G. Marleau

Modelling of CANDU reactivity control devices with the lattice code DRAGON

Abstract The lattice code DRAGON has been used for modelling the normal operating conditions in CANDU reactors. The integral transport equation is first solved using the collision probability (CP) formalism for 2-D cluster geometries representing standard CANDU cells. Whereas the usual tracking procedure only permits isotropic reflection at the cell boundary, we investigate the effects on a completely reflected cluster cell of the cyclic-tracking procedure that can also treat specular reflection. For CANDU reactivity devices located perpendicularly to the fuel channels, the standard CP formalism is applied to 3-D supercell geometries containing zones of mixed cylindrical and rectangular geometries. A symmetric two-bundle model allows most of the surfaces to be located in the moderator regions, thus reducing discrepancies introduced by the assumption of isotropic boundary currents. Using a single basic definition for the tracking files, efficient algorithms for computation and normalization of CP pertinent to these cell and supercell models are also described. Numerical results include reactivity worths for adjuster rods and zonal control units (ZCU) of a typical CANDU reactor.

A Transport Method for Treating Three-Dimensional Lattices of Heterogeneous Cells

AbstractA new ray-tracing method for the calculation of collision probabilities within arbitrary three-dimensional geometries has been developed. This method is used to discretize the neutron transport equation for heterogeneous rectangular cells containing zones of mixed cylindrical and rectangular geometry. For multicell applications, the interface current (IC) method provides the coupling between cells. The solution to the IC equations over multicell domains consisting of rectangular three-dimensional cells is improved by using an alternate direction implicit iteration scheme with variational acceleration. Results include comparisons of this technique with SHETAN for simple geometries and the analysis of a three-dimensional extension of a two-dimensional 15 × 15 pressurized water reactor benchmark problem.

Analytic reductions for transmission and leakage probabilities in finite tubes and hexahedra

Analytic reductions are used to simplify evaluation of the transmission probabilities in a hexahedron and of the five independent probabilities (two transmission and three leakage probabilities) that are required for a finite tube. The four- and five-dimensional numerical integrations required for transmission and leakage probabilities are reduced to one and two dimensions, respectively.

Adjoint and Generalized Adjoint Flux Calculations Using the Collision Probability Technique

Abstract Computation of adjoint and generalized adjoint fluxes may present some difficulties, especially when relying on the collision probability technique in transport theory. This paper proposes a simple method to compute those adjoint flux and generalized adjoint fluxes associated with homogenized and condensed cross sections. By defining a pseudo adjoint flux, one can apply an algorithm, similar to that required for the evaluation of the direct neutron flux, to adjoint flux calculations. Because of the presence of the scattering source, a multigroup iterative procedure is used in DRAGON for the direct flux solution. We show that this procedure can be easily modified in such a way that the performance of the solution algorithm is preserved for the adjoint problem. Finally, a generic adjoint algorithm is presented to deal with generalized adjoint fluxes’ computation.

Perturbation theory for lattice cell calculations

Abstract Generalized perturbation theory (GPT) can be used as a means to evaluate sensitivity coefficients or to approximate variations in integrated lattice parameters resulting from small changes in local cell properties. Using a first-order perturbation approach, the changes in the integral parameters can be written as a sum of a direct term that takes directly into account the variations in the cell properties and an indirect term that approximates the neutron flux variations resulting from the perturbation. For a lattice cell code that relies on a collision probability technique to solve the transport equation, a problem related to the evaluation of the perturbed transport operator also arises because the collision probability matrix depends on the total cross section. A technique is presented to simulate these variations in the collision probability matrix using approximate source term variations. Comparison with exact calculations will show that the results obtained using GPT with these approximate source terms are reliable provided the perturbations remain small. Results for a parametric study of a two-dimensional pressurized water reactor 17 × 17 assembly and void reactivity calculations for a DUPIC-fueled CANDU cell are also presented.

Computation of the DP1 collision probabilities for spherical and cylindrical geometries

Abstract Most computations carried out using the interface current technique make use of the double P0 (DP0) approximation where it is assumed that the neutron current impinging on, or leaving, an external surface associated with a given region has a cosine distribution. A better approximation (the so-called double P1 approximation) consists in assuming an anisotropic flux distribution on external surfaces. This higher order approximation implies that new directional probabilities associated with the anisotropic components of the neutron currents must be computed. Here we propose to compute the double P1 (DP1) transmission probabilities associated with one-dimensional spherical and cylindrical geometries and to use these probabilities to solve the interface current equations. Our analysis will include a comparison of the DP0 and DP1 interface current approximations with the complete collision probabilities method for homogeneous and heterogeneous assemblies.

Comparison between the multi-group improved and generalized quasistatic methods for different numbers of energy groups

Abstract The improved and generalized quasistatic methods implemented into the multi-group reactor code TRIVAC-3 are solved using different numbers of energy groups ranging from one to six. The comparison between the two methods is made for total power in the reactor core and the results obtained show a similar behavior of the total power for the transient studied in a CANDU-6 reactor.

Monte Carlo Simulation of Inclined Reactivity Control Rod and Boron Poisoning for the Canadian-SCWR Supercell

The Canadian-SCWR is a heavy-water moderated supercritical light-water-cooled pressure tube reactor. It is fueled with CANada deuterium uranium (CANDU)-type bundles (62 elements) containing a mixture of thorium and plutonium oxides. Because the pressure tubes are vertical, the upper region of the core is occupied by the inlet and outlet headers render it nearly impossible to insert vertical control rods in the core from the top. Insertion of solid control devices from the bottom of the core is possible, but this option was initially rejected because it was judged impractical. The option that is proposed here is to use inclined control rods that are inserted from the side of the reactor and benefit from the gravitational pull exerted on them. The objective of this paper is to evaluate the neutronic performance of the proposed inclined control rods. To achieve this goal, we first develop a three-dimensional (3D) supercell model to simulate an inclined rod located between four vertical fuel cells. Simulations are performed with the SERPENT Monte Carlo code at five axial positions in the reactor to evaluate the effect of coolant temperature and density, which varies substantially with core height, on the reactivity worth of the control rods. The effect of modifying the inclination and spatial position of the control rod inside the supercell is then analyzed. Finally, we evaluate how boron poisoning of the moderator affects their effectiveness.

Comments on âInvestigation of Interface-Current Solution Techniques for Coupled Heterogeneous Cellsâ

(1996). Comments on “Investigation of Interface-Current Solution Techniques for Coupled Heterogeneous Cells”. Nuclear Science and Engineering: Vol. 122, No. 2, pp. 283-285.

Sensitivity of Cross Sections to Isotopic Densities for Subgroup Resonance Self-Shielding Calculations

Abstract The sensitivity coefficients of self-shielded cross sections to isotopic densities are computed for a subgroup resonance self-shielding model. The method we propose is based on the derivatives of the collision probabilities used in the slowing-down equation. In this work, we look at how the sensitivities vary as a function of the position inside a fuel pin or of the position of a fuel pin within an assembly. Moreover, we evaluate the importance of the superhomogenization factors, used to correct self-shielded cross sections for the subgroup method, on the cross-section sensitivities. We also present a comparison with the Monte Carlo code Serpent where the sensitivity coefficients are approximated using a finite difference method.