Fluid-structure coupled calculation numeric methods - Homogenization method regarding tube bundles vibratory analysis

L' he fluid-structure interaction (or FSI) problem is a vast field of study that includes many different industrial configurations and needs to be tackled when the dynamic behavior of a structure is influenced by the presence of a fluid. The study of this type of problem can be complex, both from the point of view of physical analysis and the numerical treatment of the corresponding equations. In the most general case, to build a numerical model, it is necessary to couple the calculation codes that solve the equations governing the behavior of the structure and the fluid. In the case of vibratory analysis of structures coupled with a fluid, it is possible to model the system's behavior using a simpler set of equations: for the fluid in particular, the Euler equation (incompressible, non-viscous "flow" model) or the Helmholtz equation (compressible, non-viscous "flow" model) can be used to describe the physics of the problem. The IFS is then described by a system of equations for which numerical resolution using the finite element method is particularly well suited. However, finite element/finite element coupling methods quickly reach their limits in the case of systems involving a large number of fluid-coupled structures, particularly tubular bundles. In such cases, specific modeling techniques are required: computational methods based on homogenization techniques have been developed to meet this need. The aim of this article is to present the principles of a homogenization method and its application to calculating the behavior of immersed tubular beams. The presentation is divided into four sections: the first provides a few basic reminders of the notions of fluid/structure interaction and inertial effect in the general case; the second and third sections then develop the theoretical principles and numerical implementation of a homogenization method for describing inertial effects for tubular beams; two validation examples and an application example are studied in the fourth section. Bibliographical references are provided in the "Further reading" section of this article.