Modeling Coupled Bending, Axial, and Torsional Vibrations of a CANDU® Fuel Rod Subjected to Multiple Frictional Contact Constraints

Abstract

In this paper, a comprehensive dynamic model is developed based on a three-node higher-order mixed finite element for simulating the coupled bending, axial, and torsional vibrations of a CANDU® fuel rod. The continuous CANDU® fuel rod is discretized in the spatial domain using the mixed structural finite elements. The approximate discrete equations of motion of an unconstrained CANDU® fuel rod are then derived in terms of the finite element nodal variables by means of the Lagrange equations. An implicit incremental displacement Newmark time stepping scheme combined with a Bozzak relaxation scheme is employed to seek a numerical solution in the time domain. In handling the multiple unilateral frictional constraints at a time step, the sub-structuring method is used to eliminate all interior degrees of freedom. The coupled gap equations in the directions of all probable contact points and the their associated frictional forces in the two tangential directions (axial and circumferential) are reduced, through variable transformations, to a set of standard linear complementarity problem (LCP) for which a solution can be obtained using the Lemke algorithm. Proportional type of damping is introduced to the system to model the structural damping of the fuel rod. Friction is treated as 2D friction for axial and circumferential direction relative to the pressure tube surface. The contact forces in radial direction and the frictional forces in the axial and circumferential directions along with the sliding velocities are computed for each occurring contact. All these parameters are used to assess the material loss of the pressure tube. Results for bending vibration, axial and torsional vibrations of an outer fuel rod in a CANDU®6 fuel bundle with three bearing pads are obtained using the proposed approach and compared with the independently obtained results, available in the literature for frictionless contact cases. Good agreement is observed. The work presented in this paper is part of the effort undertaken at Ryerson University to develop a CANDU® fuel string vibration code for fretting and wear in a fuel channel.