Heat Transfer In Rod Bundles Research Articles

Investigation on turbulent heat transfer to lead-bismuth eutectic flows in rough rod bundles for nuclear applications

Liquid lead-bismuth eutectic corrosion and the deposition of corrosion particles can lead to surface roughening of rod bundles, which impacts the convective heat transfer characteristics of the rod bundles. In this study, the Kays turbulent Prandtl number model and the SSTk‐ω turbulence model were validated using the existing models. Then, the validated model was used to simulate the convective heat transfer in different rough rod bundles. Based on the numerical simulation results, a new Nusselt number correlation for liquid lead-bismuth eutectic within the rough rod bundle was developed. The applicable range of the new correlation is P/D = 1.1–1.5, Pe = 400–4000, and ε/De = 0.0015–0.009. The error between the Nusselt number obtained from the correlation and the numerical simulation results is within 20 %.

Subchannel thermal–hydraulic analysis of a wire-wrapped 19-pin rod bundle in the NACIE-UP facility

Based on the experimental campaign performed on the NACIE-UP (NAtural Circulation Experiment-Upgraded) facility, the benchmark activity was proposed by ENEA to qualify and validate the numerical tools for the Heavy Liquid Metal (HLM) system. Xi’an Jiaotong University participated in the benchmark exercise of subchannel validation and the self-developed subchannel code YAOGUANG was applied to the thermal hydraulic analysis. The performed two tests with different power distributions on the Fuel Pin bundle Simulator (FPS) were simulated, characterized by transition from forced to natural circulation. The applicability of this code to the stable state and mass flow rate transient was evaluated by comparing the numerical outcomes with the experimental results. Then the effect of the non-uniform heating on the thermal field was analyzed. The results indicate that this subchannel code has good accuracy in simulating both steady state and transient conditions with uniform power distribution. For the non-uniform case, the subchannel calculations can capture the general trend of temperature distributions, with a larger simulation deviation observed. This discrepancy is mainly due to the limitations of existing models adopted because they didn’t consider the impacts of non-uniform conditions on the flow and heat transfer in rod bundles. Finally, the influence of non-uniform heating is mainly manifested as the increase of axial and radial temperature gradients and it helps to flatten the radial thermal field to some degree.

Direct Numerical Simulation of Heat Transfer in a 7-Pin Wire-Wrapped Rod Bundle

The Sodium-Cooled Fast Reactor (SFR) is a promising concept chosen in the Generation IV International Forum as a possible design for pursuing the sustainable use of nuclear energy. Its core consists of multiple hydraulically isolated assemblies, with a tightly packed triangular lattice array of fuel pins enclosed in a hexagonal duct present within each assembly. Helical wire spacers are wrapped along the axis of the rods to maintain a gap between them, inducing a secondary flow, increasing the channel mixing, and enhancing convective heat transfer. In this study, a direct numerical simulation campaign is conducted for a simplified 7-pin wire wrapper geometry, with Reynolds numbers ranging from Re = 1000 to 10 000 and a Prandtl number of Pr = 0.005, to investigate heat transfer in low-flow conditions. The wire wrapper case is compared to a bare bundle case with seven pins. The results are discussed, and heat transfer predictions are compared between our numerical results and classic correlations. An anisotropy invariant map is obtained for the above-mentioned cases, and turbulent kinetic energy and turbulent heat flux budgets are computed and analyzed. Our findings provide unique insights into the flow behavior within a wire-wrapped bundle.

CFD investigation of flow and heat transfer of supercritical CO2 in wire wrapped rod bundle

Computational fluid dynamics is increasingly applied to reactor safety analysis, and the applicability evaluation of turbulence model can effectively improve the calculation accuracy. In this paper, the applicability of six turbulence models and two near wall models is compared for simulation of flow and heat transfer of supercritical carbon dioxide in wire wrapped rod bundle. According to experimental data under various conditions, the applicability of turbulence models and near wall models is respectively evaluated from wall temperature and surface heat transfer coefficient. The results show that SST k–ω model combined with low-Re model can simulate the change of wall temperature and surface heat transfer coefficient in critical state best, and the average relative error (Tw and h) is 6.88% and 13.17%. When CO2 is heated into supercritical state in the latter 900 mm of wire wrapped rod bundle, the relative error (Tw and h) calculated by RNG k–ω model is 5.94% and 18.02%. The grids number of low Re method is nearly double of the grids number of wall function method. Therefore, the simulation results computed by wall function method at supercritical region are also acceptable due to the low computational consumption. This paper researches the applicability of turbulence model and near wall model to enhance the accuracy of simulation of flow and heat transfer in supercritical CO2 reactor rod bundle.

Numerical and experimental analysis of LBE flow and heat transfer characteristics in hexagonal rod bundles

Lead-bismuth eutectic (LBE) is a liquid with low Prandtl number and high thermal conductivity, generally used as the coolant in lead-cooled fast reactors of Generation-IV. The traditional Reynolds analogy is not appropriate for LBE, hence the theoretical analysis and experimental measurements are studied to interpret the flow and heat transfer of LBE in this article. In this way, a single-rod experiment on flow and heat transfer for LBE is performed and a new empirical correlation is fitted. To analyze the behavior of flow and heat transfer for low Prandtl number fluids, and also to validate the turbulence model and new correlation in the hexagonal rod bundles. The CFD simulations are performed for the XJTU 7-rod bundle, the KIT 19-rod bundle, and the ENEA 37-rod bundle based on ANSYS Fluent. The convective heat transfer coefficient of LBE, the temperature of heating wall at different sub-channels, and the temperature non-uniformity are investigated in this paper, to reveal the flow and heat transfer characteristics of LBE. The results show that the deviations of the section averaged Nusselt number are in 25%, and the deviations of the local temperature of LBE and heating wall are in 10℃. Grid spacers will result in a 30% rise in the section averaged Nusselt number, which will improve the turbulent intensity and heat transfer. Temperature non-uniformity is reduced as the Peclet number is increased. The validations demonstrate that the new empirical correlation provides accurate convective heat transfer coefficient predictions for LBE flow and heat transfer in hexagonal rod bundles with a relative derivation in 20%, which can be used as a reference for additional LBE simulations and experiments.

Quasi-periodic large-scale vortex structure in bod bundle lattice with micro ribs

Quasi-periodic large-scale vortex structure (QLVS) is highly accounted for the local flow and heat transfer and turbulent mixing in rod bundles. The vortex structures between rod bundles with different rib heights are analyzed, and the morphology of QLVS is clarified. The mechanism of the QLVS is studied from the perspective of hydrodynamics, and the formation and development process of the QLVS are analyzed in detail. Combined with the criterion of QLVS, the rotation, deformation and velocity changes of small disturbance are analyzed. With the increase of the height of the micro-rib, QLVS is introduced and gradually enhanced. The velocity gradient between different fluid layers is a key factor in the formation and development of QLVS structures. This research can provide theoretical support for the design and optimization of rod bundle lattices.

Study on the flow and heat transfer characteristics of liquid sodium in a hexagonal 7-rod bundle

The flow and heat transfer characteristics of liquid metal sodium are different from the ordinary fluids, which brings great challenges to the CFD simulation in the sodium-cooled fast reactor (SFR). Therefore, the accurate flow and heat transfer models are particularly significant in the high fidelity three dimensional analysis of liquid metal reactors. In this paper, the OpenFOAM solver implemented with k – ε – kθ – εθ turbulent heat transfer model was developed and used to study the flow and heat transfer characteristics of liquid metal sodium. Firstly, the proposed thermal hydraulic models were validated against the thermal hydraulic experiment of single-phase liquid sodium in a 7-rod bundle. The key thermal hydraulic parameters, such as the Nusselt number, pressure drop and frictional coefficient, were compared with the experimental data. Results show that the developed OpenFOAM solver with new implemented model performs well and the simulated results were in good agreement with the experimental data. Then the thermal–hydraulic characteristics of liquid sodium in the bend rod bundle were investigated. The effects of bending angle, Reynolds number on peak wall temperature and Nusselt number were investigated. CFD results suggest that the heat transfer in the bend rod bundle is highly sensitive to the bending angle but not to Reynolds number. Two opposite-direction cross flows were formed in the sections before and after the maximum bend position, which reveals the formation and disappearance of hot spot in the narrow gap.

Adaptation of the Turbulence Model to the Heat Transfer in a Hexagonal Rod Bundle

Adaptation of the Turbulence Model to the Heat Transfer in a Hexagonal Rod Bundle

Numerical simulation of the thermal-hydraulic characteristics of supercritical carbon dioxide in a wire-wrapped rod bundle

A wire-wrapped spacer was considered in the fuel-assembly design of a supercritical carbon dioxide (SCO2) reactor to improve the heat transfer between the coolant and fuel elements. However, there is still a lack of understanding and detailed evaluation of the performance of the wrapped wire. In this study, the turbulent flow and heat transfer of SCO2 in a rod bundle were numerically investigated considering the fluid–solid conjugate interaction. Emphasis was placed on revealing the effects of wire shape, wire pitch and number of wire thread on the heat transfer and pressure drop. The performance evaluation criterion (PEC) was adopted to evaluate the performance of spacers. It was found that the heat transfer in the wire-wrapped rod bundle was enhanced compared to that in the bare rod bundle. The trapezoid-shaped wire shows a larger PEC than the circular- and rectangular-shaped wires. In addition, the PEC increased with the wire pitch first but declined subsequently, showing a peak with a wire pitch between 180 and 240 mm. The wire-wrapped spacer with two threads was recommended because of its high heat transfer efficiency and relatively low flow pressure drop.

Development of a correlation for mixed convection heat transfer in rod bundles

A correlation is developed to predict mixed convection heat transfer of water flow in rod bundles. The rod bundles are 5 × 5 and the Re number ranges from 1 × 103 to 3 × 104 in the experiment. In the forced convection region, the Dittus-Boelter correlation predicts well with the experimental data. However, in the mixed convection region, the correlations reported in the literature are all deviated from the measured data. Moreover, based on the classical form of buoyancy parameter, Gr*/Re3.425/Pr0.8, the experimental data of circular channels extracted from literature are compared with the measured data. The comparison shows that the buoyancy parameters of the onset point of heat transfer impairment (HTI), turning point of HTI and onset point of heat transfer enhancement (HTE) in rod bundles are very close to that in circular channels, but the maximum degree of HTI in bundles is significantly weaker than that in circular channels. The experimental data indicate that the circumferential heat transfer is significantly uneven in HTI region, which result in the differences of buoyancy parameter of turning point in different circumferential directions and eventually lead to the weaker overall degree of HTI in bundles. Considering the derivation method of the classical form of buoyancy parameter proposed by Rouai, a new buoyancy parameter form for rod bundle channels is derived based on the Dittus-Boelter correlation for forced convection heat transfer and the Cheng and Todreas’s correlation for friction factors in rod bundles. Based on the new buoyancy parameter form, a new correlation to predict mixed convection heat transfer in rod bundles is proposed and provides good prediction accuracy.

Numerical simulation of three-dimensional flow and heat transfer characteristics of liquid lead–bismuth

Liquid lead-bismuth cooled fast reactor is one of the most promising reactor types among the fourth-generation nuclear energy systems. The flow and heat transfer characteristics of lead-bismuth eutectic (LBE) are completely different from ordinary fluids due to its special thermal properties, causing that the traditional Reynolds analogy is no longer recommended and appropriate. More accurate turbulence flow and heat transfer model for the liquid metal lead-bismuth should be developed and applied in CFD simulation.In this paper, a specific CFD solver for simulating the flow and heat transfer of liquid lead-bismuth based on the k - ε - kθ- εθ model was developed based on the open source platform OpenFOAM. Then the advantage of proposed model was demonstrated and validated against a set of experimental data. Finally, the simulation of LBE turbulent flow and heat transfer in a 7-pin wire-wrapped rod bundle with the k - ε - kθ- εθ model was carried out. The influence of wire on the flow and heat transfer characteristics and the three-dimensional distribution of key thermal hydraulic parameters such as temperature, cross-flow velocity and Nusselt number were studied and presented.Compared with the traditional SED model with a constant Prt = 1.5 or 2.0, the k - ε - kθ- εθ model is more accurate on predicting the turbulence flow and heat transfer of liquid lead-bismuth. The average relative error of the k - ε - kθ - εθ model is reduced by 11.1% at most under the simulation conditions in this paper. This work is meaningful for the thermal hydraulic analysis and structure design of fuel assembly in the liquid lead-bismuth cooled fast reactor.

Experimental and numerical investigation on heat transfer of supercritical water flowing upward in 2 × 2 rod bundles

This paper presents the investigation of heat transfer of supercritical water flowing upward in 2 × 2 rod bundles, both experimentally and numerically. The experiment conditions are as follows: pressures from 22.9 MPa to 26.1 MPa, mass fluxes ranging from 450 kg/m2/s to 1500 kg/m2/s and heat fluxes ranging from 0.4 MW/m2 to 1.5 MW/m2. Four heated-rods of 8 mm outer diameter formed 2 set of experiment sections with pitch to diameter ratio (P/D ratio) 1.18 and 1.3. Heat transfer coefficients between the heated rod and fluid were conducted by 3 different methods and the effect of spacer grids was clearly observed. The experiment results show that heat transfer to supercritical water in rod bundles is strongly affected by flow channels and spacer grids. Moreover, a large database of heat transfer in rod bundles was carried out and HTC were compared with tube and annuli with the equivalent hydraulic diameter. The phenomenon of heat transfer difference in rod bundle circumferential direction and enhancement heat transfer in downstream of spacer grids were observed and investigated. In addition, Computational Fluid Dynamics (CFD) method was applied to give a deep insight of velocity profile, spacer effect and heat transfer enhancement in this research.

Direct numerical simulation of turbulent flow and heat transfer in a hexagonal rod bundle

The aspects of numerical simulation of heat transfer in a flow along the hexagonal rod bundle are discussed in the present work. The direct numerical simulation is used to investigate the flow with Reynolds and Prandtl numbers varying in the range from 2500 to 10000 and 0.0043 to 7 correspondingly. The obtained simulation results demonstrate good agreement with available experimental data and semi-empirical correlations for the thermo-hydraulic characteristics of the channel. The empirical correlations for the Nusselt number distributions summarizing the results of the numerical simulations are proposed. The preliminary calculations have shown that the modelled time averaging interval is comparable with the initial transition time interval. This observation allows applying the approach, proposed in [7], to speed up the simulations.

Heat transfer in rod bundles cooled by supercritical water – Experimental data and correlations

The paper presents the results of a comparative evaluation of existing correlations for the prediction of heat transfer to supercritical pressure water against experimental data for bundles of heated rods. It is shown that the method, developed by the authors for the engineering calculation of the heat transfer coefficient in the supercritical region of the coolant parameters, makes it possible to describe the experimental data for smooth rod bundles with an error of less than 15%. In the case of rod bundles with wrapped wire, the same method gives values of the heat transfer coefficient, which are on average about 8% lower compared to the experimental data obtained. This is connected with the intensification of heat transfer due to swirling the flow and can be considered as a margin when estimating the limiting temperature of the heat transfer wall. Based on the comparison of the calculation results by different methods, the problems of choosing the ratio for determining the heat transfer coefficient in fuel assemblies of reactors with supercritical pressure water are discussed.

ИССЛЕДОВАНИЯ ТЕПЛООБМЕНА В ПУЧКАХ ТВЭЛОВ ПРИ СВЕРХКРИТИЧЕСКОМ ДАВЛЕНИИ ВОДЫ

Calculations to substantiate the characteristics of a reactor cooled by water with supercritical steam parameters and an adjustable neutron spectrum require clarification of data on heat transfer characteristics. The features and data on heat transfer in round pipes and rod bundles at supercritical pressures (SCP) are considered. In analysis of hydrodynamics and heat transfer dates with the flow of water of supercritical parameters in round pipes, an area of both more intense and degraded convective heat transfer was detected compared to subcritical pressures. It is assumed that one of the reasons for the deteriorated heat exchange is the presence of a near-wall layer consisting of a "gas" phase with low thermal conductivity and a central flow region in the form of a liquid-like phase having a lower temperature. A brief review of data on heat transfer in round tubes and rod bundles with SCP is presented. Since experiments on water are complex and expensive, many results, including the SSC RF - IPPE, were obtained on model media (CO2 and freon-12). Shown that despite the diversity of recommendations on the boundary regime with the deterioration of heat transfer, the proposed ratios give a different dependence of the heat flux density on the mass velocity. They do not consider the influence of such parameters as pressure, channel geometry, temperature of heat exchange surface, etc., they are obtained for a narrow range of parameters. And only extensive analytical studies of Yu.A. Zeigarnik et al. (JIHT RAS, NRU "MEI") allowed to summarize the data on heat transfer in round pipes at SCP. Only limited data was obtained by Russian, Ukrainian and Chinese specialists in heat transfer in bundles with a small number of pipes. The results of Chinese experts have shown that heat transfer in rod bundles at supercritical water pressures is higher and more stable than when water moves in pipes and annular channels. In close bundles, the deterioration of heat transfer occurred at low mass velocities and high heat fluxes, and in widespread deterioration of heat transfer was not observed. The growth of heat transfer in the rod bundles is promoted by mixing with spacer and mixing grids, which destroy the wall barrier layer, which prevents the transfer of heat under supercritical pressure from the wall to the center of the flow. The accumulation of new experimental data and additional analysis of research are necessary. A description and technical characteristics of the thermo-hydraulic facilities of the SCP on water (SVD-1 and SVD-2) and freon-12 (STF) available at SSC RF - IPPE is provided. The results of experiments at SSC RF - IPPE and technical approach and methodology of future experiments in hydrodynamics and heat transfer at SCP is presented and discussed.

Capabilities of high y+ wall approaches in predicting heat transfer to supercritical fluids in rod bundle geometries

The present paper summarises the results of the simulation of heat transfer to supercritical water in rod-bundle geometries by a CFD code, using wall function models. Two different sets of experimental data were considered, concerning both relatively high and low mass flux conditions and inlet temperature spanning from low to near-critical values.In past analyses, the unsuitability of low-Reynolds number turbulence models was observed in predicting heat transfer in rod bundles, when both high mass and heat flux values were imposed; in fact, large overestimations of wall temperatures were reported in such conditions. This motivated to try simpler models, such as the wall function approach, in order to investigate if, though expectedly not very accurate, they could at least reproduce the experimental data at an acceptable level.As reported in the present paper, the selected models, which adopt a “high y+” wall treatment (indicating wall functions in the STAR-CCM+ code), seem reasonably able at reproducing the general observed experimental trends. The present understanding of the phenomena and the available modelling techniques unfortunately do not allow obtaining better results when the wall or fluid temperature approach the pseudocritical value. However, the comparison with results obtained by low-Reynolds models shows that, at least when facing operating conditions similar to the ones considered in the present work, a downgrading of the adopted modelling techniques may be beneficial and allows obtaining reasonable results. Analyses were also performed considering conditions far from the pseudo-critical temperature, in which low-Reynolds models had provided good performance, reporting that the wall function approach seems effective also in these cases for obtaining first guess results.

Experimental Study on Heat Transfer Enhancement Effect with Different Shapes of Mixing Vanes in Sub-Channels of 6×6 Rod Bundle

In the present study, single-phase heat transfer characteristics for downstream flow in the support grid of 6×6 rod bundle were investigated. It has been known that a turbulence generation due to a support grid with split mixing vanes enhances heat transfer in rod bundle but its heat transfer enhancement actually affects to relatively shorter distance. On the other hand, it has been also turned out that a support grid with large scale vortex flow (LSVF) mixing vanes results in heat transfer enhancement to a longer distance. Based on the results of literatre survey, single-phase water heat transfer experiments were performed for Reynolds numbers at around 30,000, and the heat transfer enhancement effect with both i) the split mixing vanes and ii) the LSVF mixing vanes was compared in this study. The key results showed that the effect of heat transfer enhancement in rod bundle region by the split mixing vanes was maintained up to the length of 15Dh behind the spacer grid. For the Reynolds numbers at around 30,000, it was also observed that the effect using the LSVF mixing vanes was stronger at about 3% when compared to the case using the split mixing vanes only for the distance ranging from 1 to 15Dh behind the spacer grid.

Mixed convection heat transfer in a 5 × 5 rod bundles

In order to investigate the buoyancy effect on heat transfer in rod bundles, experiments were performed at low flow rate with Reynolds number ranging from 1×103 to 3×104 in a 5×5 squarely arrayed rod bundles. The diameter of the rods are 10mm with a pitch of 13.3mm, and the length of the test section is about 3m. The rods are heated uniformly by a DC power, and cooled by pressurized water. The experimental data indicates that Weisman’s correlation predicts well within a deviation less than 10% in forced turbulent convection, but overestimates the Nusselt number in mixed convection conditions. It’s been found that mixed convection heat transfer in rod bundles is similar to that in simple channels, with increasing of free convection component, the heat transfer tends to be impairs firstly, and then followed by enhancement. The experimental data also indicates that buoyancy effect on heat transfer should not be neglected even when Reynolds number is about 15,000 under some certain heating conditions. New empirical correlations have been proposed for the prediction of forced turbulent convection heat transfer and mixed convection heat transfer in rod bundles respectively.

A circumferentially non-uniform fuel model and its application to thermal-hydraulic code

In the fuel assemblies in reactor core, the distribution of temperature is not uniform in the fuel rod along the circumferential direction. The circumferential temperature difference could be neglected for conventional assembly design but increases significantly in a tight lattice. To investigate the circumferential non-uniformity of heat transfer in rod bundles, this paper firstly establishes mathematical model and makes theoretical analyses, based on which influential non-dimensional numbers are summarized. Then, a semi-empirical correlation describing this phenomenon is proposed based on theoretical results and CFD sensitivity analyses. Finally, a three-dimensional model for cylindrical fuel is introduced in the thermal-hydraulic code to predict circumferential heat transfer non-uniformity in different geometry and flow conditions. To validate this model, some results are compared with experimental data of bundle test for subcritical and supercritical water. The three-dimensional fuel model for sub-channel code is a new numerical tool to predict the peak cladding and fuel temperature and can be applied in thermal-hydraulic analysis of fuel assemblies of tight lattice design. Copyright © 2017 John Wiley & Sons, Ltd.

CFD analyses of mixed and forced convection in a heated vertical rod bundle

Abstract The effects of spacer grid blockage ratio and spacer grid spacing on heat transfer in a vertical rod bundle are presented in this study. A 3-D model of a 1/8th cross-section of a subchannel with and without spacer grids has been considered for CFD simulation. The inlet flow Reynolds number (Re) was varied from 1640 to 12,000 to investigate the flow effect on heat transfer. A suitable turbulence model was selected for this study by comparing the local Nusselt number (Nu) in the subchannel with previously published experimental data. The simulation results predicted the experimental data satisfactorily with maximum 10% deviation when compared with published experimental data for a pitch-to-diameter (P/D) ratio of 1.25 and maximum 7% deviation for a P/D ratio of 1.5. Different spacer grid blockage ratios (0.1, 0.2, 0.3, and 0.4) were studied and the dependence of the pressure drop on the Re at the grid was analyzed. Furthermore, the effect of the spacer grid spacing was investigated. The simulation results were found to compare very well with some notable correlations found in the literature.