A Homogenisation Method for a FSI Problem: Application to a Tube Bundle Row

A research program is ongoing at CEA in the framework of ASTRID project, for developing and validating tools for the analysis of the mechanical dynamic behaviour of Fast Breeder Reactor (FBR) cores. In this context, Fluid Structure Interaction is a recurring problem, especially in case of tube bundles in nuclear reactor cores or steam generators. The large number of elements makes modelling difficult to perform and any direct numerical simulation at whole core scale unachievable. In order to overcome this limitation, we resort to homogenisation techniques which allow to describe the global dynamic behaviour of the whole fluid-structure system. The purpose of this study is to better understand the effects of the spatial variation of the tube displacement field on the whole bundle dynamics. Thanks to multiple scales, a complete development of the problem is conducted. An analysis of the effects of spatial variations of the long scale displacement field on the tube bundle’s dynamics is led. As a first step we consider the homogenisation of Euler linear equations that gives us the possibility to make a thorough assessment of the problem with the extension to follow to Navier-Stokes equations.