Dancoff Factor Research Articles

Physics Studies on BWR Void Simulated Cores, (II)

The steam void effect on core reactivity and flux distribution was experimentally studied on cores loaded with fuel assemblies of various void fractions. The voids were simulated by hollow polyethylene tubes. The local flux distributions within the assembly cells of various void fractions have already been discussed in Part (I) of the present series of papers. The study proved that the reactivity calculation can be improved by considering the double heterogeneity that characterizes an assembly lattice simulating the BWR core, by means of the following treatments: (a) Consideration of the spatial variation of the thermal neutron spectrum around water gaps. This gave good results for the analyses of local flux distributions, (b) Adoption of the effective Dancoff factor, which evaluates the difference in the resonance neutron shielding effect between fuel rods lining the water gap and those others closed in by similar rods.

Equivalence Relation Based on an Improved Rational Approximation

The equivalence relation between heterogeneous and homogeneous reactor systems was first established by Chernick & Vernon by using the rational approximation for the collision probabilities. The aim of this paper is to introduce refinements into the rational approximation. The parameters introduced are evaluated by separate considerations and are shown to be related to the Dancoff & Bell factors. Throughout this work, narrow resonance considerations are invoked since partial neglect of scattering complicates the issue being studied.

Intermediate Resonance Absorption in Heterogeneous Media

Resonance absorption in heterogeneous media with intermediate-mass moderators is investigated under the assumption that the flux is spatially flat in each region. Intermediate resonance parameters are introduced for scattering by all species present in the system and an intermediate resonance approximation is developed for calculating them. An improved rational representation for the lump escape probability is used and the calculation of the Dancoff factor is modified to account for the intermediate nature of the scattering-removal process by the outside moderator. The resonance integrals from the intermediate resonance approximation are compared with those from Monte Carlo and ZUT computer code calculations for the 6.7-eV resonance of 238U. The intermediate-resonance approximation results are found to be in good agreement with the Monte Carlo results. The ZUT results have large errors for heavy moderators, especially in undermoderated systems. Equivalence among heterogeneous systems and between heterogeneous and homogeneous systems is discussed. In the former case, an equivalence through the intermediate parameters is established.

Dancoff Factor in Arrayed-Type Cladded Fuel Lattice

Dancoff Factor in Arrayed-Type Cladded Fuel Lattice

Dancoff Factor in Arrayed-Type Cladded Fuel Lattice

Dancoff Factor in Arrayed-Type Cladded Fuel Lattice

Improvements to the Theory of Resonance Escape in Heterogeneous Fuel: II. The Dancoff Factor and the Equivalence Theorem in Cluster-Type Fuel

Improvements to the Theory of Resonance Escape in Heterogeneous Fuel: II. The Dancoff Factor and the Equivalence Theorem in Cluster-Type Fuel

Temperature Coefficient of Water Lattices

Temperature coefficients of slightly enriched UO2-H2O lattices were measured in the Ozenji Critical Facility and analyzed in terms of critical parameters. The lattices studied were mainly those of 2.5% enriched UO2, 10 mm in diameter and clad in 0.8 mm thick Al tube, and with water to fuel volume ratios of 2.5 and 1.5. Analyses were made with Deutsch's four factor critical equation and also with three group one dimensional diffusion calculations. The result shows the importance of the influence of the reflector, which is the largest positive contribution to the temperature coefficient, being about 1×10-4 Δk/k/°C. This was experimentally demonstrated by measuring the coefficient for a core with an inner reflector water gap. Analyses also show that the discrepancy between experiment and calculation, which increases from 0.2 to 0.7×10-4 Δk/k/°C as the water to fuel volume ratio decreases, may be mostly resolved by applying corrections for the space-dependent spectrum within the cell using the THERMOS code and for the effect of Dancoff factor with the TUZ-ZUT code. Calculation with these corrections applied reproduces experiment within an accuracy of about 0.2×10-4 Δk/k/°C over the temperature range of 20° to 70°C.

Improvements to the Theory of Resonance Escape in Heterogeneous Fuel: I. Regular Arrays of Fuel Rods

This paper gives a new and very simple method of calculating Dancoff factors in regular arrays of cylindrical fuel rods. This method is readily applicable to canned fuel, and comparisons with Monte Carlo calculations show that its accuracy is adequate for practical purposes. The paper also gives an extension of the standard equivalence theorem which, unlike the theorem itself, is accurate enough for practical work. This extension enables the resonance integrals of regular arrays to be calculated from the Dancoff factor and from calculations of the resonance integral in homogeneous mixtures. These methods have been compared with the very accurate Monte Carlo calculations of Levine; the result is most satisfactory.

Temperature Coefficient of Water Lattices

Temperature coefficients of slightly enriched UO2-H2O lattices were measured in the Ozenji Critical Facility and analyzed in terms of critical parameters. The lattices studied were mainly those of 2.5% enriched UO2, 10 mm in diameter and clad in 0.8 mm thick Al tube, and with water to fuel volume ratios of 2.5 and 1.5. Analyses were made with Deutsch's four factor critical equation and also with three group one dimensional diffusion calculations. The result shows the importance of the influence of the reflector, which is the largest positive contribution to the temperature coefficient, being about 1×10-4 Δk/k/°C. This was experimentally demonstrated by measuring the coefficient for a core with an inner reflector water gap. Analyses also show that the discrepancy between experiment and calculation, which increases from 0.2 to 0.7×10-4 Δk/k/°C as the water to fuel volume ratio decreases, may be mostly resolved by applying corrections for the space-dependent spectrum within the cell using the THERMOS code and for the effect of Dancoff factor with the TUZ-ZUT code. Calculation with these corrections applied reproduces experiment within an accuracy of about 0.2×10-4 Δk/k/°C over the temperature range of 20° to 70°C.