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.     

Single phase transport within bare rod arrays at laminar, transition and turbulent flow conditions

A theoretical analysis has been performed to study molecular and turbulent transport phenomena between subchannels of infinite bare rod arrays at laminar, transition and turbulent flow conditions. For this investigation, the theoretical approach of Ramm and Johannsen for predicting turbulent momentum and heat transfer in rod bundles has been extended to evaluate three-dimensional temperature fields. Results are presented enabling the prediction of the onset and growth of laminarization in typical subchannels of square and triangular rod arrays. These results are further applied to interpret the characteristic effects of variations in Reynolds number, Prandtl number or geometric spacing on integral exchange parameters as the thermal mixing flow rate and mixing length scale. These results are of particular significance relative to the explanation of recent data from tracer-type mixing experiments and also exhibit the importance of secondary flow effects on turbulent intersubchannel energy transport. In view of these findings, the physical relevance of current correlations derived from integral-type experiments to numerically predict exchange coefficients for use in lumped parameter subchannel analysis codes is discussed.     

Prediction of the single-phase turbulent mixing rate between two parallel subchannels using a subchannel geometry factor

This paper presents a simple method for predicting the single-phase turbulent mixing rate between adjacent subchannels in nuclear fuel bundles. In this method, the mixing rate is computed as the sum of the two components of turbulent diffusion and convective transfer. Of these, the turbulent diffusion component is calculated using a newly defined subchannel geometry factor F^* and the mean turbulent diffusivity for each subchannel which is computed from Elder's equation. The convective transfer component is evaluated from a mixing Stanton number correlation obtained empirically in this study. In order to confirm the validity of the proposed method, experimental data on turbulent mixing rate were obtained using a tracer technique under adiabatic conditions with three test channels, each consisting of two subchannels. The range of Reynolds number covered was 5000–66 000. From comparisons of the predicted turbulent mixing rates with the experimental data of other investigators as well as the authors, it has been confirmed that the proposed method can predict the data in a range of gap clearance to rod diameter ratio of 0.02–0.4 within about ±25% for square array bundles and about ±35% for triangular array bundles.     

Local thermal–hydraulic behaviour in tight 7-rod bundles

Advanced water-cooled reactor concepts with tight lattices have been proposed worldwide to improve the fuel utilization and the economic competitiveness. In the present work, experimental investigations were performed on thermal–hydraulic behaviour in tight hexagonal 7-rod bundles under both single-phase and two-phase conditions. Freon-12 was used as working fluid due to its convenient operating parameters. Tests were carried out under both single-phase and two-phase flow conditions. Rod surface temperatures are measured at a fixed axial elevation and in various circumferential positions. Test data with different radial power distributions are analyzed. Measured surface temperatures of unheated rods are used for the assessment of and comparison with numerical codes.In addition, numerical simulation using sub-channel analysis code MATRA and the computational fluid dynamics (CFD) code ANSYS-10 is carried out to understand the experimental data and to assess the validity of these codes in the prediction of flow and heat transfer behaviour in tight rod bundle geometries. Numerical results are compared with experimental data. A good agreement between the measured temperatures on the unheated rod surface and the CFD calculation is obtained. Both sub-channel analysis and CFD calculation indicates that the turbulent mixing in the tight rod bundle is significantly stronger than that computed with a well established correlation.     

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.     

Core thermal–hydraulic design

The core thermal–hydraulic design for the HTTR is carried out to evaluate the maximum fuel temperature at normal operation and anticipated operation occurrences. To evaluate coolant flow distribution and maximum fuel temperature, we use the experimental results such as heat transfer coefficient, pressure loss coefficient obtained by mock-up test facilities. Furthermore, we evaluated hot spot factors of fuel temperatures conservatively.As the results of the core thermal–hydraulic design, an effective coolant flow through the core of 88% of the total flow, is achieved at minimum. The maximum fuel temperature appears during the high-temperature test operation, and reaches 1492 °C for the maximum through the burn-up cycle, which satisfies the design limit of 1495 °C at normal operation. It is also confirmed that the maximum fuel temperature at any anticipated operation occurrences does not exceed the fuel design limit of 1600 °C in the safety analysis.On the other hand, result of re-evaluation of analysis condition and hot spot factors based on operation data of the HTTR, the maximum fuel temperature for 160 effective full power operation days is estimated to be 1463 °C. It is confirmed that the core thermal–hydraulic design gives conservative results.     

Averaging methods of the gap heat transfer coefficients and the loss form coefficients of nuclear reactor cores loaded with different fuel bundles

When performing transient analysis in heterogeneous nuclear reactors loaded with different types of fuel bundles is necessary to model the reactor core by a few representative fuel elements with average properties of a region containing a large number of fuel elements. The properties of these representative fuel bundles are obtained by averaging the thermal–hydraulic properties of the fuel elements contained in each region. In this paper we study the different ways to perform the averaging of the thermal–hydraulic properties that can have an influence on the transient results for licence purposes. Also we study the influence of the different averaging methods on the peak clad temperature (PCT) evolution for a LOCA, and on the critical power ratio (CPR) in the hot channels for a turbine trip transient without bypass credit.     

Analyses on fluid flow and heat transfer inside Calandria vessel of CANDU-6 using CFD

In a CANada Deuterium Uranium (CANDU) reactor, fuel channel integrity depends on the coolability of the moderator as an ultimate heat sink under transient conditions such as a loss of coolant accident (LOCA) with a coincidence of a loss of emergency core cooling (LOECC), as well as a normal operating condition. This study presents the assessments of moderator thermal–hydraulic characteristics in the normal operating condition and one transient condition for CANDU-6 reactors, using a general purpose three-dimensional computational fluid dynamics code. This study consists of two steps. First, an optimized calculation scheme is obtained by many-sided comparisons of the predicted results with the related experimental data, and by evaluating the fluid flow and temperature distributions. Then, in the second step, with the optimized scheme, the analyses for real CANDU-6 of normal operating condition and transition condition have been performed. The present model has successfully predicted the experimental results and also reasonably assessed the thermal–hydraulic characteristics of the real CANDU-6 with 380 fuel channels. Flow regime map with major parameters representing the flow pattern inside Calandria vessel has also proposed to be used as operational and/or regulatory guidelines.     

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.     

Mass velocity and cold-wall effects on critical heat flux in an advanced light water reactor

The characteristics of Critical Heat Flux (CHF) were investigated for a square array of rod bundles which could possibly be loaded into an integral-type advanced light water reactor. The parametric effects of the mass velocity and the unheated rod were examined by conducting CHF experiments with 5 × 5 test bundles in a Freon-loop. The influence of a cold wall on the CHF was interpreted by introducing a simple phenomenological model which accounts for the influence of a thermal mixing inside the boiling channel. A local parameter CHF correlation applicable to an integral-type reactor was developed from the CHF data base for square-arrayed rod bundles. The local thermal–hydraulic conditions calculated by the subchannel analysis code MATRA were used for the optimization of the correlation coefficients. Correction factors for the low mass velocity, spacer grids, and the non-uniform axial power shapes have been devised which reflected the results of the data assessment and the experimental observations. As a result of the thermal margin evaluation at steady state conditions, it was revealed that the integral-type reactor core has a greater DNBR margin than a typical 1000 MW_e PWR core.     

From discovery to recognition of periodic large scale vortices in rod bundles as source of natural mixing between subchannels—A review

The mixing of cooling fluid in rod bundles from one subchannel to another through the gaps between the rods reduces the temperature differences in the coolant as well as along the perimeter of the rods. The phenomenon of natural mixing was first intensively investigated in the 1960s and remains a topic of research up to the present time. The paper describes the main stations on the way to understand the nature of the flow in rod bundles and generally in compound channels with the focus on work performed at Research Center Karlsruhe (FZK).¹Earlier, it was noticed that the mixing rates where higher than could be accounted for by turbulent diffusion alone. For more than 20 years attempts were made to prove experimentally and by code application that secondary flows could account for the measured mixing rates, although the measured secondary flow velocities were much too low. Measurements of the turbulence structure by hot wire anemometry confirmed the existence of cyclic flow pulsations, which had been postulated earlier on the basis of thermocouple measurements. More sophisticated hot wire measurements revealed the nature of these pulsations as periodic, coupled to gap width and Reynolds number. Finally, the extension of the investigation to other compound channel types and flow visualization revealed the true nature of the mixing process as a vortex train moving along the gap between rods or in the narrow part of a compound channel. These findings have been confirmed by LES calculations. Based on these results CFD codes with improved turbulence models calculated successfully the flow in rod bundles including the macroscopic oscillations.     

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。     

脉动流下棒束通道内流场与湍流特性的PIV实验研究

事故条件下路基核反应堆以及受到海洋条件附加惯性力影响的浮动核反应堆一回路冷却剂会处于非稳定流动状态,进而改变冷却剂的流动和传热特性,影响反应堆的安全运行。本文应用锁相粒子图像测速（PIV）以及折射率匹配技术分别对脉动流条件下有无定位格架棒束通道内瞬时速度进行了测量。实验结果表明：对于不带定位格架的棒束通道,加速使得靠近通道壁面附近流体速度变大,而靠近中心区域流体速度变小。此外湍流强度分量随流体加速而逐渐变小,随流体减速而逐渐增加。对于流向压力梯度驱动的周期性脉动流,横向脉动速度均方根分量u′滞后于流向脉动速度均方根分量v′,且二者都滞后于流速的变化;对于带定位格架的棒束通道,带有搅浑翼的定位格架强烈的交混作用极大地减小了流体加速度对棒束通道内速度分布和湍流强度带来的影响。实验结果有助于更加清晰地揭示脉动流在棒束通道中的作用机理。     

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。     

Turbulent flow simulation in a wire-wrap rod bundle of an LMFBR

The pressure drop and heat transfer characteristics of wire-wrapped 19-pin rod bundles in a nuclear reactor subassembly of liquid metal cooled fast breeder reactor (LMFBR) have been investigated through three-dimensional turbulent flow simulations. The predicted results of eddy viscosity based turbulence models (k-?, k-ω) and the Reynolds stress model are compared with those of experimental correlations for friction factor and Nusselt number. The Re is varied between 50,000 and 150,000 and the ratio of helical pitch of wire wrap to the rod diameter is varied from 15 to 45. All the three turbulence models considered yield similar results. The friction factor increases with reduction in the wire-wrap pitch while the heat transfer coefficient remains almost unaltered. However, reduction in the wire-wrap pitch also enhances the transverse flow velocity in the cross-sectional plane as well as the local turbulence intensity, thereby improving the thermal mixing of coolant. Consequently, the presence of wire wrap reduces temperature variation within each section of the subassembly. The associated reduction in differential thermal expansion of rods is expected to improve the structural integrity of the fuel subassembly.     

Evaluation of the conduction shape factor with a CFD code for a liquid–metal heat transfer in heated triangular rod bundles

A heat transfer due to conduction through a coolant itself is not negligible in a liquid–metal cooled reactor (LMR). This portion of a heat transfer is frequently described with a conduction shape factor during the thermal-hydraulic design of an LMR. The conduction shape factor, which is highly dependent on a pitch-to-diameter (P/D) ratio, is defined as the ratio of the local conduction heat flux at a gap between two subchannels to the reference heat flux calculated by the averaged subchannel temperatures. The shape factors in heated triangular rod arrays for three different pitch-to-diameter ratios are generated through CFX calculations in the present study. The flow paths of 1.0–2.0 m in length are meshed into 180,000–360,000 volumes depending on the flow velocities. The SSG Reynolds stress model is used as a turbulent model in the calculations. The evaluated data fell between the heated-rod data and the plane-source data obtained by theoretical investigations. The conduction shape factors were found to be independent of the heating pattern of the rod arrays. Based on the evaluated data, a correlation for a liquid sodium coolant is suggested, which will improve the accuracy of the subchannel analysis codes for the thermal-hydraulic design of an LMR. When it is compared with the existing correlations, the suggested correlation is expected to enhance the reliability of the conduction shape factor because the data is evaluated by a more realistic numerical experiment.     

Measurements of the flow characteristics of the lateral flow in the 6 × 6 rod bundles with Tandem Arrangement Vanes

It is very important to increase the heat transfer efficiency in rod bundles in order to prevent the hot spot on the surface of fuel rods in view of the thermal hydraulic safety of nuclear power plants. It is representative to mount vanes in the support grid, which generate swirling flow. It is necessary to measure the flow pattern for investigating the thermal hydraulic flow characteristics in subchannels. In this study, it is performed to measure experimentally the flow field in cross-sections of the 6 × 6 rod bundles with new type vanes - Tandem Arrangement Vanes (TAV) by using Laser Doppler Anemometry. Through measurements, data are acquired at a nominal Reynolds number of 50,000 and for three streamwise locations at 3, 10, and 20 hydraulic diameters. Many previous experimental studies by the existing split mixing vanes show small turbulent length scales and short retention time till 10D_h after spacer grid. On the other hand, the TAVs proposed in the present study generate the big enforced swirl flow more than 20D_h after spacer grid and heat transfer effect are maintained through this distance.     

Experimental and numerical investigation of counter-current stratified flows in horizontal channels

Counter-current flow regimes of air and water are investigated in the WENKA test facility at the Forschungszentrum Karlsruhe. With the fluorescent-particle image velocimetry (PIV) measurement technique, velocity and velocity fluctuations are measured up to the free surface. A statistical model is presented to correlate the measured void fraction with the turbulent kinetic energy calculated from the measured velocity fluctuations. The experimental data are used to develop a phase interaction model to simulate stratified flows. Two different approaches are compared for turbulence modelling. The Prandtl mixing length model and an extended k–ω model for the two-phase region are applied to supercritical flow conditions.