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.     

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.     

Heat transfer to liquid metals flowing turbulently and longitudinally through closely spaced rod bundles : Part I

This paper presents results of a theoretical study of heat transfer to liquid metals in fully developed turbulent, in-line flow through unbaffled, spacer-free rod bundles. The bundles have equilateral triangular arrangement; and the rod spacings, rod design, and ranges of independent variables covered were chosen with reference to liquid-metal-cooled nuclear reactor applications. Three different sets of thermal boundary conditions are considered: (A) uniform heat flux in the axial direction with uniform temperature in the circumferential direction, on the outer surface of the cladding; (B) uniform heat flux in both directions, on the outer surface of the cladding; and (C) uniform heat flux in both directions on the inner surface of the cladding. The results of the third set are presented in Part II.     

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.     

稠密栅元棒束内流动行为的CFD数值模拟

国内针对稠密栅元组件内流体的流动和传热特征展了大量的实验研究,但目前仍缺乏对稠密栅元通道内冷却剂流动特性的全面认识.本文对矩形和三角形稠密栅元通道内的空气湍流流动进行了数值研究.结合实验数据,系统地验证了涡粘性和雷诺应力两类湍流模型模拟稠密栅元内流动特征的适用范围.结果表明:SSG雷诺应力模型对流动有较好的模拟,但在棒壁窄缝处的计算结果与实验数据存在较大的差距;在y+<20时,SSG模型对近壁面区域网格的疏密不敏感;在y+较小时,二阶ω模型出现数值震荡.     

Numerical Simulation of Fluid Flow and Heat Transfer of Supercritical Fluids in Fuel Bundles

A supercritical water-cooled reactor (SCWR) was proposed as a kind of generation IV reactor in order to improve the efficiency of nuclear reactors. Although investigations on the thermal-hydraulic behavior in SCWR have attracted much attention, there is still a lack of CFD study on the heat transfer of supercritical water in fuel channels. In order to understand the thermal-hydraulic behavior of supercritical fluids in nuclear reactors, the local fluid flow and heat transfer of supercritical water in a 37-element fuel bundle has been studied numerically in this work. Results show that secondary flow appears and the cladding surface temperature (CST) is very nonuniform in the fuel bundle. The maximum cladding surface temperature (MaxCST), which is an important design parameter for SCWR, can be predicted and analyzed using the CFD method. Due to a very large circumferential temperature gradient in cladding surfaces of the fuel bundle, the precise cladding temperature distributions using the CFD method is highly recommended.     

两流程2×2棒束超临界水传热实验研究

为支持欧盟2×2燃料组件入堆考核实验,开展了2×2棒束内超临界水传热实验研究。设计了两流程实验段,两流程之间通过矩形金属框隔离。2×2加热棒束通过定位格架安装在金属框中,超临界水通过第1流程向下流动然后进入第2流程冷却加热棒,第1流程通过金属框吸收第2流程流体的热量而温度升高。在2×2棒束横截面上存在明显的周向温度分布不均匀性。系统分析了实验参数包括质量流速、热流密度和实验压力对棒束平均换热系数的影响。结果表明,系统参数对棒束传热的影响规律与对单管和环管的一致。     

超临界水四棒束传热数值分析

超临界水冷堆(SCWR)开发的关键是棒束内超临界水(SCW)的热工水力特性。本文针对超临界水四棒束流动传热实验进行CFD数值模拟,SSG湍流模型的计算结果与实验结果吻合良好。分析结果表明,流动方向对棒束截面内流量分布有显著影响。与下降流相比,尽管上升流时棒束间流动搅混较弱,但上升流时棒束截面流量及壁面周向温度分布更加均匀,加热棒壁面温度更低。可见,棒束横截面上的流量分布是影响加热棒壁面流动传热的主要因素。     

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.     

An analytical method of evaluating the effect of rod displacement on circumferential temperature and heat flux distributions in turbulent flow through unbaffled rod bundles

An analytical method of evaluating the circumferential variations of temperature and heat flux fields inside and around a displaced fuel rod in triangular rod bundles in turbulent flow is presented with illustrative examples. The analysis consists mainly of the derivation of the simultaneous solutions of a set of heat conduction equations for fuel, cladding and coolant under the assumption of fully developed flow and heat transfer conditions. The local coolant velocity distribution, which is necessary for deriving the temperature field in coolant, is determined by solving the Navier-Stokes equation and the turbulent mixing of coolant is taken into consideration. The results show how the circumferential variations in the temperature and heat flux fields on the outer surface of the cladding increase the lower the ratio and the larger the fuel rod displacement due to thermal conduction and peripheral coolant flow velocity distribution.     

CFD analysis of thermal-hydraulic behavior of supercritical water in sub-channels

Investigations on the thermal-hydraulic behavior in the supercritical water-cooled reactor (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 fluids. In this paper, computational fluid dynamics (CFD) analysis is carried out to study the thermal-hydraulic behavior of supercritical water flows in sub-channels of a typical SCWR fuel assembly using commercial CFD code CFX-5.6. Three types of sub-channels, e.g. regular sub-channel, wall sub-channel and corner sub-channel, are analyzed. Effects of various parameters, such as boundary conditions and pitch-to-diameter ratios, on the mixing phenomenon in sub-channels and heat transfer are investigated. The turbulent mixing in tight lattice (P/D = 1.1) is lower than that in wide lattice (P/D > 1.1), whereas, the effect of pitch-to-diameter ratio on the turbulent mixing is slight at P/D > 1.1. The amplitude of turbulent mixing in wall sub-channel is slightly higher than that in regular sub-channel and is close to that in corner sub-channel. The mixing coefficient in the sub-channel at P/D ≥ 1.2 is in the range from 0.022 to 0.028. The results also show unusual behavior of turbulent mixing in the vicinity of the pseudo-critical point, and further investigation is needed. The mass mixing due to cross flow in wall sub-channel is much stronger than that in regular sub-channel at a same pitch-to-diameter ratio. The mass mixing in wall and regular sub-channels, especially at small pitch-to-diameter ratio, brings an unfavorable feedback to the heat transfer and strengthens the non-uniformity of the circumferential distribution of heat transfer. The strong mass mixing in corner sub-channel should be paid attention.     

2×2棒束内超临界水传热特性实验研究

以中国超临界水冷堆（CSR1000）燃料组件研发为研究背景,采用实验辅以理论分析的方法,开展2×2棒束结构内超临界水工质的传热特性研究。实验工况范围为:压力（P）23~25 MPa;质量流速（G）680~1400 kg/(m2?s);热流密度（q）174~968 kW/m2。实验结果表明,随着q的增加、G的减小,2×2棒束的传热性能减弱;随着P从23 MPa变化到25 MPa,2×2棒束的传热性能变化微弱; 2×2棒束内超临界水的传热特性既与边界层和主流的物性差异程度有关,又受流道各子通道之间的流动传热不均匀性影响;基于实验数据进行多元线性回归分析,获得2×2棒束内超临界水换热关系式,约88.9%的实验数据与该换热关系式的计算值偏差范围在±25%内。      

CFD investigation of helical wire-wrapped 7-pin fuel bundle and the challenges in modeling full scale 217 pin bundle

Flow and temperature distributions of sodium in a heat generating fuel pin bundle with helically wound spacer wire have been predicted from basic principles by solving the three-dimensional conservation equations of mass, momentum and energy, for a wide range of Reynolds number. Turbulence has been modeled using the k– turbulence model. The geometry details of the bundle and heat flux from the fuel pin are similar to that of the Indian Prototype Fast Breeder Reactor (PFBR) that is currently under construction. The focus of the study is to assess the effect of transverse flow in promoting flow and temperature uniformity. It is seen that the ratio of maximum transverse velocity to the maximum axial velocity is nearly equal to the tangent of the rolling up angle of the spacer wire. Due to the wire wrap, the difference in bulk sodium temperature between the peripheral and central sub-channels is reduced to by a factor of 4 when compared to that without spacer wire. The film drop at the junction between wire and the pin is found to be only 70 °C. The predicted results are found to be in close agreement with that of the experimental results reported in literature. The present study considers a 7-pin bundle assembly of one helical pitch. The computational time and memory required for a 217 pin with 15 pitches assembly is ascertained to be 500 times that required for the current study. Hence, research activities have been directed towards developing a parallel CFD code and structural mesh generation software.     

A turbulence model study for simulating flow inside tight lattice rod bundles

Performances of various turbulence models are evaluated for calculation of detailed coolant velocity distribution in a tight lattice fuel bundle. The individual models are briefly outlined and compared with respect to the prediction of wall shear stress and velocity field, for a fully developed flow inside a triangular lattice bundle. Comparisons clearly show the importance of proper modeling of the turbulence-driven secondary flows in subchannels. A quadratic k– model, which showed promising capability in this respect, is adjusted in its coefficients, and the adjusted model is applied to fully developed flow in an infinite triangular array, with various Reynolds numbers. The results show that the inclusion of adequate anisotropy modeling enables to accurately reproduce the wall shear stress distribution and velocity field in tight lattice fuel bundles.     

7棒束紧密栅元流体流动传热数值研究

紧密栅元内的流体流动传热研究对高转化比反应堆燃料组件的优化有十分重要的意义。本文采用CFD方法对7棒束紧密栅元棒束通道内流体流动传热现象进行了数值模拟,并与7棒束紧密栅元内氟利昂流体传热的实验结果进行对比分析,详细分析了定位格架对棒束内流体传热流动的影响。结果表明：数值计算所得的非加热棒的壁面温度和实验吻合良好,定位格架的存在对其下游流体流动、棒束最高温度分布及交混系数有明显的影响,棒束某些位置因流动滞止导致温度大幅上升,在设计中应加以注意。     

2×2稠密棒束内超临界水的传热特性试验研究

在压力p=23～28 MPa、质量流速G=350～1 000 kg/(m²•s)、热流密度q=200～1000 kW/m²的试验参数范围内,对2×2棒束内超临界水的传热特性进行了试验研究。试验得到了加热管周向壁温分布规律,并就出现周向温度差异的原因进行了分析。此外,给出了压力、质量流速及热流密度等系统参数对平均传热特性的影响,分析了低质量流速下出现的传热恶化现象。试验结果表明：加热管周向壁温并不均匀,边角子通道壁温最高,中心子通道壁温最低,周向壁温的高低与横截面流通面积的不均匀性紧密相关。随着热流密度的提高或质量流速的降低,超临界水的传热受到抑制,当q/G增大到一定程度时,棒束内发生传热恶化。     

棒束内超临界水传热实验研究

在中国广核集团有限公司和上海交通大学共建的超临界水多功能实验装置上,针对两种不同节径比(P/D)的棒束通道开展了超临界水流动传热实验,获得了传热实验数据,观测到了通道内棒束间明显的周向温度不均匀现象和定位格架导致的传热强化现象。通过对各种热工水力参数的实验研究,得出超临界水流动传热结论:随热流密度的增加,传热系数逐渐减小,棒束壁温周向不均匀程度逐渐增加;随质量流速的增加,传热系数逐渐增大,棒束壁温周向不均匀程度逐渐减小;随压力的逐渐升高,传热系数少许降低;随P/D的减小,棒束通道内的传热明显增强。     

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。     

Numerical analysis of heat transfer in supercritical water cooled flow channels

Research activities are ongoing worldwide to develop nuclear power plants with a supercritical water cooled reactor (SCWR) with the purpose to achieve a high thermal efficiency and to improve their economical competitiveness. However, there is still a big deficiency in understanding and prediction of heat transfer in supercritical fluids. In this paper, heat transfer of supercritical water has been investigated in various flow channels using the computational fluid dynamics (CFD) code CFX-5.6 to provide basic knowledge of the heat transfer behaviour and to gather the first experience in the application of CFD codes to heat transfer in supercritical fluids. Three different flow channels are selected, i.e. circular tubes, the sub-channel of a square-array rod bundle and the sub-channel of a triangular-array rod bundle. The effect of mesh structures, turbulence models, as well as flow channel configurations is analysed. Based on the present results, recommendations are made on the application of turbulence models to the heat transfer of supercritical fluids in various flow channels. A new definition for the onset of heat transfer deterioration is proposed. A strong non-uniformity of heat transfer is observed in sub-channel geometries. This non-uniformity has to be taken into account in the design of fuel assemblies of SCWR.     

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.