Investigation of multiplicity of power distributions in a nuclear reactor under reactivity feedback effects

Abstract

A nonlinear reactor model was developed taking into account several feedback effects such as the moderator and fuel temperatures, xenon absorption, and soluble boron concentration through energy balance relations in the core. The resulting equation belongs to a class of nonlinear boundary value problems, and it is shown through bifurcation theory that there may exist multiple steady-state solutions for a range of parameters which correspond to various design and operatign conditions., We obtained solutions from the nonlinear reactor model for a range of the parameters, i.e., for a set of macroscopic absorptioncross sections, moderator and fuel temperature coefficients, and boron concentration. For particular values of feedback constants, the number of solutions was multiple for a range of the parameters. The solution diagram and bifuraction diagram were obtained for several feedback constant. Moreover, stability analysis was applied to each solution in order to investigate whether the solution corresponding to the parameters is stable or not. The solution diagram consists of one bifurcation point and two limit points, one bifurcation point and one limit point, or only one bifurcation point, depending on the values of the feedback constants. In the solution diagram consisting of one bifurcation point and two limit points, the intermediate solution is unstable and the rest are stable. The solution diagram consisting of one bifurcation point and one limit point has either no solution beyond a critical value of a parameter, or two solutions below a critical value of the parameter of which the higher solution is unstable and the lowr solution is stable. The solution diagram consisting of one bifurcation point has only one stable solution beyond a critical value of the parameter, or none otherwise. Temperature feedbacks with negative moderator temperature coefficient, negative fuel temperature coefficient, and xenon feedback function in the direction of stabilizing t...