Analysis of dynamical flow structure in a square arrayed rod bundle

Large eddy simulation (LES) of turbulent flow in a bare rod bundle was performed, and a new concept about the flow structure that enhances heat transport between subchannels was proposed. To investigate the geometrical effect, the LES was performed for three different values of rod diameter over pitch ratio (D/P = 0.7, 0.8, 0.9). The computational domain containing 4 subchannels was large enough to capture large-scale structures wide across subchannels. Lateral flow obtained was unconfined in a subchannel, and some flows indicated a pulsation through the rod gap between subchannels. The gap flow became strong as D/P increased, as existing experimental studies had reported. Turbulence intensity profile in the rod gap suggested that the pulsation was caused by the turbulence energy transferred from the main flow to the wall-tangential direction. This implied that the flow pulsation was an unsteady mode of the secondary flow and arose from the same geometrical effect of turbulence. This implication was supported by the analysis results: two-points correlation functions of fluctuating velocities indicated two length-scales, P-D and D, respectively of cross-sectional and longitudinal motions; turbulence stress in the cross-sectional mean flow contained a non-potential component, which represented energy injection through the unsteady longitudinal fluid motion.     

Gas-cooled fast breeder reactor fuel bundle irradiations in the BR2 helium loop

In the BR2 helium loop at Mol, Belgium, a 12-pin test fuel element of gas-cooled fast breeder reactor (GCFR) design and materials will be irradiated at a 500 W/cm maximum pin rating and a 700°C maximum cladding temperature to a target burnup of 60 MWd/kg (extension to 100 MWd/kg is intended). The design of the test element and the loop is described in detail. To fabricate the test element, parts of the GCFR fuel development had to be anticipated. Preliminary out-of-pile testing was successfully performed, and irradiation is scheduled to start in early 1977 and will be completed between mid-1978 and mid-1979, depending on the final burnup objective. GCFR operating conditions will be completely simulated except for the full size of the fuel element and the fast neutron flux. In combination with out-of-pile performance testing of full-size dummy elements and fast flux experience from the liquid metal fast breeder reactor program, the helium loop irradiation is regarded as an adequate basis for the design of a fuel element for a GCFR demonstration plant serving as the final test bed.     

On turbulence models for rod bundle flow computations

In commercial computational fluid dynamics codes there is more than one turbulence model built in. It is the user responsibility to choose one of those models, suitable for the problem studied. In the last decade, several computations were presented using computational fluid dynamics for the simulation of various problems of the nuclear industry. A common feature in a number of those simulations is that they were performed using the standard k–ε turbulence model without justifying the choice of the model. The simulation results were rarely satisfactory. In this paper, we shall consider the flow in a fuel rod bundle as a case study and discuss why the application of the standard k–ε model fails to give reasonable results in this situation. We also show that a turbulence model based on the Reynolds stress transport equations can provide qualitatively correct results. Generally, our aim is pedagogical, we would like to call the readers attention to the fact that turbulence models have to be selected based on theoretical considerations and/or adequate information obtained from measurements.     

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.     

Laser doppler measurements of flow in a rod bundle

A two component laser doppler velocimeter with polarized beams and frequency shift was used to measure the turbulent flow field for axial flow between the rods of a nine rod, square pitch rod bundle. Parameters measured include mean axial and lateral velocities, turbulence intensities and the friction factor. The axial velocities for 10000 to 40000 Reynolds number are slightly higher than those reported by Rowe. The maximum lateral velocities measured are about 1% of the bulk velocity; somewhat larger than suggested by earlier authors. Axial and lateral turbulence intensities are larger than those in pipe flows.     

Turbulent flow in a model nuclear fuel rod bundle containing partial flow blockages

Local velocity and turbulence intensity measurements were obtained with a laser Doppler anemometer near flow blockages in an unheated 7 × 7 rod bundle. Sleeve blockages were positioned on the center nine rods to create area reductions of 70 and 90% in the center four subchannels of the bundle. Experimental results indicated that extensive flow disturbances existed downstream from the blockage clusters and showed that only minor disturbances can be expected upstream from the blockages. Recirculation zones for both 70 and 90% blockages were detected downstream from the blockage clusters and persisted for approximately three to five subchannel hydraulic diameters, depending on the degree of the blockage. The experimental velocity results obtained with blockage clusters located midway between grid spacers were successfully predicted using the COBRA subchannel computer program.     

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.     

Numerical simulation of turbulent flow in a 37-rod bundle

The unsteady Reynolds averaged Navier–Stokes equations, combined with a Reynolds stress model, were solved numerically to determine fully developed isothermal turbulent flow in a 60° sector of a 37-rod bundle. It was found that this flow contained large-scale coherent structures, which affected strongly the local velocity fluctuations, especially near the gaps between rods or between rods and the surrounding wall. The time-averaged mean velocity and Reynolds stresses were in good agreement with experimental results in a similar channel. Coherent velocity fluctuations at different locations throughout the entire rod bundle were strongly correlated with each other.     

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.     

Turbulent transports by secondary flow vortices in a rod bundle

Experimental data on secondary flow vortices in a rod bundle with pitch-to-diameter ratio show weak vortices with the average velocity magnitude only about 0.1% of the mean bulk velocity. The question then arises, how important these weak vortices could still be as a transport mechanism in turbulent flows. The transport of axial momentum by these vortices is analysed quantitatively. While a minor importance is observed for the transport in radial direction, it is found that about half of the total transport in circumferential direction is due to the secondary flow vortex convection. Based on the analogy between the transport of momentum and heat, it is expected in nonisothermal situations that, in radial direction, the contribution can improve the heat transfer coefficient and contribute to better economy of heat transfer installations. In circumferential direction, the contribution helps to smooth out circumferential temperature differences, improves the heat removal from heated surfaces and, through a decrease of the maximum surface temperature, it contributes to passive safety of heat transfer installations.     

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.     

Anisotropic modelling of tube bundle flow during steam generator wet layup

Tube bundle flow can be considered as a porous medium flow and a fluid continuum can be established by introducing the porosity which is a ratio of fluid volume to total volume. Darcy's flow regime applies for the tube bundle flow of low Reynolds number during steam generator wet layup circulation. A general three-dimensional formulation appears as a steady-state heat conduction equation with source term and anisotropic conductivities. Solution to such an equation with appropriate boundary conditions can be obtained by any finite element computer program which solves anisotropic heat conduction problems. Capability of anisotropic modelling has been demonstrated by a sample problem of axisymmetric tube bundle flow with orthotropic hydraulic conductivities which are derived according to the existing empirical correlations for friction factors.     

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.     

An experimental study of turbulent flow through a square-array rod bundle

Using laser-Doppler anemometry and calibrated Preston tubes, experiments were performed in water (80°C, 0.6 MPa) to obtain information on the distributions of wall shear stresses, mean axial velocities and turbulence intensities for fully developed adiabatic flow through a six-rod bundle at a Reynolds number of 5 × 10⁵. The rods were arranged in a square array with a pitch to a diameter ratio of 1.15 and a wall-distance to diameter ratio of 0.62. The core flow in the central subchannel appears to be similar to pipe flow, but in the gap regions much higher turbulence intensities are encountered. The skewed wall shear stress profiles together with the deformed constant-velocity lines suggest the presence of secondary flows in the corner subchannels.     

Heat transfer and hydraulic resistance in tightly packed corridor bundle of rods

Results are given of an experimental investigation into heat transfer to mercury and to a sodium-potassium alloy and into the temperature field of a tight corridor bundle of rods. The experimental equipment is described and a method is given for performing the experiments. We discuss experimental data on the hydraulic resistances of tight bundles. A comparison is made of heat transfer to molten metals in tight corridor bundles and bundles arranged in a chess-board pattern.The authors would like to thank A. I. Leipunskii for his interest shown in the work and for his valuable comments. S. P. Rogov, S. G. Povsten', N. F. Kozlov, and A. M. Barabanov took part in the work.     

The hexagonal bundle heat transfer and fluid flow experiment agathe hex

Problems of heat transfer and fluid flow in gas-cooled reactor fuel elements have been studied at the Swiss Federal Institute for Reactor Research (EIR) for 14 years. Since 1967, the activities have been directed toward gas-cooled fast breeder reactors (GCFRs). The aim of analytical and experimental studies has been to develop analytical models and comprehensive computer codes for the prediction of temperature and pressure distributions in GCFR fuel element configurations. The models developed at EIR are based on the results of specific experiments. Full-scale experiments in actual geometry are being carried out to verify the computer codes for a wide range of parameters. This paper describes the heat transfer loop and the test sections designed to verify GCFR thermohydraulic design codes.     

Fully developed rod bundle flow over a large range of Reynolds number

In an investigation of the fluid mechanics of single phase reactor cores, extensive measurements of mean axial velocity, wall shear stress and all six Reynolds stresses have been made in fully developed flow through a square pitched rod bundle array with pitch to diameter ratio of 1.107. The range of Reynolds numbers, based on bulk velocity and hydraulic diameter was 22600 to 207600. The mean secondary flow velocities could not be measured at any Reynolds number, implying that they were always less than about 1% of the bulk velocity. The axial momentum integral equation is used to show that the wall shear stress distribution is determined primarily by the pressure gradient and the transverse shear stress |ovbar|uw, a result that confirms the negligible size of the mean secondary flow. The implications of the results for current engineering calculation methods are discussed.     

Impact of gas in sodium flow on the temperature variation in an LMFBR rod bundle

The impact of gas in sodium flow on the temperature variation in an LMFBR rod bundle was studied in two types of experiments: (1) The gas fraction of the subchannels as well as the gas bubble spectra across the outlet of an unheated 61-rod bundle with wire spacers were measured in water/air flow. The distributions of the gas fractions at the inlet of the bundle were performed under uniform and non-uniform conditions. The results show that the distribution of the averaged gas fractions between the individual subchannels at the outlet of the bundle was almost the same as the distribution at the inlet. The measured bubble spectra show a dependency existing between the bubble frequencies, the bubble lengths, and the gas fraction in a subchannel. (2) A model for computing the transient temperature distributions within a heated rod was supported by experiments performed in a sodium/argon flow. For slug flow conditions a comparison indicates that the measured variations of wall temperatures can be well interpreted as being functions of the bubble contact time, rod power, and gas fraction in the flow.     

Experimental and numerical simulation of air-water two-phase flow in the rod bundle with grid spacer

1 Introduction Grid spacer is the key part of reactor fuel assem-bly. The presence of spacers in fuel assemblies affectsvarious thermal-hydraulic characteristics of the reactorcore. The grid spacer with fine performance can im-prove thermal-hydraulic performance of the core fuelassembly and enhance the critical heat flux withouttoo much augment of the pressure loss. As a result,the implementation of grid spacer with high thermalperformance provides more thermal margin, then in-creases s…