Single-phase convective heat transfer in rod bundles

The convective heat transfer for turbulent flow through rod bundles representative of nuclear fuel rods used in pressurized water reactors is examined. The rod bundles consist of a square array of parallel rods that are held on a constant pitch by support grids spaced axially along the rod bundle. Split-vane pair support grids, which create swirling flow in the rod bundle, as well as disc and standard support grids are investigated. Single-phase convective heat transfer coefficients are measured for flow downstream of support grids in a rod bundle. The rods are heated using direct resistance heating, and a bulk axial flow of air is used to cool the rods in the rod bundle. Air is used as the working fluid instead of water to reduce the power required to heat the rod bundle. Results indicate heat transfer enhancement for up to 10 hydraulic diameters downstream of the support grids. A general correlation is developed to predict the heat transfer development downstream of support grids. In addition, circumferential variations in heat transfer coefficients result in hot streaks that develop on the rods downstream of split-vane pair support grids.     

Analysis of data and recommendations on heat transfer by liquid metals in rod bundles

Translated from Atomnaya Énergiya, Vol. 65, No. 6, pp. 423–426, December, 1988.     

Pressure drop and heat transfer in gas-cooled rod bundles

Extensive experimental and analytical investigations of fluid flow and heat transfer in gas-cooled rod bundles have been carried out. Different bundle geometries with partially or fully roughened rod surfaces were tested in a carbon dioxide loop. An advanced and comprehensive measuring control and instrumentation are important design features of this experiment. Comprehensive thermal hydraulic subchannel analysis computer codes have been developed in order to assist fuel element design calculation for gas-cooled reactors. The experiments, codes and their verification procedure are described and the results of comparisons between measured and calculated pressure and temperature distributions are given.     

Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 2: Correlations for horizontal rod bundles based on theoretical results

Natural convection heat transfer from horizontal rod bundles in N_xm × N_ym arrays (N_xm, N_ym = 5–9) in liquid sodium was numerically analyzed for three types of the bundle geometry (in-line rows, staggered rows I and II). The unsteady laminar two-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady state. The PHOENICS code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, R_f, ranging from 0.0637 to 63.1 (q = 1×10⁴ to 7×10⁶ W/m²). S_x/D and S_y/D for the rod bundle, which are the ratios of the distance between center axes on the abscissa and the ordinate to the rod diameter, respectively, were ranged from 1.6 to 2.5 on each bundle geometry. The spatial distribution of Nusselt numbers, Nu, on horizontal rods of a bundle was clarified. The average value of Nusselt number, Nu_av, for three types of bundle geometry with various values of S_x/D and S_y/D were calculated to examine the effect of the array size, S/D and R_f on heat transfer. The bundle geometry for the higher Nu_av value under the condition of S_x/D×S_y/D = 4 was examined by changing the ratio of S_x/S_y. A correlation for Nu_av for the three types of bundle geometry above mentioned including the effects of S_x/D and S_y/D was developed. The correlation can describe the theoretical values of Nu_av for the three types of bundle geometry in N_xm × N_ym arrays (N_xm, N_ym = 5–9) for S_x/D and S_y/D ranging from 1.6 to 2.5 within 10% difference.     

Turbulent heavy liquid metal heat transfer along a heated rod in an annular cavity

Heavy liquid metals (HLM) are considered as coolant and spallation material in accelerator driven systems (ADS), because of their good molecular heat conductivity. This property leads to a separation of the spatial extension of thermal and viscous boundary layers. Commercially available computational fluid dynamic codes (CFD) assume an analogy of momentum and energy transfer, which is problematic for liquid metals flow. Therefore, benchmark experiments are required, in order to validate codes or modify existing models used therein. Within this article an experimental and numerical study of a thermally developing turbulent lead bismuth (PbBi) flow along a uniformly heated rod in a circular tube is presented. Local temperatures and velocity distributions are measured using thermocouples and Pitot tubes. The data are compared to simulation results computed with the CFX code package. The measured velocity profiles coincide nearly perfect with the simulation results. However, discrepancies up to 7% between the measured and computed temperatures appear. A minor part of the deviations can be explained by the imperfect experimental set-up. But, the measured shape of the thermal boundary is different to the calculated one, indicating the inadequateness of the presently used models describing the turbulent heat transport within the thermal boundary layer.     

Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles

Heat transfer in upward flows of supercritical water in circular tubes and in tight fuel rod bundles is numerically investigated by using the commercial CFD code STAR-CD 3.24. The objective is to have more understandings about the phenomena happening in supercritical water and for designs of supercritical water cooled reactors. Some turbulence models are selected to carry out numerical simulations and the results are compared with experimental data and other correlations to find suitable models to predict heat transfer in supercritical water. The comparisons are not only in the low bulk temperature region, but also in the high bulk temperature region. The two-layer model (Hassid and Poreh) gives a better prediction to the heat transfer than other models, and the standard k– high Re model with the standard wall function also shows an acceptable predicting capability. Three-dimensional simulations are carried out in sub-channels of tight square lattice and triangular lattice fuel rod bundles at supercritical pressure. Results show that there is a strong non-uniformity of the circumferential distribution of the cladding surface temperature, in the square lattice bundle with a small pitch-to-diameter ratio (P/D). However, it does not occur in the triangular lattice bundle with a small P/D. It is found that this phenomenon is caused by the large non-uniformity of the flow area in the cross-section of sub-channels. Some improved designs are numerically studied and proved to be effective to avoid the large circumferential temperature gradient at the cladding surface.     

Evaluation of the conduction shape factor with a CFD code for a liquid–metal heat transfer in heated triangular rod bundles

A heat transfer due to conduction through a coolant itself is not negligible in a liquid–metal cooled reactor (LMR). This portion of a heat transfer is frequently described with a conduction shape factor during the thermal-hydraulic design of an LMR. The conduction shape factor, which is highly dependent on a pitch-to-diameter (P/D) ratio, is defined as the ratio of the local conduction heat flux at a gap between two subchannels to the reference heat flux calculated by the averaged subchannel temperatures. The shape factors in heated triangular rod arrays for three different pitch-to-diameter ratios are generated through CFX calculations in the present study. The flow paths of 1.0–2.0 m in length are meshed into 180,000–360,000 volumes depending on the flow velocities. The SSG Reynolds stress model is used as a turbulent model in the calculations. The evaluated data fell between the heated-rod data and the plane-source data obtained by theoretical investigations. The conduction shape factors were found to be independent of the heating pattern of the rod arrays. Based on the evaluated data, a correlation for a liquid sodium coolant is suggested, which will improve the accuracy of the subchannel analysis codes for the thermal-hydraulic design of an LMR. When it is compared with the existing correlations, the suggested correlation is expected to enhance the reliability of the conduction shape factor because the data is evaluated by a more realistic numerical experiment.     

A new description of liquid metal heat transfer in closed conduits

Heat transfer with liquid metals in conduits with fully developed flow is analyzed. Four typical regions are distinguished, for which different equations hold. The influence of Prandtl number and of relative roughness are investigated. Physical conclusions are illustrated for circular tubes and computed results compared with liquid metal heat transfer formulae currently in use. A new formula for the friction factor is proposed.     

Matrix calculation of radiant heat transfer in LWR fuel bundles under accident conditions

A computer code was developed for calculating the radiant heat transfer in a LWR fuel bundle under accident conditions. The calculation method is a modular one: a fuel bundle or its part is divided into unit cells, each of which is composed of a coolant subchannel surrounded by several segments of solid or imaginary faces. The view factor matrix in each cell is expanded over the whole bundle using the concept of ‘boundary face’ between cells, and the resultant heat transfer equations are simultaneously solved for solid wall temperatures. The geometrical flexibility of this method is suitable for treating various simulation experiments for accidents. The method is also effective for repeated calculations of the radiant heat transfer reflecting state or material property changes when analyzing fuel rod behaviour under accident conditions.     

Momentum losses and convective heat transfer in rod bundles — An overview

A critical survey is made of the prediction methods available for analysing the momentum and heat transfer characteristics of axial flow in a clustered rod bundle. The Navier-Stokes and energy equations are presented, their solution procedure is outlined and the boundary layer approximation discussed. Four levels of approximation to these equations, namely, slug flow, integral methods, eddy diffusivity and turbulence energy models are examined and their limitations presented for a simple situation. Consideration is then given to the problem of extending these models to more complex situations such as, variable property flows, rough surfaces and flow blockages.     

Investigation on heavy liquid metal cooling of ADS fuel pin assemblies

In the framework of accelerator driven sub-critical reactor systems heavy liquid metals are considered as coolant for the reactor core and the spallation target. In particular lead or lead bismuth eutectic (LBE) exhibit efficient heat removal properties and high production rate of neutrons.However, the excellent heat conductivity of LBE-flows expressed by a low molecular Prandtl number of the order 10⁻² requires improved modeling of the turbulent heat transfer. Although various models for thermal hydraulics of LBE flows are existing, validated heat transfer correlations for ADS-relevant conditions are still missing. In order to validate the sub-channel codes and computational fluid dynamics codes used to design fuel assemblies, the comparison with experimental data is inevitable.Therefore, an experimental program composed of three major experiments, a single electrically heated rod, a 19-pin hexagonal water rod bundle and a LBE rod bundle, has been initiated at the Karlsruhe Liquid metal Laboratory (KALLA) of the Karlsruhe Institute of Technology, in order to quantify and separate the individual phenomena occurring in the momentum and energy transfer of a fuel assembly.     

The flow and heat transfer characteristics of turbulent flow in typical rod bundles in ocean environment

The flow and heat transfer characteristic of turbulent flow in typical 4 and 7 rod bundles in ocean environment is investigated theoretically. In ocean environment, the periodic variation of secondary flow in 7 rod bundles is not obvious. Because of the velocity oscillation, there is a periodic heat accumulation on the tube wall. And the restriction of the channel wall on the rolling motion is considerable. In 7 rod bundles, because of the restriction of the channel wall, the effect of the additional force perpendicular to flowing direction is limited, and the turbulent flowing and heat transfer is mainly determined by the axial turbulent intensity and inlet velocity. However, in the 4 rod bundles, the restriction of the channel wall is small. The effect of the additional force perpendicular to flowing direction on the flowing and heat transfer is significant. And the additional force perpendicular to flowing direction can also affect the Reynolds stress.     

Magnetohydrodynamically enhanced heat transfer in a liquid metal system

The phenomena of liquid metal flow under the influence of magnetic and electric fields are important in the development and design of nuclear and metallurgical plants, such as the blanket cooling systems of fusion or fast breeder reactors and electromagnetic stirring devices. In this study, a computer code that models recirculating flows in two dimensions using a k − ε turbulence model is expanded to include the magnetohydrodynamic (MHD) effects of applied electric and magnetic fields. This modified code is then used to examine the effect of MHD stirring on the heat transfer characteristics of a liquid metal cooling system. Using liquid sodium properties, various thermophysical properties are investigated. The results indicate that a significant increase in the rate of heat transfer is obtainable when the heat transfer system is operated in the presence of MHD stirring.     

Experimental and numerical study on lead-bismuth heat transfer in a fuel rod simulator

As a task of the EU project IP EUROTRANS towards development of an Accelerator Driven System (ADS) dedicated to the transmutation of long-lived fission products, experiments and simulations were performed on the TALL test facility at KTH to investigate thermal hydraulics along a single fuel rod simulator cooled by lead-bismuth eutectic (LBE). The fuel rod simulator is concentrically inserted in a tube, so that an annular channel is formed for LBE flow. This paper presents the measured temperature profiles in the annular channel, and the comparisons with the simulation results of the CFX code. The primary objective is to help understanding the LBE heat transfer characteristics and qualifying the turbulence and heat transfer modeling for LBE application. The quantitative comparison between the calculated and measured temperatures of the LBE indicates that the simulation underestimates the experiment at most radial and axial positions. Finally the uncertainties in measurement and the deficiency in turbulence models resulting in such a disagreement were discussed, which will be directive and beneficial to future work in the field.     

Validation of frey for the safety analysis of LWR fuel using transient fuel rod experiments

The analysis and comparison of severe light water reactor transient experiments are presented from the FREY verification and validation effort. The purpose of this study was to validate the predictive capabilities of the code for severe transient analysis. The FREY code, developed under the sponsorship of the Electric Power Research Institute, uses a two-dimensional finite-element computational method for the thermomechanical analysis of LWR fuel rods under steady state and transient conditions. A total of 10 test fuel rods from experimental programs conducted in both the Power Burst Facility and the Transient Reactor Test Facility have been used in this study. The fuel rods were selected from the following test programs: Power Coolant Mismatch Tests, PCM-2 and PCM-4: Reactivity Initiated Accident Test, RIA 1–2; Loss-of-Coolant Accident Test, LOC-3; First Fuel Rod Failure Test, FRF-1; and Irradiation Effects Test, IE-3. The test programs used in this study cover a large range of code applications for severe transient analysis. The methods used to model the fuel, cladding, and coolant geometry are discussed in addition to experimental data comparisons. The results of the PCM-2, RIA 1–2, and FRF-1 analyses are presented to highlight the full two-dimensional modeling capabilities of FREY and to compare the thermal and mechanical measurements with FREY's prediction. The comparisons show good general agreement, with a tendency for FREY to overpredict the peak cladding surface temperature for a few cases where strong three-dimensional effects have been identified.