Benchmark Simulation of Turbulent Flow through a Staggered Tube Bundle to Support CFD as a Reactor Design Tool. Part I: SRANS CFD Simulation

Time-invariant and time-variant numerical simulations of flow through a staggered tube bundle array, idealizing the lower plenum (LP) subsystem configuration of a very high temperature reactor (VHTR), were performed. In Part I, the CFD prediction of fully periodic isothermal tube-bundle flow using steady Reynolds-averaged Navier-Stokes (SRANS) equations with common turbulence models was investigated at a Reynolds number (Re) of 1.8 × 10⁴, based on the tube diameter and inlet velocity. Three first-order turbulence models, standard k-ε turbulence, renormalized group (RNG) k-ε, and shear stress transport (SST) k-ω models, and a second-order turbulence model, Reynolds stress model (RSM), were considered. A comparison of CFD simulations and experiment results was made at five locations along (x, y) coordinates. The SRANS simulation showed that no universal model predicted the turbulent Reynolds stresses, and generally, the results were marginal to poor. This is because these models cannot accurately model the periodic, spatiotemporal nature of the complex wake flow structure.     

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.     

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.     

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.     

Numerically simulating the thermal-hydraulic characteristics within the fuel rod bundle using CFD methodology

With the dramatic progress in the computer processing power, computational fluid dynamics (CFD) methodology can be applied in investigating the detailed knowledge of thermal-hydraulic characteristics in the rod bundle, especially with the spacer grid. These localized information, including flow, turbulence, and heat transfer characteristics, etc., can assist in the design and the improvement of rod bundles for nuclear power plants. In this paper, a three-dimensional (3D) CFD model with the Reynolds stresses turbulence model is proposed to simulate these characteristics within the rod bundle and subsequently to investigate the effects of different types of grid on the turbulent mixing and heat transfer enhancement. Two types of grid designs are used herein, including the standard grid and split-vane pair one, respectively. Based on the CFD simulations, the secondary flow can be reasonably captured in the rod bundle with the grid. The split-vane pair grid would enhance both the flow mixing and the heat transfer capability more than the standard grid does, as clearly shown in the simulation results. In addition, compared with the results of experiment and correlation, the present predicted result for the Nusselt (Nu) number distribution downstream the grid shows reasonable agreement for the standard grid design. However, there is discrepancy in the decay trend of Nu number between the prediction and measurement for the split-vane pair gird. This would be improved by adopting the finer mesh (y⁺ < 1) simulation and Low-Reynolds form turbulence model, which is our future research work.     

CFD analysis of PWR core top and reactor vessel upper plenum internal subdomain models

One aspect of the Westinghouse AP1000™¹ reactor design is the reduction in the number of major components and simplification in manufacturing. One design change relative to current Westinghouse reactors of similar size is that AP1000 reactor vessel has two nozzles/hot legs instead of three. With regard to fuel performance, this design difference creates a different flow field in the reactor vessel upper plenum. The flow exiting from the core and entering the upper plenum must turn toward one of the two outlet nozzles and flow laterally around numerous control rod guide tubes and support columns. Also, below the upper plenum are the upper core plate and the top core region of the 157 fuel assemblies and 69 guidetube assemblies.To determine how the lateral flow in the top of the core and upper plenum compares to the current reactors a CFD model of the flow in the upper portion of the AP1000 reactor vessel was created.Before detailed CFD simulations of the flow in the entire upper plenum and top core regions were performed, conducting local simulations for smaller sections of the domain provided crucial and detailed physical aspects of the flow. These sub-domain models were used to perform mesh sensitivities and to assess what geometrical details may be eliminated from the larger model in order to reduce mesh size and computational requirements. In this paper, CFD analysis is presented for two subdomain models: the top core region and control rod guide tube region. These models are chosen for simulation because guide tube and top core region (including top grid, top nozzle, and hold-down device) are the major components of upper plenum effecting the flow patterns and pressure distribution.The top core region, corresponding to ¼ of fuel assembly, includes components as upper part of the fuel assemblies (top grid, fuel rods, top nozzle), core component hold-down devices, and upper core plates. These components distribute the core flow to different sections of guidetube regions. Mesh sensitivity studies have been conducted for each individual part in order to determine the proper geometrical simplifications. Pressure drop measurement data are compared with the predicted CFD results and act as a guideline for the mesh selection.The guidetube region includes control rod guidetubes themselves, adjacent support columns and open regions. In this study, two models of subdomains are analyzed: (1) a ¼ section of one control rod guide tube by itself and (2) a representative unit cell containing two ¼ sections of adjacent control rod guide tubes and one ¼ section of a neighboring support column.Predicted flow rates at each of the outflow locations in conjunction with results from the mesh sensitivity studies provide guidance on (1) what geometry to preserve or remove, (2) what geometry can be simplified to reduce the required mesh, and (3) an estimate of the total mesh required to model the entire upper plenum and top fuel domain.The commercial CFD code STAR-CCM+ is employed to generate the computational mesh, to solve the Reynolds-averaged Navier–Stokes equations for incompressible flow with a Realizable k–? turbulence model, and to post-process the results.     

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。     

基于核主泵性能预测的数值模拟精度研究

为提高核主泵在全工况点的数值模拟精度,研究了数值模拟过程中近壁面网格尺度、湍流模型、流动状态3种因素对计算精度的影响。结果表明,在定常状态下,重整化群（RNG） k-ε湍流模型和标准壁面函数法在近壁面网格尺度（y+）为50左右时具有较高的计算精度,并且其计算精度高于RNG k-ε增强壁面函数法、低雷诺数k-ε和剪切应力传输（SST）k-ω这3种湍流模型的计算精度,但上述不同网格尺度和湍流模型的计算结果均存在较大的计算误差;采用非定常计算时的计算精度明显高于定常计算,能够反映出扬程曲线在关死点附近的驼峰现象,效率的计算精度也有一定改善,更适合于对核主泵进行性能预测。      

Numerical Simulation of Heat Transfer of Supercritical Fluids in Circular Tubes Using Different Turbulence Models

In this study, the heat transfer of supercritical fluids in vertical and horizontal circular tubes has been investigated numerically to understand the thermal-hydraulic behavior of supercritical fluids. The simulations are carried out using different turbulence models and the numerical results are compared with the experimental data to evaluate the accuracy and applicability of those turbulence models. Six turbulence models are used in this study, the LB low-Re k-? model, the LS low-Re k-? model, the RNG k-? model, the realizable k-? model, the standard k-? model, and the Reynolds stress model. The comparison shows that the Reynolds stress model gives better agreement with the experimental data than other turbulence models studied in this work.     

CFD studies on the phenomena around counter-current flow limitations of gas/liquid two-phase flow in a model of a PWR hot leg

In order to improve the understanding of counter-current two-phase flow and to validate new physical models, CFD simulations of a 1/3rd scale model of the hot leg of a German Konvoi pressurized water reactor (PWR) with rectangular cross section were performed. Selected counter-current flow limitation (CCFL) experiments conducted at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) were calculated with ANSYS CFX using the multi-fluid Euler–Euler modelling approach. The transient calculations were carried out using a gas/liquid inhomogeneous multiphase flow model coupled with a shear stress transport (SST) turbulence model.In the simulation, the drag law was approached by a newly developed correlation of the drag coefficient (Höhne and Vallée, 2010) in the Algebraic Interfacial Area Density (AIAD) model. The model can distinguish the bubbles, droplets and the free surface using the local liquid phase volume fraction value. A comparison with the high-speed video observations shows a good qualitative agreement. The results indicate also a quantitative agreement between calculations and experimental data for the CCFL characteristics and the water level inside the hot leg channel.     

CFD analysis of flow field in a triangular rod bundle

The flow field was investigated in subchannels of VVER-440 pressurized water cooled reactors’ fuel assemblies (triangular lattice, P/D = 1.35). Impacts of the mesh resolution and turbulence model were studied in order to obtain guidelines for CFD calculations of VVER-440 rod bundles. Results were compared to measurement data published by Trupp and Azad in 1975. The study pointed out that RANS method with BSL Reynolds stress model using a sufficient fine grid can provide an accurate prediction for the turbulence quantities in this lattice. Applying the experiences of the sensitivity study thermal hydraulic processes were investigated in VVER-440 rod bundle sections. Based on the examinations the spacer grids have important effects on the cross flows, axial velocity and outlet temperature distribution of subchannels therefore they have to be modeled satisfactorily in CFD calculations.     

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.     

CFD investigation of vertical rod bundles of supercritical water-cooled nuclear reactor

The commercial CFD code STAR-CD v4.02 is used as the numerical simulation tool for the supercritical water-cooled nuclear reactor (SCWR). The numerical simulation is based on the real full 3D rod bundles’ geometry of the nuclear reactors. For satisfying the near-wall resolution of y⁺ ≤ 1, the structure mesh with the stretched fine mesh near wall is employed. The validation of the numerical simulation for mesh generation strategy and the turbulence model for the heat transfer of supercritical water is carried out to compare with 3D tube experiments. After the validation, the same mesh generation strategy and the turbulence model are employed to study three types of the geometry frame of the real rod bundles. Through the numerical investigations, it is found that the different arrangement of the rod bundles will induce the different temperature distribution at the rods’ walls. The wall temperature distributions are non-uniform along the wall and the values depend on the geometry frame. At the same flow conditions, downward flow gets higher wall temperature than upward flow. The hexagon geometry frame has the smallest wall temperature difference comparing with the others. The heat transfer is controlled by P/D ratio of the bundles.     

CFD and DNS methodologies development for fuel bundle simulations

Development and application of computational fluid dynamics (CFD) and direct numerical simulation (DNS) approaches to the reproduction of coolant flow inside nuclear fuel bundles are discussed, focusing on the advantages and limitations of the different methodologies and on their synergetic potential. High Reynolds number flow cases are analyzed with the adoption of an improved anisotropic turbulence model, which includes a non-linear stress strain correlation and an enhanced near wall treatment. The capability of the model to predict the coolant flow distribution inside rod bundles is shown and discussed on the base of comparison with experimental data for a variety of geometrical and Reynolds number conditions. In particular predictions for wall shear stresses, velocity, and secondary flow distributions are shown. Moreover, DNS computations are performed adopting an algorithm based on the finite difference method, extended to boundary fitted coordinate systems in order to efficiently concentrate grids near the distorted wall boundaries. The validity and significance of the results is discussed underlying the importance of the insights into the turbulence structure. The calculations are further extended to higher Reynolds numbers, which cannot in general be treated with DNS approach, renouncing to the estimation of the higher-order moments, but limited to the evaluation of the averaged velocity profiles, turbulence intensities and Reynolds stresses.     

ADS无窗靶件自由界面模拟实验和数值研究

冷却剂自由界面形态的形成和控制是加速器驱动的次临界系统(ADS)无窗靶件设计的关键技术之一。采用水介质对无窗靶件模型的自由界面特征进行了实验和数值研究。实验中采用激光诱导荧光的示踪方法实现了流场的可视化,得到Re=30000～50000范围内的自由界面和可视化流场。在高Re工况下,流场中出现大尺度的非稳定涡结构,随着Re的降低,流场中涡结构的紊乱程度增加。分别采用大涡模型（LES）和两方程动能-特征耗散率模型（kω-SST）对无窗靶件实验工况进行了数值分析,计算结果表明,LES能较好地模拟实验中所得的流场现象和界面特征。     

CFD simulation of bubble column

Three-dimensional simulations of gas-liquid flow in the bubble column using the Euler-Euler approach is presented. The attempt is made to assess the performance and applicability of different turbulence models namely, k-?, k-? RNG, k-ω, Reynolds stress model (RSM) and large eddy simulation (LES) using a commercial code (ANSYS-CFX). For this purpose, the predictions are compared against the experimental data of Kulkarni et al. (2007). Performance of the turbulence models is assessed on basis of comparison of axial liquid velocity, fractional gas hold-up, turbulent kinetic energy and turbulent eddy dissipation rate. All the non-drag (turbulent dispersion, virtual mass and lift force) and drag force were incorporated in the model. The low-Reynolds number treatment of the k-ω yields a better qualitative prediction than the k-? model. The RSM predictions are comparable with LES results and seemed to give better prediction near the sparger, where the flow is more anisotropic and gives a clue why RANS approaches fails to predict the flow in this region. However, the large eddy simulations showed good agreement with the experimental data, but requires higher computational time than RSM.     

Two fluid model for two-phase turbulent jets

Eulerian two-fluid models are widely used in nuclear reactor safety and CFD. In these models turbulent diffusion of a dispersed phase must be formulated in terms of the fluctuating interfacial force and the Reynolds stresses. The interfacial force is obtained using the probability distribution function approach by Reeks (1992). This paper is the first application of this force to a case of engineering interest outside homogeneous turbulence. An Eulerian multidimensional two-fluid model for a cylindrical two-phase dispersed particle jet is proposed and compared with experimental data. The averaged conservation equations of mass and momentum are solved for each phase and the turbulent kinetic energy equation is solved for the continuous phase. The turbulent diffusion force and the Reynolds stresses are constituted within the context of the k- model of turbulence. A dissipation term has been added to the k- model for the turbulence modulation by the particles. Once the constitutive relations have been defined, the two-fluid model is implemented in a computational fluid dynamics code. It is shown that when the particles are very small the model is consistent with a convection-diffusion equation for particle transport where the diffusivity is defined according to Taylor's model (Taylor, G.I., 1921. Diffusion by continuous movements. Proc. London Math. Society, A20, pp. 196–211). The two-fluid model is also compared against two experimental data sets. Good agreement between the model and the data is obtained. The sensitivity of the results to various turbulent mechanisms is discussed.     

紧密栅棒束子通道间周期性大尺度涡的CFD模拟

为准确评估紧密栅棒束子通道间的搅混现象,采用开源计算流体力学（CFD）软件OpenFOAM 2.0并基于k-ω的显式几何雷诺应力湍流模型对两种子通道内的周期性大尺度涡结构进行模拟,研究了紧密栅子通道间周期性大尺度涡波长、峰值频率等参数的变化规律。结果表明,周期性涡结构存在一个很强的峰值频率,其平均最大频率随雷诺数（Re）呈线性增加,但其平均波长（λ）不随Re变化,只与子通道的结构参数有关;周期性涡结构导致两个子通道间存在很强的周期性的流动震荡,是紧密栅子通道湍流搅浑得到强化的主要原因。      

上游带弯头的T型管内混合流动数值模拟的湍流模型评价

T型管是研究冷热流体混合流动及其引起的温度振荡现象的典型几何模型,而上游带弯头的T型管又是一不可忽视的特殊情形。本文运用计算流体力学软件,采用3种湍流模型（RNG k-ε 模型、SSG雷诺应力模型、LES模型）对上游带弯头T型管内冷热流体的交混现象进行模拟,并与实验数据进行了对比。结果表明：非混合区域如上游弯头内,RNG k-ε 模型、SSG雷诺应力模型的模拟结果与实验结果较吻合,而在混合区内LES模型的模拟结果更能表征实际流动。     

CFD simulations of light gas release and mixing in the Battelle Model-Containment with CFX

In this validation work two turbulence models (k– and SST model) and two grids (a finer hybrid grid and a tetrahedral coarser grid) are considered in order to model helium release and dispersion. Simulation results are compared against an experiment of jet release phenomena in the Battelle Model Containment facility (BMC), a multi-compartment facility with a total volume of about 560 m³. In the selected test, HYJET Jx7, helium was released into the containment at a speed of 42 m/s over a time of 200 s. Although the k– model is the most commonly used turbulence model in most Computational Fluid Dynamics (CFD) applications, it does not provide the most accurate predictions for this application. Alternatively the SST turbulence model has been employed giving more accurate results. This investigation provides a further confirmation that the validation of commercial CFD codes is always required in order to select the more suitable physical models and computational grids for each specific application.