Homogenisation method for the modal analysis of tube bundle with fluid–structure interaction modelling

The present paper is concerned with the modal analysis of a two-dimensional tube bundle with fluid–structure interaction (FSI) modelling. The numerical modelling of FSI effects is performed with a homogenisation approach, using a method whose principles have been presented in a previous paper for the modal analysis of a nuclear reactor with internal structures and FSI modelling [J.F. Sigrist, D. Broc, Homogenisation method for the modal analysis of a nuclear reactor with internal structures modelling and fluid structure-interaction coupling, Nucl. Eng. Des. 237 (2007) 431–440]. The method is adapted here in the case of tube bundle and compared with the classical approach, based on a direct finite element discretisation of the coupled problem with all tubes modelling. The theoretical background of the method is recalled, the numerical implementation in a finite element code is exposed and a comparison of the “homogenisation” and “coupled” methods is proposed in the case of a 10 × 10 tube bundle. Calculation of eigenmode shapes, frequencies and effective masses with the two methods is performed; it is concluded that: (i) the computational time is significantly lowered when using the homogenisation method instead of the coupled method, since the problem size is reduced by 90%; (ii) the tube bundle dynamic is described in a space-averaged manner, which is sufficient to account for the main inertial coupling effects. Extension of the method to a three-dimensional case can now be considered; implementation of the method in a commercial finite element code is also currently investigated.