Sensitivity theory applied to a transient thermal-hydraulics problem

A new method for sensitivity analysis of transient nonlinear problems is developed and applied to a reactor thermal-hydraulics problem. The method resembles the differential sensitivity methods currently used in the linear problems of reactor physics, but it is applicable to nonlinear systems as well. The equations governing heat transfer and fluid flow in a fuel pin and surrounding coolant are given and used to derive a second set of equations (commonly known as the "adjoint equations") used in the sensitivity analysis. Both systems contain one second-order parabolic and one first-order hyperbolic partial differential equation. Difference equations are derived to approximate both systems and the convergence properties of these discrete systems are evaluated, yielding a useful analysis of the numerical solution. The solution functions are used to derive sensitivity coefficients for any desired integral response. These sensitivity coefficients are used in a first-order perturbation theory to predict changes in a response resulting from changes in parameter values. The results of a test problem are shown, verifying that this procedure is indeed useful for a wide variety of sensitivity calculations.