Numerical investigation of supercritical water-cooled nuclear reactor in horizontal rod bundles

The commercial CFD code STAR-CD v4.02 is used as a numerical simulation tool for flows in the supercritical water-cooled nuclear reactor (SCWR). The basic heat transfer element in the reactor core can be considered as round rods and rod bundles. Reactors with vertical or horizontal flow in the core can be found. In vertically oriented core, symmetric characters of flow and heat transfer can be found and two-dimensional analyses are often performed. However, in horizontally oriented core the flow and heat transfer are fully three-dimensional due to the buoyancy effect. In this paper, horizontal rods and rod bundles at SCWR conditions are studied. Special STAR-CD subroutines were developed by the authors to correctly represent the dramatic change in physical properties of the supercritical water with temperature. In the rod bundle simulations, it is found that the geometry and orientation of the rod bundle have strong effects on the wall temperature distributions and heat transfers. In one orientation the square bundle has a higher wall temperature difference than other bundles. However, when the bundles are rotated by 90° the highest wall temperature difference is found in the hexagon bundle. Similar analysis could be useful in design and safety studies to obtain optimum fuel rod arrangement in a SCWR.     

Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles

Heat transfer in upward flows of supercritical water in circular tubes and in tight fuel rod bundles is numerically investigated by using the commercial CFD code STAR-CD 3.24. The objective is to have more understandings about the phenomena happening in supercritical water and for designs of supercritical water cooled reactors. Some turbulence models are selected to carry out numerical simulations and the results are compared with experimental data and other correlations to find suitable models to predict heat transfer in supercritical water. The comparisons are not only in the low bulk temperature region, but also in the high bulk temperature region. The two-layer model (Hassid and Poreh) gives a better prediction to the heat transfer than other models, and the standard k– high Re model with the standard wall function also shows an acceptable predicting capability. Three-dimensional simulations are carried out in sub-channels of tight square lattice and triangular lattice fuel rod bundles at supercritical pressure. Results show that there is a strong non-uniformity of the circumferential distribution of the cladding surface temperature, in the square lattice bundle with a small pitch-to-diameter ratio (P/D). However, it does not occur in the triangular lattice bundle with a small P/D. It is found that this phenomenon is caused by the large non-uniformity of the flow area in the cross-section of sub-channels. Some improved designs are numerically studied and proved to be effective to avoid the large circumferential temperature gradient at the cladding surface.     

CFD in supercritical water-cooled nuclear reactor (SCWR) with horizontal tube bundles

The commercial CFD code STAR-CD 4.02 is used as a numerical simulation tool for flows in the supercritical water-cooled nuclear reactor (SCWR). The basic heat transfer element in the reactor core can be considered as round tubes and tube bundles. Reactors with vertical or horizontal flow in the core can be found. In a vertically oriented core, symmetric characters of flow and heat transfer can be found and two-dimensional analyses are often performed. However, in a horizontally oriented core the flow and heat transfer are fully three-dimensional due to the buoyancy effect. In this paper, horizontal tubes and tube bundles at SCWR conditions are studied. Special STAR-CD subroutines were developed by the authors to correctly represent the dramatic change in physical properties of the supercritical water with temperature. From the study of single round tubes, the Speziale quadratic non-linear high-Re k-? turbulence model with the two-layer model for near wall treatment is found to produce the best results in comparison with experimental data. In tube bundle simulations, it is found that the temperature is higher in the top half of the bundle and the highest tube wall temperature is located at the outside tubes where the flow rate is the lowest. The secondary flows across the bundle are highly complex. Their main effect is to even out the temperature over the area within each individual recirculation region. Similar analysis could be useful in design and safety studies to obtain optimum fuel rod arrangement in a SCWR.     

Analytical prediction of friction factors and Nusselt numbers of turbulent forced convection in rod bundles with smooth and rough surfaces

A simple analytical method was developed for the prediction of the friction factor, f, of fully developed turbulent flow and the Nusselt number, Nu, of fully developed turbulent forced convection in rod bundles arranged in square or hexagonal arrays. The friction factor equation for smooth rod bundles was presented in a form similar to the friction factor equation for turbulent flow in a circular pipe. An explicit equation for the Nusselt number of turbulent forced convection in rod bundles with smooth surface was developed. In addition, we extended the analysis to rod bundles with rough surface and provided a method for the prediction of the friction factor and the Nusselt number. The method was based on the law of the wall for velocity and the law of the wall for the temperature, which were integrated over the entire flow area to yield algebraic equations for the prediction of f and Nu. The present method is applicable to infinite rod bundles in square and hexagonal arrays with low pitch to rod diameter ratio, P/D<1.2.     

Evaluation of fluid flow in the lower core of a PWR with Code_Saturne

In order to better understand the stresses to which fuel rods are subjected, we need to improve our knowledge of the fluid flow inside the core. The first spacer grid region is of particular interest, as fuel rod fretting has sometimes been observed at that level. Entry conditions depend on the geometry of the lower core plate and of the assembly nozzles. Distribution of flow in the downcomer and lower plenum is also a factor. A series of calculations are thus run with the incompressible Navier–Stokes solver, Code_Saturne, using a classical RANS turbulence model. The first calculations involve a global geometry, including part of the cold legs, downcomer, lower plenum, and lower core of a pressurized water reactor. The level of detail includes most obstacles below the core. The lower core plate and the fuel rod assemblies above it cannot be well represented within a practical mesh size, so that a head loss model is used. Different types of assemblies can be represented through different head loss coefficients. We make full use of Code_Saturne’s non-conforming mesh possibilities to represent a complex geometry, being careful to retain a good mesh quality. Steady-state or near steady-state results are obtained, which may be used as realistic entry conditions for full core calculations at assembly width resolution, and beyond those, mechanical strain calculations. We are especially interested in more detailed flow conditions and in the lower core area, so as in the future to quantify vibrational input. This requires a much higher resolution, which is limited to a scale of a few assemblies for practical reasons. At this scale, most of the features of the fuel rods, nozzles, and guide tubes are represented, though the geometry of the spacer grids is still much simplified, and details such as debris-trapping grids are ignored. Different meshes are used for different fuel types. For the moment, a constant velocity upstream of the lower core plate is used as an inlet condition. We have also built a small lower fuel rod assembly mock-up (1/5 scale 7 × 7 tube, 3 × 3 assemblies) with which we plan to obtain detailed flow information, and better qualify the use of our CFD codes with regards to this type of application.     

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。     

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.     

A CFD simulation process for fast reactor fuel assemblies

A CFD modeling and simulation process for large-scale problems using an arbitrary fast reactor fuel assembly design was evaluated. Three-dimensional flow distributions of sodium for several fast reactor fuel assembly pin spacing configurations were simulated on high performance computers using commercial CFD software. This research focused on 19-pin fuel assembly “benchmark” geometry, similar in design to the Advanced Burner Test Reactor, where each pin is separated by helical wire-wrap spacers. Several two-equation turbulence models including the k-? and SST (Menter) k-ω were evaluated. Considerable effort was taken to resolve the momentum boundary layer, so as to eliminate the need for wall functions and reduce computational uncertainty. High performance computers were required to generate the hybrid meshes needed to predict secondary flows created by the wire-wrap spacers; computational meshes ranging from 65 to 85 million elements were common. A general validation methodology was followed, including mesh refinement and comparison of numerical results with empirical correlations. Predictions for velocity, temperature, and pressure distribution are shown. The uncertainty of numerical models, importance of high fidelity experimental data, and the challenges associated with simulating and validating large production-type problems are presented.     

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 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.     

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 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.     

A second order turbulence model based on a Reynolds stress approach for two-phase boiling flow and application to fuel assembly analysis

High-thermal performance PWR (pressurized water reactor) spacer grids require both low-pressure loss and high critical heat flux (CHF) properties. Numerical investigations on the effect of angles and position of mixing vanes and to understand in more details the main physical phenomena (wall boiling, entrainment of bubbles in the wakes, recondensation) are required.In the field of fuel assembly analysis or design by means of CFD codes, the overwhelming majority of the studies are carried out using two-equation Eddy Viscosity Models (EVM), especially the standard K-? model, while the use of Reynolds Stress Transport Models (RSTM) remains exceptional.The simulation of swirling flow generated by the mixing vanes plays an important role for the prediction of the CHF for the fuel assemblies. For this reason, according to [14] and [Mimouni et al., 2009b], rotation effects and RSTM model are more specifically addressed in the paper.Before comparing performance of EVM and RSTM models on fuel assembly geometry, we performed calculations with simpler geometries, the DEBORA case and the ASU-annular channel case. ASU-annular channel case has already been addressed in [14] and [Mimouni et al., 2009b].Then, a geometry closer to actual fuel assemblies is considered. It consists of a rectangular test section in which a 2 × 2 rod bundle equipped with a simple spacer grid with mixing vanes is inserted. The influence of the turbulence model on target variables linked to CHF limitation will be discussed. Moreover, the sensitivity to the mesh refinement will be particularly examined. The study of this case is a further step towards the modelling of the two-phase boiling flow in real-life grids and rod bundles.     

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.     

Simulations of turbulence, heat transfer and mixing across narrow gaps between rod-bundle subchannels

Turbulent flow and temperature fields were determined numerically in a rectangular duct containing a heated rod. As the spacing δ between the rod and the duct wall decreased from 0.10D (D is the rod diameter) to 0.03D, coherent turbulent kinetic energy and temperature fluctuations dramatically increased in the gap region, but, for δ = 0.01D, coherent fluctuations essentially disappeared. As δ/D → 0, the frequency of coherent fluctuations decreased and cross-gap mixing weakened, contrary to predictions based on extrapolated available empirical correlations.     

Fluid-to-fluid modeling of critical heat flux in 4 × 4 rod bundles

Fluid-to-fluid modeling of critical heat flux (CHF) is to simulate the CHF behaviors for water by employing low cost modeling fluid, and the flow scaling factor is the key to apply the technique to fuel bundles. The CHF experiments in 4×4 rod bundles have been carried out in Freon-12 loop in equivalent nuclear reactor water conditions (P=10.0–16.0 MPa, G=488.0–2100.0 kg/m² s, X_cr=−0.20–0.30). The models in fluid-to-fluid modeling of CHF is verified by the CHF data for Freon-12 obtained in the experiment and the CHF correlation for water obtained by Nuclear Power Institute of China (NPIC) in the same 4×4 rod bundles. It has been found that the S.Y. Ahmad Compensation Distortion model, the Lu Zhongqi model, the Groeneveld model and Stevens–Kirby model overpredict the bundles CHF values for water. Then an empirical correlation of flow scaling factor is proposed. Comparison of the CHF data in two kinds of test sections for Freon-12, in which the distance of the last grid away the end of heated length is different, shows that the spacer grid, which is located at 20 mm away from the end of the heated length, has evidently influenced on the CHF value in the 4×4 rod bundles for Freon-12. This is different from that for water, and the need for further work is required.     

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。     

A comparative CFD investigation of helical wire-wrapped 7, 19 and 37 fuel pin bundles and its extendibility to 217 pin bundle

Preliminary investigations of sodium flow and temperature distributions in heat generating fuel pin bundles with helical spacer wires have been carried out. Towards this, the 3D conservation equations of mass, momentum and energy have been solved using a commercial computational fluid dynamics (CFD) code. Turbulence has been accounted through the use of high Reynolds number version of standard k– model, with uniform mesh density respecting wall function requirements. The geometric details of the bundle and the heat flux in are similar to that of the Indian Prototype Fast Breeder Reactor (PFBR) that is currently under construction. The mixing characteristics of the flow among the peripheral and central zones are compared for 7, 19 and 37 fuel pin bundles and the characteristics are extended to a 217 pin bundle. The friction factors of the pin bundles obtained from the present study is seen to agree well with the values derived from experimental correlations. It is found that the normalized outlet velocities in the peripheral and central zones are nearly equal to 1.1–0.9, respectively which is in good agreement with the published hydraulic experimental measurements of 1.1–0.85 for a 91 pin bundle. The axial velocity is the maximum in the peripheral zone where spacer wires are located and minimum in the zones which are diametrically opposite to the respective zone of maximum velocity. The sodium temperature is higher in the zones where the flow area and mass flow rates are less due to the presence of the spacer wires though the axial velocity is higher there. It is the minimum in the peripheral zones where the circumferential flow is larger. Based on the flow and temperature distributions obtained for 19 and 37 pin bundles, a preliminary extrapolation procedure has been established for estimating the temperatures of peripheral and central zones of 217 pin bundle.     

Implementation and assessment of the renormalization group (RNG), quadratic and cubic non-linear eddy viscosity k– models in GOTHIC

In GOTHIC, the standard k– model is used to model turbulence. However, for practical reasons, one usually employs relatively large meshes near physical boundaries (walls). In an attempt to enhance the turbulence modelling in the code for simulation of mixing driven by highly buoyant discharges, in the framework of this simplified approach appropriate for containment analysis codes, we have implemented three additional models which are modifications/extensions of the standard k– model: the renormalization group k– model, and the non-linear (quadratic and cubic) eddy viscosity k– models. These models which for the time being, are only implemented in the ‘gas’ phase, were tested with different simple test-problems and their predictions were compared to the corresponding ones of the standard k– model. Furthermore, a simple study was performed to assess the sensitivity of the predictions to the mesh size.