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.     

Two-dimensional simulations of natural convection/radiation heat transfer for BWR assembly within isothermal enclosure

Abstract

The current scoping study identifies the significant heat transfer effects for a 7 × 7 boiling water reactor (BWR) assembly within an isothermal basket opening inside a transport cask. A two-dimensional finite volume mesh is constructed that models the assembly components and cover gas. Computational fluid dynamics (CFD) simulations calculate the buoyancy induced gas motion, conduction and radiation within the components. Simulations use different basket surface temperatures, fuel heat generation rates and cladding surface emissivities, for both nitrogen and helium cover gases at atmospheric pressure. An analytical conduction/radiation model is developed for the thermal resistance between the channel and basket. Results using buoyancy induced gas motion compared to stagnant gas simulations show that natural convection is significant only at low basket temperatures, with nitrogen gas. Helium and high basket temperature simulations exhibit no significant temperature reduction from natural convection. Simulations with varying cladding emissivity ? show that a 10% increase in ? causes a 7˙2% decrease in the interior temperature difference for nitrogen and a 5˙3% decrease for helium.     

Experemental investigations of transcritical heat transfer on an electrically heated model of a fuel assembly

The purpose of this work was to obtain experimental information on the temperature state of fuel elements in the transcritical region and to develop methods for calculating the heat-emission coefficient. The following region of regime parameters was investigated: pressure 11.7–16.7 MPa, temperature at the entrance into the fuel-assembly model 200–285°C, mass velocity 700–1900 kg/(m²·sec). The existence of a definite transcritical power reserve was confirmed experimentally. The results of the investigations showed that in the experimental range of regime parameters the coolant temperature at the entrance into the fuel-assembly model has the strongest effect on the transcritical reserve. As temperature increases, the transcritical reserve increases. A method for calculating the heat-emission coefficient in the transcritical region was developed on the basis of the experimental data obtained, 5 figures. 2 references. Translated from Atomnaya énergiya, Vol. 88. No. 4, pp. 257–260, April, 2000. Original article submitted July 8, 1998: resubmitted December 15, 1999.     

Numerical investigation of a heat transfer within the prismatic fuel assembly of a very high temperature reactor

The complex geometry of the hexagonal fuel blocks of the prismatic fuel assembly in a very high temperature reactor (VHTR) hinders accurate evaluations of the temperature profile within the fuel assembly without elaborate numerical calculations. Therefore, simplified models such as a unit cell model have been widely applied for the analyses and designs of prismatic VHTRs since they have been considered as effective approaches reducing the computational efforts. In a prismatic VHTR, however, the simplified models cannot consider a heat transfer within a fuel assembly as well as a coolant flow through a bypass gap between the fuel assemblies, which may significantly affect the maximum fuel temperature. In this paper, a three-dimensional computational fluid dynamics (CFD) analysis has been carried out on a typical fuel assembly of a prismatic VHTR. Thermal behaviours and heat transfer within the fuel assembly are intensively investigated using the CFD solutions. In addition, the accuracy of the unit cell approach is assessed against the CFD solutions. Two example situations are illustrated to demonstrate the deficiency of the unit cell model caused by neglecting the effects of the bypass gap flow and the radial power distribution within the fuel assembly.     

A fast and reliable calculation model for BWR fuel assembly burnup analyses

A code called superb has been developed for the BWR fuel assembly burnup analyses using a supercell model. Each of the characteristic heterogeneities of a BWR fuel assembly like water gap, poisoned pins, control blade etc. is treated by invoking the appropriate supercell concept. The burnup model of superb is so devised as to strike a balance between accuracy and speed. This is achieved by building isotopic densities in each fuel pin separately while the depletion equations are solved only in a few group of pins or burnup zones and the multigroup neutron spectra are differentiated in fewer group of pincell types. Multiple fuel ring burnup is considered only for Gd isotopes. A special empirical formula allows the microscopic cross section of Gd isotopes to be varied even during burnup integration.The supercell model has been tested against Monte-Carlo results for the fresh cold clean Tarapur fuel assembly with two Gd fuel pins. The burnup model of superb has been validated against one of the most sophisticated codes lwr-wims for a benchmark problem involving all the complexities of a BWR fuel assembly.The agreement of superb results with both Monte-Carlo and lwr-wims results is found to be excellent.     

Core heat transfer analysis during a BWR LOCA simulation experiment at ROSA-III

The ROSA-111 test facility is a 1/424-th volumetrically scaled BWR/6 simulator with an electrically heated core to study the thermal-hydraulic response during a postulated loss-of-coolant accident (LOCA). Heat transfer analyses for 5, 15, 50 and 200% break tests were conducted to understand the basic heat transfer behavior in the core under BWR LOCA conditions and to obtain a data base of post-critical heat flux (CHF) heat transfer coefficients and quench temperature. The results show that the convective heat transfer coefficient of dried-out rods at the core midplane during a steam cooling period is less than approximately 120 W/m²K. It is larger than existing data measured at lower pressures during a spray cooling period. Bottom-up quench temperatures are given by a simple equation: the sum of the saturation temperature and a constant of 262 K. Then the heat transfer model in the RELAP4/MODE/U4/J3 code was revised using the present results. The rod surface temperature behavior in the 200% break test was calculated better by using the revised model although the model is very simple.     

Subchannel analysis in BWR fuel bundles

Steady-state two-phase-flow calculations have been performed with the multidimensional drift-flux code canal. Flow-regime-dependent drift-flux parameters have been used to evaluate the flow quantities in the subchannels. Consistent modeling of the mixing components, e.g. divergence cross-flow, turbulent mixing and void drift effect, has resulted in the good prediction capability of canal. Measurements of subchannel exit mass flux and quality from simulated BWR rod bundles have been used to assess the code capability. A wide range of operating conditions has been taken into consideration in addition to variations in uniform and nonuniform radial heat-flux profile. Comparison has been made with the familiar subchannel code cobra iiic. Prediction of corner subchannel quality and mass flux by canal are nearly always found to be better than cobra iiic. The overall performance of the drift-flux code canal is comparable to that obtained from advanced two-fluid codes. A review of the conservation equations and constitutive relations shows that the countercurrent transverse flow velocities are essential for accurate prediction of subchannel flow conditions.     

Experimental study on void fraction in a simulated BWR fuel assembly (evaluation of cross-sectional averaged void fraction)

Void fraction measurement of a vertical (4 x 4) rod bundle has been conducted in a steam-water two phase flow, using an advanced X-ray CT scanner. A large amount of rod bundle data was obtained. It was found from the results that the cross-sectional averaged void fraction data for a rod bundle can be correlated by the Drift-Flux model and that the Zuber-Findlay correlation underestimates the data in a void fraction area of 80% or more. This is because the data range over which this correlation was developed, does not cover this experimental range. Therefore, a modified correlation was developed based on the authors' data.     

Experimental data on burn-out in a simulated BWR fuel bundle

Critical heat flux (CHF) experiments have been carried out on a 16-rod test section having the typical geometry of boiling water reactor (BWR) fuel elements and in particular a 366 cm length. Heat fluxes were uniform, both axially and radially. The tests were carried out for the CNEN Plutonium Program on CISE's 8 MW IETI-3 facility, at 71 kg/cm² abs, mass velocities of 12–200 g/cm² s and inlet sub-cooling of 15–180°C. Each corner rod was instrumented with four separate thermocouples to detect nnd locate the initiation of CHF, while the other rods were instrumented with four-junction thermopiles.     

Comparing VVR-M reactor fuel assembly heat technological capabilities

Translated from Atomnaya Énergiya, Vol. 67, No. 2, pp. 97–100, August, 1989.     

View factor for radiant heat transfer between the wall and end of a cylinder

Many engineered devices include cylinders because of their inherent strength and symmetry, thereby introducing a need for the view factor for radiative heat transfer between the wall and end of a cylinder. This paper presents a generic evaluation of the view factor that is applicable to a wide variety of calculations of radiative heat transfer.     

BWR fuel reloads design using a Tabu search technique

We have developed a system to design optimized boiling water reactor fuel reloads. This system is based on the Tabu Search technique along with the heuristic rules of Control Cell Core and Low Leakage. These heuristic rules are a common practice in fuel management to maximize fuel assembly utilization and minimize core vessel damage, respectively. The system uses the 3-D simulator code CM-PRESTO and it has as objective function to maximize the cycle length while satisfying the operational thermal limits and cold shutdown constraints. In the system tabu search ideas such as random dynamic tabu tenure, and frequency-based memory are used. To test this system an optimized boiling water reactor cycle was designed and compared against an actual operating cycle. Numerical experiments show an improved energy cycle compared with the loading patterns generated by engineer expertise and genetic algorithms.     

Effect of anisotropic scattering in neutronics analysis of BWR assembly

The anisotropic scattering effect to keff is studied for UO₂ and MOX fueled BWR assemblies. The anisotropic scattering effect increases the assembly k_∞ by 0.44% Δk for the UO₂ assembly with 0% void fraction, and by 0.21% Δk for the MOX assembly with 0% void fraction. This is because the anisotropic scattering effect flattens the intra-assembly thermal flux, and the absorption rate in the surrounding water gap is decreased, but the absorption rates in the MOX fuel rods are increased compared to the UO₂ rods. Therefore, the total decrease in absorption rates in the UO₂ assembly is relatively large, and the k_∞ is increased in the UO₂ assembly. The dependence of the anisotropic scattering effect on the void fraction is investigated, and the significant difference of 0.62% Δk/k is found for the 0% and the 80% void fractions. The BWR assemblies with Gd rods are also considered. Furthermore, the usefulness of the transport cross section is investigated, and it is found that the transport cross section gives reasonable anisotropic scattering effect, though not satisfactory.     

Analysis of core physics experiments on irradiated BWR MOX fuel in the REBUS program

Critical experiments were performed in the REBUS program on a core loaded with a test bundle including 16 irradiated BWR-type MOX rods of average burnup of 61 GWd/t. The experimental data were analyzed using diffusion, transport, and continuous-energy Monte Carlo calculation codes coupled with nuclear data libraries based on JENDL-3.2 or JENDL-3.3. Biases in effective multiplication factors of the critical cores were ?1.0%Δk for the diffusion calculations (JENDL-3.2), ?0.3%Δk for the transport calculations (JENDL-3.3), and 0.2%Δk for the Monte Carlo calculations (JENDL-3.2). The measured core fission rate and co-activation rate distributions were generally well reproduced using the three types of calculations. The burnup reactivity determined using the measured water level reactivity coefficients was ?2.41 ± 0.08%Δk/kk’, which also agreed with the results of the three type of calculations within the measurement and calculation errors. The most probable isotopic inventories in the irradiated MOX rods was tentatively obtained by using the ratios of the calculation to chemical assay data on a pellet sample, and the burnup reactivity was reanalyzed to split the calculation error into those due to the inventory and reactivity calculations. This approach showed that the inventory calculation error compensated the reactivity calculation error.     

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.     

An assessment of the BWR fuel box-lattice-cell homogenization procedures with the Tarapur BWR incore and excore measurements

A code system has been developed to provide the incorefuel-management guidelines to the Tarapur BWR reactors. Constant checking of the design calculational methods is rendered possible by the steady flow of operating data from the Tarapur units over the last few cycles. The operating data include cold/hot criticals and detailed flux/power maps. Besides these, the burnups and isotopic composition of a few irradiated fuel pins obtained by mass-spectrometric analyses, are also available for validation of the BWR core and lattice-cell modelling.The calculated eigen values for different power levels and at different core average burnups are found to have a spread of less than 0.25% ΔK. Analyses of a number of TIP measurements show that the core power distribution can be predicted in a satisfactory manner for uncontrolled fuel bundles and non-peripheral fuel assemblies (<10%). For prediction of cold-criticals the void-history effects are found to be unimportant.The pin burnups and isotopic densities of important U and Pu isotopes relative to ²³⁸U have been compared with mass-spectrometric measurements. The pin-burnup profile comparison is found to be good for fuel pins, which are not near water gaps. Deviation histograms of various isotopes are presented in this paper. ²³⁵U is predicted within ± 3% (r.m.s.). The total Pu is overpredicted by 5–8%, while the quality of Pu is predicted within ± 1.0% (r.m.s.).