AN EFFICIENT VARIATIONAL SOLUTION OF THE TRANSIENT RADIAL-AZIMUTHAL HEAT TRANSPORT IN NUCLEAR FUEL ROD ARRAYS

An efficient variational method was developed for transient radial-azimuthal heat conduction in nuclear rod bundles under Loss-of-Coolant Accident conditions. The method is fast running, gives the solution in a readily usable form, is easy to program, uses the same algorithm for one-dimensional and two-dimensional calculations, and is compatible with modular computer codes used in the nuclear industry.;A comparison was made with the explicit finite-difference method. The criteria were: (1) maximum clad and fuel temperature histories; (2) maximum azimuthal temperature differences; and (3) shape of azimuthal temperature profiles. It was found that, on the average, the variational method is three times faster and at least as accurate. Effective heat transfer coefficient and gap conductance azimuthal profiles were linked to trial functions to limit computer calculations to the minimum necessary for required accuracy.;Azimuthal temperature variations in a rod bundle were studied using the variational method. A parametric study was conducted to investigate how errors in parameters and simplifying assumptions affect azimuthal temperature variations. Errors in rod emissivity and its azimuthal profile were found to strongly affect azimuthal temperature differences and shape of azimuthal temperature profiles. Also, errors in convective heat transfer coefficient during core heat-up affect azimuthal temperature profiles, but to a lesser extent than errors in emissivities; during core rewetting an azimuthal profile of convective heat transfer coefficient is necessary for detailed modeling. Trial functions with a cosine profile in the azimuthal direction (for short CPU times) can be used in thermal-hydraulic modeling to improve the accuracy of the predicted clad surface temperatures as compared to the one-dimensional radial conduction model.;The trial functions for the temperature fields in fuel and cladding regions are parabolic in the radial direction. A Fourier series in place of the constant term of the parabola takes into account azimuthal variations at the inner or outer radius. Finally, a second Fourier series in place of the coefficient of the variable term of the parabola takes into account variations in maximum radial temperature differences in the azimuthal direction.