Mathematical model for studying boiling water cooled reactor power resonance instability

The mathematical model of dynamics of a tank type boiling water cooled reactor with natural circulation is developed. The reactor is represented as a system with feedback taking into account void and Doppler reactivity effects. Calculation of the power effect is based on the perturbation theory with account for dynamic parameter spatial (along core height) dependence. The fuel temperature is described by a system of non-stationary equations of heat transfer for a cylindrical three-zone fuel element (fuel, gap, can) and steam content dynamics is described by non-stationary equations of continuity and energy conservation for two-phase flow. Boundary value problems are solved in linear approximation. Analytical solutions determining the dynamics of fuel mean temperature and steam-water mixture density are obtained using the Laplace transformation. An example of the VK-50 reactor dynamic characteristics calculation by means of described technique is given. The model is recommended for calculational studies into boiling water cooled reactor power resonance instability