Turbulent momentum transport in rod bundles

An experimental investigation was performed with air to obtain detailed information on the velocity and turbulence distribution for parallel turbulent flows through subchannels of rod bundles. Experimental results were obtained for wall and corner subchannels of rod bundles of four parallel rods. The pitch-to-diameter ratios were varied between 1.07 and 1.4. The Reynolds numbers ranged from 6 × 10⁴ to 2 × 10⁵, depending on the rod bundle arrangement.On the basis of the data measured, the eddy viscosities in the directions normal and parallel to the wall were calculated. The experimental results of the velocity and wall shear stress distributions are compared with the predictions by the VELASCO code. There are considerable differences between computed and experimental results especially for low pitch-to-diameter ratios. The reasons for the discrepancies are discussed together with the results of attempts to adjust the VELASCO code against the experimental data.     

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.     

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.     

Numerical simulation of turbulent flow in a 37-rod bundle

The unsteady Reynolds averaged Navier–Stokes equations, combined with a Reynolds stress model, were solved numerically to determine fully developed isothermal turbulent flow in a 60° sector of a 37-rod bundle. It was found that this flow contained large-scale coherent structures, which affected strongly the local velocity fluctuations, especially near the gaps between rods or between rods and the surrounding wall. The time-averaged mean velocity and Reynolds stresses were in good agreement with experimental results in a similar channel. Coherent velocity fluctuations at different locations throughout the entire rod bundle were strongly correlated with each other.     

Developed single phase turbulent flow through a square-pitch rod cluster

An experimental study of developed single phase turbulent flow through a square pitched array of rod bundles is described. Measurements were made at two spacings (p/d = 1.194, 1.107) of the mean velocity distribution and wall shear stress variation, together with the six terms of the symmetrical Reynolds stress tensor. The departure of the turbulent flow structure from axisymmetric pipe flow, particularly in the rod gap region, was found to depend strongly on the (p/d) ratio.     

Pressure drop and velocity distribution in rod bundles with spacer grids

The paper contains experimental data and analysis of the pressure drop of turbulent flow through rod bundles. For laminar flow the dependence of the pressure drop on the pitch-to-diameter and wall-to-diameter ratios is discussed on the basis of theoretical analysis. In addition, correlations for the calculation of the pressure loss due to spacer grids are presented and compared with experimental data.Detailed measurements of the velocity distribution in a full bundle of 19 rods are compared with predictions for fully developed turbulent flow. Moreover, detailed measurements of the velocity distributions upstream and downstream of spacer grids typical for LMFBRs are discussed together with the mass flow separation and redistribution between the subchannels. The mass flow distribution found experimentally is compared with the predictions by a subchannel code. The status of experimental knowledge is shown.     

Multi-recycling in the ENHS and the equilibrium core

This work investigates the effect of initial fuel composition, power density and number of recycles on the pitch-to-diameter (P/D) ratio and TRans-Uranium isotopes (TRU) loading required for attaining one of the most important design goals of the Encapsulated Nuclear Heat Source (ENHS) – nearly zero burnup reactivity swing over the 20 years of core life. It is found that the required P/D ratio is sensitive to, primarily, the initial concentration of the short-lived isotope ²⁴¹Pu in the fuel loaded into the first core and to the core power density. The longer is the cooling time of the TRU from LWR spent fuel the smaller becomes the relative ²⁴¹Pu concentration and the smaller becomes the fraction of ²⁴¹Pu lost via radioactive decay and, hence, the smaller needs be the conversion ratio required for nearly zero burnup reactivity swing and the larger can be the P/D ratio. Likewise, the higher is the ENHS power density, the smaller becomes the fraction of ²⁴¹Pu lost via radioactive decay and the larger becomes the P/D required for the first core. The optimal P/D ratio tends to increase with the number of times the fuel is recycled from one ENHS core to the next one. The optimal P/D ratio for the equilibrium composition core is in between 1.53 and 1.59. For a given discharge burnup it tends to somewhat increase with the equilibrium core power density. However, if structural materials will be developed to enable a 20 years core life at elevated power densities, the higher the power density the smaller is the required equilibrium P/D ratio.     

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.     

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.     

Measurements of turbulent velocity and temperature in axial flow through a heated rod bundle

Fully developed turbulent air flow in a heated 37-rod bundle with a pitch to diameter ratio of 1.12 has been investigated. Measurements were performed with a hot-wire probe with x-wires and a temperature wire. Besides the distributions of the mean velocity, mean fluid temperature, the wall shear stress and wall temperature, the turbulent quantities such as the turbulent kinetic energy, the Reynolds-stresses and the turbulent heat fluxes were measured and compared with data from isothermal flow and heated flow in pipes.     

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.     

The flow and heat transfer characteristics of turbulent flow in typical rod bundles in ocean environment

The flow and heat transfer characteristic of turbulent flow in typical 4 and 7 rod bundles in ocean environment is investigated theoretically. In ocean environment, the periodic variation of secondary flow in 7 rod bundles is not obvious. Because of the velocity oscillation, there is a periodic heat accumulation on the tube wall. And the restriction of the channel wall on the rolling motion is considerable. In 7 rod bundles, because of the restriction of the channel wall, the effect of the additional force perpendicular to flowing direction is limited, and the turbulent flowing and heat transfer is mainly determined by the axial turbulent intensity and inlet velocity. However, in the 4 rod bundles, the restriction of the channel wall is small. The effect of the additional force perpendicular to flowing direction on the flowing and heat transfer is significant. And the additional force perpendicular to flowing direction can also affect the Reynolds stress.     

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。     

带格架四棒束超临界水流动传热数值分析

棒束内超临界水流动传热是超临界水堆堆芯热工水力研究的重要内容,但对其认识还十分有限。本文针对四棒束内超临界水的流动传热现象开展数值模拟,特别分析了定位格架对棒束通道内流动和传热的影响。结果表明,采用SSG湍流模型计算所得到的棒束壁面温度和实验结果吻合良好,定位格架的存在影响下游流体的速度分布,显著提高格架下游的传热特性,交混系数有大幅上升,使得加热棒周向壁面温度分布更加平均,最高温度出现位置发生改变。     

Laminar convection in wall sub-channels and transport rates for finite rod-bundle assemblies by superposition

Finite rod-clusters in circular, square and hexagonal shells have been divided along the symmetry lines into a number of interior, wall and corner subchannels. Laminar fluid flow and heat transfer results have been generated for these subchannels with varying pitch-to-diameter and wall distance-to-diameter ratios. Wall shear stress and temperature variations for typical wall subchannels are presented. Friction factor values for finite bundles are then obtained by superposing the results of the subchannels that constitute the bundles. The values so generated are in excellent agreement with previous work in the literature obtained by the method of symmetry sectors. Considerable disagreements were, however, observed in the superposed values of Nusselt number, apparently due to conduction effects.     

On the fluctuating wall pressure field in tube banks

This paper presents the experimental analysis of pressure and velocity fluctuations of the cross flow in tube banks, with triangular and square arrangements, and four different aspect ratios. Air is the working fluid, driven by a centrifugal blower, passed by a settling chamber and a set of honeycombs and screens, before reaching the tube bank at an incidence angle of 90°. Both triangular and square arrangements have pitch-to-diameter ratios P/D=1.60, 1.26, 1.16 and 1.05, with Reynolds numbers, calculated with the tube diameter and the velocity of the flow in the narrow gap between the tubes, from Re=4×10⁴ to 7×10⁴. Velocity and velocity fluctuations were measured by a constant-temperature hot-wire anemometer, while pressure fluctuations were measured by a piezo-resistive pressure transducer mounted inside one of the tubes in the bank. Behavior of fluctuating quantities is described by means of dimensionless root mean square values and autospectral density functions, while their interdependence is discussed based on cross-correlation functions.     

海洋条件对棒束间湍流流动传热的影响

对海洋条件下典型7棒束和4棒束通道内的流体流动传热特性进行理论分析.分析结果表明,在海洋条件下,由于流速的波动,加热管壁上始终有周期性变化的蓄热存在.在7棒束通道内,由于四周壁面和加热管管壁的限制作用,垂直于流动方向的附加力对流体的影响非常小,流体的流动和传热特性主要由轴向湍流强度和入口流速决定.而在4棒束通道内,由于...     

Numerical simulation of flows in tight-lattice fuel bundles

The flow in tight rod bundles is characterized by long-term, large-scale coherent patterns in the stream-wise direction.

In the present work, the issue of simulating these structures through unsteady CFD simulations employing periodic boundary conditions in the stream-wise direction, will be addressed. The validity of the approach is assessed through the comparison of a large eddy simulation (LES) for similar flow conditions inside a simplified geometry and experimental data.

A powerful statistical tool (proper orthonormal decomposition) is used to analyze the time varying solution. The flow field has been decomposed into a series of normal modes, identifying the structures responsible for the flow transfer between sub-channels. Additional insights on the physics of these coherent structures are obtained.

An unsteady Reynolds averaged Navier–Stokes simulation (URANS) of the flow in a rod bundle has then been carried out. The comparison between numerical results and experimental results [Krauss, T., Meyer, L., 1998. Experimental investigation of turbulent transport of momentum and energy in a heated rod bundle. Nucl. Eng. Design 180, 185–206] proves that accuracy can be achieved for averaged statistics such as stream-wise velocity, turbulent intensity and wall shear stresses.     

Distributed parameter analysis for the prediction of the fine structure of flow and temperature fields in wire-wrapped fuel pin bundle geometries

This paper describes the numerical method of a distributed parameter analysis code SPIRAL for the calculation of fluid flow and temperature in arbitrary channel geometries, discusses the numerical method in the modeling and solution of the problem, and presents some results, including comparison with experiments.

The derivation and solution of the finite element equations is discussed. In order to overcome difficulties arising from the geometry, the Galerkin finite element method using isoparametric elements was employed, and a procedure of finite element generation using curvilinear coordinate system was developed.

The SPIRAL code permits calculation of the fine structure of the multi-dimensional steady-state single-phase fluid flow and temperature fields in LMFBR fuel pin subassemblies in the presence of wire spacers. Calculated results are presented for crossflow velocity distributions and crossflow pressure drop characteristics in a tube bundle geometry with and without wire spacers, natural convection and heat transfer in horizontal annuli, flow in a wire-wrapped 7-pin bundle geometry and fully developed turbulent flow in a parallel 4-rod array contained in a rectangular duct.     

不同棒束结构稠密栅元通道内的湍流CFD研究

采用URANS（UnsteadyReynoldsAveragedNavierStokes）方法对不同棒束结构稠密栅元通道（P/D=1.001～1.2）内的湍流流动进行CFD模拟。研究分析了不同Re（Re=5000~215000）的湍流流动的主流速度、壁面剪应力、湍动能等参数。研究表明：在较稠密的棒束（P/D<1.1）通道内,P/D的变化对子通道内主流速度和剪应力分布均有较大影响。本文的模拟结果也验证了在达到临界P/D前（即使δ/D<0.011）,交混因子Y和δ/D成反比关系。对于固定的棒束结构（P/D=1.062）,当Re达到一定值（Re=9600）时,子通道内主流速度和剪应力分布对Re的变化不敏感。