length. These phenomena are simulated by Computational Fluid Dynamics (CFD). The CFD methods employed here are those of Direct Numerical Simulation (DNS) of turbulence, Large Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS) equations approach. Complicated turbulent flow structure is due to strong anisotropy in the non-uniform channel geometry that is characterized by wide open channels connected by a narrow gap. The secondary flows in subchannels play an important role in transporting small eddies generated in the wider region toward the narrow gap. Periodic cross-flow oscillations are calculated to appear in the vicinity of the gap region, and the coherent structure is transported in the main flow direction. This macroscopic flow process prevails in the low Re turbulent flow regime and is called as global flow pulsation. Finally a brief discussion is made on their influences onto the mixing between two subchannels that must be taken into account during natural circulation decay heat removals.     

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。     

Measurements of the flow characteristics of the lateral flow in the 6 × 6 rod bundles with Tandem Arrangement Vanes

It is very important to increase the heat transfer efficiency in rod bundles in order to prevent the hot spot on the surface of fuel rods in view of the thermal hydraulic safety of nuclear power plants. It is representative to mount vanes in the support grid, which generate swirling flow. It is necessary to measure the flow pattern for investigating the thermal hydraulic flow characteristics in subchannels. In this study, it is performed to measure experimentally the flow field in cross-sections of the 6 × 6 rod bundles with new type vanes - Tandem Arrangement Vanes (TAV) by using Laser Doppler Anemometry. Through measurements, data are acquired at a nominal Reynolds number of 50,000 and for three streamwise locations at 3, 10, and 20 hydraulic diameters. Many previous experimental studies by the existing split mixing vanes show small turbulent length scales and short retention time till 10D_h after spacer grid. On the other hand, the TAVs proposed in the present study generate the big enforced swirl flow more than 20D_h after spacer grid and heat transfer effect are maintained through this distance.     

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.     

Assessment of the interchannel mixing model with a subchannel analysis code for BWR and PWR conditions

The influence of the interchannel mixing model employed in a traditional subchannel analysis code was investigated in this study, specifically on the analysis of the enthalpy distribution and critical heat flux (CHF) in rod bundles in BWR and PWR conditions. The equal-volume-exchange turbulent mixing and void drift model (EVVD) was embodied to the COBRA-IV-I code. An optimized model of the void drift coefficient has been devised in this study as the result of the assessment with the two-phase flow distribution data for the general electric (GE) 9-rod and Ispra 16-rod test bundles. The influence of the subchannel analysis model on the analysis of CHF was examined by evaluating the CHF test data in rod bundles representing PWR and BWR conditions. The CHFR margins of typical light water nuclear reactor (LWR) cores were evaluated by considering the influence on the local parameter CHF correlation and the hot channel analysis result. It appeared that the interchannel mixing model has an important effect upon the analysis of CHFR margin for BWR conditions.     

CFD analysis of thermal–hydraulic behavior of heavy liquid metals in sub-channels

CFD analysis was carried out for thermal–hydraulic behavior of heavy liquid metal flows, especially lead–bismuth eutectic, in sub-channels of both triangular and square lattices. Effect of various parameters, e.g. turbulence models and pitch-to-diameter ratio, on the thermal–hydraulic behavior was investigated. Among the turbulence models selected, only the second order closure turbulence models reproduce the secondary flow. For the entire parameter range studied in this paper, the amplitude of the secondary flow is less than 1% of the mean flow. A strong anisotropic behavior of turbulence is observed. The turbulence behavior is similar in both triangular and square lattices. The average amplitude of the turbulent velocity fluctuation across the gap is about half of the shear velocity. It is only weakly dependent on Reynolds number and pitch-to-diameter ratio. A strong circumferential non-uniformity of heat transfer is observed in tight rod bundles, especially in square lattices. Related to the overall average Nusselt number, CFD codes give similar results for both triangular and square rod bundles. Comparison of the CFD results with bundle test data in mercury indicates that the turbulent Prandtl number for HLM flows in rod bundles is close to 1.0 at high Peclet number conditions, and increases by decreasing Peclet number. Based on the present results, the SSG Reynolds stress model with semi-fine mesh structures is recommended for the application of HLM flows in rod bundle geometries.     

Coolant mixing in a fuel pin assembly utilizing helical wire wrap spacers

Coolant mixing in a helically wire-wrapped, 217 pin, full-scale model of an LMFBR fuel assembly is presented. Salt-injection-conductivity techniques were employed, using water as the coolant. Over four hundred probes were concentrated in a one-sixth sector of the assembly to exhaustively measure the salt distribution.The basic results are presented for use in the verification of thermal hydraulic computer codes and wire-wrap mixing models. Interior channel gross mixing rates were about 9%/cm (effectively 3% per cm per gap); this was more than three times the natural turbulence level. There existed only a small peripheral (swirl) flow around the bundle; its direction averaged only slightly greater than half helical wire wrap angle. The results were reduced into an effective turbulent mixing model, and a wire-wrap forced diversion cross flow model is also presented.     

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.     

CFD analysis of thermal-hydraulic behavior in SCWR typical flow channels

Investigations on thermal-hydraulic behavior in SCWR fuel assembly have obtained a significant attention in the international SCWR community. However, there is still a lack of understanding and ability to predict the heat transfer behavior of supercritical water. In this paper, CFD analysis is carried out to study the flow and heat transfer behavior of supercritical water in sub-channels of both square and triangular rod bundles. Effect of various parameters, e.g. thermal boundary conditions and pitch-to-diameter ratio on the thermal-hydraulic behavior is investigated. Two boundary conditions, i.e., constant heat flux at the outer surface of cladding and constant heat density in the fuel pin are applied. The results show that the structure of the secondary flow mainly depends on the rod bundle configuration as well as the pitch-to-diameter ratio, whereas, the amplitude of the secondary flow is affected by the thermal boundary conditions, as well. The secondary flow is much stronger in a square lattice than that in a triangular lattice. The turbulence behavior is similar in both square and triangular lattices. The dependence of the amplitude of the turbulent velocity fluctuation across the gap on Reynolds number becomes prominent in both lattices as the pitch-to-diameter ratio increases. The effect of thermal boundary conditions on turbulent velocity fluctuation is negligibly small. For both lattices with small pitch-to-diameter ratios (P/D < 1.3), the mixing coefficient is about 0.022. Both secondary flow and turbulent mixing show unusual behavior in the vicinity of the pseudo-critical point. Further investigation is needed. A strong circumferential non-uniformity of wall temperature and heat transfer is observed in tight lattices at constant heat flux boundary conditions, especially in square lattices. In the case with constant heat density of fuel pin, the circumferential conductive heat transfer significantly reduces the non-uniformity of circumferential distribution of wall temperature and heat transfer, which is favorable for the design of SCWR fuel assemblies.