An Approximate Calculation Method of the λ, ωp and ωd Eigenvalue Problem of the Group Diffusion Equation

Abstract

The approximate solutions of the 1, w p and a,, eigenvaluc problems of the group-diffusion equation for a multi-region reactor are obtained by expandivg neutron fluxes into finite numbers of eigenfunctions satisfying the Helmholtz equation and the boundary condition at the extrapolated boundary of the reactor. The original eigenvalue problem is reduced to that of an asymmetric real matrix for the vector whose components constitute the expansion coefficients. For the numerical calculation of the real matrix thus derived, to dctermine the higher 1, w p and w,, modes, the QR iteration method based on numerically stable unitary transformation, in comhination with inverse iteration is effective in saving computation time.The R, w p and od modes obtained by the above method are expressed by a linear combination of a comparatively small number of simple clementary functions, and are thus of high practical value in the numerical calriilotion of higher order perturbations and for exmniniug space-dependent reactor dynamics.

An attempt to solve neutron transport equation inside supercritical water nuclear reactors using the Boubaker Polynomials Expansion Scheme

“…This scheme is applied through setting the expression: The main advantage of this step lies in Equation 10 which ensures verifying the four boundary conditions in Equation 9, at the earliest stage of resolution protocol. In fact, due to the properties of the Boubaker polynomials (Weber and Weigel, 1988;Yildirim et al, 2010;Yoshikawa and Wakabayashi, 1970;Yousif et al, 2010;Zeng-Hua et al, 2004), and since The solution is then assigned to the set of pondering real…”

“…Several nuclear reactor types have been used in the last decades. Very high temperature (VHT), supercriticalwater-cooled (SWC) and molten-salt (MS) reactors are among the most known (Gallaway et al, 2008;Yoshikawa and Wakabayashi, 1970;Yousif et al, 2010;Corradini, 2009).…”

Higher Order αMode Eigenvalue Calculation by Monte Carlo Power Iteration

“…Higher order mode calculations usually require subtraction of lower order eigenfunctions from the fission source distribution as represented by Hotelling's method. 11,12) Monte Carlo methods, however, have difficulties to make subtraction since Monte Carlo methods define the neutron flux distribution by many particles being randomly distributed throughout a fissionable system. Some attempts to perform higher order criticality eigenvalues without subtraction technique have been done by Booth 4,5) and Yamamoto.…”