Sensitivity And Uncertainty Analysis of the TRIGA Mark II Reactor Using First and Second Order Perturbation Theory

During the last years, perturbation techniques have been widely implemented for the analysis of the sensitivity and propagation of uncertainty in simulations of physical systems, such as nuclear reactors, due to changes in control or external parameters. The use of first and second order perturbation theory allows the generation of perturbation coefficients employing a weight function used to define the response of interest and the solution of the system of differential adjoint equations. If slightly variations of the operational parameters as the coolant inlet temperature or the reactivity occurs, the first order perturbation theory is sufficient to obtain satisfactory results, especially if the focus is on the steady state values at the end of the transient. In particular, the adjoint perturbation theory has different performances according to the section of the transient is under investigation. If the interest involves all the duration of the transient, the second term correction is needed to obtain acceptable results. The latter are also affected by the selection of the variables subject to variation of the control parameter and to which the perturbation theory is applied. This paper discusses the application of the first and second order adjoint perturbation theory to the analysis of the sensitivity and uncertainty propagation of the Pavia TRIGA Mark II reactor. A simplified model is used to describe the evolution of the neutron flux, the fuel and coolant temperature and their feedback on the reactivity of the system. The results show that second-order corrections are able to reproduce the response system with a slight difference with respect to the direct solution of differential equations. Errors lower than 0.1% (compared with the direct solution) are found with variations of up to 10% of the control parameter. The approach can be easily extended to take into account variations of reactivity by effect of the accumulation of neutronic poisons in long transients or eventually attaching the entire heat transfer problem, taking into account the heat exchangers subsystems and variations in the water supply.