Dancoff Factor Research Articles

The Characteristics and Subgroup Methods in Square Light Water Reactor Cell Calculations

The effect caused by the circular approximation of the geometry for cell calculations in light water reactors is studied using the continuous-energy Monte Carlo code MVP. It was found that the kinf values were underestimated with this approximation of the geometry, especially in the case of a mixed-oxide fuel cell. To treat the square geometry, including the resonance calculation, KRAM-B was developed based on the two-dimensional neutron transport code KRAM as a deterministic cell calculation code. KRAM-B solves the neutron transport equation using a combination of the subgroup method and the characteristics method. The subgroup method is able to perform the resonance calculation faster than the ultrafine energy group calculation and predict the resonance cross section more accurately than the Dancoff factor method. It was found that the kinf values and the effective microscopic resonance cross sections by KRAM-B agreed well with the reference MVP results.

Calculation of the Dancoff Factor for Pebble Bed Reactors

The double heterogeneity of the core of pebble bed–type high-temperature reactors (HTRs) requires special attention when lattice codes are applied to a unit cell of such systems. As the self-shielding of the resonance absorption takes place in the small fuel grains in the pebbles, the grain-lattice calculation should apply a Dancoff factor for the grain lattice yet take into account the finiteness of the grain lattice in a pebble and the possibility of a neutron reaching another pebble. In a study of HTR lattices, the Dancoff factor was calculated using the DANCOFF-MC program. For a finite lattice of fuel grains in the fuel region of a pebble, the space-dependent Dancoff factor was calculated, and it was averaged over the volume of the fuel in one pebble. This single-pebble Dancoff factor was further corrected to include the effect of other pebbles. The sensitivity of the Dancoff factor to core composition and the sensitivity of core calculations to the Dancoff factor are discussed, and a numerical example is given.

Analytical Calculation of the Average Dancoff Factor for a Fuel Kernel in a Pebble Bed High-Temperature Reactor

An analytical expression was derived for the average Dancoff factor of a fuel kernel (Cfk) in a pebble of a high-temperature gas-cooled reactor. This Dancoff factor accounts for the probability that a neutron escaping from a fuel kernel enters another fuel kernel, in the same pebble or in other pebbles, without colliding with a moderator nucleus in between. If the fuel zone of the pebble is thought to be of infinite dimensions, the Dancoff factor becomes equal to the so-called infinite-medium Dancoff factor . The has been determined by the evaluation of three existing analytical expressions and by two Monte Carlo calculations performed with the MCNP-4A code, for various coated-particle densities. The Dancoff factor Cfk can be written as times a correction factor. The latter has been calculated for different fuel zone radii and pebble shell thicknesses. For the standard pebble, Cfk as a function of the number of coated particles has been calculated both analytically and with MCNP. The results of both methods are in good agreement. The analytical calculation method is preferred because it consumes practically no CPU time and obviates the building of MCNP models.

A comparison of first-flight probabilities in multiregion cylindrical and spherical cells

First-flight probabilities for lattice integral transport calculation, reported in the literature under different assumptions, are compared. Errors on calculated escape and collision probabilities in cells with variable number of annular regions are assessed, as well as differences in the Dancoff factor approximations, in cylindrical and spherical geometries. Numerical examples for selected situations show, in some cases, significant discrepancies among the results.

Criticality calculation for cluster fuel bundles using grey Dancoff factor

This paper applies the grey Dancoff factor calculated by Monte Carlo method to the criticality calculation for cluster fuel bundles. Dancoff factors for five symmetrically different pin positions of CANDU37 and CANFLEX fuel bundles in full three-dimensional geometry are calculated by Monte Carlo method. The concept of equivalent Dancoff factor is introduced to use the grey Dancoff factor in the resonance calculation based on equivalence theorem. The equivalent Dancoff factor which is based on the realistic model produces an exact fuel collision probability and can be used in the resonance calculation just as the black Dancoff factor. The infinite multiplication factors based on the black Dancoff factors calculated by collision probability or Monte Carlo method are overestimated by about 2 mk for normal condition and 4 mk for void condition of CANDU37 and CANFLEX fuel bundles in comparison with those based on the equivalent Dancoff factors.

In-Rod Effective Cross Sections of Resonance Absorbers Evaluated with Routine Cell Codes

The radial distribution of capture rate and effective cross section in fuel rods of radii R, forming a light water reactor (LWR) lattice, is derived with routine cell calculations. Any internal radial subrange (r1,r2) is treated through the assessment of absorption in the two corresponding annular absorbers (r1,R) and (r2,R). The lattice of the latter absorbers, whose pitch is exactly the original LWR lattice pitch, is equivalenced to a lattice of solid cylindrical rods. Thus, for example, to obtain a tenfold radial distribution, ten routine cell calculations are required.In determining the radius s of a cylinder equivalent to the annulus (r,R), the neutron escape from the annulus is first preserved by making the s rod have a circumference of where G is the “sticking” probability in the annulus for neutrons entering it from within. The radius s is then the result of making the solid rod and the annulus have the same average chord. In addition, a lattice is assigned to the s rods such that the original Dancoff factor is preserved. Finally, a Bell factor is determined for the s rod such that the actual grayness of the annulus (r,R) is preserved.A special program for transport-related probabilities is invoked in obtaining the sticking and Dancoff probabilities just described, as well as the Bell factor.Application of the theory was conducted with the ELCOS system BOXER cell code. Three benchmarks were considered. The first was the one suggested by Tellier et al. for a fuel pin of a typical pressurized water reactor cell. The second was almost identical to the first, except that the fuel was saturated with hydrogen to generate a flatter radial distribution than in the first benchmark. The third benchmark was based on detailed space-energy calculations for a boiling water reactor rod, performed in 1978.All three benchmark testings resulted in satisfactory comparisons. Hence, the present theory may provide a practical, routine way of obtaining the in-rod distribution of absorption and cross section, calling just for a repeated use of straightforward cell calculations.

96/04975 Avoid the unexpected. Use a 3D CAD model before building or maintenance

The XPZ code is developed for the lattice physics computation in the high temperature reactors (HTRs). This paper introduces the methodologies adopted in the XPZ code, including the resonance treatment, equivalent homogenization, transport calculation, and burnup calculation. Emphasis is put on the treatment of the double heterogeneity effect, which involves the following two strategies. Firstly, the Dancoff factor obtained from the double-heterogeneous model is used in the resonance treatment. Secondly, with considering the spatially self-shielding effect in dispersed particles, the fuel compact is equivalently homogenized into a homogeneous media so that the conventional transport calculation can be applied. The effectiveness and accuracy of the methodologies are examined against Monte Carlo solutions. Numerical results demonstrate that the XPZ code is promising for lattice physics computations in HTRs.

Monte Carlo Calculation of Dancoff Factors in Irregular Geometries

Monte Carlo program is described that calculates Dancoff factors in arbitrary arrangements of cylindrical or spherical fuel elements. The fuel elements can have different diameters and material com...

Application of Multiband Method to Pin Cell Calculations

Abstract In order to accurately calculate effective neutron cross sections in the resonance energy region, the multiband method has been applied to cell calculations. Cell calculations for UO2 and MOX fuels of light water reactors have been performed and the results were compared with those of a continuous energy Monte Carlo code VIM and the conventional self-shielding method using the Dancoff factor. The k∞values calculated by the multiband method agreed with those of the VIM calculations within 0.20% Δk for the UO2 fuel cell and within 0.30% Δk for the MOX fuel cell, respectively, whereas the Dancoff factor method yielded about l.l%Δk errors for the two cells. The element- wise contribution to this error was investigated, and it was found that the effective microscopic cross sections, particularly those for the giant resonances of 238U, calculated by the multiband method were in good agreement with those of VIM. It was also found that interference effect between 238U and 235U resonances in the UO2 fuel and that between 238U and 239Pu resonances in the MOX fuel made about 0.20%Δk contributions to k∞ in both fuel cells.

Application of Multiband Method to Pin Cell Calculations.

Abstract In order to accurately calculate effective neutron cross sections in the resonance energy region, the multiband method has been applied to cell calculations. Cell calculations for UO2 and MOX fuels of light water reactors have been performed and the results were compared with those of a continuous energy Monte Carlo code VIM and the conventional self-shielding method using the Dancoff factor. The k∞values calculated by the multiband method agreed with those of the VIM calculations within 0.20% Δk for the UO2 fuel cell and within 0.30% Δk for the MOX fuel cell, respectively, whereas the Dancoff factor method yielded about l.l%Δk errors for the two cells. The element- wise contribution to this error was investigated, and it was found that the effective microscopic cross sections, particularly those for the giant resonances of 238U, calculated by the multiband method were in good agreement with those of VIM. It was also found that interference effect between 238U and 235U resonances in the UO2 fuel and that between 238U and 239Pu resonances in the MOX fuel made about 0.20%Δk contributions to k∞ in both fuel cells.

A WIMS-Based Calculational Route for Pebble-Bed Fuel

This paper reports that a WIMS-based calculational route for pebble-bed fuel has been established. An outstanding advantage of the WIMS code is its integrated route from basic lattice data to burnup-dependent lattice cross sections. The problem in applying WIMS to pebble-bed fuel is that it lacks spherical geometry. This problem is solved by establishing a number of practical equivalences enabling the replacement of a lattice of spherical fuels by a lattice of cylindrical fuels. A special program was written to convert physical data into WIMS input files, including the Dancoff factor required for resonance shielding in the multilayer multicell pebble lattice. This capacity provides all that is necessary to generate core-homogenized cross sections directly applicable to core studies. Also generated are zone-homogenized cross sections; in some cases, their use in a transport code results in more accurate core-homogenized cross sections. In terms of the fuel infinite criticality factor, this added accuracy is in the range of 1 to 3 mk for fuel free of absorbers or fuel carrying boron-only absorbers; it is in the range of 3 to 12 mk for fuel carrying hafnium absorbers.

Application of Multiband Method to KUCA Tight-Pitch Lattice Analysis

The multiband method has been applied to analyses of critical experiments related to the high-conversion core at the Kyoto University Critical Assembly in order to accurately treat the resonance self-shielding in heterogeneous cells. Three-band parameters were generated using the self-shielding table installed in the SRAC code, and used to calculate the cell-averaged cross sections. The k ∞ values calculated by this method have been compared to those by the VIM Monte-Carlo calculation, the SRAC fine group calculation, Dancoff factor method and/or Tone's method self-shielding calculation. The k∞ values calculated by the present method agree with those by the VIM calculation within 0.3%Δk for all the cases considered.

Application of Multiband Method to KUCA Tight-Pitch Lattice Analysis.

The multiband method has been applied to analyses of critical experiments related to the high-conversion core at the Kyoto University Critical Assembly in order to accurately treat the resonance self-shielding in heterogeneous cells. Three-band parameters were generated using the self-shielding table installed in the SRAC code, and used to calculate the cell-averaged cross sections. The k∞, values calculated by this method have been compared to those by the VIM Monte-Carlo calculation, the SRAC fine group calculation, Dancoff factor method and/or Tone's method self-shielding calculation. The k∞ values calculated by the present method agree with those by the VIM calculation within 0.3%Δk for all the cases considered.

Evaluation methods of resonance absorption for system with pellet surrounded by fuel solution.

KEYWORDS: uranium dioxidebenchmarkscriticalityfuel pelletsfuel solutionsresonance absorptionMonte Carlo methodcalculation methodsDancoff factor methodTone's methodPEACO methodcomparative evaluations

Generalized Dancoff Factor in Complex Lattice Arrangement

Click to increase image sizeClick to decrease image sizeKEYWORDS: Dancoff factorcollision probabilitygeneralized blacknessPROTEUS-LWHCR coresresonance cross sectionsequivalent theoremmultiregion plate cellslowing-down theoryslowing-down

Generalized Dancoff factor in complex lattice arrangement.

Generalized Dancoff factor in complex lattice arrangement.

Equivalence Resonance Integrals for Lattices of Annular Absorber Rods

Resonance integrals for lattices of annular rod absorbers can be accurately determined by ordinary equivalence relation procedures. This is demonstrated for water lattices of annular uranium rods whose inner cylindrical zone is either a void or water filled. The equivalence cross section, needed to enable the use of tabulated homogeneous integrals, is given by a formula recently developed. There are three parameters in the formula that need estimation: a Dancoff factor for the lattice, the probability of neutrons entering the inner rod zone to collide there, and a Bell factor. Ways and means to estimate these parameters are discussed and demonstrated. The interpolation of resonance integrals from entries in existing tables of homogeneous integrals is performed with an accurate technique. Results of the equivalence-based calculations are compared with results by the integral transport RABBLE code.

Incorporation of clad effects into Sauer's method for computing Dancoff factors

A simple method is presented to modify Sauer's approximation for the lattice Dancoff factor to account for clad interactions. It is shown that for some tight-pitch lattices the difference in Dancoff factors with and without clad present may cause up to 0.5% difference in k eff. The present technique has the advantages of: (a) being easy to implement into existing codes; (b) having negligible impact on execution time; and (c) showing good agreement with sophisticated methods.

Effect of the loss of coolant on the resonance escape probability

In the analysis of the loss of coolant accident in natural uranium reactors of the Atucha or Candu type, the influence of the coolant voiding on the resonance escape probability appears to be of great importance. In this paper we study this effect on the resonance absorption, analyzing its behaviour vs coolant density. We use the codes COCAP and WIMS, ∗ ∗ We have used WIMS D version of this code. in which the shadowing among pins in the cluster, or the Dancoff effect, is taken into account with different models. In COCAP, the Dancoff factor calculation based on Carlvik's method shows a remarkable dependency on the coolant density, and its values at very low densities lead to an overestimation of the cell reactivity. It is shown that the inclusion of a Bell factor in the definition of the cluster effective surface improves the agreement with experimental results.

Disadvantage Factor in a Cell with Thin Moderator

A monoenergetic disadvantage factor is introduced by extending the method of Amouyal & Benoist(1)–(3) so as to permit the treatment of a cell with thin moderator. To take into account the flux depression in a fuel rod, the blackness of the fuel rod is introduced into the calculation as in the paper by Amouyal et al. The Wigner-Seitz equivalent cylindrical cell method is incorrect for closely packed lattices. To cover this shortcoming, an extended Dancoff factor is introduced to take into account the interference among fuel rods. This factor can be easily calculated in a homogeneous system, and so no consideration is necessary to account for the shadowing effect by other fuel rods. The result obtained is similar to that from the collision- probability method but can be calculated more easily. And improvement over the Amouyal-Benoist method is thus obtained.