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.     

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.     

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.     

Thermal-hydraulic performance analysis of a subchannel with square and triangle fuel rod arrangements using the entropy generation approach

The present paper discusses entropy generation in fully developed turbulent flows through a subchannel,arranged in square and triangle arrays. Entropy generation is due to contribution of both heat transfer and pressure drop. Our main objective is to study the effect of key parameters such as spacer grid, fuel rod power distribution,Reynolds number Re, dimensionless heat power ω, lengthto-fuel-diameter ratio λ, and pitch-to-diameter ratio ξ on subchannel entropy generation. The analysis explicitly shows the contribution of heat transfer and pressure drop to the total entropy generation. An analytical formulation is introduced to total entropy generation for situations with uniform and sinusoidal rod power distribution. It is concluded that power distribution affects entropy generation.A smoother power profile leads to less entropy generation.The entropy generation of square rod array bundles is more efficient than that of triangular rod arrays, and spacer grids generate more entropy.     

The structure of turbulent flow in triangular array rod bundles

A wind tunnel study of fully developed uniform-density turbulent flow through triangular array rod bundles is described. Measurements were made for three tube spacings (

Full-size image (<1K)

) over a Reynolds number range of 12 000–84 000. The data include friction factors, local wall shear stresses, and the distributions of mean axial velocity, Reynolds stresses and eddy diffusivities. The secondary flow pattern is from the available evidence.     

A scale analysis of the turbulent mixing rate for various Prandtl number flow fields in rod bundles

The turbulent mixing rate is a very important variable in the thermal–hydraulic design of nuclear reactors. In this study, the turbulent mixing rate for the flow through rod bundles is estimated with the scale analysis on the flow pulsation generated by periodic vortices that is pointed out as a main cause of the mixing in rod bundles. Based upon the assumption that turbulent mixing is composed of molecular motion, isotropic turbulent motion (turbulent motion without the flow pulsation), and flow pulsation, the scale relation is derived as a function of P/D, Re, and Pr. The derived scale relation is compared with the published experimental results and shows good agreement. Since the scale relation is applicable to various Prandtl number fluid flows, it is expected to be useful for the thermal–hydraulic analysis of liquid metal coolant reactors as well as moderate Prandtl number coolant reactors.     

Turbulent momentum transport in rod bundles

An experimental investigation was performed with air to obtain detailed information on the velocity and turbulence distribution for parallel turbulent flows through subchannels of rod bundles. Experimental results were obtained for wall and corner subchannels of rod bundles of four parallel rods. The pitch-to-diameter ratios were varied between 1.07 and 1.4. The Reynolds numbers ranged from 6 × 10⁴ to 2 × 10⁵, depending on the rod bundle arrangement.On the basis of the data measured, the eddy viscosities in the directions normal and parallel to the wall were calculated. The experimental results of the velocity and wall shear stress distributions are compared with the predictions by the VELASCO code. There are considerable differences between computed and experimental results especially for low pitch-to-diameter ratios. The reasons for the discrepancies are discussed together with the results of attempts to adjust the VELASCO code against the experimental data.     

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.     

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.     

Heat transfer to liquid metal: Review of data and correlations for tube bundles

Four sets of experimental data (total of 658 data points) for heat transfer to liquid metals (NaK of different compositions and Hg) flowing in a triangular or square lattice of cylindrical rods with pitch-to-diameter ratios of 1.1 up to 1.95 for a wide range of Peclet numbers (30-5000) were reviewed, and analysed using a number of correlations recommended for liquid metal flowing in tube bundles. A new correlation has been derived as a best fit to the data analysed. The quality of the correlations was estimated quantitatively by comparing their predictions with the test data. The estimated accuracies of the correlations for the different test conditions are presented in the paper and can be used to help to select the heat transfer models for designing complex systems cooled by liquid metals, e.g. Generation-IV lead- or sodium-cooled nuclear reactor cores, heat exchangers, etc.     

A stepwise development and validation of a RANS based CFD modelling approach for the hydraulic and thermal-hydraulic analyses of liquid metal flow in a fuel assembly

The demand of reliable and clean energy at affordable prices poses a formidable challenge to the world. The initiatives from various international organizations reserve an important role for liquid metal cooled reactor systems. Assessment of such reactors usually involves unconventional thermal-hydraulics. Consequently, Reynolds Averaged Navier Stokes (RANS) based Computational Fluid Dynamics (CFD) approaches are expected to play a vital role along with various ongoing experiments for the design and the safe operation of these nuclear reactors. One of the major issues is the heat transport in the fuel assembly by the liquid metal. The known difficulties in heat transfer experiments, especially with liquid metals, necessitate the application of RANS in computing details of flow and temperature distribution.Considering these aspects, a four step approach is described in the current paper. As a first step, the heat transfer in a liquid metal flow inside a heated tube is analyzed using a RANS approach and then compared with some of the empirical correlations. The computed Nusselt number reveals the required development length of the thermal boundary layer in liquid metal. Furthermore, these simulations reveal the need of further assessment of this approach and all the existing correlations, and the care that should be taken while applying one of these correlations. In the second step, numerical simulations of the flow of heavy liquid metal around a heated rod in an annular cavity confirm that a RANS strategy can be employed in liquid metal flows. Furthermore, a comparison between computed and experimental non-dimensional axial temperature at the heated rod surface shows that among the considered turbulence models the use of a Baseline-Reynolds Stress Model (BSL-RSM) with automatic wall treatment (AWT) can be preferred for complex geometries. This is also demonstrated in the third step by computing the flow distribution in a triangular arrangement of a fuel assembly and by comparing with an existing hydraulics experiment in rod-bundle. These analyses reveal that the use of the BSL-RSM turbulence model with AWT allows prediction of the cross-flow in this rod-bundle. As the forth and last step, the integral TEGENA (TEmperatur- und GEschwindigkeitsverteilungen in Stabbündel mit turbulenter NAtriumströmung) experiment has been selected for further assessment of RANS based CFD approach in computing both the flow and temperature field. A comparison with literature demonstrates that the use of symmetric boundary condition in such a tightly packed parallel rod-bundle leads to a distorted flow field. The experimentally and the computationally obtained temperature field at a plane in the outlet reveal its acceptable predictive capability. Furthermore, application of two different Reynolds Stress Models yields almost the same temperature distribution as a result of the use of simple first-order gradient model for the turbulent heat fluxes. Consequently, these four steps support the use of this modelling approach for investigating the heat transport in (heavy) liquid metals. Finally, the preferred RANS approach has been applied for thermal-hydraulic evaluation in the square arrangement of a bare rod-bundle as is to be employed in the European Lead-cooled reactor System (ELSY). Also, the influence of rod pitch-to-diameter ratio has been analyzed by numerically re-arranging these rods in the different square lattice. Moreover, arranging the bare rods in triangular lattice at the different rod pitch-to-diameter ratios shows the effect of the square and triangular lattice in thermal-hydraulics. Lastly, comparisons with some of the existing heat transfer correlations for the triangular and the rectangular lattice allows us to identify preferred correlations for these lattice arrangements of bare and liquid metal cooled rod-bundles.     

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.     

Experimental investigation of turbulent transport of momentum and energy in a heated rod bundle

Turbulent air flow in a central channel of heated 37-rod bundles with triangular array at two different pitch-to-diameter ratios (P/D=1.12 and P/D=1.06) was investigated. Measurements were performed with a hot-wire probe with x-wires and an additional temperature wire. Time mean velocities, time mean fluid temperatures, wall shear stresses and wall temperatures, turbulent quantities such as the turbulent kinetic energy, all Reynolds stresses and all turbulent heat fluxes were measured at two different pitch-to-diameter ratios in a central channel of the bundle. It is shown that with decreasing gap width the turbulence field in rod bundles deviates significantly from that in a circular tube. Also, data on the power spectral density functions of the velocity and temperature fluctuations are presented. These data show the existence of large-scale periodic fluctuations of velocity and temperature in the gap region of two adjacent rods. These fluctuations are responsible for the high intersubchannel heat and momentum exchange. Spectral measurements with two hot wire probes imply a distinct similarity of motion of vortices in adjacent subchannels of the bundle.     

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.     

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.     

绕丝棒束组件低流速时摩擦阻力实验研究

钠冷快堆在事故停堆余热排放期间,堆芯组件内钠流为自然循环流动,流速很低,因此准确确定绕丝棒束组件低流速时的摩擦阻力系数对钠冷快堆非能动余热排出系统的设计具有重要意义。本文以水为流动介质,准确测量了37棒和19棒绕丝棒束组件在低流速（Re<1 000）时的摩擦阻力系数。实验结果表明,随着流速的降低,绕丝棒束组件的摩擦阻力系数迅速升高,流动从层流向过渡流转变时,摩擦阻力系数有明显跃升。将实验测量值与绕丝棒束摩擦阻力系数经验公式的计算结果进行比较,发现在低流速时,经验公式计算结果较实验测量值明显偏小,同时经验公式计算的绕丝棒束层流向过渡流转变的临界Re较实验值偏大。     

Numerical investigation of bent pipe flows at transitional Reynolds number

The correct evaluation of flows at transitional Reynolds number in nuclear reactors is gaining higher importance in relation to the accident analysis for buoyancy-driven flows which dominate the heat decay removal process. In the present paper a comparative study of different turbulence modeling and wall treatment for the evaluation of a fluid flow in transitional Reynolds number, is presented employing computational fluid dynamics (CFD). The relative performance of the models is assessed through benchmarking of fully developed pipe flow at Reynolds number 4900 and of a 90° bend pipe at Reynolds number 5000. Predictions of velocity profiles at different locations are compared to both experimental and accurate numerical simulations.It has been found that the predictions between the models can vary considerably in particular in relation to the different wall treatment employed on the wall. The results show the concerns about the employment of the available turbulence models and wall treatments in low Reynolds number flow regimes and explanation is provided in relation to their formulation.     

Proper orthogonal decomposition of the flow in a tight lattice rod-bundle

Axial coolant flow inside a tightly packed rod bundle presents a complex behavior; experimental analysis had clearly shown that when reducing the pitch-to-diameter ratio (P/D) the turbulence field in rod bundles deviates significantly from that in a circular tube. Moreover for extremely tight configurations the existence of large-scale periodic “flow oscillations” has been shown, which is responsible for the high inter-sub-channel heat and momentum exchange. A complete understanding of these oscillations has still to be achieved; the evidence shown to this point suggests that the oscillations are connected to interactions between coherent structures in adjacent sub-channels. Moreover, the coherent structures show a truly three-dimensional pattern (i.e., structures in different gaps tend to interact) that has not been fully investigated up to this point.A fully transient simulation of turbulence has been performed for an infinite tight triangular lattice. In this case it has been performed with Large Eddy Simulation (LES) at Re = 6400 and P/D = 1.05. A database of snapshots of the flow field has then been collected and proper orthogonal decomposition (POD), a powerful statistical technique, has been applied in order to obtain the most energetic modes of turbulence. The results obtained highlight the presence of several travelling waves propagating in the streamwise direction. The spatial modulation of the travelling waves offers a phenomenological explanation for observed de-coherence effects between the velocity signal in different gaps. It also provides additional insight into the three dimensional structure of the flow oscillations.     

Reprint of: Rod bundle vortex networks, gap vortex streets, and gap instability: A nomenclature and some comments on available methodologies

This note introduces the following terms, which apply to large-scale, vortical, coherent structures, appearing in flows through tightly packed rod bundles and other channels that have narrow gap regions: the term gap instability describes the mechanism of generation of such structures in the gap region in laminar and turbulent flows; the term gap vortex street describes the chain of counter-rotating vortices which from on either side of a single gap; and the term rod bundle vortex network describes the set of mutually dependent gap vortex streets that appear in rod bundles and other channels with multiple gaps. Moreover, this notes summarizes the capabilities and limitations of available CFD methods for simulating flows in rod bundles.     

Investigations on the flow and temperature distribution downstream of local coolant blockages in rod bundle subassemblies

Experimental and theoretical investigations are reported on the flow and temperature distribution in local recirculating flows in rod bundles, downstream of a blockage. A mean coolant temperature in this recirculation zone can be calculated from the dimension of the recirculation zone and the mass exchange rate with the main flow. Similarity analysis for recirculating flow in a simple geometry without rods shows that with a sufficiently high Reynolds number, similar geometry and similar heat distribution, the dimensionless temperature fields in recirculating flows are equal and independent of the Reynolds and Prandtl numbers. This result is also observed to be true for rod bundles, justifying temperature distribution measurements to be performed with water instead of sodium. Typical results are given.