Kanchhi Singh

Solution of the multigroup diffusion equation in hex-z geometry by finite Fourier transformation

A 3-D multigroup diffusion theory computer code, FINFOR, based on the finite Fourier transformation method has been developed for hexagonal geometry. The code estimates the eigenvalue and core flux/power distributions. In the present method, the currents on the surfaces of the hexagon have been assumed to be constant. The volume source has been approximated by an incomplete third-degree polynomial in the X-Y plane and by a quadratic polynomial in the axial direction. These approximations are consistent and it is shown that this combination gives good results. Equations are cast in the form of response matrix equations and are solved by a conventional fission source iteration scheme. Outer iterations are accelerated using a coarse mesh rebalancing technique. The code has been validated by analysing two benchmark problems and the results found to be satisfactory.

Reconstruction of pin power in fuel assemblies from nodal calculations in hexagonal geometry

Abstract A new formulation based on maximum entropy and minimum cross-entropy methods has been worked out for pin power reconstruction in hexagonal fuel assemblies. These methods help in estimation of boundary fluxes at the surfaces of an assembly using the values from nodal calculations. Representing the heterogeneities in the assembly using fine meshes, the diffusion equation in it is solved using finite difference (FD) technique. The results of a numerical problem formulated for the purpose have been compared with those obtained from (i) detailed fine-mesh (FD) estimations for the core as a whole and (ii) the imbedded estimations applied for the box. The boundary fluxes in the imbedded method are obtained using cubic splines at the surfaces of the assembly. Numerical difficulties encountered while imposing neutron currents as additional constraints in the entropy methods are also discussed.

A finite fourier transform method for three dimensional steady state reactor core calculations

Abstract A method based on finite Fourier transform technique has been developed to solve the steady state multigroup neutron diffusion equation for reactor core calculations in X-Y/X-Y-Z geometry. In the present work, the neutron source in a node is approximated by a 5 point quadratic in X-Y plane and a quadratic in axial direction. The partial currents on the surfaces of the node have been assumed to be constant and equal to their average values. The equations cast in response matrix form are solved by standard fission source iterative approach. The outer iterations are accelerated using a coarse mesh rebalancing scheme. The algorithm has been implemented in a computer code finfor-sqr . The code has been validated by analysing a few benchmark problems.

Solution of the multigroup diffusion equation in triangular-z geometry using finite Fourier transformation

The finite Fourier transform method has been applied in triangular-z geometry to solve the multigroup diffusion equation. In 2-D, the method is applied by using a quadratic polynomial approximation for the current on the surfaces of the triangular region and a complete cubic polynomial in the xy plane for the source inside the region. In 3-D, the extension to the axial direction is made by treating the current as constant, whereas the source is approximated by a quadratic polynomial. The method has been implemented in the computer code FINFOR-T. The code is suitable for predicting the eigenvalue and the power distribution for cores employing large-sized VVER-type assemblies (lattice pitch ~23.5 cm). The numerical studies reported here for the two problems relating to VVER-type cores demonstrate the accuracy of the method for the above class of problems.