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.     

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.     

Simulation of turbulent flow inside different subchannels in tight lattice bundle

In this paper, both steady and unsteady Reynolds Averaged Navier Stokes (RANS and URANS) methodology are applied to the prediction of turbulent flow inside different subchannels in tight lattice bundles.Two typical configurations of subchannels (i.e., wall subchannel and center subchannel) are chosen to be investigated. In this work the application of different turbulence models implemented in the commercial code CFX v12 is shown. The validity of the methodology is assessed by comparing computational results of axial velocity, wall shear stress and turbulent intensity distributions with the experimental data (Krauss, 1996; Krauss and Meyer, 1998). This study shows that RANS simulation with anisotropic turbulent model produces excellent agreement with experiment, whereas it failed to predict the flow behavior accurately in the case of tightly packed geometries (P/D < 1.1). On the other hand, the URANS simulation is in good agreement with the results in tightly packed geometries with flow oscillation in the gap region. The effects of the Reynolds number and the bundle geometry on the flow oscillation are investigated in details.     

Analysis of low Reynolds number turbulent flow phenomena in nuclear fuel pin subassemblies of tight lattice configuration

This paper focuses on the numerical simulation of low Reynolds (Re) number turbulence flow phenomena in tightly packed fuel pin subassemblies and in channels of irregular shape such as eccentric annuli. Highlighted phenomena include (i) turbulence-driven secondary flows inside a subchannel, (ii) local turbulent-laminar transition in the narrow gap region, and (iii) global flow pulsation across the gap along the channel length. These phenomena are simulated by Computational Fluid Dynamics (CFD). The CFD methods employed here are those of Direct Numerical Simulation (DNS) of turbulence, Large Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS) equations approach. Complicated turbulent flow structure is due to strong anisotropy in the non-uniform channel geometry that is characterized by wide open channels connected by a narrow gap. The secondary flows in subchannels play an important role in transporting small eddies generated in the wider region toward the narrow gap. Periodic cross-flow oscillations are calculated to appear in the vicinity of the gap region, and the coherent structure is transported in the main flow direction. This macroscopic flow process prevails in the low Re turbulent flow regime and is called as global flow pulsation. Finally a brief discussion is made on their influences onto the mixing between two subchannels that must be taken into account during natural circulation decay heat removals.     

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.     

On the transport mechanisms in simulated heterogeneous rod bundle subchannels

Experimental results are presented on fully developed turbulent flow through simulated heterogeneous rod bundle subchannels. The emphasis of this study is on the universality of the cross-gap turbulence convection transport with respect to symmetric versus asymmetric subchannels. The flow passage was formed by a rod asymmetrically mounted in a trapezoidal duct. The Reynolds number based on the equivalent hydraulic diameter and bulk average axial velocity is 26 300. The measurements include mean axial velocities, r.m.s. values of the fluctuating velocity components and the energy density spectra. The results demonstrate the existence of an unusual region near the asymmetric rod-to-wall gap characterized by high levels of axial turbulence intensity with a remarkably different type of distribution compared with a normal boundary layer. It is also shown that the strength of the cross-gap transport is subchannel geometry dependent. The distributions of wall shear stress and turbulence kinetic energy indicate that mean convection by secondary flow is also an important transport mechanism that should be taken into account in the analysis of momentum/heat transfer in rod bundle subchannels.     

Simulation of flow pulsations in a twin rectangular sub-channel geometry using unsteady Reynolds Averaged Navier-Stokes modelling

An unsteady Reynolds Averaged Navier-Stokes (URANS) based turbulence model, the Spalart-Allmaras (SA) model, was used to investigate the flow pulsation phenomena in compound rectangular channels for isothermal flows. The studied geometry was composed of two rectangular sub-channels connected by a gap, on which experiments were conducted by Meyer and Rehme (1994) and were used for the validation of numerical results. Two case studies were selected to study the effect of the advection scheme. The results from the first order upwind advection scheme had clear symmetry and periodicity. The frequency of flow pulsations was under predicted by almost a factor of two. Due to inevitable numerical diffusion of the first order upwind scheme, a second order accurate in space advection scheme was also considered. The span-wise velocity contours, velocity vector plots, and time traces of the velocity components showed the expected cross-flow mixing between the sub-channels through the gap. The predicted kinetic energy in the unsteady velocity fluctuations showed two clear peaks at the edges of the gap. The dynamics of the flow pulsations were quantitatively described through temporal auto-correlations and power spectral functions. The numerical predictions were in agreement with the experiments. Studies on the effect of the Reynolds number and the computational length of the domain were also performed. The numerical results reproduced the relationship between the Reynolds number and the frequency of the flow pulsations. The impact of the channel length was tested by simulating a longer channel with respect to the base case. It was found that the channel length did not significantly affect the numerical predictions. Simulations were also performed using the standard k-? model. While the flow pulsations were predicted with this model, the frequency of the pulsation was in poor agreement with the experimentally measured value.     

Analysis of flow distribution a PWR fuel rod bundle model containng A 90% blockage

An experimental investigation, covering a Reynolds number range from 2 × 10³ to 3.5 × 10⁴, was conducted to study the velocity and turbulence intensity distributions due to the presence of a blockage in an unheated 7 × 7 rod bundle. The blockage configuration, consisting of a 4 × 4 rod array, created a maximum flow area reduction of 90% in the central nine subchannels. The blockage sleeve length was 38.3 × rod diameter and the 90% blockage zone length extended for 16.4 × rod diameter. The results showed that upstream of the blockage, the flow was not influenced by the blockage until it reached the location where the inlet taper section of the swelling started. At the downstream end, the flow disturbance was extensive and persisted over a distance of about 83 rod diameters. Compared to the downstream velocity profiles, the turbulence intensity measurements however showed a faster recovery from the blockage influence. At the higher Reynolds number, velocity profiles calculated using the COBRA subchannel computer code compared consistently with the experimental data. The general flow behaviour of the various subchannels was reasonably well predicted. However, at low Reynolds number, due mainly to the frictional form loss calculation scheme in COBRA and uncertainty in the flow transition, the flow diversion due to the blockage to the surrounding unblocked subchannels was overestimated. The influence of the degree of recovery from the rod swelling on the flow was also studied using COBRA.     

CFD analyses in tight-lattice subchannels and seven-rod bundle geometries of a Super Fast Reactor

This paper presents CFD analyses in heat unsymmetric subchannels and heat symmetric seven-rod bundle geometries of a Super Fast Reactor (Super FR) fuel assembly using STAR-CD. The purpose of CFD analyses in heat unsymmetric subchannels is to evaluate the effect of the power differences on the heat transfer in subchannels of the Super Fast Reactor. For heat symmetric seven-rod bundles, the effects of the gap clearance between the fuel rod and the assembly wall and the displacement of the fuel rod on the circumferential temperature distributions and Maximum Cladding Surface Temperature (MCST) are analyzed. The results show that larger power difference between fuel rods gives larger circumferential temperature difference of the hottest fuel rods. Considering cross flow between edge and ordinary subchannels, 1 mm gap between the fuel rod and the assembly wall is better for small MCST although the circumferential temperature difference in edge subchannel is large. MCST increases exponentially with the displacement. The relative error of displacement should be less than 1% if the allowable increment of MCST due to displacement is less than 6 °C.     

Fuel performance analysis for PWR cores

Attainable discharge burnups for oxide and hydride fuels in PWR cores were investigated using the TRANSURANUS fuel performance code. Allowable average linear heat rates and coolant mass fluxes for a set of fuel designs with different fuel rod diameters and pitch-to-diameter ratios were obtained by VIPRE and adopted in the fuel code as boundary conditions. TRANSURANUS yielded the maximum rod discharge burnups of the several design combinations, under the condition that specific thermal-mechanical fuel rod constraints were not violated. The study shows that independent of the fuel form (oxide or hydride) rods with (a) small diameters and moderate P/Ds or (b) large diameters and small P/Ds give the highest permissible burnups limited by the rod thermal-mechanical constraints. TRANSURANUS predicts that burnups of ∼74 MWd/kg U and ∼163 MWd/kg U (or ∼65.2 MWd/kg U oxide-equivalent) could be achieved for UO₂ and UZrH_x fuels, respectively. Furthermore, for each fuel type, changing the enrichment has only a negligible effect on the permissible burnup. The oxide rod performance is limited by internal pressure due to fission gas release, while the hydride fuel can be limited by excessive clad deformation in tension due to fuel swelling, unless the fuel rods will be designed to have a wider liquid metal filled gap. The analysis also indicates that designs featuring a relatively large number of fuel rods of relatively small diameters can achieve maximum burnup and provide maximum core power density because they allow the fuel rods to operate at moderate to low linear heat rates.     

A finite element LES for high-Re flow in a short-elbow pipe with undisturbed inlet velocity

The paper is concerned with a large-eddy simulation (LES) for a high-Reynolds-number flow in a short-elbow pipe, which can potentially be employed in the primary piping system of the Japan Sodium-cooled Fast Reactor (JSFR). The basic performance of the LES is studied for an elbow pipe flow without turbulence at inlet boundary at Re = 1.2 × 10⁶ by comparison with a flow observed in a 1/3-scale water experiment, where the flow disturbance at the pipe inlet is small. In setting up the computational conditions, special care was taken to ensure that the mesh subdivision was suitable for the simulation of the pipe flow through a theoretical consideration. We discuss the effects of the turbulence model (Smagorinsky model, WALE model) and the inlet velocity profile on the results. The mechanism of the pressure fluctuation and the origin of the fluid force are also discussed with the aid of spectral analysis and the visualization of essential hydraulic quantities.     

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.     

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.     

Evaluation of a numeric procedure for flow simulation of a 5 × 5 PWR rod bundle with a mixing vane spacer

The fuel assemblies of the Pressurized Water Reactors (PWR) are constituted of rod bundles arranged in a regular square configuration by spacer grids placed along its length. The presence of the spacer grids promote two antagonist effects on the core: a desirable increase of the local heat transfer downstream the grids and an adverse increase of the pressure drop due to the constriction on the coolant flow area. Most spacer grids are designed with mixing vanes which cause a cross and swirl flow between and within the subchannels, enhancing even more the heat transfer performance in the grid vicinity. The improvement of the heat transfer increases the departure from the nucleate boiling ratio, allowing higher operating power in the reactor. Due to these important thermal and fluid dynamic features, experimental and theoretical investigations have been carried out in the past years for the development of spacer grid design. More recently, the Computational Fluid Dynamics (CFD) using three dimensional Reynolds Averaged Navier Stokes (RANS) analysis has been used efficiently for this purpose. Many computational works have been performed, but the appropriate numerical procedure for the flow in rod bundle simulations is not yet a consensus. This work presents results of flow simulations performed with the commercial code CFX 11.0 in a PWR 5 × 5 rod bundle segment with a split vane spacer grid. The geometrical configuration and flow conditions used in the experimental studies performed by Karoutas et al. were assumed in the simulations. To make the simulation possible with a limited computational capacity and acceptable mesh refinement, the computational domain was divided in 7 sub-domains. The sub-domains were simulated sequentially applying the outlet results of a previous sub-domain as inlet condition for the next. In this study the k–ε turbulence model was used. The simulations were also compared with those performed by Karoutas et al. in half a subchannel and In et al. in one subchannel computational domains. Comparison between numerical and experimental results of lateral and axial velocities along of the rod bundle show good agreement for all evaluated heights downstream the spacer grid. The present numerical procedure shows better predictions than Karoutas et al. model especially further from the spacer grid where the peripheral subchannels have more influence in the average flow.     

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。     

Evaluation of a numeric procedure for flow simulation of a 5 × 5 PWR rod bundle with a mixing vane spacer

The fuel assemblies of the Pressurized Water Reactors (PWR) are constituted of rod bundles arranged in a regular square configuration by spacer grids placed along its length. The presence of the spacer grids promote two antagonist effects on the core: a desirable increase of the local heat transfer downstream the grids and an adverse increase of the pressure drop due to the constriction on the coolant flow area. Most spacer grids are designed with mixing vanes which cause a cross and swirl flow between and within the subchannels, enhancing even more the heat transfer performance in the grid vicinity. The improvement of the heat transfer increases the departure from the nucleate boiling ratio, allowing higher operating power in the reactor. Due to these important thermal and fluid dynamic features, experimental and theoretical investigations have been carried out in the past years for the development of spacer grid design. More recently, the Computational Fluid Dynamics (CFD) using three dimensional Reynolds Averaged Navier Stokes (RANS) analysis has been used efficiently for this purpose. Many computational works have been performed, but the appropriate numerical procedure for the flow in rod bundle simulations is not yet a consensus. This work presents results of flow simulations performed with the commercial code CFX 11.0 in a PWR 5 × 5 rod bundle segment with a split vane spacer grid. The geometrical configuration and flow conditions used in the experimental studies performed by Karoutas et al. were assumed in the simulations. To make the simulation possible with a limited computational capacity and acceptable mesh refinement, the computational domain was divided in 7 sub-domains. The sub-domains were simulated sequentially applying the outlet results of a previous sub-domain as inlet condition for the next. In this study the k-ε turbulence model was used. The simulations were also compared with those performed by Karoutas et al. in half a subchannel and In et al. in one subchannel computational domains. Comparison between numerical and experimental results of lateral and axial velocities along of the rod bundle show good agreement for all evaluated heights downstream the spacer grid. The present numerical procedure shows better predictions than Karoutas et al. model especially further from the spacer grid where the peripheral subchannels have more influence in the average flow.     

Comparison of thermo-hydraulic performances of large scale vortex flow (LSVF) and small scale vortex flow (SSVF) mixing vanes in 17 × 17 nuclear rod bundle

Spacer grids in the nuclear fuel rod assembly maintain a constant distance between rods, secure flow passage and prevent the damage of the rod bundle from flow-induced vibration. The mixing vanes attached to the spacer grids generate vortex flows in the subchannels and enhance the heat transfer performance of the rod bundle. Various types of mixing vanes have been developed to produce cross flows between subchannels as well as vortex flows in the subchannels.The shapes of the mixing vane have been improved to generate larger turbulence and cross flow mixing. In the present study, two types of large scale vortex flow (LSVF) mixing vanes and two types of small scale vortex flow (SSVF) mixing vanes are examined. SSVF-single is conventional split type and SSVF-couple is split type with different arraying method. LSVF mixing vane has different geometry and arraying method to make large scale vortex. 17 × 17 rod bundle with eight spans of mixing vanes is simulated using the IBM 690 supercomputer. The FLUENT code and IBM supercomputer is employed to calculate the flow field and heat transfer in the subchannels.Turbulence intensities, maximum surface temperatures of the rod bundle, heat transfer coefficients and pressure drops of the four kinds of mixing vanes are compared. LSVF mixing vanes produced higher turbulence intensity and heat transfer coefficient than SSVF mixing vanes. Consequently, LSVF mixing vane increases the thermal efficiency and safety of the rod bundle.     

Measurements of frequencies and spatial correlations of coherent structures in rod bundle flows

Cross-wire anemometry was used to identify and characterize coherent flow pulsations in isothermal air flow near the gap regions of a five-rod bundle with a design pitch-to-diameter ratio of 1.149 and contained in a quasi-trapezoidal duct. It was confirmed that such pulsations are quasi-periodic and contribute significantly to the velocity fluctuations across the gap. The frequency of pulsations was found to decrease with diminishing rod–wall gap size in the range between 0.015D and 0.250D, where D is the rod diameter. The pulsations in a rod–wall gap and an adjacent rod–rod gap were strongly coupled and occurred at the same frequency as one rod was displaced towards the duct wall.     

Numerical study on flow and heat transfer characteristics in the rod bundle channels under super critical pressure condition

In this study, the 3D flow and heat transfer characteristics in rod bundle channels of the super critical water-cooled reactor were numerically investigated using CFX codes. Different turbulent models were evaluated and the flow and heat transfer characteristics in different typical channels were obtained. The effect of pitch-to-diameter ratio (P/D) on the distributions of surface temperature and heat transfer coefficient (HTC) was analysed. For typical quadrilateral channel, it was found that HTC increases with P/D first and then decreases significantly when P/D is <1.4. There exists a “flat region” at the maximum value when P/D is 1.4. If P/D is larger than 1.4, heat transfer deterioration (HTD) occurs as main stream enthalpy is quite small. Furthermore, the HTD under low mass flow rate and the non-uniformity of circumferential temperature were also discussed.     

Very-Large Eddy Simulation (V-LES) of the flow across a tube bundle

A new turbulence modelling approach (Very-Large Eddy Simulation; V-LES) is developed and compared to conventional RANS and LES for a flow across a tube bundle. The method, which belongs to the large-scale simulation category, represents a good compromise between efficiency and precision, and may thus be used for industrial problems for which LES remains computationally expensive under high to very-high Reynolds number flow conditions. It can also be used for gas-liquid two-phase flows such as pressurized thermal shocks. The method is a sort of blend between U-RANS and LES, in that it resolves very large structures - way larger than the grid size - and models all subscale of turbulence using a two-equation model, by reference to RANS. The original model is shown here to share the same characteristics as the Detached Eddy Simulation (DES) approach, in that when the filter width is smaller than the wall-distance at which viscous effects are negligible (f_μ = 1), the fixed filter width is replaced by the wall distance. First conclusions to be drawn from its extension here is that the flow must be resolved in three-dimensions, under transient conditions, with refined grids. Sensitivity to various computational parameters has been addressed: grid, filter width, domain size, and inflow conditions. This modelling strategy is proved to provide the flow unsteadiness in three-dimensions, while saving computational cost compared to LES. The method is computationally efficient (it can be applied using an implicit solver which permits a higher CFL than with LES; typically 1 versus 0.1), and numerically robust. The computational cost decreases with increasing filter width, though at the expenses of the quality of the results.