Variational Determination of Transient Radial-Azimuthal Temperature Distributions in Fuel Rods for Loss-of-Coolant-Accident Analysis

An efficient variational method was developed to solve the transient radial-azimuthal heat conduction problem in nuclear fuel rods under loss-of-coolant-accident (LOCA) conditions. The method is efficient in that it is fast, accurate, and compatible with the modular accident analysis codes already in use in the nuclear industry. The methodology uses the Lebon-Labermont restricted variational principle, with parabolic trial functions in the radial direction and circular trial functions in the azimuthal direction, to reduce the transient heat conduction problem in the rod to a set of first-order ordinary differential equations in time. These equations are then solved by an explicit technique. The solution is in a readily usable form (i.e., averages and gradients can be determined without interpolation) and the same algorithm is used for both one- and two-dimensional problems. The solution technique allows changing the trial functions at every time step to obtain an accurate solution with minimum computing time. The methodology is implemented for a single rod under hypothetical LOCA conditions in order to (a) investigate the sensitivity of the predicted radial-azimuthal temperature distributions to the choice of the trial functions, (b) investigate the importance of nonlinearity effects (i.e., temperature dependence of thermal properties) on rod response, and (c) compare the variational and finite difference techniques with respect to computation time and accuracy of the results. It is shown that the variational technique leads to substantial reduction in computing time (more than a factor of 3) for comparable accuracy.