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.     

Analysis of flow distribution in a PWR fuel rod bundle model containing a blockage - Part 2. A non-coplanar blockage

An experimental investigation, covering a Reynolds number range from 1900 to 9800, was conducted to study the influence of a non-coplanar blockage on the velocity and turbulence intensity distributions in an unheated 7 X 7 rod bundle. Using the blockage sleeves from a previous 61% coplanar blockage study, the non-coplanarity was obtained by axially staggering these sleeves in a prescribed manner. The results showed that the introduction of non-coplanarity did not result in significant changes from the overall bundle flow behaviour with a coplanar blockage. The effect on the flow immediately upstream and downstream of the blockage and within the blockage was less pronounced, thereby resulting in a smaller degree of flow diversion. The blockage zone, despite being effectively longer than the coplanar geometry, did not seem to adversely influence the downstream flow recovery process. Indeed the recovery to an undisturbed flow profile was more rapidly established. Complete flow recovery was attained for both the non-coplanar and coplanar blockage geometries at the same axial location in the rod bundle. Predictions from the COBRA subchannel computer code again agreed reasonably with the experimental data.     

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.     

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.     

Cold-neutron tomography of annular flow and functional spacer performance in a model of a boiling water reactor fuel rod bundle

Dryout of the coolant liquid film at the upper part of the fuel pins of a boiling water reactor (BWR) core constitutes the type of heat transfer crisis relevant for the conditions of high void fractions. It is both a safety concern and a limiting factor in the thermal power and thus for the economy of BWRs. We have investigated adiabatic, air-water annular flows in a scaled-up model of two neighboring subchannels as found in BWR fuel assemblies using cold-neutron tomography. The imaging of the double suchannel has been performed at the ICON beamline at the neutron spallation source SINQ at the Paul Scherrer Institute, Switzerland. Cold-neutron tomography is shown here to be an excellent tool for investigating air-water annular flows and the influence of functional spacers of different geometries on such flows. The high-resolution, high-contrast measurements provide the spatial distributions of the coolant liquid film thickness on the fuel pin surfaces as well as on the surfaces of the spacer vanes. The axial variations of the cross-section averaged liquid hold-up and its fraction in the gas core shows the effect of the spacers on the redistribution of the two phases.     

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.     

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.     

Thermal equivalence between nuclear fuel rod model and experimental heater simulator

Method of formulating nuclear fuel rod model (typical materials for pellet and clad, including usual gas-gap), which is thermally equivalent to multi-layer experimental heater simulator (any materials in contact, and/or without/with gas-gap) is presented. Thermally equivalent typical fuel rod model is defined. To validate it, the HECHAN model able to use different layouts of multi-layer rod/simulator geometry with constant and/or temperature dependent thermal–physical properties is used. Comparison with measured data for cladding surface temperatures in both pre- and post-CHF regimes proved applicability of this approach in transients. The rod model is easy to define, without changing the source of standard thermal–hydraulic code—only through input deck. It is qualified for further use in COBRA 3-CP and COBRA-TF codes for their validation on experiments using the particular heater simulator design.     

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.     

An analytical solution to fuel-and-cladding model of the rewetting of a nuclear fuel rod

An exact solution of the quasi-steady two-dimensional conduction equation for the rewetting of a nuclear fuel rod in water reactor emergency core cooling is obtained for a fuel-and-cladding model. A method of solving non-separable differential equations is presented, which is used in the present analysis. The recently developed theorem of orthogonality of piecewise continuous eigenfunctions is also used to handle the composite rod in the present model. The present analysis reveals that the wet front velocity increases with the increase of the gap resistance between the fuel and the cladding, and approaches a limiting value, which is equal to the wet front velocity of the tube of cladding alone, as the gap resistance becomes infinite. For convenience in practical application, the results of the present analysis are correlated in simple expressions.     

RANS modeling for flow in nuclear fuel bundle in pressurized water reactors (PWR)

This paper presents use of Reynolds-averaged Navier-Stokes (RANS) based turbulence model for single-phase CFD analysis of flow in pressurized water reactor (PWR) assemblies. An open source code called OpenFoam was used for computational fluid dynamics (CFD) study using computational meshes generated using Shari Harpoon. The PWR assembly design used in this analysis represents a 5 × 5 pin design including structural grid equipped with mixing vanes. The design specifications used in this study were obtained from the experimental setup at Texas A&M University and the results obtained are used to validate the CFD software, algorithm, and the turbulence model used in this analysis.     

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.     

BACCHUS; A numerical approach to two-phase flow in a rod bundle

We present in this paper the computer code BACCHUS, to analyze the thermal-hydraulics in a rod bundle in single or two-phase flow regime. The model is 2-D and uses the porous body approach. The two-phase model is an extension of the classical homogeneous model, and includes a differential non-equilibrium equation. Results are shown for the extension of the boiling region in a 19-pin bundle.     

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.     

Prevention of fuel rod ballooning in nuclear power plants

Possible means of eliminating ballooning as a mode of failure of fuel rods due to overheating are described. Ballooning tends to block cooling passages and hence render energency cooling inoperative. Means proposed involve altering the shape of the yield locus so that the plastic strain increment vector lies in the axial rather than the circumferential direction of the fuel rod. Proposed changes in yield locus are accomplished by texturing of the zirconium cladding or by grooving or by wrapping the fuel rod.     

Structural impact stability of commercial nuclear fuel rod

The United States Nuclear Regulatory Commission (USNRC) requires that all licensees evaluate the potential for handling accidents that may occur during the transfer of fuel from the reactor vessel to the spent fuel pool. In this process, a bottom end drop scenario resulting in the release of radiological fissions products is of primary concern. For this reason, the U.S. Code of Federal Regulations requires that each applicant provide an analysis and evaluation of accident conditions that present a risk to public health and safety at the facility of operation. Furthermore, as stated in the USNRC Regulatory Guide 1·183, the number of fuel rods damaged during a handling accident such as that described above should be based on a conservative analysis that considers the most limiting case pertaining to weight, drop height and the compression, torsion and shear stresses on the irradiated fuel rods with the potential damage of adjacent fuel assemblies being considered. It is further recommended by the USNRC that the limiting mode of failure associated with such a postulated handling accident is that of elastic buckling, which should be evaluated through application of Euler’s static load limit. However, as will be shown in this article, the lack of inertial terms and assumed axially continuous compressive load present in Euler’s solution result in an overly conservative design limit when applied to a transient impact analysis. In an effort to illustrate the conservative nature of this recommended design limit, the theories and limitations of closed form static buckling are introduced, followed by a more rigorous treatment of dynamic pulse buckling, and finally, a complete solution via the finite element method. It may be concluded from the results of this investigation that elastic instability during a transient impact event develops only at loads well beyond Euler’s critical load. Such results require that an alternative stress based limit be introduced, which establishes a more reasonable design limit for evaluating the structural integrity of a spent fuel assembly bottom end drop scenario.     

The structure of turbulent flow through a wall subchannel of a rod bundle

An experimental investigation was performed to establish reliable information on the transport properties of turbulent flow through subchannels of rod bundles. Detailed data were measured of the distributions of the time-mean velocity, the turbulence intensities in all directions and hence, the kinetic energy of turbulence, of the shear stresses in the directions normal and parallel to the walls and of the wall shear stresses for a wall subchannel of a rod bundle of four parallel rods. The pitch to diameter ratio of the rods equal to the wall to diameter ratio was 1.07, the Reynolds number of this investigation was Re = 8.7 × 10⁴.On the basis of the data measured the eddy viscosities in the directions normal and parallel to the walls were calculated. Thus, detailed data of the eddy viscosities in direction parallel to the walls in rod bundles were obtained for the first time. The experimental results were compared with predictions by the VELASCO code. There are considerable differences between calculated and measured data of the time-mean velocity and the wall shear stresses. Attempts to adjust the VELASCO code against the measurements were not successful. The reasons of the discrepancies are discussed.