A quasi-static orthogonal method for solving spatial-time neutron kinetics equations in non-steady processes

Abstract

Neutron spatial-time kinetics equations are composed of multiple mutually coupling variables, and solving the equations is relatively complex and time-consuming. Thus, it is difficult to meet the demand for actual fast calculations. In the present work, the quasi-static orthogonal (QSO) method is proposed to solve space-time reactor neutron kinetics equations for a cylindrical homogeneous core. Under the conditions of quasi-static approximation, the neutron flux density is decomposed into a range function and shape function using the factorization method. The analytical solutions in the axial and radial directions of the shape function are obtained using this QSO method. Also, the range function is transformed into the form of a point reactor model for the series solutions. Then the analytical solutions of the three-dimensional spatial-time reactor neutron kinetic equations are derived under non-steady state conditions. Applying the results to the operating reactors departs from the steady state conditions, and the variation of neutron flux density with time and space is obtained. Compared with other analytical methods and numerical solutions, this QSO method is relatively simple and effective under the conditions of the non-steady and delayed neutron impact.