Unsteady numerical simulations of the single-phase turbulent mixing between two channels connected by a narrow gap

This paper focuses on the unsteady numerical simulation of the turbulent flow in two types of geometry containing a narrow gap with the explicit algebraic Reynolds stress model. The model was first validated through the comparison of simulation results inside a rectangular channel containing a cylinder and the corresponding experimental data. The structures of the oscillation were correctly reproduced. Simulation of turbulent mixing between circular channels connected by a narrow gap was carried out with the validated model. Because of the influence of the strong anisotropic turbulent flow in the gap region, the mixing rate was dramatically enhanced by the cyclic and almost periodic flow pulsation. The calculation results of the turbulent mixing rate showed good agreement with the experiment and the maximum error was less than 15%.     

矩形通道内脉动层流相位差实验研究

对流量脉动条件下矩形通道内的相位差进行了实验研究，通过建立的脉动层流相位差数学模型，对脉动周期、脉动振幅、通道结构尺寸和流体性质等因素进行了分析，并将实验数据与理论模型结果进行对比。结果表明：矩形通道内，脉动层流的流量变化滞后于压降变化，存在相位差，该相位差仅与脉动周期、流道结构尺寸和流体性质有关，与压降相对振幅无关。     

矩形通道内层流脉动流动相位差分析

通过建立数学模型,对大宽高比矩形通道单相低频脉动层流流动特性进行了分析。研究结果表明：低频率流量脉动未引起流体的速度分布变化,压降与流量间存在相位差,相位差仅与通道窄边尺寸、流体粘性及脉动周期相关。脉动周期及流体粘性越大,相位差越小;窄边尺寸越大,相位差越大。通过建立模型对上述现象进行了分析。     

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。     

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。     

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.     

CFD analyses of liquid metal flow in sub-channels for Gen IV reactors

Some of the limitations of Reynolds Averaged Navier Stokes (RANS) based Computational Fluid Dynamics CFD codes in computing the flow and temperature field in a rod-bundle are well known. An in-house validation campaign has indicated that the Baseline Reynolds Stress Model (BSL-RSM) with automatic wall treatment is preferred for RANS analyses of a rod-bundle using the CFX code.As a first step in the present paper, the employed CFX code has been assessed with the analyses of a liquid sodium flow in a rod-bundle as in the TEGENA (TEmperatur- und GEschwindigkeitsverteilungen in Stabbündel mit turbulenter NAtriumströmung) experiment. For this RANS analysis, the full cross-section is modelled to avoid numerical issues associated with symmetric boundary conditions.The influence of pitch-to-diameter ratio (p/d) and rod arrangements on thermal-hydraulics is analyzed by applying the assessed modeling approach. For this purpose, rod-bundles with different p/d are arranged in a square and triangular lattice. The computational sub-channels make use of periodic boundary conditions. RANS computed axial velocity normalized with the friction velocity shows the presence of a logarithmic outer region for both arrangements. Similar behavior was reported based on a Large Eddy Simulation (LES) approach. The analyses reveal that the intensity of secondary flow increases with decreasing p/d for both arrangements. RANS analyzed normal Reynolds stresses normalized with centerline velocity in the smallest gap of rod-bundle reveal their anisotropy. Furthermore, the analyses show that the Nusselt numbers increase with p/d for described flow conditions and for both arrangements. Following observations of flow oscillations in a tight lattice rod-bundle as in Hooper's experiment, as a final step, unsteady RANS simulations for hydraulic analyses using a rod-bundle with small p/d are presented with two commercial CFD codes, namely, CFX and STAR-CCM+. In particular, the analysis of Hooper's hydraulics experiment with a tight lattice rod-bundle having a p/d of 1.1 demonstrates the existence of flow oscillations or instabilities as inferred in the experiment.     

摇摆状态下矩形通道内弹状流压力模型

本文通过可视化方法对竖直与倾斜条件下矩形通道内弹状流单元的参数进行研究,尝试给出摇摆状态下矩形通道内弹状流压力模型。通过图像处理给出气弹段空泡份额以及两相速度的计算关系式,并验证漂移流模型在液弹段的适用性,给出弹状流单元的长度份额以及空泡份额的计算关系式。根据实验结果给出摇摆条件下矩形通道内弹状流压力组分的模型,并重点分析摩擦压降模型的适用程度。结果表明,弹状流压力模型可很好地预测摇摆条件下矩形通道内的压力。     

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.     

Numerical and modeling issues in application of CFD to flow in a simplified plenum relevant to a prismatic VHTR

Computational Fluid Dynamics (CFD) calculations have been performed for turbulent flow inside a plenum model that resembles a section of the lower plenum of a typical helium-cooled prismatic Very High Temperature Reactor (VHTR). Different Reynolds Averaged Navier-Stokes (RANS) based turbulence models are employed to investigate the capability in capturing unsteady large scale coherent structures due to vortex shedding at two different Reynolds numbers. A grid convergence study is conducted with those models which were able to capture unsteady vortex shedding. The non-linear interaction of mesh quality, turbulence model and numerical scheme lead to flow regime changes with significantly different unsteady behaviors. This makes it difficult to assess numerical and modeling uncertainty using the procedures available in the literature. Some remedies to overcome this difficulty are recommended. The numerical uncertainty in the local values of velocity components at selected locations inside the plenum, as well as the uncertainty associated with derived quantities such as wall shear stress at critical locations are calculated and reported. Since there are no experiments corresponding to the present cases simulated, the current analysis can be considered as a blind application of the proposed uncertainty estimation procedures.     

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.     

超临界水冷堆类三角形子通道流动传热特性研究

基于类三角形子通道超临界水的传热试验,建立了超临界水冷堆三角形子通道物理模型。采用雷诺应力湍流模型SSG,在压力为23～28 MPa、质量流速为700～1300 kg/(m²•s)、热流密度为200～1000 kW/m²参数范围内,对棒径8 mm、栅距比为1.4的子通道内超临界水流动与传热特性进行了数值研究。分析了系统参数对流动和传热特性的影响,对比了不同焓区的二次流特性。结果表明：采用SSG模型对超临界水冷堆三角形子通道内流动传热的CFD模拟结果与试验数据较吻合。质量流速越高,传热能力越强;子通道换热系数峰值随压力的提高而减小;热负荷越高,内壁温度越高;在大比热容区换热系数峰值随热流密度的增大而明显减小,传热存在恶化趋势。超临界区子通道内在与主流垂直方向形成了明显的二次流,存在6个对称的漩涡,二次流速最大值出现在子通道窄缝区间隙。通道内不同焓区二次流结构相似,但二次流强度随焓的提高而增大。     

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.     

矩形通道中两相流变密度模型空泡份额计算

基于Bankoff的圆管内和无限长平板间两相流变密度模型空泡份额计算式的推导，结合流体在管道中的流场分布特征，建立了矩形通道中两相流流场分布规律方程，导出了变密度模型在矩形通道中空泡份额的计算式，并对3种通道计算的结果进行了对比分析。计算结果与原有Bankoff模型符合得很好。     

高流速下窄矩形通道内临界热流密度试验研究

在常压下,对具有窄间隙的矩形通道进行了下降流大流速临界热流密度试验研究。研究发现：大流速下临界热流密度随着流速的增加而呈线性增加,随出口含汽量的增加而减小Sudo公式的预测值较试验值要小在人口参数相同时。即相同的人口过冷度和质量流速式矩形通道的长度对临界热流密度的影响较小;如果从出口质量流速和出口含汽量来看,在相同的出口参数下,长度的增加将显著降低临界热流密度。     

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.     

钠冷快堆乏燃料组件自然循环冷却瞬态过程的数值模拟研究

应用Fluent程序,对处于氩气中的钠冷快堆乏燃料组件自然循环冷却瞬态过程进行了三维数值模拟。计算获得了乏燃料组件内部冷却剂通道和外部区域的热工水力学现象及变化规律。结果表明:利用标记区域分割方法,将燃料棒间隙网格划分为绕丝网格和绕丝周边流体域网格,能在棒束区生成高质量结构化网格;在氩气自然循环冷却瞬态过程中,棒束区内子通道氩气流量增加速度落后于边子通道,内子通道升温更快;乏燃料组件棒束区温度在轴向呈现中心高、边缘低的分布特征;为避免包壳温度超过设计值,乏燃料组件处于氩气中的时间不宜超过6min。     

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。     

湍流边界层内暗斑拟序结构的可视化实验研究

采用氢气泡流动显示技术,以水为工质,对竖直矩形通道湍流边界层内的暗斑拟序结构进行了可视化实验研究,流动雷诺数Re =3009。根据暗斑形成过程中其上游边界处是否产生涡旋,将暗斑划分为两种类型：三涡旋暗斑和双涡旋暗斑。对暗斑的形成过程及其速度分布进行了初步研究。通过与平板边界层内暗斑拟序结构对比发现：矩形通道内暗斑的发展时间较短,且其内部流体的速度增量较小。